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  • 1
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    In:  EPIC3Springer, Berlinpp. (Lecture Notes in Mathematics ; 1725) Remark (September 2002): The original edition is now out of print. A slightly revised version (compare `Errata' and `Additions' under: {http://www.awi-bremerhaven.de/Modelling/LGCA+LBM/} is availab, Berlin, Springer, 308, 308 p., ISBN: 3-540-66973-6
    Publication Date: 2019-07-17
    Description: Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.
    Repository Name: EPIC Alfred Wegener Institut
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    In:  EPIC3Naturwissenschaften, Springer, 71(12), pp. 599-608, ISSN: 0028-1042
    Publication Date: 2014-06-04
    Repository Name: EPIC Alfred Wegener Institut
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  • 3
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    Bulletin of mathematical biology 46 (1984), S. 967-969 
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    Notes: Abstract It is observed that a dynamical continuity equation for biomass distribution yields the asymptotic steady-state exponential dependencen=A exp( $$ - m/\bar m$$ ) exhibited by certain fishery data, wherem is the biomass of an individual,n is the number of individuals per unit biomass interval, andA, $$\bar m$$ are positive constants. This dynamical approach to biomass distribution is an alternative to the global maximization principle proposed recently by Lurié and Wagensberg.
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    Bulletin of mathematical biology 46 (1984), S. 971-972 
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    Bulletin of mathematical biology 46 (1984), S. 973-974 
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    Bulletin of mathematical biology 46 (1984), S. 11-17 
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    Notes: Abstract Linear birth and death processes are used to derive simple expressions for sequential extinction times and gene fixation probabilities in asexual populations.
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  • 7
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    Bulletin of mathematical biology 46 (1984), S. 1-10 
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    Notes: Abstract We are here concerned with the functionf which assigns to each pointP of an object the numberf(P) which is the shortest distance fromP to the border. This function appears in various guises in diverse biological studies. The functionf(P) is itself a measure of shape—or more precisely, an infinite set of measures, one for each point (and hence, in view of its geometric definition, usually in a form inconvenient for use). Thus in this paper we sought a reasonable representative of this infinite set of measures, namely themean of the numbersf(P) asP ranges over all points of the entity. Computability studies are developed for various classes of shapes. For example, (1) the mean for a lamina bounded by a polygon circumscribable about a circle of radiusr isr/3; (2) the mean for a domain bounded by a polyhedron circumscribable about a sphere of radiusr isr/4. The transition from pointwise to piecewisef(P), especially in the non-convex case, requires working with inequalities.
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    Bulletin of mathematical biology 46 (1984), S. 19-40 
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    Notes: Abstract A mathematical model for traveling bands of motile and chemotactic bacteria in the presence of cell growth and death is examined. It is found that asymptotic traveling wave solutions exist in the absence of chemotaxis, due to the balance of growth, death and random motility. Thus random motility confers the ecological advantage of population propagation through migration into nutrient-rich regions. The presence of chemotaxis amplifies this advantage by moving more cells into higher nutrient concentration regions, resulting in larger and faster bands. Therefore there seem to be two types of traveling bands that can be attained by chemotactic bacteria in the presence of growth and death: (1) these growth/death/motility bands; and (2) pure chemotactic ‘Keller-Segel'-type bands. Comparison to experimental observations by Chapman in 1973 indicate that the latter seem to be formed. The relationship between these two types of solution is at present uncertain. The growth/death/motility bands may have relevance on longer time or distance scales characteristic of microbial ecological systems.
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    Bulletin of mathematical biology 46 (1984), S. 115-125 
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    Notes: Abstract Based on the principle of minimum power, a mathematical model of the pathological functional state of the oxygen transport system is presented. The model is used to determine the optimal functional parameters of the oxygen transport system in hyperthyroidism, anemia and hypertension. Theoretical results are compared with clinical data.
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    Bulletin of mathematical biology 46 (1984), S. 139-153 
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    Notes: Abstract A modified SIRS model is developed as a framework for the study of epizootiological dynamics in an insect-pathogen system. Linearized stability analysis reveals that the system with one immune and one susceptible host class can exhibit stable, periodic or unstable behavior depending on model parameters. In general, high pathogenicity, short pathogen propagule lifespan and high host reproductive rate are stabilizing influences. Pathogen transmissibility and propagule production/host do not influence local stability. The effect of seasonal host reproduction is studied because most insect hosts are seasonal in temperate climates. The basic stability dependence on model parameters holds except as modified by the length of the reproduction interval. The results of this study are compared with the recent work of Anderson and May.
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    Bulletin of mathematical biology 46 (1984), S. 175-184 
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    Notes: Abstract The random predator-prey type interactions of the population species in a random varying environment have been investigated. The Fokker-Planck equation for the transition probability, corresponding to the stochastic differential equations established from Lotka-Volterra equations by the introduction of randomness and variability, has been integrated in the form of a path integral. The transition probabilities for extinction or survival of one or several species have been approximately evaluated and investigated.
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    Bulletin of mathematical biology 46 (1984), S. 155-174 
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    Notes: Abstract If two microbial populations compete for a single resource in a homogeneous environment with time invariant inputs they cannot coexist indefinitely if the resource competed for is not renewed by biological activity within the system. Mathematical studies have shown that in a predator-prey system, where the resource (prey) is self-renewing, the two competitors (predators) can coexist in a limit cycle. This suggests that if the resource competed for is renewed by biological activity within the system coexistence can occur in any microbial system provided that it exhibits the same features as, but without being, a predator-prey one. A food chain involving commensalism, competition and amensalism is presented here. Two subcases are considered. It is only when maintenance effects are taken into account that coexistence, in limit cycles, can occur for this system. Limit cycle solutions for the system are demonstrated with the help of computer simulations. Some necessary conditions for coexistence are presented, as are some speculations regarding the possible physical explanations of the results.
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    Bulletin of mathematical biology 46 (1984), S. 127-137 
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    Notes: Abstract The branching structure of the mammalian arterial tree has been known to be close to that of an optimal conduit system of the minimum work model characterized as the branch system of constant wall shear rate. The physiological mechanism producing such construction was considered to be based on the local response of arterial caliber induced by the wall shear stress (shear rate × blood viscosity) and thereby maintaining this stress constant, which was previously observed at the canine common carotid artery shunted to the external jugular vein. The stress levels at various parts of the arterial system estimated from available data fell within ±50% of the mean (15 dyn/cm2), which was consistent with the value predicted from the model. Theoretical analyses on the cost function of the model indicated that the suspected variation of shear rate levels in the arterial tree due to the anomalous changes in blood viscosity which might bring about 3- to 4-fold differences between the minimum and maximum shear rates would cause less than 10% increase in the total energy cost. It was concluded that a local adaptive response to wall shear stress is the mechanism which effectively optimizes the design of the arterial tree.
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    Bulletin of mathematical biology 46 (1984), S. 185-185 
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    Bulletin of mathematical biology 46 (1984), S. 187-203 
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    Notes: Abstract The structure of the genetic code is related to a Gray code, which is a plausible theoretical model for an amino acid code. The proposed model implies that the most important factor in shaping the code was the effects of mistakes in translation, not effects of mutations. Another possible implication is that the preservation of stiffness and flexibility at appropriate places in a protein chain is as important in protein structure as the appropriate placement of hydrophilic (external) and hydrophobic (internal) residues. Other results are a simple conceptualization of the relationships among the 20 amino acids and their relations to their codons. The detailed relationships are summarized in the following ‘similarity alphabet’: ala, thr, gly, pro, ser; asp, asn, glu, gln, lys; his, arg, trp, tyr, phe; leu, met, ile, val, cys; (ATGPS DNEQK HRWYF LMIVC in the one-letter code). This alphabet falls into four groups of amino acids: small, external, large, internal. The approximate relation of the groups to their codons is expressed as: the first base of a codon controls size—a purine means a small amino acid, a pyrimidine means large; the middle base controls cloisterednes—purine means external, pyrimidine means internal. These relationships express the minimum change principle upon which the code appears to be founded.
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    Bulletin of mathematical biology 46 (1984), S. 269-282 
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    Notes: Abstract A theoretical study of the Brusselator model with non-uniform distribution of component A and a concentration-dependent diffusion coefficient has been performed. Numerical simulation reveals that a variable diffusion coefficient alters the bifurcation pattern and the stability properties of the steady-state as well as periodic solutions. A simple approximate method, based on one-point collocation, has been proposed to analyze the bifurcation phenomena for the case of fixed boundary conditions and low system size.
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    Bulletin of mathematical biology 46 (1984), S. 283-294 
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    Notes: Abstract In this paper the effects of the occurrence of cut trees in the topological analysis of branching patterns have been studied. It is assumed that branches are removed at random from the trees. We prove that, for both the segmental and terminal growth models, the probability distributions of the cut trees are identical to those of complete trees.
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    Bulletin of mathematical biology 46 (1984), S. 247-268 
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    Notes: Abstract The goal of this work is an examination of capillary exchange models as mathematical operators. The concentration function relations for the Krogh cylinder of a single capillary, basic to many organ models, are studied via the theory of operators on the Lebesgue normed spacesL p[0,∞], (1〈-p〈-∞). A discussion is included of theL p -normsvis-à-vis the coefficient of variation currently used in finding capillary parameters and evaluating parameter searches. The capillary model determines two operators on the space of locally integrable functions: O K (relating extravascular concentration to intravascular) and K a, k (relating intravascular concentration to input), wherek is the ratio of permeabilitysurface area (PS) to extravascular volume, and α is the ratio of PS to flow. These operators are shown to induce contractive (‖O K ‖ p 〈-1, ‖K a, k ‖ p 〈-1), isotone, linear operators onL p . The uniform convergence relation $$K_{a,k} = \mathop {\lim _{(p)} }\limits_{N \to \infty } \left( {\sum\limits_{n = 0}^N {P_n (a)O_k^n } } \right)$$ (as operators onL p) is derived, whereP n (a) is the Poisson probabilitye −a a n /n!. For the important special cases ofp=∞, 1, 2 the norms are found (‖Ok‖=‖Ka,k‖p=1). Consideration is also given to the norms and operators when the functions involved are limited to a finite interval of time.
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    Bulletin of mathematical biology 46 (1984), S. 295-326 
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    Notes: Abstract One particular kind of structure offers possible explanations, for long-term memory, efficient consolidation of stored information from the environment, clustering of data strings and multimodal functioning. It is a possible model for pieces of neural structure and its use offers a uniform method for both studying and constructing an extensive class of mechanisms.
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    Bulletin of mathematical biology 46 (1984), S. 327-332 
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    Notes: Abstract Levenshtein dissimilarity measures are used to compare sequences in application areas including coding theory, computer science and macromolecular biology. In general, they measure sequence dissimilarity by the length of a shortest weighted sequence of insertions, deletions and substitutions required, to transform one sequence into another. Those Levenshtein dissimilarity measures based on insertions and deletions are analyzed by a model involving valuations on a partially ordered set. The model reveals structural relationships among poset, valuation and dissimilarity measure. As a consequence, certain Levenshtein dissimilarity measures are shown to be metrics characterized by betweenness properties and computable in terms of well-known measures of sequence similarity.
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    Bulletin of mathematical biology 46 (1984), S. 337-337 
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    Bulletin of mathematical biology 46 (1984), S. 333-336 
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    Notes: Abstract It is pointed out that the methane flux measured experimentally for certain ponds and swamps is quantitatively consistent with a commensal dependence of Methanobacteria on O2-chemotactic motile aerobic bacteria. The Methano species is thereby shielded from oxygen and provided with carbon dioxide for the anaerobic production of methane.
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    Bulletin of mathematical biology 46 (1984), S. 357-370 
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    Notes: Abstract A sufficient condition is given for stochastic boundedness persistence of a top predator in generalized Lotka-Volterra-type stochastic food web models in arbitrary bounded regions of state space. The main result indicates that persistence in the corresponding deterministic system is preserved in the stochastic system if the intensities of the random fluctuations are not too large.
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    Bulletin of mathematical biology 46 (1984), S. 371-377 
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    Notes: Abstract One of Bobisud's models for the evolution of cannibalism is reanalyzed by applying the method of finding evolutionarily stable strategies (or ESS's). It is demonstrated that ‘no cannibalism’ never will be an ESS if the initial rate of cannibalism is too large. It is further demonstrated that individual selection may even result in the evolution of cannibalism during food abundance. Some empirical case studies are briefly discussed in relation to this model.
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    Bulletin of mathematical biology 46 (1984), S. 379-387 
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    Notes: Abstract A computer algorithm is presented which equiprobably generates any member of the set of all directed trees withk labeled terminal nodes and unlabeled interior nodes. The algorithm requires roughlyk 2 /2 storage locations. The one-time initialization requiresO(k 2 ) time, while generating each tree requiresO(k) time.
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    Bulletin of mathematical biology 46 (1984), S. 515-527 
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    Notes: Abstract The comparison of several sequences is central to many problems of molecular biology. Finding consensus patterns that define genetic control regions or that determine structural or functional themes are examples of these problems. Previously proposed methods, such as dynamic programming, are not adequate for solving problems of realistic size. This paper gives a new and practical solution for finding unknown patterns that occur imperfectly above a preset frequency. Algorithms for finding the patterns are given as well as estimates of statistical significance.
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    Bulletin of mathematical biology 46 (1984), S. 501-514 
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    Notes: Abstract A new development is introduced here in the use of dynamic programming in finding pattern similarities in genetic sequences, as was first done by Needleman and Wunsch (1969). A condition of pattern similarity is defined and an algorithm is given which scans any set of similarities and screens out those which fail to meet the condition. When the set to be scanned contains every pair of segments, one from each of two given sequences of lengthsm andn (i.e. every possible location for a pattern similarity), then it completes the scan in a number of computational steps proportional tom·n, leaving those pairs of segments which satisfy the similarity condition. The algorithm is based on the concept of match density, as suggested by Goad and Kanehisa (1982).
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    Bulletin of mathematical biology 46 (1984), S. 529-543 
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    Notes: Abstract This paper concerns sequences of letters in which certain “distinguished” words are of interest. Such sequences arise as data in numerous fields including genetics and neuroscience. A probability distribution is given for the number of occurrences of a chosen word in a randomized sequence of letters. Such words are considered “favored” if they occur more than expected at random. Favored words have been discovered in nerve impulse trains and may reflect a neural coding scheme.
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    Bulletin of mathematical biology 46 (1984), S. 545-552 
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    Notes: Abstract As the volume of protein sequence data grows, rapid methods for searching the protein sequence database become of primary importance. Rigorous comparison of sequences is obtained with the well-known dynamic programming algorithms. However, these algorithms are not rapid enough to use for routinely searching the entire database. In this paper we discuss some methods that can be used for rapid searches.
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    Bulletin of mathematical biology 46 (1984), S. 553-566 
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    Notes: Abstract We give algorithms for computing the extent of similarity between two or three sequences of letters. The similarity measures we consider include a penalty for inserting gaps within the sequence in order to enhance similarity. The magnitude of the penalty for gaps is assumed to be independent of their size in order to accommodate certain biological applications. Our algorithm for three sequence comparisons, which is based on solving a system of recursive equations, improves upon the efficiency of existing methods. Although the system of recursive equations utilized by the algorithm is quite complicated as it stands, it has none the less been simplified by appeal to combinatorial considerations.
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    Bulletin of mathematical biology 46 (1984), S. 567-577 
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    Notes: Abstract Well-known dynamic programming algorithms exist for comparing two finite sequences inO(N 2) time and storage, whereN is the common sequence length. Extensions to the comparison ofM finite sequences requireO((2N) M) time and storage, making such algorithms difficult even forM=3. A simple generalization of the sequences makes it possible to obtain some results about the geometry of sequence alignments. These ideas suggest heuristic approaches to problems of comparing several sequences. IfM sequences are known to be related by a binary tree, they can be aligned inO(MN 2) time andO(N 2+NM) storage.
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    Bulletin of mathematical biology 46 (1984), S. 661-672 
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    Notes: Abstract Protein sequences of the Dayhoff databank of 1984 have been analyzed to evaluate the occurrences of the 400 dipeptides and 8000 tripeptides. Expected values and standard deviations for the di- and tripeptides were determined by Monte Carlo and binomial approximation. A condensed format containing this information, labeled a uniqueness diagram, is presented and made available in the form of a microfiche.
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    Bulletin of mathematical biology 46 (1984), S. 827-844 
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    Notes: Abstract In two-state sliding filament models of muscle contraction a partial differential equation must be solved to find the cross-bridge distribution functionn(x, t). In this paper the analytical form of this function is obtained by integration along the characteristic line and special cases are presented in which the explicit expression forn(x, t) can be completely determined. These analytical solutions provide a direct mathematical connection between the microscopic contraction parameters contained in the kinetic theories and macroscopic muscle dynamics and are thus used to investigate what parameters influence the transient contractile tension in typical experimental conditions. The results of this investigation are consistent with relevant aspects of muscle physiology.
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    Bulletin of mathematical biology 46 (1984), S. 845-857 
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    Notes: Abstract Experiments on random binary, ternary, etc. (P=2, 3,…, 10) switching nets are reported. Behavioral cycle lengths are examined as functions of output variety,P, input connectance,K, and net size,N. Overall, output variety appears an influential, well-behaved net property. Strong, but well-behaved interactions appear among net variables. In high connectance nets, median cycle length grows approx. asP N/2. Other factors constant, one-connected nets show the shortest cycles, and connectance effects appear to converge asymptotically aroundN. Data for cycle length as a function of net size suggest a concavity not compatible with the Kauffman “square root law” (Kauffman, 1969). Evidence of a positive relationship between cycle length and run-in length is found in two-input nets; weaker evidence is obtained that in higher connectance nets this relationship becomes negative in sign. The “modular complexity” ofP〉2 nets is examined briefly.
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    Bulletin of mathematical biology 46 (1984), S. 869-877 
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    Notes: Abstract The influence of topographical situation on the spread of infection is studied. The investigation is based on a multigroup model. The population under consideration is thought to be divided into subpopulations living in regions that are separated from each other by natural barriers (mountains). Infection is carried from one region to another by migrating infectives. Migration is possible only along the river system so that the structure of the epidemiological network is that of a symmetric tree. The results allow comparison of the velocity of propagation of the epidemic for different geographical situations and allow quantification of the “channel-effect”, according to which mountainous regions are channels rather than barriers to the spread of an epidemic.
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    Bulletin of mathematical biology 62 (2000), S. 37-59 
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    Notes: Abstract In Xenopus and Drosophila, the nucleocytoplasmic ratio controls many aspects of cell-cycle remodeling during the transitory period that leads from fast and synchronous cell divisions of early development to the slow, carefully regulated growth and divisions of somatic cells. After the fifth cleavage in sea urchin embryos, there are four populations of differently sized blastomeres, whose interdivision times are inversely related to size. The inverse relation suggests nucleocytoplasmic control of cell division during sea urchin development as well. To investigate this possibility, we developed a mathematical model based on molecular interactions underlying early embryonic cell-cycle control. Introducing the nucleocytoplasmic ratio explicitly into the molecular mechanism, we are able to reproduce many physiological features of sea urchin development.
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    Bulletin of mathematical biology 62 (2000), S. 17-35 
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    Notes: Abstract The irregular sequence of counts of a microbial population, in the absence of observable corresponding environmental changes (e.g., temperature), can be regarded as reflecting the interplay of several unknown or random factors that favor or inhibit growth. Since these factors tend to balance one another, the fluctuations usually remain within bounds, and only by a coincidence—when all or most act in unison—does an ‘outburst’ occur. This situation can be represented mathematically as a sequence of independent random variables governed by a probability distribution. The concept was applied to reported microbial counts of ground meat and wastewater. It is found that the lognormal distribution could serve as a model, and that simulations from this model are indistinguishable from actual records. The parameters of the lognormal (or other) distribution can then be used to estimate the probability of a population outburst, i.e., an increase above a given threshold. Direct estimation of the outburst probability based on frequency of occurrence is also possible, but in some situations requires an impractically large number of observations. We compare the efficiency of these two methods of estimation. Such methods enable translation of irregular records of microbial counts into actual probabilities of an outburst of a given magnitude. Thus, if the environment remains ’stable’ or in dynamic equilibrium, the fluctuations should not be regarded merely as noise, but as a source of information and an indicator of potential population outbursts even where obvious signs do not exist.
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    Bulletin of mathematical biology 62 (2000), S. 121-153 
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    Notes: Abstract During an immune response, the affinity of antibodies that react with the antigen that triggered the response increases with time, a phenomenon known as affinity maturation. The molecular basis of affinity maturation has been partially elucidated. It involves the somatic mutation of immunoglobulin V-region genes within antigen-stimulated germinal center B cells and the subsequent selection of high affinity variants. This mutation and selection process is extremely efficient and produces large numbers of high affinity variants. Studies of the architecture of germinal centers suggested that B cells divide in the dark zone of the germinal center, then migrate to the light zone, where they undergo selection based on their interaction with antigen-loaded follicular dendritic cells, after which they exit the germinal center through the mantle zone. Kepler and Perelson questioned this architecturally driven view of the germinal center reaction. They, as well as others, argued that the large number of point mutations observed in germinal center B cell V-region genes, frequently 5 to 10 and sometimes higher, would most likely render cells incapable of binding the antigen, if no selection step was interposed between rounds of mutations. To clarify this issue, we address the question of whether a mechanism in which mutants are generated and then selected in one pass, with no post-selection amplification, can account for the observed efficiency of affinity maturation. We analyse a set of one-pass models of the germinal center reaction, with decaying antigen, and mutation occurring at transcription or at replication. We show that under all the scenarios, the proportion of high affinity cells in the output of a germinal center varies logarithmically with their selection probability. For biologically realistic parameters, the efficiency of this process is in clear disagreement with the experimental data. Furthermore, we discuss a set of, possibly counterintuitive, more general features of one-pass selection models that follow from our analysis. We believe that these results may also provide useful intuitions in other cases where a population is subjected to selection mediated by a selective force that decays over time.
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    Bulletin of mathematical biology 62 (2000), S. 61-86 
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    Notes: Abstract Simple predator-prey models often predict extreme instability in interactions where the prey are depressed well below their carrying capacity. Although the behaviour of some laboratory systems conforms to this pattern, field and mesocosm studies generally show prolonged co-existence of prey and predator. Prominent among the possible causes of this discrepancy are the effects of spatial heterogeneity. In this paper we show that both discrete and continuous representations of the spatial Rosenzweig-McArthur model with immobile prey can be stabilized by self-organized prey heterogeneity. This concordance of behaviour closely parallels that which we have previously established in the context of invasion waves. We use the continuous model variant to calculate the characteristic spatial scales of the self-organized structures. The discrete variant forms the basis of a simulation study demonstrating the variety of stable structures and elucidating their relation to the history of the system. We note that all stable prey distributions take the form of a network of occupied patches separated by prey-free regions, and liken the process which generates such assemblages to the formation of a landscape mozaic.
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    Bulletin of mathematical biology 62 (2000), S. 395-398 
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    Bulletin of mathematical biology 62 (2000), S. 229-240 
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    Notes: Abstract Multistage mathematical models of carcinogenesis (when applied to tumor incidence data) have historically assumed that the growth kinetics of cells in the malignant state are disregarded and the formation of a single malignant cell is equated with the emergence of a detectable tumor. The justification of this simplification is, from a mathematical point of view, to make the estimation of tumor incidence rates tractable. However, analytical forms are not mandatory in the estimation of tumor incidence rates. Portier et al. (1996b, Math. Biosci. 135, 129–146) have demonstrated the utility of the Kolmogorov backward equations in numerically calculating tumor incidence. By extending their results, the cumulative distribution function of the time to a small observable tumor may be numerically obtained.
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    Bulletin of mathematical biology 62 (2000), S. 321-336 
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    Notes: Abstract An analytic formalism developed earlier to describe the time evolution of the basic enzyme reaction is extended to fully competitive systems. Time-dependent closed form solutions are derived for the three nominal cases of competition: even, slow and fast inhibitors, allowing for the first time the complete characterization of the reactions. In agreement with previous work, the time-independent Michaelis-Menten approach is shown to be inaccurate when a fast inhibitor is present. The validity of the quasi-steady-state approximation on which the present framework is based is also revised.
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    Bulletin of mathematical biology 62 (2000), S. 87-99 
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    Notes: Abstract A simple model of macroparasitic infections has been used to evaluate the potential use of parasites as biological tags of fish populations. In the model, the parasite-host interaction is regulated by a birth-death process, and parasites can only be acquired by the non-specific migratory host population in a particular area of the space domain. In this case, we show that parasites can be succesfully used for stocks identification and to describe the migratory routes taken by some marine fish species.
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    Bulletin of mathematical biology 62 (2000), S. 155-161 
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    Notes: Abstract We investigate the effect of migration between local populations of a single discrete-generation species living in a ring or an array of habitats. The commonly used symmetric dispersal assumption is relaxed to include the biologically more reasonable asymmetric dispersion. It is demonstrated analytically that density independent migration has no effect on the equilibrium stability of individual populations. However, the positive equilibrium may be destabilizing if the migration is density dependent in such a way that it increases with increasing population density at the source patch.
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    Bulletin of mathematical biology 62 (2000), S. 101-120 
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    Notes: Abstract A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling. For different parameter values, single cell models can exhibit bursting, beating and a myriad of other complex oscillations. A procedure for finding asymptotic estimates of the thresholds between these (synchronous) behaviors in the cellular aggregates is described for the heterogeneous case where the coupling strength is strong. This procedure is tested on a model of a strongly coupled heterogeneous collection of bursting and beating cells. Since isolated pancreatic β-cells have been observed to both burst and beat, this test of the spatial averaging techniques provides a possible explanation to measured discrepancies between the electrical activities of isolated β-cells and coupled collections (islets) of β-cells.
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    Bulletin of mathematical biology 62 (2000), S. 595-632 
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    Notes: Abstract We describe the dynamics of competing species in terms of interactions between spatial moments. We close the moment hierarchy by employing a Gaussian approximation which assumes that fluctuations are independent and distributed normally about the mean values. The Gaussian approximation provides the lowest-order systematic correction to the mean-field approximation by incorporating the effect of fluctuations. When there are no fluctuations in the system, the mean equations agree with the Gaussian approximation as the fluctuations are weak. As the fluctuations gain strength, they influence the mean quantities and hence the Gaussian approximation departs from the mean-field approximation. At large fluctuation levels, the Gaussian approximation breaks down, as may be explained by the bimodality and skewness of the fluctuation distribution of the partial differential equation.
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    Notes: Abstract The multipole approach to the inverse electrocardiological problem consists of estimating the multipole components of the cardiac electric generator, starting from the measured body surface potential. This paper presents a critical investigation of the basic premise for the applicability of the multipole approach, namely the convergence of the multipole equivalent generator for the heart on the surface of an inhomogeneous body conductor. As an extension to multipole theory, a criterion for the convergence is derived. Based on realistic models for the body conductor and the cardiac electric generator, we observe that the criterion is not strictly satisfied in realistic conditions. Numerical simulations with the same models point out that the multipole equivalent generator is indeed not convergent in the strict mathematical sense. On the other hand, we show that the multipole equivalent generator yields a rather close approximation of the electrocardiological potential for intermediate values of the order of the multipole generator. A discussion is given on how to explain the apparently ambiguous results for the estimation of cardiac multipole components.
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    Bulletin of mathematical biology 62 (2000), S. 633-656 
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    Notes: Abstract The continuous model of Anderson et al. (1981), Nature 289, 765–771, is successful in describing certain characteristics of rabies epizootics, in particular, the secondary recurrences which follow the initial outbreak; however, it also predicts the occurrence of exponentially small minima in the infected population, which would realistically imply extinction of the virus. Here we show that inclusion of a more realistic distribution of incubation times in the model can explain why extinction will not occur, and we give explicit parametric estimates for the minimum infected fox density which will occur in the model, in terms of the incubation time distribution.
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    Bulletin of mathematical biology 62 (2000), S. 657-674 
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    Notes: Abstract The processes whereby developing neurones acquire morphological features that are common to entire populations (thereby allowing the definition of neuronal types) are still poorly understood. A mathematical model of neuronal arborizations may be useful to extract basic parameters or organization rules, hence helping to achieve a better understanding of the underlying growth processes. We present a parsimonious statistical model, intended to describe the topological organization of neuritic arborizations with a minimal number of parameters. It is based on a probability of splitting which depends only on the centrifugal order of segments. We compare the predictions made by the model of several topological properties of neurones with the corresponding actual values measured on a sample of honeybee (olfactory) antennal lobe neurones grown in primary culture, described in a previous study. The comparison is performed for three populations of segments corresponding to three neuronal morphological types previously identified and described in this sample. We show that simple assumptions together with the knowledge of a very small number of parameters allow the topological reconstruction of representative (bi-dimensional) biological neurones. We discuss the biological significance (in terms of possible factors involved in the determinism of neuronal types) of both common properties and cell-type specific features, observed on the neurones and predicted by the model.
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    Bulletin of mathematical biology 62 (2000), S. 483-499 
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    Notes: Abstract We re-visit previous analyses of the classical Michaelis-Menten substrate-enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt ≈ 0 for the basic enzyme reaction at high enzyme concentration. For the first time, an approximate solution for the concentrations of the reactants uniformly valid in time is reported. Numerical simulations are presented to verify this solution. We show that an analytical approximation can be found for the reactants for each initial condition using the appropriate quasi-steady-state assumption. An advantage of the present formalism is that it provides a new procedure for fitting experimental data to determine reaction constants. Finally, a new necessary criterion is found that ensures the validity of the reverse quasi-steady-state assumption. This is verified numerically.
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    Bulletin of mathematical biology 62 (2000), S. 799-848 
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    Notes: Abstract We analytically study the dynamics of evolving populations that exhibit metastability on the level of phenotype or fitness. In constant selective environments, such metastable behavior is caused by two qualitatively different mechanisms. On the one hand, populations may become pinned at a local fitness optimum, being separated from higher-fitness genotypes by a fitness barrier of low-fitness genotypes. On the other hand, the population may only be metastable on the level of phenotype or fitness while, at the same time, diffusing over neutral networks of selectively neutral genotypes. Metastability occurs in this case because the population is separated from higher-fitness genotypes by an entropy barrier: the population must explore large portions of these neutral networks before it discovers a rare connection to fitter phenotypes. We derive analytical expressions for the barrier crossing times in both the fitness barrier and entropy barrier regime. In contrast with ‘landscape’ evolutionary models, we show that the waiting times to reach higher fitness depend strongly on the width of a fitness barrier and much less on its height. The analysis further shows that crossing entropy barriers is faster by orders of magnitude than fitness barrier crossing. Thus, when populations are trapped in a metastable phenotypic state, they are most likely to escape by crossing an entropy barrier, along a neutral path in genotype space. If no such escape route along a neutral path exists, a population is most likely to cross a fitness barrier where the barrier is narrowest, rather than where the barrier is shallowest.
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    Bulletin of mathematical biology 62 (2000), S. 925-941 
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    Notes: Abstract Measures of sexual dimorphism have been used extensively to predict the social organization and ecology of animal and human populations. There is, however, no universally accepted measure of phenotypic differences between the sexes. Most indices of sexual dimorphism fail to incorporate all of the information contained in a random data set. In an attempt to have a better alternative, an index is proposed to measure sexual dimorphism in populations that are distributed according to a probabilistic mixture model with two normal components. The index calculates the overlap between two functions that represent the contribution of each sex in the mixture. In order to assess such an index, sample means, variances and sizes of each sex are needed. As a consequence, the sample information used is greater than that used by other indices that take intrasexual variability into account. By evaluating some examples, our proposed index appears to be a more realistic measure of sexual dimorphism than other measures currently used.
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    Bulletin of mathematical biology 62 (2000), S. 1001-1001 
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    Bulletin of mathematical biology 62 (2000), S. 1191-1194 
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    Bulletin of mathematical biology 62 (2000), S. 1087-1108 
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    Notes: Abstract While retinal defocus is believed to be myopigenic in nature, the underlying mechanism has remained elusive. We recently constructed a theory of refractive error development to investigate its fundamental properties. Our Incremental Retinal-Defocus Theory is based on the principle that the change in retinal-defocus magnitude during an increment of genetically-programmed ocular growth provides the requisite sign for the appropriate alteration in subsequent environmentally-induced ocular growth. This theory was tested under five experimental conditions: lenses, diffusers, occlusion, crystalline lens removal, and prolonged nearwork. Predictions of the theory were consistent with previous animal and human experimental findings. In addition, simulations using a MATLAB/SIMULINK model supported our theory by demonstrating quantitatively the appropriate directional changes in ocular growth rate. Thus, our Incremental Retinal-Defocus Theory provides a simple and logical unifying concept underlying the mechanism for the development of refractive error.
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    Bulletin of mathematical biology 62 (2000), S. 1163-1189 
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    Notes: Abstract A dynamic energy budget (DEB) model describes the rates at which organisms assimilate and utilize energy from food for maintenance, growth, reproduction and development. We study the dynamic behavior of one particular DEB model, Kooijman’s κ rule model, whose key assumption is that somatic and reproductive tissues are competing for energy. We assume an environment in which the food density fluctuates either periodically or stochastically (pink noise). Both types of fluctuations stimulate growth; the magnitude of the (average) increase in size depends on both the strength and duration of the fluctuations. In a stochastic environment, the risk of mortality due to starvation increases with increasing fluctuation intensity. The mean lifespan is also a function of the model parameter κ characterizing the partitioning of energy between somatic and reproductive tissues. Organisms committing a large fraction of resources to reproduction endure periods of food shortage relatively well. The effects of food fluctuations on reproduction are complex. With stochastic food, reproduction in survivors increases with increasing fluctuation intensities, but lifetime reproduction decreases. Periodic fluctuations may enhance reproduction, depending on the value of κ. Thus, a variable food supply stimulates growth, increases mortality and may enhance reproduction, depending on life history.
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    Transformation groups 5 (2000), S. 35-59 
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    Topics: Mathematics
    Notes: Abstract In this paper we extend Drinfeld's current realization of quantum affine algebrasU q(ĝ) and of the Yangians in several directions: we construct current operators for non-simple roots of g, define a new braid group action in terms of the current operators, and describe the universalR-matrix for the corresponding “Drinfeld” comultiplication in the forms of an infinite product and of certain integrals over current operators.
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    Transformation groups 5 (2000), S. 325-350 
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    Notes: Abstract IfS=G Exp (iW) is a complex open Ol'shanskiî semigroup, whereW is an open elliptic cone, then we considerG-biinvariant domainsD=G Exp (iD g)S. First we show that the representation ofG×G on eachG-biinvariant irreducible reproducing kernel Hilbert space in Hol(D) is a highest weight representation whose kernel is the character of a highest weight representation ofG. In the second part of the paper we explain how to construct biinvariant Kähler structures on biinvariant Stein domains and show by a certain Legendre transform that the so obtained symplectic manifolds are isomorphic to domains in the cotangent bundleT * (G).
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    Transformation groups 5 (2000), S. 181-204 
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    Notes: Abstract We study Cartier divisors on normal varieties with the action of a reductive groupG. We give criteria for a divisor to be Cartier, globally generated and ample, and apply them to a study of the local structure and the intersection theory of aG-variety. In particular, we prove an integral formula for the degree of an ample divisor on a variety of complexity 1, and apply this formula to computing the degree of a closed 3-dimensional orbit in any SL2-module.
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    Circuits, systems and signal processing 19 (2000), S. 385-398 
    ISSN: 1531-5878
    Keywords: Recovery of distorted signals ; almost periodic signals ; bandlimited signals ; nonlinear systems ; nonlinear distortion
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    Notes: Abstract It is shown that thePQ theorem can be used to solve a certain signal recovery problem in which the transmitted and received signals are almost periodic functions. In this problem the signal to be recovered, which is bandlimited, is nonlinearly distorted and then bandlimited to the original band. Related signal recovery results are also given. These related results, unlike thePQ theorem, are applicable in settings in which the underlying signal space is not a Hilbert space or even a space that is complete.
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    Circuits, systems and signal processing 19 (2000), S. 411-421 
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    Keywords: Periodic filters ; lifted model ; minimal realization ; reachability ; observability
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    Notes: Abstract Practical applications in signals and systems often deal with lifted models of periodic digital filters, to which well-known methods and computing software for linear time-invariant (LTI) systems can be applied in the analysis and synthesis of periodic filters. When the design of a periodic filter is based on the lifted model, the resultant filter is usually in the lifted LTI form and needs to be further converted into the periodic form for implementational and computational purposes. In this paper, we present a computational procedure for obtaining a minimal realization of periodic digital filters from the fifted model.
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    Circuits, systems and signal processing 19 (2000), S. 451-466 
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    Keywords: Direction finding ; high-order statistics ; root-MUSIC ; robustness
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    Notes: Abstract Several typical situations unfavorable for second-order direction-finding methods are known to be easily overcome by means of higher-order techniques. In turn, in typical situations unfavorable for higher-order methods, second-order algorithms often perform quite well. Therefore, appropriately combining covariance- and cumulant-based techniques into one scheme, it is possible to obtain an algorithm with an improved robustness. In this paper, we propose two modifications of such combined methods, referred to asmixed-order root-MUSIC.
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    Notes: Abstract The spectrum of platinum is studied in the region from 250 to 1250 Å. The twenty-two 5d6s-5d6p spectral lines of the PtIX are assigned. All levels of the 5d6s configuration are found. The assignment of the previously known 5d6p levels is confirmed and their positions are refined. The 5d 2, 5d6s, and 5d6p configurations are theoretically described by the method of orthogonal operators. These calculations are compared with the data obtained by a conventional method using the Cowan program.
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    Optics and spectroscopy 88 (2000), S. 1-6 
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    Notes: Abstract The process of resonant multiphoton ionization of a hydrogen atom in the ground 1s state is studied by direct numerical integration of the nonstationary Schrödinger equation for a quantum system in an electromagnetic field. The dependence of photoionization probability on the radiation intensity is found to be nonmonotonic. It is established that the minima of ionization correspond to multiphoton resonances between the ground state and one of the excited (Rydberg) atomic states perturbed by the laser field. It is shown that ionization is suppressed due to rearrangement of Rydberg states in a strong electromagnetic field and is accompanied by efficient Raman Λ transitions, which connect a set of closely lying Rydberg states via the continuum.
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    Optics and spectroscopy 88 (2000), S. 96-101 
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    Notes: Abstract An analysis of a specific feature of the interaction of an ultrashort pulse with a slit is made. Analytical expressions for a monochromatic wave in the form of an ultrashort pulse diffracted by an infinite slit are obtained.
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    Notes: Abstract The observation of “spatial-modulation” resonances of saturated absorption in the interaction of iodine-127 vapors with a superposition of frequency-nondegenerate TEM01 and TEM10 transverse modes of a linear laser is reported. The modulation of the total radiation power of the probing wave, recorded at twice the beating frequency of transverse modes of the laser, is interpreted to be the result of the transformation of modulation of the spatial distribution of the field into its amplitude modulation under the action of nonlinearly absorbing iodine vapors. Resonances of saturated absorption of the weak line R(127)11-5 of iodine-127 (633 nm) in an extracavity cell are observed by the method proposed.
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    Optics and spectroscopy 88 (2000), S. 127-131 
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    Notes: Abstract The shape of the transmission band of an active interferometer, a resonator with amplification and absorption cells excited by an external signal, is studied. Upon tuning the external signal frequency, the narrow saturated absorption resonances can be observed in the transmission band of the interferometer. It is shown that, by varying the gain, the resonance absorption amplitude can be compensated for one order of smallness in pressure. The effect of amplitude and frequency noises of the external signal on the results obtained is studied.
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    Optics and spectroscopy 88 (2000), S. 38-41 
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    Notes: Abstract The electronic and spatial structures of the impurity hydroxyl ion in LiF, NaF, and KF crystals are studied using a molecular cluster model by the Hartree-Fock-Roothaan method in the semiempirical INDO (intermediate neglect of differential overlap) approximation. The equilibrium geometry of the impurity ion is determined. The hydroxyl ion is oriented in all the three matrices along the 〈110〉-axis, which is caused by the formation of the selected chemical bond between the hydrogen ion and the nearest lattice fluorine ion located on the same axis. The optical absorption energies are calculated.
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    Optics and spectroscopy 88 (2000), S. 50-54 
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    Notes: Abstract Processes of the electron-hole pair generation and excited-state relaxation at earlier stages of the latent image formation in the AgBr nanocrystals are studied theoretically. The experimental dependence of the photographic blackening D in the field of the intense laser light on the light pulse energy I is analyzed in the range of pulse durations τi from 10−13 to 10−8 s. The values of I needed to obtain a fixed blackening D at τi∼10−10 s exceeded those at τi∼10−8 s by three orders of magnitude. However, as τi further decreased to hundreds of fs, these values decreased by two orders of magnitude. It is shown that experimental nonmonotonic dependences can be explained by saturation of the one-photon interband generation of electron-hole pairs accompanied by the development of the two-photon generation. For shortest pulses and, correspondingly, greatest light intensities, the pair generation rate varies more strongly than upon usual two-photon absorption, which is caused by the resonance optical Stark effect.
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    Notes: Abstract A study is reported of the scattering of surface magnetic polaritons in the vicinity of second-order spin-reorientational phase transitions, which is caused by spatial fluctuations of the order parameter. A four-sublattice antiferromagnet α-Fe2O3 is used as an example to derive expressions for the vacuum-scattered radiation near exchange magnetic-vibration frequencies. The scattering of surface magnetic polaritons is shown to be resonantly enhanced in characteristic regions of their spectrum. Estimates made for α-Fe2O3 indicate a possibility of experimental observation of surface magnetic-polariton scattering from fluctuations of the refractive index near second-order spin-reorientational phase transitions.
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  • 71
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    Astronomy letters 26 (2000), S. 49-60 
    ISSN: 1562-6873
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Phase retrieval of a signal given its intensity is considered as a problem of statistically estimating a set of unknown parameters, the Zernike coefficients. Specifically, the phase problem is presented in the context of classical wave optics in the Fresnel approximation. Investigating the stability in this case suggests first learning if the Zernike coefficients can be restored in principle. If this is indeed the case, it then suggests determining the accuracy of their estimation. The stability of a solution to the phase problem depends, as it does for the other inverse problems, on the spectrum of the Fisher information matrix. An explicit representation of the Fisher matrix is given, and its spectrum is calculated for in-focus and out-of-focus images of a pointlike source. Simulations show that the solutions in the latter case are generally stable, so the coefficients of the Zernike series can be determined with an acceptable accuracy. The principal components, the mutually independent combinations of aberrations that are a generalization of the coefficients of the well-known Karhunen-Loeve decomposition, are calculated. As an example of this approach, the maximum-likelihood method is used to determine the aberrations of the optical system.
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    Optics and spectroscopy 88 (2000), S. 151-157 
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    Topics: Physics
    Notes: Abstract The afterglow of a discharge in helium with a small admixture of hydrogen is studied spectroscopically (p=40 Torr, [e]≤1011 cm−3). The time-resolved measurements of intensities of the first four lines of the Balmer series are performed. The concentrations of metastable helium atoms and molecules are evaluated from the relative intensity of the absorption lines. The ratios of excitation transfer rates from atoms He(2 3 S 1) k 1(n) and molecules of helium He2(a 2sσ 3Σ u + ) k 2(n) to atomic hydrogen H*(n) are measured to be k 1(n=3)/k 2(n=3)=0.04±0.02 and k 1(n=4)/k 2(n=4)=0.01±0.02. The ratios of excitation rate constants k 2(n) corresponding to different states H(n) are measured to be k 1(n=4)/k 2(n=3)=0.023±0.01; k 1(n=5)/k 2(n=3)≤0.013; and k 1(n=6)/k 2(n=3)≤0.007.
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    Optics and spectroscopy 88 (2000), S. 238-241 
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    Topics: Physics
    Notes: Abstract An analysis is made of the dynamics of the transverse structure of the field in the scheme of a layer of a medium with nonlinear amplitude-phase transmittance and a feedback mirror separated from it by a linear spacing. For the case of small field changes in a single passage, an approximate equation is derived, which is close in form to the equation used in the average-field approximation for nonlinear interferometers excited with external emission. For the nonlinearity of threshold type, an analytical form is presented for the field distribution corresponding to localized dissipative structures (dissitons).
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  • 74
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    Notes: Abstract The question of applicability of the approximation of an elastic isotropic medium to the description of elastooptic distortions in the second-harmonic generation in nonlinear crystals is analyzed. A method for a change to this approximation is proposed and the numerical calculation of elastooptic distortions in the secondharmonic generation is made for some crystals.
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    Optics and spectroscopy 88 (2000), S. 253-259 
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    Topics: Physics
    Notes: Abstract Results of laboratory measurements of the weak-localization effect for light scattered by surfaces with different characteristics are presented. The measurements were made in a range of phase angles of 0.2°–3.5°. The aim of the measurements was to study the influence of the choice of surface material (metal, dielectric), the size of particles of the scattering surface, their packing density, the reflectivity of a sample, and the wavelength of incident radiation on the effect. For the measurements, both nonpolarized and linearly polarized light was used. Powders of dielectric materials were found to enhance the weak-localization effect with increasing particle size, but the effect weakened starting with a certain size of the order of wavelength. The pressing of powders of dielectric transparent materials enhanced the opposition effect. This was most pronounced for samples with small-sized particles. The phase dependence of brightness became wider and more linear with decreasing reflectivity of the surface. A qualitative difference in the behavior of the phase dependence for the ratio of cross-and copolarized components was observed. For metals and metal-like materials, the ratio increased with decreasing phase angle. Dielectrics were found to have an opposite dependence.
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    Optics and spectroscopy 88 (2000), S. 297-301 
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    Topics: Physics
    Notes: Abstract Spectral and temporal characteristics of xenon flashlamps are studied theoretically for the case of high-power nonstationary discharges of microsecond lengths. It is shown that several factors affect them simultaneously under these conditions: parameters of electric discharge pulse, thermal inertia of a heated gas, and the region of transparency of a lamp envelope.
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    Optics and spectroscopy 88 (2000), S. 310-311 
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    Topics: Physics
    Notes: Abstract The spectral and luminescent properties of the Cu+ ion in an NaCl crystal are studied and the amplification is obtained at the 3d 10→3d 94P transition, which is under excitation by the fourth harmonic of an Nd:YAG laser (λ=266 nm). It is found that the short-lived absorption is related to an uncontrollable nickel impurity in the crystal.
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  • 78
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    Notes: Abstract The fine-structure parameters are calculated semiempirically in the intermediate coupling scheme for the np 5 n′p configurations of rare gas atoms and a number of ions. The calculation is based on the two-electron matrix of the energy operator, which takes into account, along with the electrostatic interaction, all magnetic interactions. Diagonalizing the energy matrix with the calculated values of the fine-structure parameters yields energy values exactly coinciding with the experimental data, as well as the coupling coefficients and the gyromagnetic ratios. The results obtained are compared with the available literature data.
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  • 79
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    Notes: Abstract The infrared and Raman spectra of the octachlorodibenzo-p-dioxine molecule are measured and all normal vibrational modes of the molecule are calculated. Each vibrational mode was assigned to the vibrations of certain functional groups of atoms in the molecule, taking into account the local symmetry characteristics of the vibration mode. A correlation of vibrational modes by their shape was established in a series of molecules: dibenzo-p-dioxine, 2,3,7,8-tetrachlorodibenzo-p-dioxine, and OCDX. The influence of substituents on vibrational frequencies was also examined.
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    Optics and spectroscopy 88 (2000), S. 380-386 
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    Notes: Abstract A theory of quasi-resonance for the model of atoms with an arbitrary number of levels is developed by the method of unitary transformation without recourse to Bloch’s equations. Corrections to the results known from the theory of adiabatic following, which refine these results and take into account dispersion of the nonlinear response of the resonant system, are obtained. The condition for quasi-resonance with a single atomic transition is shown to impose stringent limitations on the form of the nonlinear evolution equation for the electric field envelope of the pulse with dispersion of the nonlinear response taken into account, which prohibit the reduction of the equation indicated to familiar, fully integrable systems.
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    Optics and spectroscopy 88 (2000), S. 334-338 
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    Notes: Abstract The line phosphorescence spectrum of octachlorodibenzo-p-dioxine (OCDX) is obtained and interpreted. The symmetry of the lowest triplet state of this molecule is established. The vibrational frequencies found from the vibronic phosphorescence spectrum at 4.2 k are assigned to the vibrational modes of certain symmetry related to individual functional atomic groups of the molecule. The relation between contributions from the spin-orbit (SO) and vibronic-spin-orbit (VSO) interactions to the phosphorescence rate constant k ph of the OCDX molecule is found from the vibronic line intensities. It is found that the increase in the number of Cl atoms in OCDX compared to that in tetrachlorobenzo-p-dioxine results in the increase in the relative contribution of the VSO interaction to k ph.
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    Optics and spectroscopy 88 (2000), S. 327-333 
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    Notes: Abstract Using the decay of a single exponential function to a nonzero level as an example, the following numerical methods for determining lifetimes are considered: the least-squares method, the differentiation method, and two modifications of the method of moments. Domains of efficient application of one method or the other, depending on the form of the noise distribution, are determined on the basis of computer simulation in parameter space of the problem. For the Poisson noise distribution, a domain of parameters is found, where the error of determining the decay rate in the method of moments is smaller than in the least-squares method.
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    Astronomy letters 26 (2000), S. 691-698 
    ISSN: 1562-6873
    Keywords: pulsars ; neutron stars ; X-ray sources ; scattering
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    Topics: Physics
    Notes: Abstract We present the results of our comparative timing and spectral analysis of the high and low (off) states in the X-ray pulsar Her X-1 based on data from the ART-P telescope onboard the Granat observatory. A statistically significant (several mCrab) persistent flux with a simple power-law spectrum was detected during the low state. The spectral slope changed from observation to observation by almost a factor of 2. Pulsations were detected only during the high state of the source, when its flux was a factor of ∼25 larger than the low-state flux. The spectral shape of Her X-1 in its high state was complex, with the parameters depending on pulse phase.
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    Astronomy letters 26 (2000), S. 679-690 
    ISSN: 1562-6873
    Keywords: interstellar medium ; circumstellar shells
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    Topics: Physics
    Notes: Abstract The temperatures of prolate and oblate spheroidal dust grains in the envelopes of stars of various spectral types are calculated. Homogeneous particles with aspect ratios a/b≤10 composed of amorphous carbon, iron, dirty ice, various silicates, and other materials are considered. The temperatures of spherical and spheroidal particles were found to vary similarly with particle size, distance to the star, and stellar temperature. The temperature ratio T d(spheroid)/T d(sphere) depends most strongly on the grain chemical composition and shape. Spheroidal grains are generally colder than spherical particles of the same volume; only iron spheroids can be slightly hotter than iron spheres. At a/b≈2, the temperature differences do not exceed 10%. If a/b≥4, the temperatures can differ by 30–40%. For a fixed dust mass in the medium, the fluxes at wavelengths λ≥100 are higher if the grains are nonspherical, which gives overestimated dust masses from millimeter observations. The effect of grain shape should also be taken into account when modeling Galactic-dust emission properties, which are calculated when searching for fluctuations of the cosmic microwave background radiation in its Wien wing.
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    Astronomy letters 26 (2000), S. 699-724 
    ISSN: 1562-6873
    Keywords: neutron stars ; luminosity ; disk accretion ; X-ray bursters
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    Topics: Physics
    Notes: Abstract The energy release L s on the surface of a neutron star (NS) with a weak magnetic field and the energy release L d in the surrounding accretion disk depend on two independent parameters that determine its state (for example, mass M and cyclic rotation frequency f) and is proportional to the accretion rate. We derive simple approximation formulas illustrating the dependence of the efficiency of energy release in an extended disk and in a boundary layer near the NS surface on the frequency and sense of rotation for various NS equations of state. Such formulas are obtained for the quadrupole moment of a NS, for a gap between its surface and a marginally stable orbit, for the rotation frequency in an equatorial Keplerian orbit and in the marginally stable circular orbit, and for the rate of NS spinup via disk accretion. In the case of NS and disk counterrotation, the energy release during accretion can reach $$0.67\dot Mc^2 $$ . The sense of NS rotation is a factor that strongly affects the observed ratio of nuclear energy release during bursts to gravitational energy release between bursts in X-ray bursters. The possible existence of binary systems with NS and disk counterrotation in the Galaxy is discussed. Based on the static criterion for stability, we present a method of constructing the dependence of gravitational mass M on Kerr rotation parameter j and on total baryon mass (rest mass) m for a rigidly rotating neutron star. We show that all global NS characteristics can be expressed in terms of the function M(j, m) and its derivatives. We determine parameters of the equatorial circular orbit and the marginally stable orbit by using M(j, m) and an exact solution of the Einstein equations in a vacuum, which includes the following three parameters: gravitational mass M, angular momentum J, and quadrupole moment Ф2. Depending on Ф2, this solution can also be interpreted as a solution that describes the field of either two Kerr black holes or two Kerr disks.
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    Optics and spectroscopy 88 (2000), S. 619-622 
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    Notes: Abstract Results of computer simulation of the shading effect in systems of opaque spherical particles scattering light in accordance with the Lambert law are presented. Two types of systems are studied: a semi-infinite medium and statistically uniform clusters of a finite number of particles. The simulation makes it possible to obtain photometric characteristics of systems with an accuracy better than 1%. The phase dependence of the shading effect is shown to become steeper as the packing density of particles in clusters decreases and their number increases. For statistically uniform media, the following relation takes place: The lower the packing density, the more pronounced the shadow decrease in brightness with an increasing phase angle.
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  • 87
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    Notes: Abstract The generalizations of the original Fresnel theory and original theory of natural gyrotropy as manifestations of the first-order natural dispersion in uniaxial crystals are considered. The generalizations are made for magnetic crystals, taking into account the magnetic gyrotropy. The region of application of the corresponding generalized theories is found to be restricted by a particular case of the wave normal s directed parallel to the optic axis C of a uniaxial crystal.
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  • 88
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    Notes: Abstract Granular gallium films deposited in high vacuum on the rough surfaces of NaCl and KCl single crystals maintained at 400°C consist of two layers, in which two resonance bands are excited simultaneously. In isolated grains of the upper layer, a band at the normal electron oscillation frequency ω0 is excited. As a result of supercooling, the grains are in the liquid state. The gallium plasma frequency calculated from the measured ω0 and dielectric constants of NaCl and KCl coincides with that obtained by other authors by metallooptic methods. In gallium deposited on room-temperature substrates, only one resonance band is excited, with the interband absorption band superposed on its low-frequency edge.
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  • 89
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    Notes: Abstract The absolute values of probabilities of the I 1Π g − , v′, J′; J 1 Δ g − , v′, J′→C 1Π u ± , v″, J″ spontaneous transitions in the H2 molecule (for the vibrational and rotational quantum numbers v′=v″=0–3, J′=1–6, and J″=J′, J′ ±1) are calculated by using ab initio and semiempirical data on the dipole moments of the 3dπ 1Πg, 3dδ1Δg→2pπ1Πu electronic transitions. In both cases, the calculations are performed both in the adiabatic approximation and with an allowance for the nonadiabatic effect of electronic-rotational interaction. The coefficients of expansion of the wave functions of perturbed rovibronic states in the Born-Oppenheimer basis functions used in the calculations were obtained in the approximation of pure precession from experimental values of the terms. It was found that the values of transition probabilities based on the ab initio calculations systematically exceed the corresponding semiempirical data by a factor of 1.2–1.9 for the I 1Πg→C 1Π u ± transition and by a factor of 1.4–1.6 for the J 1Δ g − →C 1Π u ± transition. It was established that the difference between the ab initio and semiempirical values of electronic transition moments virtually has no effect on the dependence of the transition probabilities on the vibrational quantum numbers. The discrepancies between the results of adiabatic and nonadiabatic calculations are significant and reach two orders of magnitude, which is indicative of the important role of perturbations in the probabilities of the transitions considered.
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    Optics and spectroscopy 88 (2000), S. 705-712 
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    Topics: Physics
    Notes: Abstract Properties of collision transfer of vibrational energy in the vibrational quasi-continuum of mixed singlet-triplet levels of anthraquinone are studied by the method of time-resolved delayed fluorescence. The two-exponential fluorescence decay is analyzed in the kinetic approximation. It is shown that dependences of the intensities and decay rates of the fast and slow components on pressure can be used for estimating the rates of the establishment of the vibrational (V-V) and thermal (V-T) equilibrium. The efficiency β and the average energy 〈ΔE〉 transferred in collisions are estimated for these processes. It is found that the V-V process is characterized by high values of β, which, however, are lower in the quasi-continuum of mixed singlet-triplet states than the gas-kinetic values (β 〈 0.2). The transformation of the vibrational energy to the translational energy occurs with the low efficiency (10−2 〉 β 〉 10−5). The average energy 〈ΔE〉 transferred during a collision in the V-V process is comparable with the energy predicted by the statistical theory of ergodic transfer. The correlation between experimental and theoretical values improves when the time resolution of the experiment is sufficient for the separation of the V-V and V-T processes.
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    Optics and spectroscopy 88 (2000), S. 725-728 
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    Notes: Abstract The dynamics of switching waves in optically bistable systems on the basis of growing absorption is analyzed by quasi-optical description. A new scenario of kinks moving towards the optical beam under the action of a tubular optical beam is described. As opposed to an originally Gaussian beam focused on to the entrance face, a high intensity at the exit from the medium under the action of a collimated tubular beam is achieved due to the transformation of its profile. The structures formed are shown to be identical for both cases of action. The scenario of the development of moving switching waves found in this work is an alternative to that known in the literature earlier, which developed under the action of focused Gaussian beams and was analyzed with no regard for the variations of the phase of the optical beam.
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    Optics and spectroscopy 88 (2000), S. 852-856 
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    Notes: Abstract A new method for determining a fragment of the potential function of a bound state of a piatomic molecule from the phase of the matrix element of an electronic transition is proposed. As opposed to the method of WKB nodes [Opt. Spektrosk. 83, 906 (1997)], the new method (we call it the Franck-Condon factor phase method) is suitable for analyzing only those spectral regions free from interference structures. However, it is less demanding to the quality of experimental data and makes it possible to study situations where only a portion of the electronic band profile is accessible for analysis. Accuracy characteristics of the method are demonstrated using the analysis of the spectra of the transitions in Na2(23Σ g + (v=15, N=27; v=5, N=39)→3Σ u + ) as an example.
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    Optics and spectroscopy 88 (2000), S. 883-887 
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    Notes: Abstract The spectrum of the dielectric constant of three different samples of diamond in the 5–30-eV region is decomposed in thirteen elementary components. The main parameters of components are determined, and their nature is found on the basis of the band model.
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  • 94
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    Notes: Abstract The observation of the effect of mutual orientation of spin angular momenta of sodium atoms in the 32 S 1/2 state and helium atoms in the 23 S 1 state on the electrical conduction of a Na-He gas-discharge plasma is reported. In the experiments, a simultaneous optical orientation of atoms by the optical emission of sodium and helium lamps was carried out. The influence of the mutual orientation on the conduction was observed as a change in the high-frequency voltage across electrodes of a gas-discharge camera caused by the destruction of orientation of sodium atoms. The effect is explained by the dependence of Penning ionization in the interaction of sodium and helium atoms on the mutual orientation of spin angular momenta of partners.
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    Optics and spectroscopy 88 (2000), S. 696-704 
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    Notes: Abstract The formation of vibrational-rotational absorption spectra of small molecules in vibrationally non-equilibrium conditions, with the possibility of manifestation of partial population inversion of levels and negative absorption, is studied. Specific features of the partial inversion in linear and top molecules are analyzed. It is shown that water vapor is the best object among atmospheric gases for the realization of this effect. Formulas for the integrated line intensities and the absorption coefficient of two-and three-level nonequilibrium vibrational systems with a rotational structure are obtained. It is shown that the partial-inversion effect can be used to study weak vibrational-rotational transitions. Concrete calculations for the (000)-(010)-(020) bands of water molecules at different temperatures are made. The frequencies are determined for which negative absorption is the strongest.
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    Optics and spectroscopy 88 (2000), S. 921-925 
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    Notes: Abstract The diffraction of light by a corrugated surface of a layered structure is studied. It is shown that the excitation of waveguide modes in a layered structure substantially changes the diffraction efficiency of a corrugated structure. In the autocollimation regime, the diffraction efficiency of a grating with a moderate depth may reach 100%. An increased Q factor of leaky modes was found to be the condition of efficient interaction of light with a grating.
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    Optics and spectroscopy 88 (2000), S. 944-947 
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    Notes: Abstract The effect of reverse absorption saturation is studied in aromatic polyimides sensitized with fullerenes and a dye. The power density is estimated at which these systems can be most efficiently used to limit the laser radiation power. The data obtained are explained within the framework of the Förster model.
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    Optics and spectroscopy 89 (2000), S. 169-174 
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    Notes: Abstract Results of the experimental study of excitation of transitions of singly charged barium atoms in collisions of low-energy monokinetic electrons with barium atoms are presented. Regularities of the behavior of cross sections for excitation in spectral series of BaII are found. The results are compared with other authors’ results.
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    Optics and spectroscopy 89 (2000), S. 205-210 
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    Notes: Abstract A direct quantum-mechanical calculation of the relative intensities of lines in the resonance Raman scattering (RRS) spectra of uracil is performed by a method developed earlier by the authors on the basis of the adiabatic model in the Herzberg-Teller approximation [1]. It is shown that the main regularities in the intensity distribution of spectra can be explained only by taking into account the vibronic mixing of electronic states and the contribution to the scattering tensor components from the excited electronic states adjacent to the resonance state. The calculated results are in satisfactory agreement with the results of experimental studies of the RRS spectra of uracil excited by laser radiation at 266, 240, 218, and 200 nm.
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    Optics and spectroscopy 89 (2000), S. 211-215 
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    Notes: Abstract The burning kinetics of closely spaced equidistant holes in impurity absorption spectra of glasses and polymers is theoretically studied in an alternating electric field (alternating in the magnitude, sign, and direction). The height of barriers between wells of the burnt multiwell spectral hole depends on the shape of the distribution of impurity molecules over the Stark dipole moments. Centrally symmetric impurity molecules are considered whose Stark moment is determined exclusively by the interaction with matrix molecules. Model calculations performed for different hypothetical distribution functions of Stark moments yield substantially different kinetics. Therefore, the method described allows one to verify experimentally various hypotheses about the nature of matrix-induced Stark moments.
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