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  • Nitrogen fixation  (148)
  • Bone  (145)
  • CR: 5.17  (143)
  • Springer  (436)
  • Cambridge University Press
  • 1980-1984  (289)
  • 1975-1979  (147)
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  • 1
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    Springer
    Computing 25 (1980), S. 317-335 
    ISSN: 1436-5057
    Keywords: AMS (MOS): 65L65 ; CR: 5.17 ; AMS (MOS): 65L65 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract In this paper a general procedure to obtain spline approximations for the solutions of initial value problems for ordinary differential equations is presented. Several well-known spline approximation methods are included as special cases. It is common practice to partition the interval for which the initial value problem is defined into equidistant subintervals and to construct successively the spline approximation; thereby the spline function has to satisfy certain conditions at the knots. In the general procedure presented here additional knots are admitted in every subinterval. At these points which need not be equally spaced the spline approximation has to fulfill analogous conditions as at the original knots. Convergence and divergence theorems are proved; especially the influence of the additional knots on convergence and divergence of the method is investigated.
    Notes: Zusammenfassung In dieser Arbeit wird ein allgemeines Verfahren zur Erzeugung von Splineapproximationen für die Lösungen von Anfangswertproblemen bei gewöhnlichen Differentialgleichungen vorgestellt. Einige der bekannten Spline-approximationsmethoden sind als Spezialfälle enthalten. Eine gängige Vorgehensweise besteht darin, das Intervall, über dem das Anfangswertproblem gegeben ist, in äquidistante Teilintervalle zu zerlegen und dann sukzessive die Splineapproximation zu definieren. Hierbei wird gefordert, daß die Spline-approximation in den Knoten gewisse Bedingungen erfüllt. Bei dem hier betrachteten allgemeinen Verfahren werden in den einzelnen Teilintervallen noch zusätzliche Zwischenknoten eingeführt. In diesen Punkten, die nicht äquidistant sein müssen, werden für die Splineapproximation analoge Bedingungen wie in den Hauptknoten vorgeschrieben. Konvergenz- und Divergenzsätze werden bewiesen, insbesondere wird der Einfluß der Zwischenknoten auf Konvergenz und Divergenz des Verfahrens untersucht.
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  • 2
    ISSN: 1436-5057
    Keywords: 65L05 ; CR: 5.17 ; Numer. Analysis ; verallgemeinerte Runge-Kutta-Methoden ; steife Probleme
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract Adaptive Runge-Kutta-methods are considered. Investigations of stability for these linear implicit methods are studied. For the application a LS-stable method of order four with an adaptive stepsize control is proposed. Test results for 25 stiff initial value problems for different tolerances are discussed.
    Notes: Zusammenfassung Es werden adaptive Runge-Kutta-Verfahren betrachtet und Stabilitätsuntersuchungen für diese linear impliziten Methoden durchgeführt. Für die Anwendung wird ein LS-stabiles Verfahren vierter Ordnung mit einer angepaßten Schrittweitenkontrolle vorgeschlagen. Testergebnisse von 25 stiff Anfangswertproblemen für verschiedenen Toleranzen werden diskutiert.
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  • 3
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    Numerische Mathematik 40 (1982), S. 179-199 
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; Primary 65N30 ; Secondary 35R35 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Two problems are considered in the paper: the first of them is connected with elliptic variational inequalities and consists in developing a moving obstacle algorithm for approximating the unknown free boundary; the other problem is linked with numerical solution of the Stefan problem, which is formulated in the similar way as in the elliptic case. Some computational aspects are also discussed in the paper.
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  • 4
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    Numerische Mathematik 40 (1982), S. 207-227 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Several regularization methods for parabolic equations backwards in time together with the usual additional constraints for their solution are considered. The error of the regularization is estimated from above and below. For a “boundary value problem in time”-method, finite elements as well as a time discretization are introduced and the error with respect to the regularized solution is estimated, thus giving an overall error of the discrete regularized problem. The algorithm is tested in simple numerical examples.
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  • 5
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    Numerische Mathematik 43 (1984), S. 105-119 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new formulation of the Dirichlet problem for the biharmonic operator is presented. This gives rise to a simple numerical method to solve the above problem. Convergence is proved in the unidimensional case. Numerical results in one and two dimensional test problems are presented.
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  • 6
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    Numerische Mathematik 43 (1984), S. 175-198 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 L 10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present a difference scheme for solving a semilinear singular perturbation problem with any number of turning points of arbitrary orders. It is shown that a solution of the scheme converges, uniformly in a perturbation parameter, to that of the continuous problem.
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  • 7
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary This paper uses Augmented Lagrangian techniques for the numerical solution of equilibrium problems of compressible hyperelastic bodies subjected to large deformations. The resulting method is illustrated by several numerical examples.
    Notes: Résumé Cet article applique les techniques de Lagrangien Augmenté à la résolution numérique des problèmes d'équilibre de corps hyperélastiques compressibles soumis à de grandes déformations. La méthode obtenue est illustrée par plusieurs exemples numériques.
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  • 8
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    Numerische Mathematik 39 (1982), S. 221-230 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper Adams type methods for the special case of neutral functional differential equations are examined. It is shown thatk-step methods maintain orderk+1 for sufficiently small step size in a sufficiently smooth situation. However, when these methods are applied to an equation with a “non-smooth” solution the order of convergence is only one. Some computational considerations are given and numerical experiments are presented.
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  • 9
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    Numerische Mathematik 39 (1982), S. 309-324 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems. Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor ofε n+1 can be obtained (where ɛ is the “small” parameter andn is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.
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  • 10
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    Numerische Mathematik 39 (1982), S. 341-350 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We discuss the construction of three-point finite difference approximations and their convergence for the class of singular two-point boundary value problems: (x α y′)′=f(x,y), y(0)=A, y(1)=B, 0〈α〈1. We first establish a certain identity, based on general (non-uniform) mesh, from which various methods can be derived. To obtain a method having order two for all α∈(0,1), we investigate three possibilities. By employing an appropriate non-uniform mesh over [0,1], we obtain a methodM 1 based on just one evaluation off. For uniform mesh we obtain two methodsM 2 andM 3 each based on three evaluations off. For α=0,M 1 andM 2 both reduce to the classical second-order method based on one evaluation off. These three methods are investigated, theirO(h 2)-convergence established and illustrated by numerical examples.
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  • 11
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    Numerische Mathematik 39 (1982), S. 371-404 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The purpose of this paper is to study the approximation of the Von Karman equations by the mixed finite element scheme of Miyoshi and to follow the solutions arcs at a neighbourhood of the first eigenvalue of the linearized problem. This last problem is solved by a continuation method.
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  • 12
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    Numerische Mathematik 39 (1982), S. 449-463 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L65 ; CR: 5.17 ; AMS (MOS): 65L65 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary In [10] a general procedureV is presented to obtain spline approximations by collocation for the solutions of initial value problems for first order ordinary differential equations. In this paper the attainable order of convergence with respect to the maximum norm is characterized in dependence of the parameters involved inV; in particular the appropriate choice of the collocation points is considered.
    Notes: Zusammenfassung In [10] ist ein allgemeines VerfahrenV beschrieben, das die Lösungen von Anfangswertproblemen bei gewöhnlichen Differentialgleichungen erster Ordnung durch Splines approximiert. Die Konstruktion der Splines erfolgt hierbei mittels Kollokation. In dieser Arbeit wird die maximal erreichbare Konvergenzordnung vonV bezüglich der Maximumnorm in Abhängigkeit aller Parameter vonV charakterisiert, insbesondere wird auf die geeignete Wahl der Kollokationsknoten eingegangen.
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  • 13
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    Numerische Mathematik 40 (1982), S. 169-177 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The stability and accuracy of some explicit nonlinear methods for the numerical integration of stiff systems of ordinary differential equations are investigated. It is shown, that in the general case they can produce the essential error. The special class of stiff systems is singled out, for which these methods are highly efficient. Some numerical results are also presented.
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  • 14
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    Numerische Mathematik 40 (1982), S. 319-328 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65J05, 65L15 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Although multiparameter eigenvalue problems, as for example Mathieu's differential equation, have been known for a long time, so far no work has been done on the numerical treatment of these problems. So in this paper we extend the spectral theory for one parameter (cf. [7, II, VII]) to multiparameter eigenvalue problmes, formulate in the framework of discrete approximation a convergent numerical treatment, establish algebraic bifurcation equations for the intersection points of the eigenvalue curves and illustrate this with some numerical examples.
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  • 15
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    Numerische Mathematik 40 (1982), S. 373-406 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30, 65M20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We extend in this paper the analysis of a posteriori estimates of the space discretization error presented in a previous paper [3] for time-independent space meshes. In the context of the model problem studied there, results are given relating the effectiveness of the error estimator to properties of the solution, space meshes, and manner in which the meshes change. A procedure based upon this theory is presented for the adaptive construction of time-dependent meshes. The results of some computational experiments show that this procedure is practically very effective and suggest that it can be used to control the space discretization error in more general problems.
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  • 16
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    Numerische Mathematik 41 (1983), S. 373-398 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper introduces a new semi-implicit extrapolation method especially designed for the numerical solution of stiff systems of ordinary differential equations. The existence of a quadratic asymptotic expansion in terms of the stepsize is shown. Moreover, the new discretization is analyzed in the light of well-known stability models. The efficiency of the new integrator is clearly demonstrated by solving a series of challenging test problems including real life examples.
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  • 17
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    Numerische Mathematik 41 (1983), S. 345-371 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Maximum-norm stability and error estimates of best approximation and nonsmooth data types are derived for the approximate solution of a parabolic equation in one space variable, using the continuous in time Galerkin method based on piecewise polynomial approximating functions on a quasi-uniform mesh.
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  • 18
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study the difference equations obtained when a linear multistep method is applied to the scalar test equationdy/dt=λy and constant stepsizeh. LetS be the region of the absolute stability of the method, and letD be a closed subset ofS (on the Riemann sphere $$\mathbb{C}$$ ). It is shown that the solutions of these difference equations are bounded forn≧0, uniformly for λh∈D.S is itself closed in $$\mathbb{C}$$ iff ∂S is free of cusps. The question is studed by means of contractivity analysis and a matrix theorem, derived from the matrix theorem of Kreiss.
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  • 19
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    Numerische Mathematik 41 (1983), S. 399-422 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper presents a new theory for joint order and stepsize control in extrapolation methods. This theory defines a locally optimal order that can be determined along any trajectory to be computed. In addition, Shannon's information theory is applied to derive some ideal convergence model that is expected to describe the behavior of an extrapolation method over a large set of test problems. Extensive numerical comparisons document a drastic acceleration in stiff integration and a mild acceleration in non-stiff integration by the new device. Moreover, a significant increase in reliability, robustness, and portability of the extrapolation codes is achieved.
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  • 20
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    Numerische Mathematik 42 (1983), S. 299-310 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new approach to the problem of numerically integrating stiff differential systems is described. In this approach a linear multistep method (the basic method) is split into a kind of predictor-corrector scheme, where the predictor is also implicit. If this splitting is done in an appropriate manner, the modified method has considerably better stability properties than the basic method. As a result, splitting methods are particularly useful for problems where conventional integration methods experience stability difficulties. In particular some highly stable split linear multistep methods based on backward differentiation formulae are derived and a highly stable variable step implementation is proposed.
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  • 21
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    Numerische Mathematik 42 (1983), S. 311-322 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper presents Galerkin approximations for solutions of two dimensional interface problems by solving corresponding boundary integral equations. These are obtained by simple layer potential operators only. Due to the strong ellipticity of the integral equations the Galerkin procedure converges with optimal order. Smoothness of the given data implies high convergence rates for the layers.
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  • 22
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    Numerische Mathematik 42 (1983), S. 349-357 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper theD-stability properties of some classes of perturbed collocation methods are investigated. Among others we show the implicit Runge-Kutta methods described by Ehle-Chipman to beD-stable. We also give implicit Runge-Kutta methods that are bothD-stable andA-stable but notB-stable. Finally we indicate in what senseB-stability is stronger thanA-stability together withD-stability. The results of this paper are based on recent results of Nørsett and Wanner on perturbed collocation methods.
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  • 23
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    Calcified tissue international 33 (1981), S. 239-242 
    ISSN: 1432-0827
    Keywords: Bone ; Magnetic field ; IR light ; Light absorption constant ; Efficiency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Enhancement of photovoltage has been found in bone and its two major constituents when placed in a magnetic field in standard Hall geometry. Infrared light has been used for carrier excitation. From data obtained in this manner, values for the light absorption constant, extinction constant, mass absorption constant, and efficiency have been estimated. All these parameters increase with the increase of magnetic field. A possible explanation for the observed phenomena is presented.
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  • 24
    ISSN: 1432-0827
    Keywords: Vitamin D ; Vitamin D deficiency ; Cartilage ; Bone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary To test the importance of 24-hydroxylation of vitamin D3 on bone mineralization, rat pups born to vitamin D-deficient females were given either 25-hydroxyvitamin D3 or 24,24-difluoro-25-hydroxyvitamin D3 for 16 days beginning at the time of weaning. Following such treatment analysis of blood samples revealed no detectable 24R,25-(OH)2D3 and 1,25-(OH)2D3 in the rats given the difluoro compound while revealing the expected 24,24-difluoro-25-hydroxyvitamin D3 and 24,24-difluoro-1,25-dihydroxyvitamin D3. The rats given 25-hydroxyvitamin D3 had the expected levels of 25-hydroxyvitamin D3, 24,25-dihydroxyvitamin D3, and 1,25-dihydroxyvitamin D3. Following sacrifice at day 17, postweaning bone mineralization and modeling were studied in long bones using histological methods. Bones taken from vitamin D-deficient rats at the beginning and end of the experimental period had lesions typical of rickets. These included wide growth plates, excessive amounts of osteoid, and metaphyseal fibrosis. Following treatment with either 25-hydroxyvitamin D3 or 24,24-difluoro-25-hydroxyvitamin D3, bone mineralization returned to normal. Growth plate widths and the amount of osteoid on bone surfaces were both substantially reduced and to a similar degree in both treatment groups. Normal cartilage core formation and trabecularization of the metaphyseal primary spongiosa were also restored to a similar degree in both groups. In effect, no difference was observed in any bone parameter studied between the 25-hydroxyvitamin D3- and the 24,24-difluoro-25-hydroxyvitamin D3-treated animals. These results provide strong evidence that 24-hydroxylation of the vitamin D molecule plays little or no role in the modeling and mineralization of bone.
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  • 25
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    Calcified tissue international 33 (1981), S. 655-661 
    ISSN: 1432-0827
    Keywords: 1,25-Dihydroxyvitamin D3 ; 25-Hydroxyvitamin D3 ; 24,25-Dihydroxyvitamin D3 ; Receptors ; Bone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The hormonal metabolite of vitamin D3, 1,25-dihydroxyvitamin D3 [1,25(OH)2D3], exerts its biological effects by binding to a cytosolic receptor protein. Such a protein has been demonstrated in vitamin D3 target organs including fetal rat calvariae and more recently in rat osteogenic sarcoma cells. In this study we have compared the binding of 25-hydroxyvitamin D3 [25(OH)D3] and 24,25-dihydroxyvitamin D3 [24,25(OH)2D3] to that of 1,25-(OH)2D3 in fetal rat calvariae and osteogenic sarcoma (OS) cells. Sucrose density sedimentation, DNA-cellulose chromatography, and intracellular uptake studies have been employed to evaluate these interactions. In cytosol preparations from calvariae, [3H]-1,25(OH)2D3 bound to a 3.3S macromolecule and to a much greater extent to a 5.8S macromolecule while both [3H]25(OH)D3 and [3H]24,25(OH)2D3 bound to the 5.8S macromolecule. By incubating intact calvariae and OS cells with labeled metabolites and thus establishing binding intracellularly prior to cell disruption, we have found that the 3.3S protein which has high specificity for 1,25(OH)2D3 occurs inside the cells; the 5.8S protein, however, does not occur inside the cells but is generated after cell disruption. The [3H]-1,25(OH)2D3-receptor complex adsorbed to DNA-cellulose and was eluted from this affinity resin at 0.28M KCl. In contrast, [3H]25(OH)D3 and [3H]-24,25(OH)2D3 binding activity did not adsorb to DNA-cellulose. We conclude that, in contrast to the 3.3S protein, the 5.8S macromolecule does not fulfill receptor criteria but is rather generated by the experimental manipulation of the bone cells. Our data suggest that the vitamin D3 actions on bone are mediated only via the 3.3S receptor, and hence quantitative but not qualitative differences of the effects of the various metabolites are feasible.
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  • 26
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    Calcified tissue international 22 (1977), S. 303-313 
    ISSN: 1432-0827
    Keywords: Osteoclasts ; Sedimentation ; Isolation ; Cells ; Bone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Abstract A method is presented for separating osteoclasts from the heterogeneous population of bone and marrow cells. Cell suspensions were prepared from femora of young rabbits by mechanical dispersion. The starting cell suspension typically contained only 1.0%±0.5 osteoclasts. Following an initial 45 min of unit gravity sedimentation in a lucite chamber osteoclasts were primarily distributed in fractions 2–5. A second 45-min sedimentation of these pooled fractions yielded cell suspensions containing greater than 30% osteoclasts (as much as a 50-fold increase over starting percentages). Linear scan analysis, however, revealed that osteoclasts accounted for 73.14%±0.58 of the cell colume. Subsequent in vitro experiments demonstrated linear incorporation of3H-leucine into TCA precipitable protein for cells comprising the osteoclast fraction. Concomitant radiautographs revealed radioactive label in isolated osteoclasts.
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  • 27
    ISSN: 1432-0827
    Keywords: Bone ; Diphosphonates ; Bone resorption ; Bone formation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Male rats weighing 100 g were assigned to groups and injected daily for 10 days with vehicle (control), 0.4, 2.0, 4.0, 10.0, or 20.0 mg/kg/day of ethane-1-hydroxy-1,1-diphosphonate (EHDP) or dichloromethylene diphosphonate (Cl2MDP). The proximal tibial metaphysis and epiphysis were assayed for changes in percentage of hard tissue and bone formation parameters. From the data, information about hard tissue resorption was deduced. All doses of Cl2MDP and doses of 2.0 mg EHDP/kg/day and greater caused significant increases in percentage of hard tissues with Cl2MDP being more effective than similar doses of EHDP in decreasing bone resorption. Osteoclast population parameters were increased with all doses of both Cl2MDP and EHDP with Cl2MDP having a greater effect than similar doses of EHDP. Decreases in the proliferation of the osteoprogenitor pool parallel the decreases in osteoblasts and bone formation parameters. These decreases in osteoprogenitor pool proliferation do not account for the increases with diphosphonates in osteoclast population parameters.
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  • 28
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    Calcified tissue international 23 (1977), S. 283-289 
    ISSN: 1432-0827
    Keywords: Bone ; Resorption ; Osteoclast ; Quantitation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The stimulation of bone resorption, assessed by the release of45Ca from prelabeled bones, was associated with an increase in number of osteoclasts per bone section in parathyroid hormone (PTH)-treated bones, but not in lipopolysaccharide (LPS)-treated bones. By contrast the number of nuclei per osteoclast increased following LPS treatment, but was not affected by PTH. LPS-treated bones had more multinucleated cells, some having as many as 27 nuclei per osteoclast. More osteoclasts were adjacent to the bone collar in bones treated with LPS or PTH than in control bones. In LPS-treated bones this area also contained the largest osteoclasts, as determined by the greatest number of nuclei per osteoclast. The results suggest that LPS and PTH stimulate osteoclastic resorption by different mechanisms.
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  • 29
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    Calcified tissue international 23 (1977), S. 303-305 
    ISSN: 1432-0827
    Keywords: Albumin ; Bone ; Hydroxyapatite ; Plasma protein
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary The extractability of125I-labelled plasma albumin from bone pieces and from powdered bone has been compared after both in vivo and in vitro incorporation. The results show that albumin is more readily extracted from bone pieces than from bone powder which implies that tissue disruption exposes additional protein adsorption sites. It is suggested that incorporation of plasma albumin into calcified matrix during bone formation occurs mainly as a result of its strong interaction with bone mineral.
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  • 30
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    Calcified tissue international 23 (1977), S. 161-170 
    ISSN: 1432-0827
    Keywords: Bone ; Growth ; Rat ; Remodeling ; Tetracyclines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Notes: Summary Cortical bone remodeling along the femur diaphysis was determined in normal female rats (Sprague-Dawley) with the tetracycline technique. Three segments on the cortical bone circumference (the anterolateral, the medial, and the posterior) were found to be most suitable for the study of the remodeling process. Oxytetracycline was administered at age 60 and 75 days, and groups of animals were killed at age 75, 85, 95, and 105 days. The accumulated endosteal growth during age 60 to 75 days in the anterolateral segment was found to increase uniformly in the distal direction along the femur diaphysis. A method is described where this accumulated endosteal growth is used. This method eliminates the use of calipers to determine the section level and makes it possible to study comparable sections even after varying periods of time. The proximal part of the diaphysis showed periosteal apposition in all three segments. The periosteal apposition turned into resorption in the distal part of the diaphysis in the anterolateral and medial segments, whereas the periosteal appsition increased in the posterior segment. The endosteal growth increased in the distal direction in the anterolateral and medial segments. Irregular OTC bands made measurements of endosteal remodeling in the posterior segment impossible. The cortical width decreased in the distal direction along the femoral shaft. Comparison between the different age groups is described and also the relation between the accumulated endosteal growth and the diameter of the medullary cavity.
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    Calcified tissue international 27 (1979), S. 177-185 
    ISSN: 1432-0827
    Keywords: Calcification ; Bone ; Glycoprotein ; Golgi ; Osteoblasts
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    Topics: Biology , Medicine , Physics
    Notes: Summary The elaboration of bone matrix glycoprotein by osteoblasts of alveolar bone was investigated by radioautography after the intravenous injection of3H-fucose into young rats. At selected times after injection, animals were sacrificed by intracardiac perfusion and demineralized specimens were prepared for light and electron microscope radioautography. At 5 and 10 min after injection, when the blood fucose level was high, silver grains were restricted to the spheroidal and cylindrical saccules of the Golgi apparatus. At 20 min membrane-limited secretory granules were also labeled. By 35 min, the blood fucose level had dropped and silver grains were detected over the apical cortical cytoplasm, in association with secretory granules located therein. Some grains were present over osteoblast processes and the adjacent prebone matrix. By 4 h most of the silver grains had left the cell. At that time they were observed over prebone, adjacent to osteoblast processes, as well as over the prebone-bone junction where a distinct band of label was noted. In demineralized preparations an electron-dense granular material was present at the prebone-bone junction in association with collagen fibrils. These findings provide evidence that osteoblasts in alveolar bone synthesize fucose-containing glycoprotein and indicate that the addition of3H-fucose occurs in the Golgi apparatus. The glycoprotein passes to the apical cortical cytoplasm by way of membrane-limited secretory granules, is exteriorized, and accumulates at the site where prebone transforms into bone (the prebone-bone junction). Since this is also the site of the calcification front, the deposition of labeled glycoprotein may be related to the deposition of bone mineral.
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    Calcified tissue international 23 (1977), S. 1-5 
    ISSN: 1432-0827
    Keywords: Water ; Bone ; Homeostasis ; Structure
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    Topics: Biology , Medicine , Physics
    Notes: Summary A short review is given of the water in bone. Various analyses of bone water content are discussed, and its possible location is considered in relation to the behaviour of water in isolated components of bone. Some of the difficulties encountered in examining such microscopic phenomena as water structure in a heterogeneous system such as bone are also discussed.
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    Calcified tissue international 24 (1977), S. 41-46 
    ISSN: 1432-0827
    Keywords: Lead salt ; Bone ; Mobilization ; Hypercalcemia ; Hyperphosphatemia
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    Topics: Biology , Medicine , Physics
    Notes: Summary The present study is an investigation of the mechanism of hypercalcemia and hyperphosphatemia induced by the intravenous injection of lead acetate (Pb-Ac). A total of 118 male rats were injected with 30 mg/kg of Pb-Ac, or with 16.5 mg/kg of sodium acetate as the control. The levels of serum calcium, phosphorus and lead were then determined at various time periods after the injections. Serum calcium and phosphorus levels increased with time after Pb-Ac injection and the maximum values of calcium (17 mg%) were found after 1 h and of phosphorus (13.5 mg%) after 30 min. Both calcium and phosphorus levels reverted to the normal range after 12 h. The maximum net rates of increase of calcium and phosphorus were found immediately after Pb-Ac injection. At that time, deposition of lead at the calcifying sites of bone and incisor dentin was demonstrated by a histochemical examination. In other experiments the changes in the calcium and phosphorus contents in the medium after shaking bone powder in serum with Pb-Ac in an in vitro system were studied. It was confirmed that the calcium and phosphorus were displaced from the bone mineral, the extent of the displacement being correlated with the concentration of the Pb-Ac added to the medium, and that these displacements were very rapid reactions. These results suggest that hypercalcemia and hyperphosphatemia following Pb-Ac injection results from a direct action of lead on the bone mineral.
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    Calcified tissue international 27 (1979), S. 95-99 
    ISSN: 1432-0827
    Keywords: Bone ; Fluoride ; Analysis ; Food ; Age
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    Topics: Biology , Medicine , Physics
    Notes: Summary Recently published bone fluoride values from Iowa are very high compared to earlier reports, suggesting an increase in fluoride intake. Reanalysis of the Iowa specimens shows levels one-fourth those reported by the Iowa laboratory indicating an error in the original report. Seventeen bone specimens, collected from long-term residents of Rochester, New York, drinking 1 ppm F− water, had a mean value of 2085±270 ppm F− on an ashed-weight basis. This value is not significantly different from that predicted by the data of Zipkin et al. in 1958. These data, therefore, do not support the contention that there has been an increase in fluoride intake.
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    Calcified tissue international 24 (1977), S. 209-214 
    ISSN: 1432-0827
    Keywords: Parathyroid hormone ; Plasma calcium ; Radiocalcium ; Bone
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    Topics: Biology , Medicine , Physics
    Notes: Summary The net rate of loss of45Ca from plasma was monitored in normal, thyroparathyroidectomized (TPTX), and nephrectomized rats. Also studied was the effect of a 24 h intravenous infusion of PTH in TPTX rats. The45Ca was injected after an overnight fast and 1 to 4 h prior to the time the first blood sample was obtained. In normal rats, the net rate of loss of45Ca from plasma was slower than in TPTX rats for at least 12 h after radionuclide injection. Nephrectomy did not affect this difference between control and TPTX rats until 8 h after45Ca injection or about 18 h after nephrectomy. At this time a reversal occurred and the net rate of plasma45Ca loss in nephrectomized rats with parathyroids became faster than in TPTX nephrectomized rats. When PTH was infused at a constant rate (3 mU/g body weight/h) plasma calcium concentrations rose gradually for approximately 12 h after which a constant plasma calcium level was maintained with continued PTH infusion. During the period when plasma calcium concentrations were rising, the net rate of loss of45Ca from plasma was slower than in TPTX controls infused only with saline. However, when plasma levels stabilized, plasma45Ca disappearance rates changed such that the rate loss of45Ca from plasma became faster in PTH-infused than in TPTX controls. It is concluded that PTH increases calcium efflux from the same compartment in bone which receives calcium from plasma, thereby returning some recently deposited45Ca to plasma. In the non-equilibrated state, this returns additional45Ca to plasma causing anet decrease in the rate of loss of45Ca from plasma. However, in the equilibrated condition, when both calcium efflux from bone and influx into bone are in balance but at higher flux rates, PTH stimulates the diffusion of45Ca into other bone compartments.
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    Calcified tissue international 28 (1979), S. 103-105 
    ISSN: 1432-0827
    Keywords: Bone ; Photodensitometry, X-ray ; Radiography ; Spectrophotometry
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    Topics: Biology , Medicine , Physics
    Notes: Summary A conventional spectrophotometer was used to do radiographic photodensitometry of bone mass. An experiment to produce osteoporosis in guinea pigs required quantification of changes in bone mass. Lack of a densitometer necessitated finding another method for quantification. The method developed involved using industrial film in a closed X-ray system. Optical density of X-rays was then read in a spectrophotometer at nine femur locations. Highly significant correlations between optical density and femur calcium content and femur dry weight per millimeter were obtained. Histological sections from an animal with low optical density measurements confirmed bone loss by showing decreased cortical width and loss of trabecular bone. In addition to using readily available equipment, this method offers the advantage of being able to detect bone loss in specific areas of the bones. In addition, bones are left intact and can be used for other purposes.
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  • 37
    ISSN: 1432-0827
    Keywords: ESR ; Bone ; Enamel ; CO3-Apatite ; Paramagnetism
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    Notes: Summary Carbonate-containing hydroxyapatite, enamel, and bone were irradiated by an X-ray and investigated between 77° and 350°K by means of electron spin resonance (ESR) spectroscopy. The ESR spectrum of enamel irradiated at 77°K in vacuum and observed at the same temperature was almost the same as that of the carbonate-containing hydroxyapatite. The temperature dependence of signal intensities confirms a spin-energy exchange between the mineral and organic constituents in bone, but in enamel no or very little spinenergy exchange between the mineral and organic constituents. Considerable similarity among the ESR spectra of enamel, bone, and carbonate-containing apatite was obtained after X-ray irradiation in air at 300°K with both an X-band and a Q-band ESR spectrometer. The Q-band spectrum can be interpreted in terms of two paramagnetic species. One is identified as a CO 3 3− anion radical which has an axial symmetry withg factors of 2.0029 and 1.9972. The other species is found to be centered atg=2.0019.
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    Calcified tissue international 28 (1979), S. 33-36 
    ISSN: 1432-0827
    Keywords: Infrared, visible light ; Bone ; Collagen ; Apatite
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    Topics: Biology , Medicine , Physics
    Notes: Abstract Photovoltaic effect (infrared and visible light) is observed in bone and its two major components, collagen and apatite, at room temperature. A dimunition in the magnitude of photovoltage is observed after exposure to ultraviolet light in all the cases. The drift mobility of the charge carriers is obtained by measuring I versus V relationships in sandwich samples and relating them to the permitivity of the medium. Lifetime of the injected carriers is measured in the usual way. The data are consistent with the hypothesis that the effects are due to protonic conduction phenomena.
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    Calcified tissue international 26 (1978), S. 47-49 
    ISSN: 1432-0827
    Keywords: Matrix vesicles ; Calcospherites ; Mineralization ; Bone ; Dentin ; Cartilage ; SEM
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    Topics: Biology , Medicine , Physics
    Notes: Summary Mineral particle cluster, corresponding to calcospherites or matrix vesicle-initiated clusters in calcifying cartilage and dentin and to collagen bundle-related mineralization in lamellar bone, have been isolated from NaOCl solutions used to dissolve the organic matrix in preparation of anorganic mineralizing fronts for scanning electron microscopy.
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    Calcified tissue international 26 (1978), S. 81-84 
    ISSN: 1432-0827
    Keywords: Osteoclasts ; Bone ; Resorption
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    Topics: Biology , Medicine , Physics
    Notes: Summary Osteoclastic bone resorption involves the solubilization of the mineral salts and the degradation of noncollagen bone matrix and collagen fibrils. As no recognizable collagen fibrils have ever been reported within cytoplasmic vacuoles in osteoclasts, it is generally assumed that the collagen fibrils are digested extracellularly in the resorption zone. The extent to which lysis occurs extracellularly and whether or not the osteoclasts phagocytose the degradation products remain to be established. In the present communication, a hypothesis is presented suggesting the possibility that osteoclastic resorption of bone involves the participation of two different cell types. According to this hypothesis, osteoclastic bone resorption is initiated by osteoclasts that demineralize areas of bone and degrade noncollagen bone matrix. After the osteoclasts have moved away or become partially detached from the demineralized site, the exposed collagen fibrils are phagocytosed by mononuclear, fibroblast-like or monocyte-derived cells.
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    Calcified tissue international 26 (1978), S. 155-161 
    ISSN: 1432-0827
    Keywords: Plasma protein ; Glycoprotein ; Bone ; Glucosamine
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    Topics: Biology , Medicine , Physics
    Notes: Summary Plasmaα 2HS-glycoprotein is specifically accumulated in calcified tissues. In the present studies this glycoprotein was isolated from plasma and after iodination with iodine-125 was injected intravenously into young rabbits. The tissue distribution and plasma disappearance rate of this radioactively labeled material were determined. Of the various tissues studied, bone showed the greatest retention of labeled glycoprotein expressed as percentage of the injected dose per gram tissue relative to the plasma content. The rate of loss of iodinatedα 2HS-glycoprotein from plasma was similar to that ofα 2HS-glycoprotein labeled endogenously by using14C-glucosamine or3H-glucosamine. The uptake of exogenously labeled3I-α 2HS-glycoprotein into bone tissue expressed as a percentage of the injected dose was similar to that of endogenously labeled14C-α 2HS-glycoprotein. These results suggest that the125I-labeled material can be used to study further the metabolism ofα 2HS-glycoprotein by bone tissue.
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    Calcified tissue international 26 (1978), S. 209-213 
    ISSN: 1432-0827
    Keywords: Mithramycin ; Bone ; β-Glucuronidase ; KT medium
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    Topics: Biology , Medicine , Physics
    Notes: Summary Mithramycin suppresses bone resorption. Its effect on the synthesis and release of β-glucuronidase (a referent for lysosomal enzymes) in mouse calvarial explants was studied in an in vitro culture system. A newly described medium (designated as KT medium) was introduced in this specific study. Mithramycin initially inhibited the release of β-glucuronidase into the medium and resulted in an ultimate accumulation of this enzyme in the bone. These results suggest that inhibition of bone resorption by mithramycin may be attributed to interference in release of lysosomal enzymes from bone cells.
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  • 43
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    Keywords: Vitamin D ; Bone ; Osteoblasts ; Receptors ; 1,25-dihydroxyvitamin D3
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    Topics: Biology , Medicine , Physics
    Notes: Summary Thaw-mount autoradiographic studies after injection of3H-1,25-D3 were conducted on 18-and 20-day-old rat fetuses. In maxillary bones, ribs, and tibia, nuclear concentration of radioactivity was found in osteoprogenitor cells and osteoblasts. Osteocytes and chondrocytes in epiphyseal plates were either unlabeled or weakly labeled. In competition experiments, nuclear concentration of radioactivity was blocked by the injection of a high dose of nonradioactive 1,25-D3 prior to the administration of the labeled hormone, but not by a similar dose of nonradioactive 25-D3. The results are interpreted as indicating that osteoprogenitor cells and osteoblasts are target cells for the direct action of 1,25-D3 on fetal bone.
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  • 44
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    Keywords: Vitamin D ; Vitamin D deficiency ; Bone ; Cartilage ; Bone development
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    Notes: Summary The role of vitamin D in early skeletal development was studied by measuring serum calcium and phosphorus, osseous tissue quantity and mineralization, and endochondral bone elongation in rat fetuses and pups from vitamin D-replete and vitamin D-deficient mothers. At the 20th day of pregnancy there was a slight, yet significant, increase in the amount of osteoid on trabecular bone surfaces in fetuses from vitamin D-deficient mothers. The fetal bones otherwise appeared normal in spite of severe skeletal changes in the vitamin D-deficient mothers. After parturition, the importance of vitamin D in skeletal development becomes progressively more obvious. Serum calcium levels were slightly, yet significantly, lower in vitamin D-deficient than in vitamin D-replete pups and these levels continued to fall in the vitamin D-deficient pups through lactation and after weaning. At 3 days postpartum, there was a small, yet significant, increase in the amount of osteoid on bone surfaces of the vitamin D-deficient pups. The relative amounts of osteoid in the vitamin D-deficient pups continued to increase through lactation and after weaning when compared with vitamin D-replete pups. By the 14th day of lactation and at later periods, there were significant reductions in metaphyseal mineralized tissues in the vitamin D-deficient pups when compared with the vitamin D-replete pups. At weaning and after weaning, there were substantial increases in growth plate thickness and decreases in longitudinal bone growth in the vitamin D-deficient pups when compared with the vitamin D-replete pups. The results from this study indicate that vitamin D does not appear to play a major role in fetal skeletal development. However, after birth, vitamin D becomes progressively more important with age for normal bone development, mineralization, and endochondral growth.
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    Calcified tissue international 35 (1983), S. 481-485 
    ISSN: 1432-0827
    Keywords: Chemotaxis ; Bone ; Osteoblasts ; Bone proteins
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    Topics: Biology , Medicine , Physics
    Notes: Summary When demineralized bone matrix powder is implanted subcutaneously in the rat, the early responses involve the appearance and proliferation of mesenchymal cells at the site of implantation, followed by cartilage and bone formation. The ability of cells to migrate to the implant suggests that chemotaxis may be a critical event in this process. Therefore, using the modified Boyden chamber assay, we tested extracts of demineralized bone matrix for chemotactic activity. We have identified and partially purified, on molecular sieve chromatography, a heat labile and trypsin-sensitive protein (Mr=60,000–70,000) that is a potent chemoattractant for mouse calvaria, osteoblast-like cells (MMB-1), but not for monocytes (putative osteoclast precursors). These findings suggest that chemotactic protein(s) have a significant role in the recruitment of osteoprogenitor cells to a site of bone repair.
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    Calcified tissue international 35 (1983), S. 762-766 
    ISSN: 1432-0827
    Keywords: Enamel ; Maturation cycles ; Tetracycline ; Dentine ; Bone
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    Topics: Biology , Medicine , Physics
    Notes: Summary Uptake of tetracycline by enamel in the short-term was studied at an advanced stage of crown formation and after completion of crown formation in deciduous molars in the cat. Both secretory phase enamel and bands of postsecretory, maturation phase enamel labeled rapidly. The pattern of labeling mimicked that seen in the continuously growing, rootless incisor teeth of the rat, with narrow doublets fusing to form narrow bands with wide unlabeled intervals in the short term. This is a physiological demonstration which indicates that cyclical activity and changes may occurin vivo during the maturation phase of amelogenesis in rooted teeth. It is also noted that dentine did not, and that some circumscribed patches of bone did label in the same animals in the same time interval. Short-term tetracycline labels are lost following conventional histological processing, but are retained after freeze-drying or air-drying.
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    Calcified tissue international 36 (1984), S. S25 
    ISSN: 1432-0827
    Keywords: Remodeling ; Bone ; Stress
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    Topics: Biology , Medicine , Physics
    Notes: Summary It has long been known that the stress history of bone tissue influences its structure; however, the nature of this relationship remains largely uncharacterized. The objective of this work was to induce a quantifiable change in the stress history ofin vivo bone tissue and examine subsequent changes in structural and material properties that might occur. Continuous compressive loads were applied to the diaphysis of adult mongrel dogs for 2 months. The loads, ranging from 12–130 N, were superposed on the normal activity of the animals by implanting spring loading devices on the diaphysis of the femur. After the animals were sacrificed, mid-diaphysial specimens were subjected to compression testing to determine a structural bulk stiffness. The cross-sectional areas of original bone tissue and new bone deposition were then determined. The ash weights of selected specimens were also determined. The results indicate that a positive correlation between the increase in cross-sectional area and the superposed stress does exist. The new bone apposition was found almost entirely on the periosteal surface. Very little evidence of internal remodeling or endosteal movement was observed. The new tissue was found to have a lower ash weight and appeared to have a disorganized microstructure. Mechanical testing also suggests that the newly deposited tissue is far less stiff than the mature original bone.
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    Calcified tissue international 34 (1982), S. 439-448 
    ISSN: 1432-0827
    Keywords: Bone ; Histomorphometry ; Osteocytes ; Bone dynamics ; Histology
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    Topics: Biology , Medicine , Physics
    Notes: Summary A new semiautomatic technique combining advantages of the manual and fully automatic methods is described for obtaining quantitative static and dynamic histologic data of bone. The hardware consists of a photomicroscope, digitizing platen, digitizer, plotter/printer, floppy disc drive, and computer. The microscope is equipped with a drawing tube through which the image of the digitizing platen is projected over the optical field. The investigator selects and traces all histologic structures to be measured by moving a cursor on the digitizing platen which is visible by its projection over the histologic field. The results on accuracy and static and dynamic precision of this method show that static and dynamic parameters of bone are obtained with a degree of error (〈20%) well within the acceptable range for biologic measurements. Comparison of this method with the grid technique according to Merz and Schenck showed that for almost all micromorphometric parameters comparable absolute data are obtained. Due to the higher precision of our method, however, the number of optical fields evaluated in obtaining these comparable data could be reduced to 25% of the number of fields evaluated by the Merz and Schenck technique. The time requirements for quantitative evaluation of a histologic slide of bone by our technique are 40–50 min; 20–25 min is needed for quantitative evaluation of osteocytes.
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    Calcified tissue international 34 (1982), S. 449-455 
    ISSN: 1432-0827
    Keywords: Bone ; Histomorphometry ; Normal values ; Bone biopsies ; Sampling error
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    Topics: Biology , Medicine , Physics
    Notes: Summary Quantitative bone histology was done in undecalcified sections of iliac crest bone specimens obtained from 84 normal American individuals. Samples were obtained within 12 h after death in a vertical and horizontal manner from both the right and left iliac crests. In addition to the determination of normal values of micromorphometric parameters of bone in these healthy American subjects, the following studies were carried out: (a) comparison of variance of micromorphometric parameters of bone obtained from the right versus left iliac bone (40 pairs), (b) comparison of micromorphometric parameters of bone obtained in a vertical versus horizontal manner (12 pairs), (c) evaluation of variance with increasing distance from the compact zone in bone samples obtained in a vertical manner (44 pairs), (d) analysis of variation between bone samples obtained more anteriorly versus posteriorly along the iliac crest (N=40), (e) comparison of differences in micromorphometric parameters obtained from age-matched men versus premenopausal women (N=12), and (f) plotting of histograms for assessment of distribution of micromorphometric parameters. The results show that histomorphometric data of bone cannot be easily compared when different techniques are employed for obtaining bone samples. Sampling variations are kept smaller when bone specimens are obtained in a vertical manner. Anterior/posterior variation does not cause major sampling error. If ranges of variation are taken into account, quantitative bone histology is a valuable tool for assessment of bone structure and bone cells.
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    Calcified tissue international 35 (1983), S. 148-152 
    ISSN: 1432-0827
    Keywords: Bone ; Computed tomography ; Densitometry ; Osteoporosis ; Osteomalacia
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    Topics: Biology , Medicine , Physics
    Notes: Summary The linear attenuation coefficient (μ in cm1) of trabecular bone was modeled for different conditions of bone and marrow composition in order to assess their influence on computed tomography (CT) quantitation. A large relative change (10% of TBV at 15% TBV) of bone concentration resulted in small changes of μ: 2.3% at 60 keV, 3.4% at 44 keV, 5.2% at 29 keV. Relative changes of trabecular bone volume (TBV) on the order of 3% could be detectedin vivo by CT were it not for errors of relocation and for compositional influences on accuracy. The μ (and density) depended critically not only on amounts of bone substance and marrow but on their compositions. Normal variation in the composition of bone substance produced an uncertainty in μ equivalent to 0.5 to 1% TBV. Increases of yellow marrow produced a decrease of μ which could be mistaken for a decrease of bone concentration. The biological variation (90% confidence limit) of marrow composition gives an uncertainty at 15% TBV of about 2.4% TBV at 60 keV, 1.7% at 44 keV, and 1.3% at 29 keV. These correspond to relative uncertainities of 16, 11, and 9% respectively. These factors help explain the large accuracy errors (30%) observed in all studies of trabecular bone where single-energy CT was used. Marrow composition also can affect precision of bone measurement. Systematic shifts of red and yellow marrow could mask biological changes such as those occurring with aging or treatment.
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    Journal of molecular evolution 21 (1984), S. 19-32 
    ISSN: 1432-1432
    Keywords: Leghemoglobin ; Gene duplication ; Gene linkage ; Concerted evolution ; Nitrogen fixation ; Soybean
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    Topics: Biology
    Notes: Summary We have analyzed the sequences of soybean leghemoglobin genes as an initial step toward understanding their mode of evolution. Alignment of the sequences of plant globin genes with those of animals reveals that (i) based on the proportion of nucleotide substitutions that have occurred at the first, second, and third codon positions, the time of divergence of plant and animal globin gene families appears to be extremely remote (between 900 million and 1.4 billion years ago, if one assumes constancy of evolutionary rate in both the plant and animal lineages) and (ii) in addition to the normal regulatory sequences on the 5′ end, an approximately 30-base-pair sequence, specific to globin genes, that surrounds the cap site is conserved between the plant and animal globin genes. Comparison of the leghemoglobin sequences with one another shows that (i) the relative amount of sequence divergence in various coding and noncoding regions is roughly similar to that found for animal globin genes and (ii) as in animal globin genes, the positions of insertions and deletions in the intervening sequences often coincide with the locations of direct repeats. Thus, the mode of evolution of the plant globin genes appears to resemble, in many ways, that of their animal counterparts. We contrast the overall intergenic organization of the plant globin genes with that of animal genes, and discuss the possibility of the concerted evolution of the leghemoglobin genes.
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    Numerische Mathematik 31 (1978), S. 175-182 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary When variable stepsize variable formula methods (VSVFM's) are used in the solution of systems of first order differential equations instability arises sometimes. Therefore it is important to find VSVFM's whose zerostability properties are not affected by the choice of both the stepsize and the formula. The Adams VSVFM's are such methods. In this work a more general class of methods which contains the Adams VSVFM's is discussed and it is proved that the zero-stability of the class is not affected by the choice of the stepsize and of the formula.
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    Numerische Mathematik 30 (1978), S. 369-383 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L05, 65M10, 65M15, 65M20, 65N15, 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Backward differentiation methods up to orderk=5 are applied to solve linear ordinary and partial (parabolic) differential equations where in the second case the space variables are discretized by Galerkin procedures. Using a mean square norm over all considered time levels a-priori error estimates are derived. The emphasis of the results lies on the fact that the obtained error bounds do not depend on a Lipschitz constant and the dimension of the basic system of ordinary differential equations even though this system is allowed to have time-varying coefficients. It is therefore possible to use the bounds to estimate the error of systems with arbitrary varying dimension as they arise in the finite element regression of parabolic problems.
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    Numerische Mathematik 31 (1978), S. 1-16 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Notes: Summary We study the mixed finite element approximation of variational inequalities, taking as model problems the so called “obstacle problem” and “unilateral problem”. Optimal error bounds are obtained in both cases.
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    Numerische Mathematik 31 (1978), S. 131-152 
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    Topics: Mathematics
    Notes: Summary The right-hand sides of a system of ordinary differential equations may be discontinuous on a certain surface. If a trajectory crossing this surface shall be computed by a one-step method, then a particular numerical analysis is necessary in a neighbourhood of the point of intersection. Such an analysis is presented in this paper. It shows that one can obtain any desired order of convergence if the method has an adequate order of consistency. Moreover, an asymptotic error theory is developed to justify Richardson extrapolation. A general one-step method is constructed satisfying the conditions of the preceding theory. Finally, a simplified Newton iteration scheme is used to implement this method.
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    Numerische Mathematik 32 (1979), S. 147-157 
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    Keywords: AMS (MOS) ; 65L65 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In 1967, F.R. Loscalzo und T.D. Talbot presented a procedure for obtaining polynomial spline approximations of defect one for solutions of the initial value problem for first order ordinary differential equations. This method is generalized and investigated for spline approximations of arbitrary defect. The results are analogous to those of the defect one. In the first part of this paper the divergence problem is treated. The convergent procedures are investigated in a following second part of this paper.
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    Numerische Mathematik 32 (1979), S. 247-270 
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    Keywords: AMS(MOS): 65D05, 65N30, 41A20 ; CR: 5.17
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    Topics: Mathematics
    Description / Table of Contents: Résumé Ce travail est consacré à l'étude d'éléments finis rationnels de Wachspress (cf. [15]) sur un quadrilatère. Après avoir étudié la construction et les propriétés de ces éléments finis, on obtient une évaluation de l'erreur d'interpolation correspondante.
    Notes: Summary This paper is devoted to the study of Wachspress's rational finite elements (cf. [15]) over a quadrilateral. After studying construction and properties of these finite elements, we get an estimate of the corresponding interpolation error.
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    Numerische Mathematik 32 (1979), S. 343-358 
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    Topics: Mathematics
    Notes: Summary In the first part [5] a general procedure is presented to obtain polynomial spline approximations of arbitrary defect for the solution of the initial value problem of ordinary differential equations. The essential result is a divergence theorem in dependence of the polynomial degree and the defect of the spline functions. In this second part the convergent procedures are investigated and two convergence theorems are proved. Furthermore the question is treated, whether the convergent procedures are appropriate for the numerical solution of stiff equations. The paper is finished by a convergence theorem for a procedure producing spline approximations in a natural way by the discrete approximations of an arbitrary difference method.
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    Numerische Mathematik 31 (1978), S. 49-61 
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    Keywords: AMS (MOS): 65N20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary There are currently several highly efficient methods for solving linear systems associated with finite difference approximations of Poisson's equation in rectangular regions. These techniques are employed to develop both direct and iterative methods for solving the linear systems arising from the use ofC 0 quadratic orC 1 cubic tensor product finite elements.
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    Numerische Mathematik 33 (1979), S. 43-53 
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    Topics: Mathematics
    Notes: Summary Letu h be the finite element solution to−Δu=f with zero boundary conditions in a convex polyhedral domain Ω. Fromu h we calculate for eachz∈Ω and |α|≦1 an approximationu h −α (z) toD α u(z) with |D α u(z)−u h −α (z)|=O(h 2k−2) wherek is the order of the finite elements. The same superconvergence order estimates are obtained also for the boundary flux. We need not work on a regular mesh but we have to compute averages ofu h where the diameter of the domain of integration must not depend onh.
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    Numerische Mathematik 34 (1980), S. 235-246 
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    Topics: Mathematics
    Notes: Summary A class of extended backward differentiation formulae suitable for the approximate numerical integration of stiff systems of first order ordinary differential equations is derived. An algorithm is described whereby the required solution is predicted using a conventional backward differentiation scheme and then corrected using an extended backward differentiation scheme of higher order. This approach allows us to developL-stable schemes of order up to 4 andL(α)-stable schemes of order up to 9. An algorithm based on the integration formulae derived in this paper is illustrated by some numerical examples and it is shown that it is often superior to certain existing algorithms.
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    Numerische Mathematik 35 (1980), S. 127-142 
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    Keywords: AMS (MOS): 34G05, 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A class of approximation schemes of arbitrary accuracy, generated by a two-step recurrence relation, is devised for evolution equations of the second order. The schemes are effected via a specially constructed family of rational approximations to cos τ for τ≧0 and yield computationally efficient methods for systems of second-order ordinary differential equations and semidiscrete approximations for initial-boundary value problems for second-order hyperbolic equations.
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    Numerische Mathematik 35 (1980), S. 143-162 
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    Keywords: AMS(MOS): 65M15, 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We study the error due to the discretization in time of a nonlinear parabolic problem by a multistep method. Error estimates are obtained if the method is of the orderp (p〉1) and stronglyA(Θ)-stable $$\left( {0〈 \Theta〈 \frac{\pi }{2}} \right)$$ . The method is also applied to the Navier-Stokes equations in two dimensions.
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    Numerische Mathematik 35 (1980), S. 231-240 
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    Keywords: AMS(MOS): 65L10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The homotopy method is a frequently used technique in overcoming the local convergence nature of multiple shooting. In this paper sufficient conditions are given that guarantee the homotopy process to be feasible. The results are applicable to a class of two-point boundary value problems. Finally, the numerical solution of two practical problems arising in physiology is described.
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    Numerische Mathematik 35 (1980), S. 257-276 
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    Topics: Mathematics
    Description / Table of Contents: Résumé Considérons une équation d'évolution parabolique linéaire associée à un opérateur linéaireA(t) dépendant du tempst. Nous développons dans cet article une méthode de discrétisation, basée sur les méthodes linéaires à pas multiples, traitant de manière implicite une partie de l'opérateurA(t) indépendante du temps, l'autre partie est traitée de manière explicite. Nous étudions la stabilité et la convergence de cette méthode.
    Notes: Summary Let us consider a linear parabolic equation which is associated with a time dependent operatorA(t). In this paper, we present a method, which is founded on linear multistep methods, which discretize a time-independent part of the operatorA(t) in an implicit way, and the other part in an explicit way. We study stability and convergence for this method.
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    Numerische Mathematik 35 (1980), S. 315-341 
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    Notes: Summary We present here some new families of non conforming finite elements in ℝ3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.
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    Numerische Mathematik 35 (1980), S. 381-404 
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    Notes: Summary We study in this paper the convergence of a new mixed finite element approximation of the Navier-Stokes equations. This approximation uses low order Lagrange elements, leads to optimal order of convergence for the velocity and the pressure, and induces an efficient numerical algorithm for the solution of this problem.
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    Numerische Mathematik 45 (1984), S. 105-116 
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    Topics: Mathematics
    Notes: Summary We study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which at any nodal point is an average of gradients of linear elements on triangles incident with this nodal point. The convergence rate of the averaged gradient to an exact gradient in theL 2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.
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    Numerische Mathematik 45 (1984), S. 201-206 
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    Notes: Summary Bulirsch and Stoer have shown how to construct asymptotic upper and lower bounds on the true (global) errors resulting from the solution by extrapolation of the initial value problem for a system of ordinary differential equations. It is shown here how to do this for any one-step method endowed with an asymptotically correct local error estimator. The one-step method can be changed at every step.
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    Numerische Mathematik 28 (1977), S. 455-474 
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    Keywords: AMS(MOS): 65B05, 65M25, 65M99 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The application of extrapolation to the limit requires the existence of an asymptotic expansion in powers of the step size. In this paper one-and multi-step methods for the solution of hyperbolic systems of first order are considered. Conditions are formulated that ensure the asymptotic expansion. Methods of characteristics for quasilinear systems with two independent variables are included in this presentation. If a rectangular grid is used, also non-quasilinear systems are admissible. The main part of this paper deals with initial value problems. But it is shown that in some exceptional cases asymptotic expansions hold for initial-boundary problems, too.
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    Numerische Mathematik 37 (1981), S. 257-277 
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    Notes: Summary In theh-version of the finite element method, convergence is achieved by refining the mesh while keeping the degree of the elements fixed. On the other hand, thep-version keeps the mesh fixed and increases the degree of the elements. In this paper, we prove estimates showing the simultaneous dependence of the order of approximation on both the element degrees and the mesh. In addition, it is shown that a proper design of the mesh and distribution of element degrees lead to a better than polynomial rate of convergence with respect to the number of degrees of freedom, even in the presence of corner singularities. Numerical results comparing theh-version,p-version, and combinedh-p-version for a one dimensional problem are presented.
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    Numerische Mathematik 37 (1981), S. 405-421 
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    Notes: Abstract The discretization by finite elements of a model variational problem for a clamped loaded beam is studied with emphasis on the effect of the beam thickness, which appears as a parameter in the problem, on the accuracy. It is shown that the approximation achieved by a standard finite element method degenerates for thin beams. In contrast a large family of mixed finite element methods are shown to yield quasioptimal approximation independent of the thickness parameter. The most useful of these methods may be realized by replacing the integrals appearing in the stiffness matrix of the standard method by Gauss quadratures.
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    Numerische Mathematik 37 (1981), S. 387-404 
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    Keywords: AMS(MOS): 65N20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The treatment of a multigrid method in the framework of numerical analysis elucidates that regularity of the solution is not necessary for the convergence of the multigrid algorithm but only for fast convergence. For the linear equations which arise from the discretization of the Poisson equation, a convergence factor 0,5 is established independent of the shape of the domain and of the regularity of the solution.
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    Numerische Mathematik 38 (1982), S. 141-154 
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    Keywords: AMS(MOS): 35 A 40 ; 35 K 05 ; 65 N 15 ; 65 K 05 ; 80 A 20 ; CR: 5.17
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    Notes: Summary A nonlinear approximation technique for the numerical solution of certain free boundary problems is proposed. The method is shown for a degenerate one-dimensional Stefan problem. For this problem, an error estimate, which is independent of the used algorithm, is derived. Numerical examples are discussed.
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    Numerische Mathematik 40 (1982), S. 329-337 
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    Topics: Mathematics
    Notes: Summary A widely used technique for improving the accuracy of solutions of initial value problems in ordinary differential equations is local extrapolation. It is well known, however, that when using methods appropriate for solving stiff systems of ODES, the stability of the method can be seriously degraded if local extrapolation is employed. This is due to the fact that performing local extrapolation on a low order method is equivalent to using a higher order formula and this high order formula may not be suitable for solving stiff systems. In the present paper a general approach is proposed whereby the correction term added on in the process of local extrapolation is in a sense a rational, rather than a polynomial, function. This approach allows high order formulae with bounded growth functions to be developed. As an example we derive anA-stable rational correction algorithm based on the trapezoidal rule. This new algorithm is found to be efficient when low accuracy is requested (say a relative accuracy of about 1%) and its performance is compared with that of the more familiar Richardson extrapolation method on a large set of stiff test problems.
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    Numerische Mathematik 40 (1982), S. 339-371 
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    Notes: Summary In this first of two papers, computable a posteriori estimates of the space discretization error in the finite element method of lines solution of parabolic equations are analyzed for time-independent space meshes. The effectiveness of the error estimator is related to conditions on the solution regularity, mesh family type, and asymptotic range for the mesh size. For clarity the results are limited to a model problem in which piecewise linear elements in one space dimension are used. The results extend straight-forwardly to systems of equations and higher order elements in one space dimension, while the higher dimensional case requires additional considerations. The theory presented here provides the basis for the analysis and adaptive construction of time-dependent space meshes, which is the subject of the second paper. Computational results show that the approach is practically very effective and suggest that it can be used for solving more general problems.
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    Numerische Mathematik 41 (1983), S. 55-62 
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    Notes: Summary The finite element method with Laplace transform of time variable is proposed for the solution of hyperbolic equations. Error estimates in Hardy spaces of functions with values in Sobolev spaces are derived. Due to the isometric isomorphism of Hardy spaces with weighted Hilbert spaces these estimates are valid also for original formulations of hyperbolic equations.
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    Numerische Mathematik 41 (1983), S. 165-175 
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    Notes: Summary The extrapolated midpoint rule is a popular way to solve the initial value problem for a system of ordinary differential equations. As originally formulated by Gragg, the results are smoothed to remove the weak instability of the midpoint rule. It is shown that this smoothing is not necessary. A cheaper smoothing scheme is proposed. A way to exploit smoothing to increase the robustness of extrapolation codes is formulated.
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    Numerische Mathematik 41 (1983), S. 255-279 
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    Notes: Summary Some methods for evaluating the characteristic exponents in connection with Newton's iteration are applied for solving the eigenvalue problem related to the finite Hill's differential equation or, in particular, Mathieu's equation. By using these methods a high accuracy is achieved, furthermore a complete error analysis, which yields rather realistic error bounds, is possible.
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    Numerische Mathematik 42 (1983), S. 15-30 
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    Keywords: AMS: 65L10 ; 34C25 ; 34K10 ; CR: 5.17
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    Notes: Summary An iterative method is presented which starting from a lower or from an upper periodic solution, provides a monotone sequence converging to a periodic solution of (1). With some restrictions on the growth off, the method extends to functional differential equations of type (1′). Two numerical examples with an “a posteriori” error analysis are given.
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    Numerische Mathematik 42 (1983), S. 51-64 
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    Notes: Summary Engquist and Majda [3] proposed a pseudodifferential operator as asymptotically valid absorbing boundary condition for hyperbolic equations. (In the case of the wave equation this boundary condition is valid at all frequencies.) Here, least-squares approximation of the symbol of the pseudodifferential operator is proposed to obtain differential operators as boundary conditions. It is shown that for the wave equation this approach leads to Kreiss well-posed initial boundary value problems and that the expectation of the reflected energy is lower than in the case of Taylor- and Padé-approximations [3, 4]. Numerical examples indicate that this method works even more effectively for hyperbolic systems. The least-squares approach may be used to generate the boundary conditions automatically.
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    Numerische Mathematik 42 (1983), S. 77-95 
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    Notes: Summary Brakhage and Werner, Leis and Panich suggested to reduce the exterior Dirichlet boundary value problem for the Helmholtz equation to an integral equation of the second kind which is uniquely solvable for all frequencies by seeking the solution in the form of a combined double- and single-layer potential. We present an analysis of the appropriate choice of the parameter coupling the double- and single-layer potential in order to minimize the condition number of the integral operator.
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    Numerische Mathematik 42 (1983), S. 65-76 
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    Notes: Summary We consider here a general class of algorithms for the numerical solution of variational inequalities. A convergence proof is given and in particular a multi-grid method is described. Numerical results are presented for the finite-difference discretization of an obstacle problem for minimal surfaces
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    Numerische Mathematik 42 (1983), S. 119-123 
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    Notes: Summary Many difference methods for the numerical solution of elliptic boundary value problems lead to systems of linear equations whose matrices areM-matrices and which therefore have nonnegative inverses. In this paper it is shown, that these difference methods are at most consistent of second order.
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    Numerische Mathematik 42 (1983), S. 173-194 
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    Notes: Summary We consider the stationary Navier-Stokes equations, written in terms of the primitive variables, in the case where both the partial differential equations and boundary conditions are inhomogeneous. Under certain conditions on the data, the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. A conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved. In addition, the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given. Numerical examples, using an efficient choice of finite element spaces, are also provided.
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    Numerische Mathematik 42 (1983), S. 271-290 
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    Keywords: AMS(MOS): 65J10, 65L20, 65M10 ; CR: 5.17
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    Notes: Summary Consider a linear autonomous system of ordinary differential equations with the property that the norm |U(t)| of each solutionU(t) satisfies |U(t)|≦|U(0)| (t≧0). We call a numerical process for solving such a system contractive if a discrete version of this property holds for the numerical approximations. A givenk-step method is said to be unconditionally contractive if for each stepsizeh〉0 the numerical process is contractive. In this paper a general theory is given which yields necessary and sufficient conditions for unconditional contractivity. It turns out that unconditionally contractive methods are subject to an order barrierp≦1. Further the concept of a contractivity threshold is studied, which makes it possible to compare the contractivity behaviour of methods with an orderp〉1 as well. Most theoretical results in this paper are formulated for differential equations in arbitrary Banach spaces. Applications are given to numerical methods for solving ordinary as well as partial differential equations.
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    Numerische Mathematik 42 (1983), S. 359-377 
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    Keywords: AMS 65L05 ; 65L07 ; CR: 5.17
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    Notes: Summary This paper is concerned with the stability of multistep methods for ordinary initial-value problems on grids with variable mesh-sizes. A necessary and sufficient condition for stability is given from which generalizations of recent results by Gear et al. and by Zlatev can be obtained as special cases. As an application the stability of the variable BDF-formulas is treated.
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    Numerische Mathematik 42 (1983), S. 379-389 
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    Keywords: AMS(MOS): 65L20 ; 15A60 ; 65M20 ; CR: 5.17
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    Notes: Summary If the field of values of a matrixA is contained in the left complex halfplaneH and a functionf mapsH into the unit disc then ∥f(A)∥2≦1 by a theorem of J.v. Neumann. We prove a theorem of this type, only the field of values ofA is used for functions which are absolutely bounded by one in only part ofH. An extension can be used to show norm-stability of single step methods for stiff differential equations. The results are applicable among others to several subdiagonal Padé approximations which are notA-stable.
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    Numerische Mathematik 29 (1977), S. 65-82 
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    Notes: Summary The line method discussed in [19] is improved by considering several time slices. It is applied to parabolic initial-value problems, and with techniques similar to [16] it is proved that the root conditions of Dahlquist [5] and Widlund [17] are sufficient for stability. Stable methods up to order 6 are given and illustrated by numerical calculations.
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    Numerische Mathematik 29 (1978), S. 381-396 
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    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, a general class ofk-step methods for the numerical solution of ordinary differential equations is discussed. It is shown that methods with order of consistencyq have order of convergence (q+1) if a very simple condition is satisfied. This result gives a new aspect to previous results of Spijker; it also serves as a starting point for a new theory of cyclick-step methods, completing an approach of Donelson and Hansen. It facilitates the practical determination of high-order cyclick-step methods, especially of stiffly stable,k-step methods.
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  • 91
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    Numerische Mathematik 29 (1978), S. 409-424 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65LO5 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In a recent article [2] Frank and Überhuber define and motivate the method of iterated defect correction for Runge-Kutta methods. They prove a theorem on the order of that method using the theory of asymptotic expansions. In this paper we give similar results using the theory of Butcher series (see [4]). Our proofs are purely algebraic. We don't restrict our considerations to Runge-Kutta methods, but we admit arbitrary linear one-step methods. At the same time we consider more general defect functions as in [2].
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  • 92
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    Numerische Mathematik 29 (1978), S. 209-226 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L 10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we give a simple stability theory for finite difference approximations to linear ordinary boundary value problems. In particular we consider stability with respect to a maximum norm including all difference quotients up to the order of the differential equation. It is shown that stability in this sense holds if and only if the principal part of the differential equation is discretized in a “stable way”. This last property is characterized by root conditions which we prove to be satisfied for some classes of finite difference schemes. Our approach simplifies and generalizes some known results of the literature where Sobolev norms or merely the maximum norm are used.
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  • 93
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    Numerische Mathematik 29 (1978), S. 397-407 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 31-04, 65N05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A transformation method is developed which may be used to solve various types of boundary value problems on three-dimensional regions with an arbitrary boundary. The implementation of the method is illustrated in the solution of a potential flow problem. All computations are performed on a cubic mesh in a rectangular region.
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  • 94
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    Numerische Mathematik 29 (1978), S. 425-443 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65J05, 65L99 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Recently, a number of closely related techniques for error estimation and iterative improvement in discretization algorithms have been proposed. In this article, we expose the common structural principle of all these techniques and exhibit the principal modes of its implementation in a discretization context.
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  • 95
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    Numerische Mathematik 30 (1978), S. 93-101 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider non-inverse positive differential operators of the second order and show that error estimates can be obtained through methods of inverse positivity alone. This means a significant simplification if the operator has only one negative eigenvalue. In addition we show how to obtain Range-Domain implications for operators with mixed boundary conditions.
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  • 96
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    Numerische Mathematik 31 (1978), S. 359-375 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For the numerical solution of two-point boundary value problems a shooting algorithm based on a Taylor series method is developed. Series coefficients are generated automatically by recurrence formulas. The performance of the algorithm is demonstrated by solving six problems arising in nonlinear shell theory, chemistry and superconductivity.
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  • 97
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    Numerische Mathematik 32 (1979), S. 271-279 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 49.04 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper is concerned with the solution of the finite time Riccati equation. The solution to the Riccati equation is given in terms of the partition of the transition matrix. Matrix differential equations for the partition of the transition matrix are derived and are solved using computational methods. Examples illustrating the method are presented and the computational algorithms are given.
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  • 98
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    Numerische Mathematik 32 (1979), S. 307-332 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65Q05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper deals with the convergence of nonstationary quasilinear multistep methods with varying step, used for the numerical integration of Volterra functional differential equations. A Perron type condition (appearing in the differential equations theory) is imposed on the increment function. This gives a generalization of some results of Tavernini ([19–21]).
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  • 99
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    Numerische Mathematik 33 (1979), S. 195-210 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the mixed finite element method for the buckling problem of the thin plate by using piecewise linear polynomials. We give error estimates for the approximate eigenvalues and the eigenfunctions.
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  • 100
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    Numerische Mathematik 33 (1979), S. 69-75 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 34B15 ; 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In the first part of this paper we are dealing with theoretical statements and conditions which lead to existence and uniqueness of the solution of a nonlinear boundary value problem with delay. Next we apply this method successfully to a numerical example. The computations have been carried out at the computer Siemens 4004. The data obtained are presented in two tables.
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