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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Czechoslovak mathematical journal 48 (1998), S. 291-312 
    ISSN: 1572-9141
    Keywords: evolution triple ; optimal control ; monotone operator ; hemicontinuous operator ; parabolic system ; property (Q)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
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  • 2
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    Springer
    Discrete event dynamic systems 8 (1998), S. 353-364 
    ISSN: 1573-7594
    Keywords: scheduling ; optimal control ; time-decomposition methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper discusses dynamic methods for solving a class of multi-project scheduling problems in which rates of job performances are controllable and resources such as money, energy or manpower per time unit, are renewable and continuously divisible. The objective is to complete the projects as close to the common due date as possible. Two different ways of imposing sequential precedence relations between project jobs are explored by formulating two dynamic models and studying their relationships on the optimal solution. Efficient time-decomposition algorithms for finding either globally optimal schedules or lower bound guided near-optimal solutions are suggested and computationally tested.
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  • 3
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    Discrete event dynamic systems 8 (1998), S. 175-201 
    ISSN: 1573-7594
    Keywords: hybrid systems ; optimal control ; calculus of variations ; manufacturing systems ; queueing systems ; nonsmooth optimization ; two point boundary value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We propose a modeling framework for a class of hybrid systems which arise in many manufacturing environments and study related optimal control problems. In this framework, discrete entities have a state characterized by a temporal component whose evolution is described by event-driven dynamics, and a physical component whose evolution is described by time-driven dynamics. As a first step towards developing an optimal control theory for such hybrid systems, we formulate a problem consisting of a single-stage manufacturing process and use calculus of variations techniques to obtain structural properties and an explicit algorithm for deriving optimal policies.
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  • 4
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    Discrete event dynamic systems 8 (1998), S. 37-54 
    ISSN: 1573-7594
    Keywords: Production planning ; stochastic dynamic programming ; vanishing discount approach ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the problem of production planning in a flexible manufacturing system consisting of a single or parallel failure-prone machines producing a number of different products. The objective is to choose the rates of production of the various products over time in order to meet their demands at the minimum long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach for the average cost problem that the Hamilton-Jacobi-Bellman equation in terms of directional derivatives has a solution consisting of the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem, and in specifying an optimal control policy in terms of the potential function. The results settle a hitherto open problem as well as generalize known results.
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  • 5
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    Journal of optimization theory and applications 96 (1998), S. 589-626 
    ISSN: 1573-2878
    Keywords: Nonlinear control ; optimal control ; Hamilton–Jacobi–Bellman equation ; feedback synthesis ; successive approximation ; Galerkin approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we develop a new method to approximate the solution to the Hamilton–Jacobi–Bellman (HJB) equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB equation to a sequence of linear partial differential equations. These equations are then approximated via the Galerkin spectral method. The resulting algorithm has several important advantages over previously reported methods. Namely, the resulting control is in feedback form and its associated region of attraction is well defined. In addition, all computations are performed off-line and the control can be made arbitrarily close to optimal. Accordingly, this paper presents a new tool for designing nonlinear control systems that adhere to a prescribed integral performance criterion.
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  • 6
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    Journal of optimization theory and applications 98 (1998), S. 161-173 
    ISSN: 1573-2878
    Keywords: Robust stabilization ; optimal control ; time-delay systems ; Razumikhin-type approach
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, using a Razumikhin-type approach, the stabilization of a class of uncertain nonlinear systems with time-varying delay is considered. The proposed controller is based on a specific optimal control problem. Global asymptotic stability is guaranteed for the proposed control if some algebraic condition is met. An example illustrates the use of the main result.
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  • 7
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    Journal of optimization theory and applications 96 (1998), S. 507-532 
    ISSN: 1573-2878
    Keywords: Rigid bodies ; Hamilton–Jacobi equation ; Riccati equation ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the problem of obtaining optimal controllers which minimize a quadratic cost function for the rotational motion of a rigid body. We are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by the Euler equations. We obtain conditions which guarantee the existence of linear stabilizing optimal and suboptimal controllers. These controllers have a very simple structure.
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  • 8
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    Journal of optimization theory and applications 97 (1998), S. 11-28 
    ISSN: 1573-2878
    Keywords: Optimization ; nonlinear dynamic systems ; transformations ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with optimization of a class of nonlinear dynamic systems with n states and m control inputs commanded to move between two fixed states in a prescribed time. Using conventional procedures with Lagrange multipliers, it is well known that the optimal trajectory is the solution of a two-point boundary-value problem. In this paper, a new procedure for dynamic optimization is presented which relies on tools of feedback linearization to transform nonlinear dynamic systems into linear systems. In this new form, the states and controls can be written as higher derivatives of a subset of the states. Using this new form, it is possible to change constrained dynamic optimization problems into unconstrained problems. The necessary conditions for optimality are then solved efficiently using weighted residual methods.
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  • 9
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    Journal of optimization theory and applications 98 (1998), S. 681-700 
    ISSN: 1573-2878
    Keywords: Manufacturing systems ; bang–bang control ; dynamic programming ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The system under consideration comprises n workstations in parallel and one assembly workstation. The workstations are either reliable or unreliable and the product demand is random. The n different type parts are processed first in the parallel workstations and then are joined in the assembly workstation. By minimizing the expected discounted cost, it is shown that the optimal control policy is of the bang–bang type and can be described by a set of switching manifolds. The structural properties of the optimal policy, such as monotonicity and asymptotic behavior, are investigated. These structural properties are very useful to find the optimal policy in large-size systems. Three numerical examples are given to demonstrate the results.
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  • 10
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    Journal of optimization theory and applications 97 (1998), S. 281-297 
    ISSN: 1573-2878
    Keywords: Nonlinear ship steering dynamics ; optimal control ; saturation ; slew rate limitation ; sequential gradient-restoration algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The steering control of a ship during a course-changing maneuver is formulated as a Bolza optimal control problem, which is solved via the sequential gradient-restoration algorithm (SGRA). Nonlinear differential equations describing the yaw dynamics of a steering ship are employed as the differential constraints, and both amplitude and slew rate limits on the rudder are imposed. Two performance indices are minimized: one measures the time integral of the squared course deviation between the actual ship course and a target course; the other measures the time integral of the absolute course deviation. Numerical results indicate that a smooth transition from the initial set course to the target course is achievable, with a trade-off between the speed of response and the amount of course angle overshoot.
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  • 11
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    Biospectroscopy 4 (1998), S. 197-208 
    ISSN: 1075-4261
    Keywords: Raman spectroscopy ; protein-ligand interactions ; streptavidin complexes ; biotin analogues ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Raman spectra of anhydrous complexes of streptavidin (Strep) with biotin (Bio) and some Bio analogues [Biotin methyl ester (MEBio), desthiobiotin (DEBio), 2′-iminobiotin (IMBio), and diaminobiotin (DABio)] were recorded. The vibrational results indicate that the interaction with some of these ligands is able to modify the overall structure of the protein and this binding results in a decrease in the βsheet content and an increase in the α-helix content. To further confirm the conformational changes of the protein structure due to Bio analogue binding, the curve-fitting analysis of the amide I Raman band of neat Strep and of the complexes were performed. The intensity ratio of the components due to the β-sheet and α-helix conformations decreased in the Strep-MEBio, Strep-IMBio (pH 11), and Strep-Bio systems, whereas in all the other systems the changes were not significant. This behavior differs from that of Avi bound to the same ligands and suggests that Strep and Avi differ in their binding selectivity. A good correlation was found between the secondary structure percentages of the Avi and of the Strep complexes and ΔG°. On the basis of this linear relationship, the vibrational results allow for an acceptable evaluation of the dissociation constants of the Strep complexes, not previously reported in the literature. The present results indicate a correlation between the type of interaction and the effects of the protein-substrate bonding on the overall structure of the proteins. The amino acid residues in the binding site appear to be positioned in a such a way as to provide a precise fit of Bio. Even slight change in the substrate structure causes a weakness in the strength of the binding. The vibrational results confirm that both the imidazolidinone and the thiophan rings are important in the Strep-Bio interactions, but the former is more responsible for the high affinity of the binding. One of the Tyr residues is hydrogen bound with the ureido ring and another Tyr could be involved in the binding pocket. Trp residues do not directly bind the ligand and probably stabilize other binding site residues which in turn interact directly with Bio. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 197-208, 1998
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  • 12
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    Biospectroscopy 4 (1998), S. 209-216 
    ISSN: 1075-4261
    Keywords: high pressure ; FTIR spectroscopy ; bovine pancreatic trypsin inhibitor ; hydrogen-deuterium exchange ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Fourier transform infrared (FTIR) spectroscopy combined with resolution enhancement techniques, second-derivative and difference spectroscopies, have been used to characterize pressure-induced changes in the structural rearrangements of bovine pancreatic trypsin inhibitor (BPTI) in D2O solution at 25.0°C. According to the observed changes in the amide I′ band up to 550 MPa, the secondary structure elements of BPTI, such as the α-helix, 310-helix, β-sheet, and β-turn, are scarcely rearranged except for the loop structure of residues of 9-17 and 36-43. The polypeptide backbone is not extensively unfolded up to 550 MPa. The minor pressure-induced structural rearrangements are completely reversible. A further increase in pressure above 1000 MPa associated with the precipitation of BPTI in D2O buffer solution induces the partial structural rearrangements of the α-helix, β-turn and/or 310-helix, and β-sheet. The polypeptide backbone of BPTI is not fully unfolded even above 1000 MPa. Most of the protected backbone amide protons involved in the β-sheet remain intact in the pressure range where BPTI is not precipitated, while those involved in the α-helix and β-turn and/or 310-helix are exchanged with solvent deuterons. The protected backbone amide protons located near the surface regions are more easily exchanged with solvent deuterons by application of high pressure than those involved in the core. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 209-216, 1998
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  • 13
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    Biospectroscopy 4 (1998), S. 219-227 
    ISSN: 1075-4261
    Keywords: guanosine 5′-diphosphate ; guanosine 5′-triphosphate ; magnesium ; vibrational spectroscopy ; Raman spectroscopy ; FTIR ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Raman and infrared spectra were examined for guanosine 5′-diphosphate (GDP) and guanosine 5′-triphosphate (GTP) in aqueous solution. The vibrational modes were assigned on the basis of isotopic frequency shifts and relative intensities in the Raman and infrared spectra. The observed frequency shifts on 18O isotope labeling made it possible to identify the bands from each phosphate group (α, β, γ). Frequency shifts were observed as Mg2+ complexes with GDP and GTP. The results suggested that Mg2+ binds to GDP in a bidentate manner to the α, β P · · O bonds and in a tridentate manner to the α, β and γ P · · O bonds of Mg·GTP. The results indicate that structure of Mg2+ coordinated to GTP in aqueous solution differs somewhat to that found for Mg·ATP. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 219-227, 1998
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  • 14
    ISSN: 1075-4261
    Keywords: near-IR ; protein folding ; denaturation ; ribonuclease A ; overtone and combination bands ; 2-dimensional correlation analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: We introduce near-IR spectroscopy as an ancillary tool for monitoring structural changes of proteins in aqueous solution using ribonuclease A (RNase A) as a model protein. The thermal unfolding of RNase A results in clear spectral changes in the near-IR and the mid-IR regions. In the near-IR the most pronounced changes are observed in the spectral region between 4820 and 4940 cm-1. The strong N—H combination band found at 4867 cm-1 in the spectrum of native RNase A shifts to 4878 cm-1 upon thermal unfolding. Hydrogen-deuterium exchange experiments that validate the N—H character of this mode can also be used to estimate the number of unexchanged amide protons after exposure to D2O. The transition profiles and temperatures derived from the temperature dependence of the N—H combination mode were found to be practically identical with those derived from the temperature dependence of the C=O amide I band in the mid-IR region, demonstrating that the near-IR region can be used as a conformation-sensitive monitor for the thermally induced unfolding of proteins in H2O solution. A 2-dimensional correlation analysis was applied to the mid-IR and near-IR spectra of RNase A to establish correlations between IR bands in both regions. The correlation analysis demonstrates that the thermal unfolding of RNase A is not a completely cooperative process; rather it begins with some changes in β-sheet structure, followed by the loss of α-helical structures, and then ending with the unfolding of the remaining β-sheets. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: S19-S29, 1998
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  • 15
    ISSN: 1075-4261
    Keywords: 13C-NMR ; 57Fe-NMR ; ν(C—O) stretching vibration ; ν(Fe—C) stretching vibration ; heme proteins ; heme models ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: 13C- and 57Fe-NMR spectra of several carbon monoxide hemoprotein models with varying polar and steric effects of the distal organic superstructure, constraints of the proximal side, and solvent polarity are reported. The 13C shieldings of heme models cover a 4.0 ppm range that is extended to 7.0 ppm when several hemoglobin CO and myoglobin CO species at different pHs are included. Both heme models and heme proteins obey a similar excellent linear δ(13C) versus ν(C—O) relationship that is primarily due to modulation of π backbonding from Fe dπ to the CO π* orbital by the distal pocket polar interactions. There is no direct correlation between δ(13C) and Fe—C—O geometry. The poor monotonic relation between δ(13C) and ν(Fe—C) indicates that the iron-carbon π bonding is not a primary factor influencing δ(13C) and δ(57Fe). The δ(57Fe) was found to be extremely sensitive to deformation of the porphyrin geometry, and increased shielding by more than 600 ppm with increased ruffling was observed for various heme models of known X-ray structures. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: S57-S69, 1998
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  • 16
    ISSN: 1075-4261
    Keywords: nucleic acid ; conformation ; Raman spectroscopy ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: The structure of the packaged double-stranded DNA genome of bacteriophage T7 was compared to that of unpackaged T7 DNA using digital difference Raman spectroscopy. Spectral data were obtained at 25°C from native T7 virus (100 mg/mL), empty T7 capsids (50 mg/mL), and purified T7 DNA (40 mg/mL) in buffer containing 200 mM NaCl, 10 mM MgCl2, and 10 mM Tris at pH 7.5. At these conditions, the local conformation of T7 DNA was not affected by packaging. Specifically, the local B-form secondary structure of unpackaged T7 DNA, including furanose C2′-endo pucker, anti glycosyl torsion, Watson-Crick base pairing, and base stacking, were essentially fully (〉98%) retained when the genome was condensed within the viral capsid. However, the average electrostatic environment of T7 DNA phosphates was altered dramatically by packaging as revealed by large perturbations in the Raman bands associated with localized vibrations of the DNA phosphate groups. The change in the phosphate environment was attributed to Mg2+ ions that were packaged with the genomic DNA, and the observed Raman perturbations of genomic DNA were equivalent to those generated by a 50-100-fold increase in Mg2+ concentration in aqueous phosphodiester model compounds. The T7 data were qualitatively and quantitatively similar to those observed previously for packaged DNA of bacteriophage P22 and imply that genomic DNAs of T7 and P22 are both organized in a similar fashion within their respective capsids. The results show that the condensed genome does not contain kinks or folds that would disrupt the local B conformation by more than 2%. The present findings are discussed in relation to previously proposed models for condensation and organization of double-stranded and single-stranded viral DNA. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: S47-S56, 1998
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  • 17
    ISSN: 1075-4261
    Keywords: peroxidases ; quantum-mixed spin ; fluoride and hydroxyl complexes ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Electronic absorption and resonance Raman spectra of ferric and ferrous forms of a peroxidase from soybean seed coat (SBP) at neutral and alkaline pH values together with the spectra of the ferric-fluoride complex are reported. At neutral pH a quantum mechanically mixed spin state, resulting from the admixture of intermediate spin, S = 3/2, and high spin, S = 5/2, configurations, has been identified which coexists with five- and six-coordinate high-spin hemes. A complete conversion to a fluoride-ligated six-coordinate high-spin and a hydroxy-ligated six-coordinate low-spin heme are observed at acid pH in the presence of fluoride and at alkaline pH, respectively. The spectral features suggest that both the fluoride and hydroxo ligands are stabilized by hydrogen-bond interactions with the distal Arg residue and through a water molecule with the distal His residue. The ferrous form shows a single ν(Fe - Im) at 246 cm-1 at neutral pH. The data indicate that SBP shares many characteristics with peroxidases belonging to class III of the “plant peroxidase” superfamily. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 355-364, 1998
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  • 18
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    Biospectroscopy 4 (1998), S. 365-377 
    ISSN: 1075-4261
    Keywords: resonance Raman ; Thermus thermophilus ; oxidase ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: The terminal caa3 oxidase of Thermus thermophilus has been studied by resonance Raman spectroscopy. Using different excitation wavelengths in the Soret band region, it was possible to disentangle the resonance Raman spectra of the fully oxidized and fully reduced state in terms of the component spectra of the individual hemes a, a3, and c. For the heme a and a3 groups, the spectra reveal only minor differences compared to those of beef heart cytochrome c oxidase attributable to subtle modifications of the heme environment. These differences are not more pronounced than those between the oxidases from beef heart and Paracoccus denitrificans confirming the view that this oxidase of Th. thermophilus is a typical member of the aa3 oxidase superfamily. The heme c component spectra display far-reaching similarities with those of c-type cytochromes which serve as mobile electron carriers in the respiratory chain. These results imply that caa3 oxidase represents an integrated version of the noncovalent redox complex between cytochrome c and cytochrome c oxidase in higher organisms. On the other hand, the structural changes of cytochrome c in the noncovalent complex have no counterpart in the heme c component of the caa3 oxidase indicating a specific cytochrome c binding site for the mitochondrial enzyme. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 365-377, 1998
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  • 19
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    Biospectroscopy 4 (1998), S. 413-419 
    ISSN: 1075-4261
    Keywords: disposable soft contact lenses ; biocompatibility ; Raman spectroscopy ; hydrogels ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Disposable soft contact lenses based on HEMA-MAA hydrogels are examined using Raman and ATR/FTIR vibrational spectroscopies and thermal analysis. The main factors dealing with physical, chemical, and biological biocompatibility are evaluated in relation to those of long-wear soft contact lenses with the aim of individuating the most biocompatible lens. The Raman spectra of HEMA-MAA lenses show that some biocompatibility factors are affected by environmental conditions and, in particular, by changes in pH and ionic strength values. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 413-419, 1998
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  • 20
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    Biospectroscopy 4 (1998), S. 229-233 
    ISSN: 1075-4261
    Keywords: bopindolol ; luminescence ; oxygen radicals ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: The oxidation of bopindolol using the Co-ethylenediaminetetraacetic acid (EDTA) + H2O2 system was investigated by spectrophotometric, chemiluminescence, and fluorescence methods. The effects of oxygen free radicals scavengers and 1O2 quenchers on the light emission were measured. The obtained results show the electronically excited products of the bopindolol degradation are involved in the oxidation process. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 229-233, 1998
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  • 21
    ISSN: 1075-4261
    Keywords: metalloporphyrin ; nucleic acid ; outside binding ; CD ; MCD ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: The Soret (B0) region of free and externally DNA-bound 5,10,15,20-tetrakis(2-N-methylpyridyl)porphyrinatopalladium(II), PdP(2), was investigated by electronic magnetic circular dichroism (MCD), natural circular dichroism (CD), and optical (UV-visible) absorption spectroscopies. We conclude that four-coordinate, “thick” PdP(2) binds to the exterior of each of poly(A-T)2 and calf thymus DNA (CT DNA) by two distinctly different AT-specific minor and major groove modes, with site 5′TA3′ being favored for both modes. The minor groove mode involves an edge-on orientation of PdP(2), for which porphyrin electric dipole transition moments (edtms) μx (most perturbed direction of the bound porphyrin) and μy (least perturbed direction) have approximate orientation angles of α/β/β′ = ∼ 90°/0°/0° and ∼ 45°/0°/90°, respectively. Major groove binding is by a face-on mode, which results in the porphyrin plane being approximately parallel to the helix axis, such that νx (most perturbed direction) and μy (least perturbed direction) have approximate orientation angles of α/β/β′ = ∼ 45°/180°/90° and ∼ 45°/180°/270°, respectively. The Soret MCD and optical band alterations upon binding (i.e., sign retention of the tetragonal, genuine MCD (+) A-term on becoming the (+) pseudo-A-term of similar amplitude and small DNA-induced optical red (Δλ) and hypochromic (H) shifts) are all consistent with exterior binding perturbations of the porphyrin's pπ MOs (1a1u3a2u 4eg) by the A and T bases of each polymer being weaker than caused by intercalation. Furthermore, that the (+) A-term of PdP(2) retains the (+) sign upon binding informs that the 4eg splitting, or ΔLUMO, is less than the energy separation |1a1u-3a2u|, or ΔHOMO. For the third system, PdP(2)/poly(G-C)2, the B0 CD spectrum has two extremely weak (+) and (-) CD bands at higher and lower energy, respectively, indicating that weak outside binding (wob) interactions are taking place between the cationic porphyrin and the electron-rich phosphate backbone of this rigid polymer. The composite of our CD, MCD, and optical data are suggestive of a face-on mode at the GC major groove. Band parameter extraction is performed on the Soret CD and MCD bands of each of the three bound systems, and it is determined that (1) very little spatial rotation of molecular charge is induced during CD excitation and (2) the excited state angular momentum, 〈Lj〉, changes very little upon binding of PdP(2) to each duplex. These findings are also consistent with each PdP(2)/B-DNA interaction not being very strong. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 341-352, 1998
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  • 22
    ISSN: 1075-4261
    Keywords: ortho-aminobenzoylamino acids ; fluorescence ; protease ; peptide ; peptide synthesis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: ortho-Aminobenzoic acid (Abz) has been used as a convenient fluorescent donor group in internally quenched fluorescent peptides, which are employed as substrates for several proteolytic enzymes. As Abz is usually bound to the N-amino terminal of these peptides, it is of interest to investigate the Abz group fluorescent properties bound to different amino acids. We report in this article the optical absorption and fluorescent properties, in aqueous media, of Abz bound to the α-amino group of Ala, Gly, Leu, Ile, Val, Pro, Phe, Arg, Glu, Met, Asn, Tyr, and Trp, with monomethyl-amidated α-carboxyl group. In order to explore the origin of the drastic reduction of Abz attached to Nα amino group of prolyl-peptides, we also examined the fluorescence properties of Abz-NHCH3, Abz-N(CH3)2, and Abz-pyrrolidine. Molecular dynamics simulation and NMR data indicated a lack of periplanarity of the Abz-dimethylamide, which could be the origin of low fluorescence quantum yield of Abz-prolyl-peptides. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 395-402, 1998
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  • 23
    ISSN: 1075-4261
    Keywords: X-ray photoelectron spectroscopy ; surface analysis ; MUC1 mucin ; structure ; glycosylation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: X-ray photoelectron spectroscopy (XPS) is a surface sensitive analytical technique that measures the binding energy of electrons in atoms and molecules on the surface of a material. XPS was used to determine the distribution of the oligosaccharide side chains in the glycoprotein, MUC1 mucin. Low-resolution XPS spectra provided elemental composition of MUC1 mucin (fully glycosylated), mucin polypeptide (nonglycosylated), and carbohydrates found in mucin. The nitrogen content of MUC1 mucin was determined to be intermediate between the mucin polypeptide and the carbohydrates. Assuming a uniform distribution of carbohydrate on MUC1 mucin, the average thickness of the carbohydrate layer was calculated to be 4.9 nm using the low-resolution N 1s signals. High-resolution XPS spectra give detailed information about the chemical bonding of the surface molecules. Calculations based on the high-resolution O 1s spectra showed a carbohydrate thickness of 6.6 nm. These experimentally determined values agree reasonably well with an estimated 5 nm of carbohydrate thickness from a simple model which assume that the core protein is a rodlike molecule approximately 5 nm in diameter. Although the carbohydrate coating on the MUC1 mucin appears to be thick enough to cover the core protein entirely, fully glycosylated breast milk MUC1 mucin is susceptible to proteolytic digestion without removal of any oligosaccharide side chain, suggesting areas of exposed core protein. A possible explanation is that the oligosaccharide side chains may form patches of carbohydrate along the core protein with regions of exposed core protein. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 257-266, 1998
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  • 24
    ISSN: 1075-4261
    Keywords: pterins ; FTIR ; vibrational analysis ; solvent effects ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Fourier transform infrared (FTIR) spectra have been obtained from solution samples of the heterocycles uracil, lumazine, and violapterin and reveal interpretable carbonyl stretching frequencies. Spectra of conjugate bases of lumazine and violapterin demonstrate decreases in these carbonyl stretching frequencies upon ionization. Based on isotopic shifts from amide deuterated analogs, semiempirical QCFF/PI calculations were used to assign the vibrational frequencies in the region 1100-1800 cm-1 observed from samples in dimethylsulfoxide (DMSO) and aqueous solutions to specific normal modes. The observed deuterium shifts and the calculations suggest that, in some cases, N - H bending motions are coupled to the C=O stretching motions of the pyrimidine ring. These data suggest that for lumazine anions a change in solvent can significantly change the mixing of the N - H bending and C=O stretching vibrational motions. This implies that vibrational analysis for lumazine species in relatively noninteracting media like nonpolar solvents, mulls or pellets cannot necessarily be transferred to the system when it is dissolved in a polar, hydrogen-bonding solvent such as water. Although other explanations can be offered, our vibrational analysis suggests that the changes in normal mode composition of the predominantly C=O stretching vibrations of lumazine anion on going from dimethylsulfoxide to water solution are consistent with a change in the predominant tautomer of the heterocycle. This change appears to correspond to a shifting of the location of the remaining acidic proton to a different ring nitrogen atom. This interpretation is of interest in view of recent ab initio calculations which suggest that proton shifts may occur during the hydroxylation of lumazine as mediated by the enzyme xanthine oxidase. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 235-256, 1998
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  • 25
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    Biospectroscopy 4 (1998), S. 281-294 
    ISSN: 1075-4261
    Keywords: phosphatidylcholines ; dioleoylphosphatidylethanolamine ; mixed-chain phospholipids ; unsaturation ; hydration ; FTIR spectroscopy ; lyotropic phase transitions ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: The gradual hydration of phospholipid films can be effectively probed by Fourier transform infrared (FTIR) spectroscopy (cf. part I of this series). The hydration-induced changes observed for lipid IR-absorption bands are probably composed of contributions arising from the effects of both the direct binding of water molecules and the thereby caused conformational changes and phase transitions in the lipid molecules and assemblies, respectively. In this article, an attempt is made to attribute some of the more indicative spectroscopic results to these molecular and supermolecular processes with a view to separating their individual contributions to the relevant spectroscopic data. This is done by considering a series of suitable PLs consisting of the palmitoyl and oleoyl lecithins, DPPC, DOPC, POPC, and OPPC, and one cephalin, DOPE. This choice of PCs and DOPE means that at room temperature and different degrees of hydration, several phase states including lamellar gel and liquid crystalline as well as certain nonlamellar phases are covered. The separation of the water-binding and phase-transition contributions to the FTIR-spectroscopic data, we believe, is clearly demonstrated by interpreting the hydration-dependent wavenumber shifts of the νC=O band of the PCs. Carbonyl groups are affected to a more significant degree for lipids arrayed in the Lα phase than in the gel phase. A number of spectral features reveal the lyotropically triggered chain-melting transition as well as other structural rearrangements of PCs. This is discussed in detail and demonstrates the excellent sensitivity of the FTIR methodology for the study of such systems. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 281-294, 1998
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  • 26
    ISSN: 1075-4261
    Keywords: Fourier-transform surface-enhanced Raman scattering ; all-trans retinoic acid ; retinoic acid receptor ; silver colloids ; fluorescence ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Surface-enhanced Raman scattering and fluorescence were used to investigate the interactions of all-trans retinoic acid with the gamma-type retinoic acid receptor. Raman data revealed a significant attenuation in intensity of the bands originating from the retinoic acid polyenic chain upon receptor binding, with the spectrum being dominantly that of the β-ionone ring. Fluorescence measurements supported the hydrophobic character of the ligand binding. These novel spectroscopic results are fully consistent with the published X-ray crystallographic data and suggest that these techniques may be valuable additional tools to characterize the interactions of agonists and antagonists with residues in the ligand-binding pockets of retinoid receptor homo- and heterodimers. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 297-302, 1998
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  • 27
    ISSN: 1075-4261
    Keywords: heme vinyl groups ; hemoglobin I ; hydrogen sulfide ; Lucina pectinata ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Hemoglobin I (HbI) from the claim Lucina pectinata is a unique heme protein that binds and transfers hydrogen sulfide (H2S) to a symbiotic bacteria. The metcyano, metaquo, carbon monoxy, oxy, and deoxy complexes of HbI were studied by resonance Raman (RR) spectroscopy, and the metcyano and carbon monoxy complexes were also studied by 1H-NMR. The results indicate a unique orientation of the heme 2-vinyl group relative to other heme proteins. The RR spectra of the HbICO, metHbICN, metHbIH2O, HbIO2 and deoxyHbI heme derivatives show a band at 1621 cm-1 and a shoulder at 1626 cm-1, indicative of an out-of-plane position for one of the vinyls relative to the other one. Spin-lattice relaxation properties of protons in the metHbICN complex also suggest a unique orientation for the heme 2-vinyl group of HbI. The longitudinal relaxation time (T1) for the 2-Hα, 2-Hβc, and Hβt protons are 120 ms, 115 ms, and 135 ms, respectively. The data from both techniques suggest an out-of-plane and trans-oriented 2-vinyl group, and an in-plane and cis-oriented 4-vinyl group for the low-spin complexes of HbI. These results imply that the electron withdrawing character of the out-of-plane vinyl group contributes to the stability of the heme Fe+3 oxidation state, facilitates the binding of the H2S ligand, and promotes the stability of this ferric H2S complex. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 311-326, 1998
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  • 28
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    Biospectroscopy 4 (1998), S. S3 
    ISSN: 1075-4261
    Keywords: charge-transfer (CT1) band ; vinyl conjugation ; peroxidases ; heme cavity ; heme ligands ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Electronic absorption and resonance Raman spectra of various peroxidases and selected site-directed mutants are reported. These results and the X-ray crystal structure data are critically analyzed and underline the differences that exist between the crystal and solution states. The effect of the vinyl conjugation on the electronic absorption maxima and the influence of the ligand nature on the wavelength of the charge-transfer (CT1) band are shown to be useful probes of subtle interactions in the heme pocket. The spectroscopic differences observed between the three classes of peroxidases are discussed in terms of their structural diversity. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: S3-S17, 1998
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  • 29
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    Biospectroscopy 4 (1998), S. S41 
    ISSN: 1075-4261
    Keywords: molecular force fields ; molecular dynamics simulations ; biomembranes ; phospholipids ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: A molecular force field dedicated to molecular dynamics simulation of biomembranes was developed. It was parameterized on model compounds related to phospholipids and was able to reproduce at the same time structures, energies, and vibrational spectra. Cross terms in the potential energy function were introduced by solving the redundancy problem among internal coordinates. This force field was used in the 400-ps molecular dynamics simulation of a hydrated bilayer in the gel and liquid crystal phases. The conformational properties of the polar head groups were in particular agreement with the experimental observations using Raman scattering. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: S41-S46, 1998
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  • 30
    ISSN: 1075-4261
    Keywords: surface-enhanced Raman spectroscopy ; gold and silver island films ; silver colloids ; dimethylcrocetin ; single living cell ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Gold and silver vacuum-deposited island films were characterized by studying deposition variables such as film thickness, evaporation rate, and substrate temperature. For both metals, these parameters were correlated with the surface-enhanced Raman spectroscopy (SERS) effect and an increase in film thickness and low evaporation rates were shown to upshift the wavelength at maximum optical density (λmax) and increase the optical density of the substrates. In contrast, pre- and postdeposition annealing of gold films led to the formation of substrates that exhibited a downshift of λmax. Our spectral data also indicated that silver films are substrates that are more suited for SERS applications where high frequency visible excitations are used. Measurements on gold films classified them into two groups: thin Au films (10-50 Å) well adapted for red excitations and thicker ones that are operative in the near infrared. SERS results, which were obtained from a single HL60 cell treated with micromolar drug quantities, placed on thin gold island films indicated that these island films could be future promising substrates for SERS imaging at the cellular level. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: S71-S78, 1998
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  • 31
    ISSN: 1075-4261
    Keywords: protein secondary structure ; FTIR spectroscopy ; Fourier self-deconvolution ; factor analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Fourier self-deconvolution (FSD) was performed on protein amide I and II Fourier transform infrared (FTIR) spectra to test if the resultant increased band shape variation would lead to improvements in protein secondary structure prediction with our factor analysis based restricted multiple regression (RMR) methods. FTIR spectra of 23 proteins dissolved in H2O were measured and normalized to a constant amide I peak absorbance. The deconvolved spectra were renormalized by area so that the deconvolved spectra sets had the same area as before. Principal component analysis of the deconvolved spectra sets was carried out, which was followed by a selective multiple linear regression (RMR) analysis of the principal component loadings with regard to the fractional components (FC) of secondary structure. As compared to analyses based on the original spectra set, helix and sheet predictions were not noticeably improved by FSD; but, if a very large number of component spectra (16) were retained in the pool to select which loadings to be used in the RMR optimization, better predictions of turn and “other” resulted. The prediction quality varied depending on the deconvolution parameters used. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 93-106, 1998
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  • 32
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    Biospectroscopy 4 (1998), S. 107-111 
    ISSN: 1075-4261
    Keywords: conformational mobility ; nucleic acid dynamics ; Raman optical activity ; RNA ; temperature dependence ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: The backscattered Raman and Raman optical activity (ROA) spectra of poly(rA)-poly(rU) at 20°C and 45°C in buffered aqueous solution between 650 and 1750 cm-1 are reported. Although the intensity of the majority of the Raman bands increase by varying amounts as the temperature is raised in accordance with the well-known hypochromic effect, the reverse effect is found for the ROA signals which we attribute to thermal accessibility of a greater number of distinct conformations leading to cancellation of ROA signals. The difference ROA spectrum obtained by subtracting the spectrum recorded at 45°C from that recorded at 20°C displays a very similar sign pattern to those at both 20°C and 45°C throughout the spectral region examined. This indicates that the same average structure is maintained in this temperature range and that the thermal fluctuations are correlated through the bases, the glycosidic link, the sugar ring, and the phosphate backbone of both strands. These results indicate that ROA may be a useful new probe of the dynamics of nucleic acid in solution. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 107-111, 1998
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  • 33
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    Biospectroscopy 4 (1998), S. 113-120 
    ISSN: 1075-4261
    Keywords: FT-Raman spectroscopy ; micro-Raman technique ; Ancistrocladus heyneanus ; naphthylisoquinoline alkaloids ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: The applicability of the micro-FT-Raman technique for studying alkaloids in vitro and for observing alkaloids in plant cells is demonstrated. This technique is examined using fresh plant material of Ancistrocladus heyneanus, a tropical liana known to produce pharmacologically interesting naphthylisoquinoline alkaloids as secondary metabolites. It will be shown that it is possible to localize and identify some of these alkaloids in different parts of the plant by means of Raman microspectroscopic studies. Data on the in situ structure and the spatial distribution can be obtained, which could provide information about the biosynthesis of the alkaloids in the plant. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 113-120, 1998
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  • 34
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    Biospectroscopy 4 (1998), S. 135-144 
    ISSN: 1075-4261
    Keywords: amphotericin B ; low-density lipoprotein ; oxidation ; toxicity ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: The effect of amphotericin B on the oxidation and degradation of low- and high-density lipoproteins was investigated by UV-vis spectroscopy, electron microscopy, electrophoresis, and size-exclusion chromatography. Two formulations of the drug were used: the commercial Fungizone and a new, less toxic, liposomal formulation, AmBisome. It was shown that Fungizone strongly enhanced the oxidative deformation of low-density lipoprotein structure while AmBisome did not bind to this lipoprotein fraction and did not affect its oxidation. It was shown that amphotericin B contained in Fungizone extracted cholesterol from low-density lipoproteins which sensitized them to oxidation. Both formulations of amphotericin B studied here did not bind to high-density lipoprotein and did not affect the process of its oxidation. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 135-144, 1998
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  • 35
    ISSN: 1075-4261
    Keywords: protected surface-enhanced resonance Raman spectroscopy ; chlorophyll transformation products ; pheophytins ; geochemical transformations ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Protected surface-enhanced resonance Raman spectroscopy (PSERRS) has been used to study a number of chlorophyll transformation products that have been suggested as intermediates in the so-called Treibs hypothesis which describes the transformation of ancient chlorophyll a (chla) in the biosphere into desoxophylloerythroetioporphyrin (DPEP) found in sedimentary environments. Both Soret- and Qy-resonant PSERR spectra have been recorded, providing two-dimensional structural fingerprints containing a number of bands which enable the presence of specific peripheral substituents to be identified. Some of these marker bands can be assigned directly to vibrational modes of the particular substituents. This has allowed further characterization of the vibrational spectrum of chl a; in particular, a vinyl mode has been identified which previously was thought to be Raman silent. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 147-159, 1998
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  • 36
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    Biospectroscopy 4 (1998), S. 121-133 
    ISSN: 1075-4261
    Keywords: meso-tetraarylporphyrins ; protonated forms ; visible absorption spectra ; luminescence ; radiationless transitions ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: A comparative study of the spectral-luminescent properties (at 293 K and 77 K) of meso-tetrakis(o-tolyl)porphyrin (o-TTP) and meso-tetraphenylporphyrin (TPP), and also meso-tetrakis(n-propyl)porphyrin (TPrP) in nonaqueous acid media has been carried out with the aim to reveal effects associated with the influence of methyl groups which hinder sterically the twist of the phenyl rings enhancing their conjugation with the macrocycle in acid medium. On the basis of the spectral data it is concluded that although the introduction of the methyl groups diminishes this twist of phenyls it does not eliminate it completely (the absorption spectra of protonated o-TTP are intermediate between those of TTP and TPrP). The fluorescence spectra of the protonated forms of o-TTP and TPP at 77 K are approximately mirror-symmetrical to the Q(0-0) and Q(0-1) absorption bands; on the elevation of the temperature up to 293 K the fluorescence and absorption bands broaden, the Stokes shift largely increases, and the mirror symmetry of the spectra disappears, which is indicative of changes in solute-solvent interactions in the S1 state. The analysis of the obtained data on the energetics of photophysical processes leads to the conclusion that the significant role of radiationless deexcitation in the S1 ↝ S0 channel, characteristic of the protonated form of TPP, is retained at 77 K. The introduction of the methyl groups at the ortho positions sharply decreases the corresponding rate constant, so that the S1 ↝ T1 intersystem crossing becomes the main channel of deexcitation. The influence of heavy atoms (the Cl- and Br- anions) on the luminescence of the protonated forms has been investigated. It is shown that, analogous to the case of octaethylporphyrin investigated earlier, in nonaqueous media the protonated species of o-TTP form bis adducts of the dihydrochloride type. Contrary to this, the experiments with meso-tetrakis(p-sulfophenyl)porphyrin (TPPS) in aqueous solutions have shown that the TPPS dications do not add counterions, whereas the influence of Cl- and Br- on fluorescence is realized according to the external heavy-atom effect mechanism. For nonaqueous o-TTP solutions with admixtures of HCl and CF3COOH the short-wavelength fluorescence from the S3 (B1) level has been detected whose unusual peculiarity is its enhancement in passing from 293 K to 77 K. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 121-133, 1998
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  • 37
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    Biospectroscopy 4 (1998), S. 161-170 
    ISSN: 1075-4261
    Keywords: surface-enhanced resonance Raman scattering ; SERRS ; cytochrome c3 ; electrode modifiers ; electroreflectance voltammetry ; ER ; 11-mercaptoundecanoic acid ; 4,4′-bipyridine promoters ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Surface-enhanced resonance Raman scattering and electroreflectance voltammetry were used to investigate the effect of electrode surface modification on the structure and redox properties of cytochrome c3 immobilized on Ag surfaces. It is shown that the redox reactions of cytochrome c3 are more reversible at an 11-mercaptoundecanoic acid modified Ag electrode as compared to a bare metal surface. The heme of cytochrome c3 is in a mixed low and high spin state when adsorbed at the bare electrode, whereas only the low spin form is present on the 11-mercaptoundecanoic acid modified electrode, suggesting that the native conformation is maintained in the latter case. The reduction potential is close to that of the most positive macroscopic potential as determined by electroreflectance spectroscopy. In contrast, the reduction potential as determined by SERRS undergoes a large positive shift in the presence of 4,4′-bipyridine, the magnitude of which is dependent upon the concentration of 4,4′-bipyridine. These results indicate that the effect of the cytochrome c3 interaction with the 4,4′-bipyridine-modified surface is significantly different as compared to its interaction with the 11-mercaptoundecaodoic acid modified surface. Moreover, the results emphasize that electrode modifiers can have dramatically different effects on the redox properties of different proteins. It is well known that 4,4′-bipyridine acts as a redox promoter in the case of cytochrome c, whereas no electrochemical or electroreflectance response was observed in the case of cytochrome c3. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 161-170, 1998
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  • 38
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    Biospectroscopy 4 (1998), S. 185-195 
    ISSN: 1075-4261
    Keywords: hydrogen bonding ; van der Waals ; betacarbolines ; benzopyridines ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: A spectroscopic (UV-vis, Fourier transform IR, steady state, and time-resolved fluorescence) study of the interactions of the ground and excited singlet states of harmane (1-methyl-9H-pyrido/3,4-b/indole) with quinoline has been carried out in cyclohexane, toluene, and buffered pH = 8.7 aqueous solutions. To analyze how the number of rings in the substrate influences these interactions, pyridine and phenanthridine have also been included in this study. In cyclohexane and toluene 1 : 1 stoichiometric hydrogen-bonded complexes are formed in both the ground and the excited singlet states. As the number of rings of the benzopyridines and the solvent polarity increase hydrogen-bonding interactions weaken and π-π van der Waals interactions become apparent. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 185-195, 1998
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  • 39
    ISSN: 1075-4261
    Keywords: ultraviolet resonance Raman spectroscopy ; membrane-bound peptides ; gramicidin A ; ion channel ; tryptophan orientation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: A Raman linear intensity difference (RLID) method has been developed to determine orientations of chromophores in membrane-bound peptides and proteins. The method involves orientation of the peptide or protein in lipid bilayer membranes and measurement of intensity differences between Raman spectra excited with two orthogonal laser polarizations. Analysis of the RLID spectrum is simplified when the chromophore exhibits a vibrational mode for which the Raman band is enhanced through resonance with a single molecular electronic transition. To examine the indole ring orientations of Trp residues in the gramicidin A transmembrane channel, we have prepared analogues of gramicidin A, in which one of four Trp residues is replaced by deuterated Trp (Trp-2,4,5,6,7-d5). Two vibrational Raman bands ωd3 and ωd2 of deuterated Trp have been shown to gain intensity predominantly through resonance with the Bb and La electronic transitions, respectively, when excited at 244 and 257 nm. By examining the RLID spectra of the ωd3 and ωd2 bands of gramicidin A channels oriented in phospholipid bilayer membranes, we have determined the inclination angles of the Bb and La transition moments with respect to the channel axis in the absence and presence of Na+. The orientations of the Trp-11 and Trp-13 indole rings in the gramicidin channel structure have been derived from the inclination angles of the transition moments. The indole rings of Trp-11 and Trp-13, which are known to shift along the channel axis upon binding of Na+, do not reorient during their positional shifts. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 171-184, 1998
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  • 40
    ISSN: 1075-4261
    Keywords: dipalmitoylphosphatidylcholine ; dioleoylphosphatidylcholine ; mixed-chain phospholipids ; unsaturation ; hydration ; FTIR spectroscopy ; lyotropic phase transition ; chain-melting transition ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: An algorithm for the study of the gradual hydration of phospholipid assemblies by means of Fourier transform infrared (FTIR) spectroscopy is presented. A complete series of diacyl phosphatidylcholines (PCs) including all possible analogues with palmitoyl and oleoyl residues, namely DPPC, DOPC, POPC, and OPPC, was investigated at room temperature. The lipid samples were prepared as cast films probably consisting of aligned multilamellar bilayers. The range of water activities studied in these films was regulated by adsorption via the gas phase corresponding to relative humidities of between 0 and 100%. Analyses of the IR-spectroscopic data have concentrated mainly on determining the amounts of water incorporated by each lipid as well as the hydration-induced response observed for some absorption bands of the different lipids. The water uptake at high relative humidity (RH) increases with the portion of unsaturated acyl chains in the molecular structure of the PCs. Isothermal phase transitions triggered lyotropically have been detected in demonstrating the occurrence of the main transition in POPC and OPPC films at room temperature. Moreover, it appears that both lamellar phases, the gel as well as the liquid-crystalline phase, are not uniform. They seem to comprise an amazingly large span of order/disorder states of the lipid chains generally depending on the degree of hydration. As exemplified by the significant variation in the onset of wavenumber shifts for the PO2- and C=O stretching-vibration modes, obtained as a function of hydration, a sequence of attachment to polar lipid binding sites by water molecules was established for DPPC. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 267-280, 1998
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  • 41
    ISSN: 1075-4261
    Keywords: photon migration ; ballistic photons ; two-photon excitation ; fluorescence ; time-resolved fluorescence ; optical tomography ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: We describe spatially localized two-photon excitation in scattering media. Using femtosecond pulses at 770 nm from a Ti : Sapphire laser, we were able to excite fluorophores in capillary tubes under up to 1.5 mm of 0.5% intralipid. Displacement of the laser beam relative to the embedded samples indicates that highly localized excitation was possible with two-photon excitation, whereas one-photon excitation resulted in loss of spatial resolution due to excitation by the diffusely scattered photons. These results indicate that two-photon excitation in the scattering solution is due only to the ballistic photons, a result confirmed by frequency-domain time-resolved measurements. Selective excitation of adjacent embedded samples was found possible for two but not one-photon excitation. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 303-310, 1998
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  • 42
    ISSN: 1075-4261
    Keywords: 9-aminoacridine ; fluorescence ; SERS ; dimerization ; excimer ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Fluorescence spectroscopy and surface-enhanced Raman spectroscopy (SERS) have been applied to study the aggregation and excimer emission of 9-aminoacridine (9AA) and 9-aminoacridine hydrochloride (9AA-HCl) in aqueous solution and on silver colloids. The effect of the drug concentration, pH, and chloride concentration on these processes has been investigated. The excimer emission of 9AA is connected to the dimerization of this drug in solution: the formation of 9AA dimers is greatly favored when the drug is under the amino form at neutral and acidic pH, while at alkaline pH the imino 9AA form tends to form large-sized aggregates which cannot be excited to render excimer emission. 9AA is adsorbed on the silver surface under two different forms: strongly and weakly attached 9AA, each one corresponding to the different drug tautomers: imino and amino. The interaction of 9AA with silver induces a charge transfer from the adsorbate to the metal leading to a remarkable fluorescence quenching, a basicity decrease of the adsorbed drug and a considerable weakening of the dimer-excimer emission. Furthermore, an attribution of the main Raman features appearing in the SERS spectra has been proposed, providing marker bands for the imino and amino 9AA tautomers, and a mechanism for the molecular dimerization is also suggested. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 327-339, 1998
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    ISSN: 1075-4261
    Keywords: molecular force field ; resonance Raman intensities ; aromatic amino acids ; nucleic acid bases ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Normal modes analyses for different molecules with biological interest have been performed and checked via the calculation of resonance Raman intensities. For this purpose, molecular orbital calculations were used to determine bond order changes in the lowest-lying electronic transitions. These bond order changes were used to calculate resonance Raman intensities in order to obtain correct vibrational assignments and reliable force fields. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 379-393, 1998
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  • 44
    ISSN: 1075-4261
    Keywords: FT Raman microscopy ; qualitative analysis ; bone mineralization ; hydroxyapatite coatings ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: An optimized FT Raman microscope (inverted microscope with high throughput of radiation) was developed that allows minimal sample preparation and Raman spectroscopy without fluorescence. A quantitative determination of the mineralization of bone tissue and hydroxyapatite (HA) coatings of hip and knee prostheses was performed. The lateral resolution reached down to 10 μm. The distribution of the HA content in the coatings investigated was found to be similar all the time. This result was independent of the composition of the coatings and the history of the whole prosthesis. In the immediate vicinity of the prosthesis a large HA content could be observed that decreased to a minimum towards the periphery of the coating and increased at the site of the ongrown bone. For the interface between bone and HA coating a transitional zone was observed at a lateral distance of 30-40 μm to the implant. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 403-412, 1998
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  • 45
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    Biospectroscopy 4 (1998), S. S1 
    ISSN: 1075-4261
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: No abstract.
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  • 46
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    Biospectroscopy 4 (1998), S. S31 
    ISSN: 1075-4261
    Keywords: stratum corneum ; epidermis ; noninvasive ; lipids ; natural moisturizing factor ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Noninvasive techniques that provide detailed information about molecular composition, structure, and interactions are crucial to further our understanding of the relation between skin disease and biochemical changes in the skin, as well as for the development of penetration enhancers for transdermal drug administration. In this study we present in vitro and in vivo Raman spectra of human skin. Using a Raman microspectrometer, in vitro spectra were obtained of thin cross sections of human skin. They provided insight into the molecular composition of different skin layers. Evidence was found for the existence of a large variation in lipid content of the stratum corneum. A simple experimental setup for in vivo confocal Raman microspectroscopy of the skin was developed. In vivo Raman spectra of the stratum corneum were obtained at different positions of the arm and hand of three volunteers. They provided evidence for differences in the concentration of natural moisturizing factor at these positions. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: S31-S39, 1998
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  • 47
    ISSN: 1075-4261
    Keywords: DNA dyes ; single-stranded DNA ; oxazole yellow ; fluorescent dyes ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Interactions between short single-stranded DNA oligomers of homogeneous base composition and the fluorescent probes oxazole yellow (YO) and its homodimer YOYO are described. The oligomers included 15-mers and 30-mers of polydA, polydT, polydG, and polydC. Interactions between the dyes and DNA hybrids formed from complementary homogeneous strands of equal length were also investigated. No interactions were observed between the dyes and the monomeric monophosphate nucleosides A, G, T, or C. The dyes were found to interact much more strongly with the purine oligomers polydA and polydG than with the pyrimidine oligomers polydT and polydC. PolydA of both lengths has strong interactions with YOYO, whereas the polydG 30-mer interacts strongly with monomeric YO. The 15-mers of polydG and polydC of both lengths show little interaction with either dye. Interactions of the dyes with the polydA/polydT and polydG/polydC hybrids tend to be dominated by interactions with polydA and polydG, respectively. Although dye interactions generally were facilitated by hybridization, particularly for polydA/polydT, the interactions were similar to those with the single strands and different from those that have been observed in long double-stranded DNA. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 17-25, 1998
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    Biospectroscopy 4 (1998), S. 27-35 
    ISSN: 1075-4261
    Keywords: DNA dyes ; single-stranded DNA ; oxazole yellow ; fluorescent dyes ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Interactions between short single-stranded DNA ligands and fluorescent DNA indicator dyes were used to investigate binding selectivity of the ligands. Conformational differences among four DNA ligands of different sequence and structure, including two that form a G-quartet and two that do not, were confirmed by circular dichroism spectroscopy. Their interactions with indicator dyes YO-pro-1 iodide (YO) and YOYO-1 iodide (YOYO) were probed using measurements of dye absorbance; induced circular dichroism; and fluorescence spectra, anisotropy, and lifetime. Equilibrium binding constants and stoichiometry were determined as well. Results indicate significant differences among the dye interactions and binding stoichiometries of the four ligands. One of the G-quartet forming ligands, a 20-mer of sequence 5′-GGTTTT-GGTTTTGGTTTTGG-3′, shows distinctly different interactions from the other three ligands, all of which are 15-mers. These studies illustrate the importance of sequence and conformation in determining the binding interactions of short single-stranded DNA. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 27-35, 1998
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    Biospectroscopy 4 (1998), S. 37-46 
    ISSN: 1075-4261
    Keywords: FTIR ; cancer prognosis ; cancer grade ; tissue spectroscopy ; lymphoma ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Thirty-nine freeze-dried tissue samples from 17 lymphoid tumors (nine malignant non-Hodgkin's lymphomas) were studied by Fourier transform infrared (FTIR) spectroscopy. The absorbance ratio A1121/A1020 increased, along with the emergence of an absorbance pulse at 1121 cm-1, with increasing clinicopathological grade of malignant lymphoma. An increasing A1121/A1020 ratio from benign to malignant is evident in literature spectra from several different tissues; however, the present study is the first to comment on this effect and to propose it as an index of the cellular RNA/DNA ratio after subtraction of overlapping absorbances, if present, due to collagen or glycogen. Absorbance attributable to collagen increased with lymphoma grade and was greater in benign inflammatory tumors than in low-grade lymphomas. The A1121/A1020 trend observed here may form the basis of a universal cancer-grading parameter to assist with cancer treatment decisions and may also be useful in the analysis of cellular growth perturbation induced by drugs or other therapies. Our spectral findings may potentially be applied to cell clusters and discrete areas of tumor tissue sections using the FTIR microscope, allowing correlation with morphology and a high degree of spatial resolution. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 37-46, 1998
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  • 50
    ISSN: 1075-4261
    Keywords: cytochrome ba3 ; cytochrome aa3 ; binuclear site structure ; cyanide ; Raman spectroscopy ; normal coordinates ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: The cyanide isotope-sensitive low-frequency vibrations of ferrous cyano complexes of cytochrome a3 are studied for cytochrome ba3 from Thermus thermophilus and cytochrome aa3 from bovine heart. Cyanide complexes of ba3 display three isotope sensitive frequencies at 512, 485, and 473 cm-1. The first is primarily an Fe - C stretching motion, whereas the lower wavenumber modes are bending motions. These iron-cyanide vibrations are independent of the redox levels of the other metal centers in the protein. On the other hand, the fully reduced bovine derivative complexed with cyanide gives rise to a bending vibration at 503 cm-1 and a stretching vibration at 469 cm-1. That is, the ordering of the stretching and bending frequencies is reversed from that of the bacterial protein. These results are analyzed by normal coordinate calculations to obtain comparative models for the binuclear O2 reducing site of the two proteins. We find that the observed frequencies are consistent with a linear Fe - C - N group and larger Fe - C stretching force constant (2.558 mdyn/Å) for ba3 and a slightly bent Fe - C - N group (angle ∼ 170°) and a smaller Fe - C stretching force constant (2.335 mdyn/Å) for aa3. Thus, there are significant differences in the interaction of cyanide with ferrous a3 in the two proteins that are most likely caused by a weaker proximal histidine interaction and stronger peripheral heme electron withdrawing effects in ba3. Possible sources of these protein-induced effects are discussed. Using the analysis developed here, comparison of the FeCN stretching and bending frequencies of the ferrous bovine a3-CN complex to those obtained from the ferric a3-CN complex suggests that upon conversion of the resting to the fully reduced protein, a conformational change occurs that constrains the ligand binding site. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 1-15, 1998
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  • 51
    ISSN: 1075-4261
    Keywords: infrared spectroscopy of human tissue ; basal, parabasal, and superficial layers of cervical squamous epithelium ; cell maturation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Infrared spectral results for the different epithelial layers of human cervical squamous tissue are reported. The layers, representing different cellular maturation stages, exhibit quite different spectral patterns. Thus, infrared spectroscopy presents a powerful tool to monitor cell maturation and differentiation. Furthermore, a detailed understanding of the spectra of the individual layers of tissue permit a proper interpretation of the state of health of cells exfoliated from such tissue. Part II of this series describes the use of the spectral information presented here to interpret the infrared spectra of exfoliated cells. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 47-53, 1998
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    ISSN: 1075-4261
    Keywords: infrared spectroscopy of human tissue ; squamous epithelium ; exfoliated cells ; Chemistry ; Analytical Chemistry and Spectroscopy
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    Topics: Biology , Physics
    Notes: A comparison of infrared absorption spectra obtained from the different layers of squamous epithelium from the human cervix, and infrared spectra obtained from exfoliated cervical cells, is presented. Infrared spectroscopy has been shown (in part I of this series) to be a sensitive tool to monitor maturation and differentiation of human cervical cells; therefore, this spectroscopic technique provides new insights into the composition and state of health of exfoliated cells. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 55-59, 1998
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    Biospectroscopy 4 (1998), S. 61-71 
    ISSN: 1075-4261
    Keywords: L-tyrosine ; polarized Raman spectra ; Raman tensor ; ab initio MO calculation ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: Polarized Raman scattering measurements have been made of a single crystal of L-tyrosine by the use of a Raman microscope with the 488.0-nm exciting beam from an argon ion laser. The L-tyrosine crystal belongs to the space group P212121 (orthorhombic), and Raman scattering intensities corresponding to the aa, bb, cc, ab and ac components of the crystal Raman tensor have been determined for each prominent Raman band. A similar set of measurements has been made of L-tyrosine-d4, in which four hydrogen atoms on the benzene ring are replaced by deuterium atoms. The effects of NH3 → ND3 and OH → OD on the Raman spectrum have also been examined. In addition, depolarization ratios of some bands of L-tyrosine in aqueous solutions of pH 13 and pH 1 were examined. For comparison with these experimental results, on the other hand, ab initio molecular orbital calculations have been made of the normal modes of vibration and their associated polarizability oscillations of the L-tyrosine molecule. On the basis of these experimental data and by referring to the results of the calculations, discussions have been presented on the Raman tensors associated to some Raman bands, including those at 829 cm-1 (benzene ring breathing), 642 cm-1 (benzene ring deformation), and 432 cm-1 (Cα-Cβ-Cγ bending). © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 61-71, 1998
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  • 54
    ISSN: 1075-4261
    Keywords: FTIR microspectroscopy ; cervical cancer ; leukocytes ; lymphocytes ; erythrocytes ; semen ; mucins ; fibroblasts ; thrombocytes ; bacteria ; nylon ; Candida albicans ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: FTIR microscopy was applied to the analysis of cell types and other variables present in Pap smears to ascertain the limitations of infrared spectroscopy in the diagnosis of cervical cancer and dysplasia. It was found that leukocytes, and in particular lymphocytes, have spectral features in the phophodiester region (1300-900 cm-1) suggestive of what has previously been described as changes indicative of malignancy. Endocervical cells and fibroblasts have similar spectral features to HeLa cells and consequently could also confound diagnosis. The use of ethanol as a fixative and dehydrating agent results in retention of glycogen in cervical cell types and thus minimizes spectral changes in the glycogen region due to sampling technique. Spectra of seminal fluids exhibit strong bands in the phosphodiester/carbohydrate region; however, sperm contamination should be easily detectable by the presence of a distinctive doublet at 981/968 cm-1. Erythrocyte spectra exhibit a reduction in glycogen band intensity, but can be discerned by a relatively low-intensity νs $PO^{-}_{2}$ band. Endocervical mucin spectra exhibit a reduction in glycogen bands and a very pronounced νs $PO^{-}_{2}$ band, which is similar in intensity to the corresponding band in HeLa cells. Thrombocytes have strong bands in the phosphodiester region, but thrombocytes can be discerned from other cell types by the presence of two small broad bands at 980 and 935 cm-1. Candida albicans is characterized by strong bands in the polysaccharide region which could potentially obscure diagnostic bands if C. albicans is present in large numbers. Spectra of bacteria common to the female genital tract, in general, also have strong absorptions in the polysaccharide region; however, bacterial contamination is usually minimal and would not be expected to obscure cervical cell spectra. Nylon threads and bristles from cervical sampling implements produce characteristic IR profiles which allow for easy identification. Given the number of potential confounding variables associated with cervical cytology, a multivariate statistical or neural network analysis would appear to be necessary before the implementation of FTIR technology in clinical laboratories. © 1998 John Wiley & Sons, Inc. Biospectroscopy 4: 75-91, 1998
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    International Journal for Numerical Methods in Engineering 43 (1998), S. 425-440 
    ISSN: 0029-5981
    Keywords: numerical methods ; time-marching ; dynamics ; optimal control ; boundary-value problems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An hp-version finite element method for one-dimensional boundary value problems is presented. The method is based on a similar approach developed by the authors for solution of optimal control problems. The primary applications for the methodology include two-point- and multi-point-boundary-value problems, for example, in the time domain. Results presented for a 7-state/3-phase missile problem show that the method is very efficient for time-marching applications. Furthermore, it easily solves time-domain problems with discontinuities in the system equations and/or in the states, where the time at which these jumps (i.e. ‘events’) take place is determined by equations that govern the states. An example involving friction with intermittent sticking is presented to illustrate the power of the method. © 1998 John Wiley & Sons, Ltd.
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 387-406 
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In solving unsteady problems,domain decomposition methods may be used either for iterative preconditioning each global implicit time-step or directly (noniteratively) within a blockwise implicit time-stepping procedure, in the latter case, the inner boundary values for the subproblems are generated by explicit time-extrapolation. The overlapping variants of this method have been proved to be efficient tools for solving parabolic and first-order hyperbolic problems on modern parallel computers, because they require global communication only once per time-step. The mechanism making this possible is the exponential decay in space of the time-discrete Green's function. We investigate several model problems of convection and convection-diffusion. Favorable optimal and far-reaching estimates of the overlap required have been established in the case of exemplary standard upwind finite-difference schemes. In particular, it has been shown that the overlap for the convection-diffusion problem is the additive function of overlaps for the corresponding convection and diffusion problem to be considered independently. These results have been confirmed with several numerical test examples. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 387-406, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 89-96 
    ISSN: 0749-159X
    Keywords: finite element method ; third-order differential equation ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A splitting of a third order partial differential equation into a first-order and a second-order one is proposed as the basis for a mixed finite element method to approximate its solution. A time-continuous numerical method is described and error estimates for its solution are demonstrated. Finally, a full discretization is described based on backward Euler finite differences in time, and error estimates for the resulting approximation are established. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 89-96, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 97-114 
    ISSN: 0749-159X
    Keywords: non-Newtonian fluids ; finite elements ; error estimates ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Numerical simulation of industrial processes involving viscoelastic liquids is often based on finite element methods on quadrilateral meshes. However, numerical analysis of these methods has so far been limited to triangular meshes. In this work, we consider quadrilateral meshes. We first study the approximation of the transport equation by a Galerkin discontinuous method and prove an O(hk+1/2) error estimates for the Qk finite element. Then we study a differential model for viscoelastic flow with unknowns u the velocity, p the pressure, and σ the viscoelastic part of the extra-stress tensor. The approximations are ((Q1)2 transforms of) Qk+1 continuous for u, Qk discontinuous for σ, and Pk discontinuous for p, with k ≥ 1. Upwinding for σ is obtained by the Galerkin discontinuous method. We show that an error estimate of order O(hk+1/2) is valid in the energy norm for the three unknowns. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 97-114, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 115-141 
    ISSN: 0749-159X
    Keywords: Navier-Stokes equations ; spectral elements ; stabilization techniques ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The conforming spectral element methods are applied to solve the linearized Navier-Stokes equations by the help of stabilization techniques like those applied for finite elements. The stability and convergence analysis is carried out and essential numerical results are presented demonstrating the high accuracy of the method as well as its robustness. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 115-141, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 143-157 
    ISSN: 0749-159X
    Keywords: Normal mode stability ; spectral approximation ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The accuracy of calculating the normal modes in the numerical linear stability study of two-dimensional nondivergent viscous flows on a rotating sphere is analyzed. Discrete spectral problems are obtained by truncating Fourier's series of the spherical harmonics for both the basic flow and the disturbances to spherical polynomials of degrees K and N, respectively. The spectral theory for the closed operators [1], and embedding theorems for the Hilbert and Banach spaces of smooth functions on a sphere are used to estimate the rate of convergence of the eigenvalues and eigenvectors. It is shown that the convergence takes place if the basic state is sufficiently smooth, and the truncation numbers K and N of Fourier's series for the basic flow and disturbances tend to infinity keeping the ratio N/K fixed. The convergence rate increases with the smoothness of the basic flow and with the power s of the Laplace operator in the vorticity equation diffusion term. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:143-157, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 159-168 
    ISSN: 0749-159X
    Keywords: ADI scheme ; parabolic differential equation ; stability ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A second-order unconditionally stable ADI scheme has been developed for solving three-dimensional parabolic equations. This scheme reduces three-dimensional problems to a succession of one-dimensional problems. Further, the scheme is suitable for simulating fast transient phenomena. Numerical examples show that the scheme gives an accurate solution for the parabolic equation and converges rapidly to the steady state solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:159-168, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 297-315 
    ISSN: 0749-159X
    Keywords: elasticity equations ; least-squares ; finite elements ; error estimates ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new stress-pressure-displacement formulation for the planar elasticity equations is proposed by introducing the auxiliary variables, stresses, and pressure. The resulting first-order system involves a nonnegative parameter that measures the material compressibility for the elastic body. A two-stage least-squares finite element procedure is introduced for approximating the solution to this system with appropriate boundary conditions. It is shown that the two-stage least-squares scheme is stable and, with respect to the order of approximation for smooth exact solutions, the rates of convergence of the approximations for all the unknowns are optimal both in the H1-norm and in the L2-norm. Numerical experiments with various values of the parameter are examined, which demonstrate the theoretical estimates. Among other things, computational results indicate that the behavior of convergence is uniform in the nonnegative parameter. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 297-315, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 339-351 
    ISSN: 0749-159X
    Keywords: monotone iteration ; finite difference equation ; reaction-diffusion-convection ; time delay ; upper and lower solutions ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article we use the monotone method for the computation of numerical solutions of a nonlinear reaction-diffusion-convection problem with time delay. Three monotone iteration processes for a suitably formulated finite-difference system of the problem are presented. It is shown that the sequence of iteration from each of these iterative schemes converges from either above or below to a unique solution of the finite-difference system without any monotone condition on the nonlinear reaction function. An analytical comparison result among the three processes of iterations is given. Also given is the application of the iterative schemes to some model problems in population dynamics, including numerical results of a model problem with known analytical solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 339-351, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 353-365 
    ISSN: 0749-159X
    Keywords: Euler equations ; contact discontinuity ; finite difference schemes ; dispersion ; first-order wave equation ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We introduce a method, constructed such that numerical solutions of the wave equation are well behaved when the solutions also contain discontinuities. The wave equation serves as a model problem for the Euler equations when the solution contains a contact discontinuity. Numerical computations of linear equations and the Euler equations in one and two dimensions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 353-365, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 367-386 
    ISSN: 0749-159X
    Keywords: finite element methods ; superconvergence ; the Reissner-Mindlin plate ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A projected-shear finite element method for periodic Reissner-Mindlin plate model are analyzed for rectangular meshes. A projection operator is applied to the shear stress term in the bilinear form. Optimal error estimates in the L2-norm, the H1-norm, and the energy norm for both displacement and rotations are established and gradient superconvergence along the Gauss lines is justified in some weak senses. All the convergence and superconvergence results are uniform with respect to the thickness parameter t. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 367-386, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 407-437 
    ISSN: 0749-159X
    Keywords: Maxwell's equations ; magnetotellurics ; domain decomposition ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A collection of global and domain decomposition mixed finite element schemes for the approximate solution of the harmonic Maxwell's equations on a bounded domain with absorbing boundary conditions at the artificial boundaries are presented. The numerical procedures allow us to solve efficiently the direct problem in magnetotellurics consisting of determining the electromagnetic scattered field in a two-dimensional earth model of arbitrary conductivity properties. Convergence results for the numerical procedures are derived. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 407-437, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 549-565 
    ISSN: 0749-159X
    Keywords: boundary integral ; finite element ; Navier-Stokes equations ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article, we represent a new numerical method for solving the nonstationary Navier-Stokes equations in an unbounded domain. The technique consists of coupling the boundary integral and the finite element method. The variational formulation and the well-posedness of the coupling method are obtained. The convergence and optimal error estimates for the approximate solution are provided. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 549-565, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 519-548 
    ISSN: 0749-159X
    Keywords: miscible displacements ; finite elements ; error estimates ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Finite element methods are used to solve a coupled system of nonlinear partial differential equations, which models incompressible miscible displacement in porous media. Through a backward finite difference discretization in time, we define a sequentially implicit time-stepping algorithm that uncouples the system at each time-step. The Galerkin method is employed to approximate the pressure, and accurate velocity approximations are calculated via a post-processing technique involving the conservation of mass and Darcy's law. A stabilized finite element (SUPG) method is applied to the convection-diffusion equation delivering stable and accurate solutions. Error estimates with quasi-optimal rates of convergence are derived under suitable regularity hypotheses. Numerical results are presented confirming the predicted rates of convergence for the post-processing technique and illustrating the performance of the proposed methodology when applied to miscible displacements with adverse mobility ratios. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 519-548, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 567-579 
    ISSN: 0749-159X
    Keywords: finite difference ; finite element ; triangular grid ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We define a finite differences method for triangular grids and we show how to link it to a finite element method. From this new point of view we then analyze properties of the solution and convergence. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 567-579, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 593-606 
    ISSN: 0749-159X
    Keywords: finite difference approximations ; Poisson equation ; symbolic computation ; Mathematica ; three-dimensions ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A symbolic procedure for deriving various finite difference approximations for the three-dimensional Poisson equation is described. Based on the software package Mathematica, we utilize for the formulation local solutions of the differential equation and obtain the standard second-order scheme (7-point), three fourth-order finite difference schemes (15-point, 19-point, 21-point), and one sixth-order scheme (27-point). The symbolic method is simple and can be used to obtain the finite difference approximations for other partial differential equations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 593-606, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 717-737 
    ISSN: 0749-159X
    Keywords: parallel ; domain decomposition ; nonlinear ; elliptic equation ; space decomposition ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This work presents some space decomposition algorithms for a convex minimization problem. The algorithms has linear rate of convergence and the rate of convergence depends only on four constants. The space decomposition could be a multigrid or domain decomposition method. We explain the detailed procedure to implement our algorithms for a two-level overlapping domain decomposition method and estimate the needed constants. Numerical tests are reported for linear as well as nonlinear elliptic problems. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 717-737, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 695-716 
    ISSN: 0749-159X
    Keywords: Rosenau equation ; orthogonal spline collocation method ; differential algebraic equations (DAEs) ; implicit Runge-Kutta methods ; decay estimates ; BBM (Benjamin-Bona-Mahony) equation ; BBMB (Benjamin-Bona-Mahony-Burgers) equation ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A second-order splitting method is applied to a KdV-like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L2 and L∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin-Bona-Mahony) and BBMB (Benjamin-Bona-Mahony-Burgers) equations and the well-known decay estimates are demonstrated for the computed solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 695-716, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 781-814 
    ISSN: 0749-159X
    Keywords: hyperbolic problems ; IBVP ; multi-dimensional ; nonorthogonal mesh ; quasi-linear form ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A matricial formalism to solve multi-dimensional initial boundary values problems for hyperbolic equations written in quasi-linear based on the λ scheme approach is presented. The derivation is carried out for nonorthogonal, moving systems of curvilinear coordinates. A uniform treatment of the integration at the boundaries, when the boundary conditions can be expressed in terms of combinations of time or space derivatives of the primitive variables, is also presented. The methodology is validated against a two-dimensional test case, the supercritical flow through the Hobson cascade n.2, and in three-dimensional test cases such as the supersonic flow about a sphere and the flow through a plug nozzle. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 781-814, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 815-820 
    ISSN: 0749-159X
    Keywords: Burgers equation ; nonstandard finite difference schemes ; traveling waves ; exact solutions ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We construct a finite difference scheme for the ordinary differential equation describing the traveling wave solutions to the Burgers equation. This difference equation has the property that its solution can be calculated. Our procedure for determining this solution follows closely the analysis used to obtain the traveling wave solutions to the original ordinary differential equation. The finite difference scheme follows directly from application of the nonstandard rules proposed by Mickens. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 815-820, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 821-842 
    ISSN: 0749-159X
    Keywords: homogenization ; asymptotic analysis ; ink-jet printer ; droplet generator ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We modelize the behavior of a vibrating fluid cavity. Small nozzles are uniformly distributed in one direction on a side of the cavity. By means of asymptotic expansion in powers of the smallest dimension of the cavity, including boundary layer terms, we get the convergence of the solution of the three-dimensional problem, as well as the convergence of the solution of the “homogenized” three-dimensional problem towards the solution of the same two-dimensional problem. Numerical experiments have been carried out in order to illustrate the previous theoretical results. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 821-842, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 1-25 
    ISSN: 0749-159X
    Keywords: Finite difference ; thermoelastic contact ; nonlinear parabolic system ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article, we study a sequence of finite difference approximate solutions to a parabolic system, which models two dissimilar rods that may come into contact as a result of thermoelastic expansion. We construct the approximate solutions based on a set of finite difference schemes to the system, and we will prove that the approximate solutions converge strongly to the exact solutions. Moreover, we obtain and prove rigorously the error bound, which measures the difference between the exact solutions and approximate solutions in a reasonable norm. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 1-25, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 27-46 
    ISSN: 0749-159X
    Keywords: Parallel ; domain decomposition ; parabolic equation ; space decomposition ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank-Nicolson scheme is used for the parabolic equation, then by suitably choosing the space decomposition, only O(| log τ |) steps of iteration at each time level are needed, where τ is the time-step size. Applications to overlapping domain decomposition and to a two-level method are given for a second-order parabolic equation. The analysis shows that only a one-element overlap is needed. Discussions about iterative and noniterative methods for parabolic equations are presented. A method that combines the two approaches and utilizes some of the good properties of the two approaches is tested numerically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 27-46, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 47-61 
    ISSN: 0749-159X
    Keywords: p-version finite element method ; boundary element method ; interface problem ; preconditioning ; domain decomposition ; additive Schwarz method ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We propose and analyze efficient preconditioners for solving systems of equations arising from the p-version for the finite element/boundary element coupling. The first preconditioner amounts to a block Jacobi method, whereas the second one is partly given by diagonal scaling. We use the generalized minimum residual method for the solution of the linear system. For our first preconditioner, the number of iterations of the GMRES necessary to obtain a given accuracy grows like log2 p, where p is the polynomial degree of the ansatz functions. The second preconditioner, which is more easily implemented, leads to a number of iterations that behave like p log3 p. Computational results are presented to support this theory. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 47-61, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 63-88 
    ISSN: 0749-159X
    Keywords: Maxwell equations ; edge finite elements ; mass lumping ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Finite element and finite difference methods for approximating the Maxwell system propagate numerical waves with slightly incorrect velocities, and this results in phase error in the computed solution. Indeed this error limits the type of problem that can be solved, because phase error accumulates during the computation and eventually destroys the solution. Here we propose a family of mass-lumped finite element schemes using edge elements. We emphasize in particular linear elements that are equivalent to the standard Yee FDTD scheme, and cubic elements that have superior phase accuracy. We prove theorems that allow us to perform a dispersion analysis of the two common families of edge elements on rectilinear grids. A result of this analysis is to provide some justification for the choice of the particular family we use. We also provide a limited selection of numerical results that show the efficiency of our scheme. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 63-88, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 169-192 
    ISSN: 0749-159X
    Keywords: finite element space ; (1 + α˜)-regular mesh partition ; recovered gradient ; superconvergence ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We propose the use of an averaging scheme, which recovers gradients from piecewise linear finite element approximations on the (1 + α˜) - regular triangular elements to gradients of the weak solution of a second-order elliptic boundary value problem in the 2-dimensional space. The recovered gradients, from mid-points of element edges, are superconvergent estimates of the true gradients. This work is an extension of Levine [Levine, IMA J. Numer. Anal. 5, 407 (1985)] and follows some of the ideas therein. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:169-192, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 193-212 
    ISSN: 0749-159X
    Keywords: Cell-centered finite differences ; upwind approximations ; error estimates ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two cell-centered finite difference schemes on Voronoi meshes are derived and investigated. Stability and error estimates in a discrete H1-norm for both symmetric and nonsymmetric problems, including convection dominated, are proven. The theoretical results are illustrated with several numerical experiments. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:193-212, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 213-231 
    ISSN: 0749-159X
    Keywords: cell-centered finite volume method ; convergence ; finite element method ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The article is devoted to the study of convergence properties of a Finite Volume Method (FVM) using Voronoi boxes for discretization. The approach is based on the construction of a new nonconforming Finite Element Method (FEM), such that the system of linear equations coincides completely with that for the FVM. Thus, by proving convergence properties of the FEM, we obtain similar ones of the FVM. In this article, the investigations are restricted to the Poisson equation. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:213-231, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 233-249 
    ISSN: 0749-159X
    Keywords: Infinite domain ; semi-infinite strip ; Dirichlet-to-Neumann ; Finite element ; variable coefficients ; nonlinear elliptic PDEs ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Dirichlet-to-Neumann (DtN) Finite Element Method is a combined analytic-numerical method for boundary value problems in infinite domains. The use of this method is usually based on the assumption that, in the infinite domain D exterior to the finite computational domain, the governing differential equations are sufficiently simple. In particular, in D it is generally assumed that the equations are linear, homogeneous, and have constant coefficients. In this article, an extension of the DtN method is proposed, which can be applied to elliptic problems with “irregularities” in the exterior domain D, such as (a) inhomogeneities, (b) variable coefficients, and (c) nonlinearities. This method is based on iterative “regularization” of the problem in D, and on the efficient treatment of infinite-domain integrals. Semi-infinite strip problems are used for illustrating the method. Convergence of the iterative process is analyzed both theoretically and numerically. Nonuniformity difficulties and a way to overcome them are discussed. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:233-249, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 251-262 
    ISSN: 0749-159X
    Keywords: Moving finite element ; discontinuous Galerkin ; space-time orientation ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article deals with moving finite element methods by use of the time-discontinuous Galerkin formulation in combination with oriented space-time meshes. A principle for mesh orientation in space-time based on minimization of the residual, related to adaptive error control via an a posteriori error estimate, is presented. The relation to Miller's moving finite element method is discussed. The article deals with scalar problems; systems will be treated in a companion article. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:251-262, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 263-280 
    ISSN: 0749-159X
    Keywords: Convection-diffusion equation ; iterative methods ; fourth-order compact discretization schemes ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the convergence and performance of iterative methods with the fourth-order compact discretization schemes for the one- and two-dimensional convection-diffusion equations. For the one-dimensional problem, we investigate the symmetrizability of the coefficient matrix and derive an analytical formula for the spectral radius of the point Jacobi iteration matrix. For the two-dimensional problem, we conduct Fourier analysis to determine the error reduction factors of several basic iterative methods and comment on their potential use as the smoothers for the multilevel methods. Finally, we perform numerical experiments to verify our Fourier analysis results. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:263-280, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 281-296 
    ISSN: 0749-159X
    Keywords: singularities ; elliptic PDE ; Laplace equation ; high-order Finite Difference Schemes ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A high-order semi-analytic finite difference scheme is presented to overcome degradation of numerical performance when applied to two-dimensional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional representation of the exact solution in the vicinity of the singularities, and a conventional finite difference scheme on the remaining domain. It is shown that the L-S SFDS is “pollution” free, i.e., no degradation in the convergence rate occurs because of the singularities, and the coefficients of the asymptotic solution in the vicinity of the singularities are computed as a by-product with a very high accuracy. Numerical examples for the Laplace and Poisson equations over domains containing re-entrant corners or abrupt changes in the boundary conditions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 281-296, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 317-337 
    ISSN: 0749-159X
    Keywords: s-i-s epidemic model ; finite difference ; method of characteristics ; asymptotic behavior ; periodic solution ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A finite difference scheme along the characteristics is used to approximate the solution of an age-dependent s-i-s epidemic model. The global behavior of the discrete solution resulting from the algorithm is investigated. It is shown that a nontrivial discrete periodic solution is generated by a periodic force of infection. Sufficient (and explicit) threshold conditions for the existence and stability of a unique nontrivial periodic solution are given. Results from numerical experiments are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 317-337, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 439-465 
    ISSN: 0749-159X
    Keywords: mesh-centered finite differences ; nodal methods ; elliptic problems ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: After it is shown that the classical five-point mesh-centered finite difference scheme can be derived from a low-order nodal finite element scheme by using nonstandard quadrature formulae, higher-order block mesh-centered finite difference schemes for second-order elliptic problems are derived from higher-order nodal finite elements with nonstandard quadrature formulae as before, combined to a procedure known as “transverse integration.” Numerical experiments with uniform and nonuniform meshes and different types of boundary conditions confirm the theoretical predictions, in discrete as well as continuous norms. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 439-465, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 467-485 
    ISSN: 0749-159X
    Keywords: convection-reaction equations ; Lagrangian methods ; convective flows ; reactive solute transport problems ; exact finite difference schemes ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new nonstandard Lagrangian method is constructed for the one-dimensional, transient convective transport equation with nonlinear reaction terms. An “exact” time-stepping scheme is developed with zero local truncation error with respect to time. The scheme is based on nonlocal treatment of nonlinear reactions, and when applied at each spatial grid point gives the new fully discrete numerical method. This approach leads to solutions free from the numerical instabilities that arise because of incorrect modeling of derivatives and nonlinear reaction terms. Algorithms are developed that preserve the properties of the numerical solution in the case of variable velocity fields by using nonuniform spatial grids. Effects of different interpolation techniques are examined and numerical results are presented to demonstrate the performance of the proposed new method. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 467-485, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 487-518 
    ISSN: 0749-159X
    Keywords: A posteriori error estimates ; nonlinear parabolic PDEs ; time-dependent Navier-Stokes equations ; space-time finite elements ; θ-scheme ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Using the abstract framework of [R. Verfürth, Math. Comput. 62, 445-475 (1996)], we analyze a residual a posteriori error estimator for space-time finite element discretizations of parabolic PDEs. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizations in particular cover the so-called θ-scheme, which includes the implicit and explicit Euler methods and the Crank-Nicolson scheme. As particular examples we consider scalar quasilinear parabolic PDEs of 2nd order and the time-dependent incompressible Navier-Stokes equations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 487-518, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 581-591 
    ISSN: 0749-159X
    Keywords: iterative methods ; Hermitian splitting ; successive overrelaxation ; convection-diffusion equation ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solution of the linear system Ax = b by iterative methods requires a splitting of the coefficient matrix in the form A = M - N where M is usually chosen to be a diagonal or a triangular matrix. In this article we study relaxation methods induced by the Hermitian and skew-Hermitian splittings for the solution of the linear system arising from a compact fourth order approximation to the one dimensional convection-diffusion equation and compare the convergence rates of these relaxation methods to that of the widely used successive overrelaxation (SOR) method. Optimal convergence parameters are derived for each method and numerical experiments are given to supplement the theoretical estimates. For certain values of the diffusion parameter, a relaxation method based on the Hermitian splitting converges faster than SOR. For two-dimensional problems a block form of the iterative algorithm is presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 581-591, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 607-625 
    ISSN: 0749-159X
    Keywords: convection-diffusion-reaction equation ; finite volume method ; exponential scheme ; flux computation ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A finite volume method for the convection-diffusion-reaction equation is presented, which is a model equation in combustion theory. This method is combined with an exponential scheme for the computation of the fluxes. We prove that the numerical fluxes are second-order accurate, uniformly in the local Peclet numbers. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 607-625, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 627-648 
    ISSN: 0749-159X
    Keywords: scalar conservation laws ; dimensional splitting ; front tracking ; error bounds ; adaptive grid refinement ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Front tracking in combination with dimensional splitting is analyzed as a numerical method for scalar conservation laws in two space dimensions. An analytic error bound is derived, and convergence rates based on numerical experiments are presented. Numerical experiments indicate that large CFL numbers can be used without loss of accuracy for a wide range of problems. A new method for grid refinement is introduced. The method easily allows for dynamical changes in the grid, using, for instance, the total variation in each grid cell as a criterion for introducing new or removing existing refinements. Several numerical examples are included, highlighting the features of the numerical method. A comparison with a high-resolution method confirms that dimensional splitting with front tracking is a highly viable numerical method for practical computations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 627-648, 1998
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    Numerical Methods for Partial Differential Equations 14 (1998), S. 649-665 
    ISSN: 0749-159X
    Keywords: linear stability ; zonal flows ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The normal mode (linear) stability of zonal flows of a nondivergent fluid on a rotating sphere is considered. The spherical harmonics are used as the basic functions on the sphere. The stability matrix representing in this basis the vorticity equation operator linearized about a zonal flow is analyzed in detail using the recurrent formula derived for the nonlinear triad interaction coefficients. It is shown that the zonal flow having the form of a Legendre polynomial Pn(μ) of degree n is stable to infinitesimal perturbations of every invariant set Im with |m| ≥ n. For each zonal number m, Im is here the span of all the spherical harmonics $Y^{m}_{k}(x)$, whose degree k is greater than or equal to m. It is also shown that such small-scale perturbations are stable not only exponentially, but also algebraically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 649-665, 1998
    Additional Material: 4 Ill.
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  • 95
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    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 679-693 
    ISSN: 0749-159X
    Keywords: least squares method ; finite element method ; Volterra equation ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this article least squares approximations to Volterra integral equations are considered, both with exact integration and with quadrature. Optimal error estimates are derived, and it is shown that the same order of convergence is obtained in both cases with only modest requirements on the quadrature rule used in the latter. The most important practical setting for least squares is the case of convolution kernels, and these are also studied in this article. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 679-693, 1998
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  • 96
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    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 667-678 
    ISSN: 0749-159X
    Keywords: Method of fundamental solutions ; elliptic boundary value problems ; Stokes flow ; free surface ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the use of the Method of Fundamental Solutions (MFS) for solving Stokes flow problems with a free surface. We apply the method to the creeping planar Newtonian extrudate-swell problem and study the effect of the surface tension on the free surface. The results are in good agreement with existing finite element and boundary element solutions. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 667-678, 1998
    Additional Material: 5 Ill.
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  • 97
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    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 739-780 
    ISSN: 0749-159X
    Keywords: advection-diffusion-reaction transport equations ; characteristic methods ; error estimates ; Eulerian-Lagrangian methods ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A family of ELLAM (Eulerian-Lagrangian localized adjoint method) schemes is developed and analyzed for linear advection-diffusion-reaction transport partial differential equations with any combination of inflow and outflow Dirichlet, Neumann, or flux boundary conditions. The formulation uses space-time finite elements, with edges oriented along Lagrangian flow paths, in a time-stepping procedure, where space-time test functions are chosen to satisfy a local adjoint condition. This allows Eulerian-Lagrangian concepts to be applied in a systematic mass-conservative manner, yielding numerical schemes defined at each discrete time level. Optimal-order error estimates and superconvergence results are derived. Numerical experiments are performed to verify the theoretical estimates. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 739-780, 1998
    Additional Material: 2 Tab.
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