ALBERT

Notes: Abstract We consider the history of discovery and justify the existence in the Solar system of a new class of bodies—minicomets, i.e., bodies of cometary nature and composition but of low mass. Two classes of minicomets are distinguished: icy ones similar to the Tunguska meteorite, and snow ones, which break up at high altitudes.

Notes: Abstract We consider asymmetric periodic solutions of the double-averaged Hill problem by taking into account oblateness of the central planet. They are generated by steady-state solutions, which are stable in the linear approximation and correspond to satellite orbits orthogonal to the line of intersection of the planet’s equatorial plane with the orbital plane of a disturbing point. For two model systems [(Sun+Moon)-Earth-satellite] and [Sun-Uranus-satellite], these periodic solutions are numerically continued from a small vicinity of the equilibrium position. The results are illustrated by projecting the solutions onto the (pericenter argument-eccentricity) and (longitude-inclination) planes.

Notes: Abstract A model of gas-dynamical flow during gravitational collapse is analyzed mathematically by assuming its spherical symmetry and self-similarity. A shock wave diverging from the center emerges in this model. The physical requirements imposed on the post-shock flow at the center for the specified parameters at infinity unambiguously determine the shock front and the flow behind it.

Notes: Abstract A self-similar solution to Sedov’s problem of a strong explosion in a homogeneous medium is generalized to the case of relativistic-particle generation in a supernova remnant; the particles are accelerated by Fermi’s mechanism at the shock front and in the perturbed post-shock region. Self-similarity takes place if the thickness of the prefront is small compared to its radius and if the pressure ratio of the relativistic and nonrelativistic components at the shock front is kept constant. In the presence of relativistic particles, the time dependence of the shock-front radius remains the same as that in their absence, but the plasma parameters in the inner perturbed region change appreciably. The shell of the matter raked up by the explosion is denser and thinner than that in the nonrelativistic case, the relativistic-particle pressure in the central region remains finite, and the nonrelativistic-gas pressure at the explosion center approaches zero. The influence of relativistic particles on the transition to the radiative phase of expansion of the supernova remnant and on its dynamics is studied. It is shown that relativistic particles can decrease several-fold the remnant radius at which the transition to the radiative phase occurs.

Notes: Abstract We obtained optical spectra of four objects identified with variable radio sources. Three objects (0029+0554, 0400+0550, 2245+0500) were found to be quasars with redshifts of 1.314, 0.761, and 1.091. One object (2349+0534) has a continuum spectrum characteristic of BL Lac objects. We analyze spectra of the radio sources in the range 0.97–21.7 GHz for the epoch 1997 and in the range 3.9–11.1 GHz for the epoch 1990, as well as the pattern of variability of their flux densities on time scales of 1.5 and 7 years.

Notes: Abstract We study the effect of nova magnetodipole fields on the dynamics and structure of ejected shells by using a numerical model based on the kinetic-hydrodynamic description of plasma dynamics. Our calculations show that characteristic nonuniformities appear in the distribution of field and plasma perturbations during super-Alfvén shell expansion in the circumstellar medium.

Notes: Abstract Parathyroid hormone (PTH) paradoxically causes net bone loss (resorption) when administered in a continuous fashion, and net bone formation (deposition) when administered intermittently. Currently no pharmacological formulations are available to promote bone formation, as needed for the treatment of osteoporosis. The paradoxical behavior of PTH confuses endocrinologists, thus, a model bone resorption or deposition dependent on the timing of PTH administration would de-mystify this behavior and provide the basis for logical drug formulation. We developed a mathematical model that accounts for net bone loss with continuous PTH administration and net bone formation with intermittent PTH administration, based on the differential effects of PTH on the osteoblastic and osteoclastic populations of cells. Bone, being a major reservoir of body calcium, is under the hormonal control of PTH. The overall effect of PTH is to raise plasma levels of calcium, partly through bone resorption. Osteoclasts resorb bone and liberate calcium, but they lack receptors for PTH. The preosteoblastic precursors and preosteoblasts possess receptors for PTH, upon which the hormone induces differentiation from the precursor to preosteoblast and from the preosteoblast to the osteoblast. The osteoblasts generate IL-6; IL-6 stimulates preosteoclasts to differentiate into osteoclasts. We developed a mathematical model for the differentiation of osteoblastic and osteoclastic populations in bone, using a delay time of 1 hour for differentiation of preosteoblastic precursors into preosteoblasts and 2 hours for the differentiation of preosteoblasts into osteoblasts. The ratio of the number of osteoblasts to osteoclasts indicates the net effect of PTH on bone resorption and deposition; the timing of events producing the maximum ratio would induce net bone deposition. When PTH is pulsed with a frequency of every hour, the preosteoblastic population rises and decreases in nearly a symmetric pattern, with 3.9 peaks every 24 hours, and 4.0 peaks every 24 hours when PTH is administered every 6 hours. Thus, the preosteoblast and osteoblast frequency depends more on the nearly constant value of the PTH, rather than on the frequency of the PTH pulsations. Increasing the time delay gradually increases the mean value for the number of osteoblasts. The osteoblastic population oscillates for all intermittent administrations of PTH and even when the PTH infusion is constant. The maximum ratio of osteoblasts to osteoclasts occurs when PTH is administered in pulses of every 6 hours. The delay features in the model bear most of the responsibility for the occurrence of these oscillations, because without the delay and in the presence of constant PTH infusions, no oscillations occur. However, with a delay, under constant PTH infusions, the model generates oscillations. The osteoblast oscillations express limit cycle behavior. Phase plane analysis show simple and complex attractors. Subsequent to a disturbance in the number of osteoblasts, the osteoblasts quickly regain their oscillatory behavior and cycle back to the original attractor, typical of limit cycle behavior. Further, because the model was constructed with dissipative and nonlinear features, one would expect ensuing oscillations to show limit cycle behavior. The results from our model, increased bone deposition with intermittent PTH administration and increased bone resorption with constant PTH administration, conforms with experimental observations and with an accepted explanation for osteoporosis.

Notes: Abstract Density-independent and density-dependent, stochastic and deterministic, discrete-time, structured models are formulated, analysed and numerically simulated. A special case of the deterministic, density-independent, structured model is the well-known Leslie age-structured model. The stochastic, density-independent model is a multitype branching process. A review of linear, density-independent models is given first, then nonlinear, density-dependent models are discussed. In the linear, density-independent structured models, transitions between states are independent of time and state. Population extinction is determined by the dominant eigenvalue λ of the transition matrix. If λ ≤ 1, then extinction occurs with probability one in the stochastic and deterministic models. However, if λ 〉 1, then the deterministic model has exponential growth, but in the stochastic model there is a positive probability of extinction which depends on the fixed point of the system of probability generating functions. The linear, density-independent, stochastic model is generalized to a nonlinear, density-dependent one. The dependence on state is in terms of a weighted total population size. It is shown for small initial population sizes that the density-dependent, stochastic model can be approximated by the density-independent, stochastic model and thus, the extinction behavior exhibited by the linear model occurs in the nonlinear model. In the deterministic models there is a unique stable equilibrium. Given the population does not go extinct, it is shown that the stochastic model has a quasi-stationary distribution with mean close to the stable equilibrium, provided the population size is sufficiently large. For small values of the population size, complete extinction can be observed in the simulations. However, the persistence time increases rapidly with the population size.

Notes: Abstract Spatial pattern formation is one of the key issues in developmental biology. Some patterns arising in early development have a very small spatial scale and a natural explanation is that they arise by direct cell—cell signalling in epithelia. This necessitates the use of a spatially discrete model, in contrast to the continuum-based approach of the widely studied Turing and mechanochemical models. In this work, we consider the pattern-forming potential of a model for juxtacrine communication, in which signalling molecules anchored in the cell membrane bind to and activate receptors on the surface of immediately neighbouring cells. The key assumption is that ligand and receptor production are both up-regulated by binding. By linear analysis, we show that conditions for pattern formation are dependent on the feedback functions of the model. We investigate the form of the pattern: specifically, we look at how the range of unstable wavenumbers varies with the parameter regime and find an estimate for the wavenumber associated with the fastest growing mode. A previous juxtacrine model for Delta-Notch signalling studied by Collier et al. (1996, J. Theor. Biol. 183, 429–446) only gives rise to patterning with a length scale of one or two cells, consistent with the fine-grained patterns seen in a number of developmental processes. However, there is evidence of longer range patterns in early development of the fruit fly Drosophila. The analysis we carry out predicts that patterns longer than one or two cell lengths are possible with our positive feedback mechanism, and numerical simulations confirm this. Our work shows that juxtacrine signalling provides a novel and robust mechanism for the generation of spatial patterns.

Notes: Abstract Bioconvection occurs as the result of the collective behaviour of many microorganisms swimming in a fluid and is realized as patterns similar to those of thermal convection which occur when a layer of fluid is heated from below. We consider the phenomenon of pattern formation due to gyrotaxis, an orientation mechanism which results from the balance of gravitational and viscous torques acting on bottom-heavy micro-organisms. The continuum model of Pedley et al. (1988, J. Fluid. Mech. 195, 223–237) is used to describe the suspension. The system is governed by the Navier-Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. To examine the dependence of the horizontal pattern wavelengths on the parameters, we consider two-dimensional solutions in a wide chamber using rigid side walls. The wavelengths of the numerical computations are in good agreement with the experimental observations and we provide the first computational examples of the commonly seen ‘bottom-standing’ plumes.

Notes: Abstract This article demonstrates how perceptual constraints of predators and the possibility that predators encounter prey both sequentially (one prey type at a time) and simultaneously (two or more prey types at a time) may influence the predator attack decisions, diet composition and functional response of a behavioural predator-prey system. Individuals of a predator species are assumed to forage optimally on two prey types and to have exact knowledge of prey population numbers (or densities) only in a neighbourhood of their actual spatial location. The system characteristics are inspected by means of a discrete-time, discrete-space, individual-based model of the one-predator-two-prey interaction. Model predictions are compared with ones that have been obtained by assuming only sequential encounters of predators with prey and/or omniscient predators aware of prey population densities in the whole environment. It is shown that the zero-one prey choice rule, optimal for sequential encounters and omniscient predators, shifts to abruptly changing partial preferences for both prey types in the case of omniscient predators faced with both types of prey encounters. The latter, in turn, become gradually changing partial preferences when predator omniscience is considered only local.

Notes: Abstract Mathematical models are useful for providing a framework for integrating data and gaining insights into the static and dynamic behavior of complex biological systems such as networks of interacting genes. We review the dynamic behaviors expected from model gene networks incorporating common biochemical motifs, and we compare current methods for modeling genetic networks. A common modeling technique, based on simply modeling genes as ON—OFF switches, is readily implemented and allows rapid numerical simulations. However, this method may predict dynamic solutions that do not correspond to those seen when systems are modeled with a more detailed method using ordinary differential equations. Until now, the majority of gene network modeling studies have focused on determining the types of dynamics that can be generated by common biochemical motifs such as feedback loops or protein oligomerization. For example, these elements can generate multiple stable states for gene product concentrations, state-dependent responses to stimuli, circadian rhythms and other oscillations, and optimal stimulus frequencies for maximal transcription. In the future, as new experimental techniques increase the ease of characterization of genetic networks, qualitative modeling will need to be supplanted by quantitative models for specific systems.

Notes: Abstract This paper introduces a simple stochastic model for waterfowl movement. After outlining the properties of the model, we focus on parameter estimation. We compare three standard least squares estimation procedures with maximum likelihood (ML) estimates using Monte Carlo simulations. For our model, little is gained by incorporating information about the covariance structure of the process into least squares estimation. In fact, misspecifying the covariance produces worse estimates than ignoring heteroscedasticity and autocorrelation. We also develop a modified least squares procedure that performs as well as ML. We then apply the five estimators to field data and show that differences in the statistical properties of the estimators can greatly affect our interpretation of the data. We conclude by highlighting the effects of density on per capita movement rates.

Notes: Abstract Models of particular epidemiological systems can rapidly become complicated by biological detail which can obscure their essential features and behaviour. In general, we wish to retain only those components and processes that contribute to the dynamics of the system. In this paper, we apply asymptotic techniques to an SEI-type model with primary and secondary infection in order to reduce it to a much simpler form. This allows the identification of parameter groupings discriminating between regions of contrasting dynamics and leads to simple approximations for the model’s transient behaviour. These can be used to follow the evolution of the developing infection process. The techniques examined in this paper will be applicable to a large number of similar models.

Notes: Abstract Theoretical and empirical arguments are used to support the growth kinetics of disseminated tumors. Employing viable hypotheses, it is established that Gompertzian growth of disseminated cancer cells can be derived from a number of theoretical considerations. Empirical methods are used to validate and confirm the theoretical assertions with the use of available data.

Notes: Abstract This article presents and analyses several cases in which the use of the cut-off effect is useful. It starts from the fact that an anesthetic effect of homologous agents is always expressible as a function of their chain lengths and that the cut-off point is a point at which the function vanishes. We then investigate four categories of results: (i) whole body effects. (ii) Cases in which the anesthetics affect the Hodgkin-Huxley parameters of a nerve. (iii) Molecular mechanisms of anesthetic action. (iv) The physical chemistry of the anesthetic process. Our discussion shows that it is possible to incorporate these apparently remote results into one framework. It also shows how to compare results that were gathered by independent measuring methods. In some instances we suggest an interpretation, in others we suggest a further gathering of experimental data. One of the deductions indicates that a weakness exists in the lipid theories of anesthesia.

Notes: Abstract A frequently used measure for the extent of cooperativity in ligand binding by allosteric proteins is the Hill coefficient. Hill coefficients can be measured for steady-state kinetic data and also for transient kinetic data. Here, the relationship between the two types of Hill coefficients is analysed. It is shown that a value of 1 for the ratio of the two Hill coefficients is a test for a concerted ligand-induced transition between two conformations of the protein, in accordance with the Monod-Wyman-Changeux model. A value of 1 for this ratio has recently been observed for a series of chaperonin GroEL mutants suggesting that ATP-induced allosteric transitions in this protein are concerted.

Notes: Abstract We consider a spatially explicit metapopulation model with interaction among the two nearest neighbors to relate, with a simple mathematical expression, chaos in the local, uncoupled, populations, the degree of interaction among patches, size of the metapopulation, and the stability of the synchronized attractor. Since synchronism is strongly correlated with extinction, our results can provide useful information on factors leading to population extinction.

Notes: Abstract A group of individuals resolve their disputes by a knockout tournament. In each round of the tournament, the remaining contestants form pairs which compete, the winners progressing to the next round and the losers being eliminated. The payoff received depends upon how far the player has progressed and a cost is incurred only when it is defeated. We only consider strategies in which individuals are constrained to adopt a fixed play throughout the successive rounds. The case where individuals can vary their choice of behaviour from round to round will be treated elsewhere. The complexity of the system is investigated and illustrated both by special cases and numerical examples.

Notes: Abstract Can we express biophysical neuronal models as integrate-and-fire (IF) models with leakage coefficients which are no longer constant, as in the conventional leaky IF model, but functions of membrane potential and other biophysical variables? We illustrate the answer to this question using the FitzHugh-Nagumo (FHN) model as an example. A novel IF type model, the IF-FHN model, which approximates to the FHN model, is obtained. The leakage coefficient derived in the IF-FHN model has nonmonotonic relationship with membrane potential, revealing at least in part the intrinsic mechanisms underlying the FHN models. The IF-FHN model correspondingly exhibits more complex behaviour than the standard IF model. For example, in some parameter regions, the IF-FHN model has a coefficient of variation of the output interspike interval which is independent of the number of inhibitory inputs, being close to unity over the whole range, comparable to the FHN model as we noted previously (Brown et al., 1999).

Notes: Abstract The biased random walk undergone by chemotactic bacteria such as Escherichia coli will be influenced at the microscopic level by flow in the ambient medium. In this paper, we model swimming bacteria being advected and rotated by a simple shear flow. Under certain scaling assumptions, we obtain an advection—diffusion equation for cell density, when the chemotactic response is small, which shows a coupling between the rotation and chemotaxis. We also present an alternative method for calculating the chemotactic flux in an unbounded region which is valid for more general chemotactic responses.

Notes: Abstract The formation of the primitive streak in early avian development marks the onset of gastrulation, during which large scale cell movement leads to a trilaminar blastoderm comprising prospective endodermal, mesodermal and ectodermal tissue. During streak formation a specialized group of cells first moves anteriorly as a coherent column, beginning from the posterior end of the prospective anterior-posterior axis (a process called progression), and then reverses course and returns to the most posterior point on the axis (a process called regression). To date little is known concerning the mechanisms controlling either progression or regression. Here we develop a model in which chemotaxis directs the cell movement and which is capable of reproducing the principal features connected with progression and regression of the primitive streak. We show that this model exhibits a number of experimentally-observed features of normal and abnormal streak development, and we propose a number of experimental tests which may serve to illuminate the mechanisms. This paper represents the first attempt to model the global features of primitive streak formation, and provides an initial stage in the development of a more biologically-realistic discrete cell model that will allow for variation of properties between cells and control over movement of individual cells.

Notes: Abstract The effect of recombination on genotypes can be represented in the form of P-structures, i.e., a map from the set of pairs of genotypes to the power set of genotypes. The interpretation is that the P-structure maps the pair of parental genotypes to the set of recombinant genotypes which result from the recombination of the parental genotypes. A recombination fitness landscape is then a function from the genotypes in a P-structure to the real numbers. In previous papers we have shown that the eigenfunctions of (a matrix associated with) the P-structure provide a basis for the Fourier decomposition of arbitrary recombination landscapes. Here we generalize this framework to include the effect of genotype frequencies, assuming linkage equilibrium. We find that the autocorrelation of the eigenfunctions of the population-weighted P-structure is independent of the population composition. As a consequence we can directly compare the performance of mutation and recombination operators by comparing the autocorrelations on the finite set of elementary landscapes. This comparison suggests that point mutation is a superior search strategy on landscapes with a low order and a moderate order of interaction p 〈 n/3 (n is the number of loci). For more complex landscapes 1-point recombination is superior to both mutation and uniform recombination, but only if the distance among the interacting loci (defining length) is minimal. Furthermore we find that the autocorrelation on any landscape is increasing as the distribution of genotypes becomes more extreme, i.e., if the population occupies a location close to the boundary of the frequency simplex. Landscapes are smoother the more biased the distribution of genotype frequencies is. We suggest that this result explains the paradox that there is little epistatic interaction for quantitative traits detected in natural populations if one uses variance decomposition methods while there is evidence for strong interactions in molecular mapping studies for quantitative trait loci.

Notes: Abstract We investigate bursting behaviour generated in an electrophysiological model of pituitary corticotrophs. The active and silent phases of this mode of bursting are generated by moving between two stable oscillatory solutions. The bursting is indirectly driven by slow modulation of the endoplasmic reticulum Ca2+ concentration. The model exhibits different modes of bursting, and we investigate mode transitions and similar modes of bursting in other Hodgkin-Huxley models. Bifurcation analysis and the use of null-surfaces facilitate a geometric interpretation of the model bursting modes and action potential generation, respectively.

Notes: Abstract Mean fitness is non-decreasing in the symmetry sector of the frequency trajectory followed in competitive replication at sublinear propagation rates (parabolic time course). This sector contains the pairwise symmetric distribution of species frequencies and its neighboring states, and represents at least half the possible states of an evolving sublinear system. States in the non-symmetry sector produce a negative rate of change in mean fitness. The heterogeneous steady state attained in a finite sublinear system is destabilized by formation of a variant with above-threshold fitness. Evolution in the post-steady-state interval elevates the fitness threshold for coexistence. Contrary to the proposition that ‘parabolic growth invariably results in the survival of all competing species’, only species with sufficient fitness to avoid subthreshold fitness survive.

Notes: Abstract Restriction-modification (RM) systems are cognate gene complexes that code for an endonuclease and a methylase. They are often thought to have developed in bacteria as protection against invading genetic material, e.g., phage DNA. The high diversity of RM systems, as observed in nature, is often ascribed to the coevolution of RM systems (which ‘invent’ novel types) and phages. However, the extent to which phages are insensitive to RM systems casts doubts on the effectiveness of RM systems as protection against infection and thereby on the reason for the diversity of RM systems. We present an eco-evolutionary model in order to study the evolution of the diversity of RM systems. The model predicts that in general diversity of RM systems is high. More importantly, the diversity of the RM systems is expressed either at the individual level or at the population level. In the first case all individuals carry RM systems of all sequence specificities, whereas in the second case they carry only one RM system or no RM systems at all. Nevertheless, in the second case the same number of sequence specificities are present in the population.

Notes: Abstract Autoinhibition of neurotransmitter release occurs via binding of transmitter to appropriate receptors. Experiments have provided evidence suggesting that the control of neurotransmitter release in fast systems is mediated by these inhibitory autoreceptors. Earlier, the authors formulated and analysed a mathematical model for a theory of release control in which these autoreceptors played a key role. The key experimental findings on which the release-control theory is based are: (i) the inhibitory autoreceptor has high affinity for transmitter under rest potential and shifts to low affinity upon depolarization; (ii) the bound (with transmitter) autoreceptor associates with exocytotic machinery Ex and thereby blocks it, preventing release of neurotransmitter. Release commences when depolarization shifts the autoreceptor to a low-affinity state and thereby frees Ex from its association with the autoreceptors. Here we extend the model that describes control of release so that it also accounts for release autoinhibition. We propose that inhibition is achieved because addition of transmitter, above its rest level, causes transition of the complex of autoreceptor and Ex to a state of stronger association. Relief of Ex from this state requires higher depolarization than from the weakly associated complex. In contrast to the weakly associated complex that only requires binding of transmitter to the autoreceptor to be formed, the transition to the strongly associated complex is induced by a second messenger, which is produced as a result of the receptor binding to transmitter. The theory explains the following experimental results (among others): for inhibition via transmitter or its agonists, the magnitude of inhibition decreases with depolarization; a plot of inhibition as a function of the concentration of muscarine (an acetylcholine agonist) yields an S-shaped curve that shifts to the right for higher depolarizations; the time course of release does not change when transmitter is added; the time course of release also does not change when transmitter antagonists are added, although quantal content increases; however, addition of acetylcholine esterase (an enzyme that hydrolyses acetylcholine) prolongs release.

Notes: Abstract Simple predator-prey type models have brought much insight into the dynamics of both nonspecific and antigen-specific immune responses. However, until now most attention has been focused on examining how the dynamics of interactions between the parasite and the immune system depends on the nature of the function describing the rate of activation or proliferation of immune cells in response to the parasite. In this paper we focus on the term describing the killing of the parasite by cell-mediated immune responses. This term has previously been assumed to be a simple mass-action term dependent solely on the product of the densities of the parasite and the immune cells and does not take into account a handling time (which we define as the time of interaction between an immune cell and its target, during which the immune cell cannot interact with and/or destroy additional targets). We show how the handling time (i) can be incorporated into simple models of nonspecific and specific immunity and (ii) how it affects the dynamics of both nonspecific and antigen-specific immune responses, and in particular the ability of the immune response to control the infection.

Notes: Abstract The contact process is used as a simple spatial model in many disciplines, yet because of the buildup of spatial correlations, its dynamics remain difficult to capture analytically. We introduce an empirically based, approximate method of characterizing the spatial correlations with only a single adjustable parameter. This approximation allows us to recast the contact process in terms of a stochastic birth-death process, converting a spatiotemporal problem into a simpler temporal one. We obtain considerably more accurate predictions of equilibrium population than those given by pair approximations, as well as good predictions of population variance and first passage time distributions to a given (low) threshold. A similar approach is applicable to any model with a combination of global and nearest-neighbor interactions.

Notes: Abstract The paper looks at a formulation of physiologically structured population models within which individual development is affected by a special form of demographic stochasticity, accounting for random success or failure at exploiting available resources. This frees models from the requirement that individual development is uniquely determined by physiology and environmental conditions. An expression is derived which describes the motion of cohorts through individual state space, and the results are applied to an idealized model of Daphnia feeding on algae.

Notes: Abstract A class of autocatalytic reaction networks based on template-dependent ligation and higher-order catalysis is analysed. Apart from an irreversible ligation reaction we consider only reversible aggregation steps that provide a realistic description of molecular recognition. The overall dynamics can be understood by means of replicator equations with highly non-linear interaction functions. The dynamics depends crucially on the total concentration c 0 of replicating material. For small c 0, in the hyperbolic growth regime, we recover the familiar dynamics of second-order replicator equations with its wealth of complex dynamics ranging from multi-stability to periodic and strange attractors as well as to heteroclinic orbits. For large c 0, in the parabolic growth regime, product inhibition becomes dominating and we observe a single globally stable equilibrium tantamount to permanent coexistence. In an intermediate parameter range we sometimes observe a behavior that is reminiscent of ’survival of the fittest’. Independently replicating species (Schlögl’s model) and the hypercycle are discussed in detail.

Notes: Abstract All organisms are composed of multiple chemical elements such as carbon, nitrogen and phosphorus. While energy flow and element cycling are two fundamental and unifying principles in ecosystem theory, population models usually ignore the latter. Such models implicitly assume chemical homogeneity of all trophic levels by concentrating on a single constituent, generally an equivalent of energy. In this paper, we examine ramifications of an explicit assumption that both producer and grazer are composed of two essential elements: carbon and phosphorous. Using stoichiometric principles, we construct a two-dimensional Lotka-Volterra type model that incorporates chemical heterogeneity of the first two trophic levels of a food chain. The analysis shows that indirect competition between two populations for phosphorus can shift predator—prey interactions from a (+, −) type to an unusual (−, −) class. This leads to complex dynamics with multiple positive equilibria, where bistability and deterministic extinction of the grazer are possible. We derive simple graphical tests for the local stability of all equilibria and show that system dynamics are confined to a bounded region. Numerical simulations supported by qualitative analysis reveal that Rosenzweig’s paradox of enrichment holds only in the part of the phase plane where the grazer is energy limited; a new phenomenon, the paradox of energy enrichment, arises in the other part, where the grazer is phosphorus limited. A bifurcation diagram shows that energy enrichment of producer—grazer systems differs radically from nutrient enrichment. Hence, expressing producer—grazer interactions in stoichiometrically realistic terms reveals qualitatively new dynamical behavior.

Notes: Abstract For a smooth oriented surface Σ, denote byM(Σ) the set of all ways to represent Σ as a result of gluing together standard spheres with holes (“the Lego game”). In this paper we give a full set of simple moves and relations which turnM(Σ) into a connected and simply-connected 2-complex. Results of this kind were first obtained by Moore and Seiberg, but their paper contains serious gaps. Our proof is based on a different approach and is much more rigorous.

Notes: Abstract The kernel of a certain derivation of the polynomial ringk [6] is shown to be nonfinitely generated overk (a field of charactersitic zero), thus giving a new counterexample to Hilbert's Fourteenth Problem. As a corollary, we obtain a new proof for Roberts' well-known counterexample in dimension seven.

Notes: Abstract The theorem of Hochster and Roberts says that, for every moduleV of a linearly reductive groupG over a fieldK, the invariant ringK[V] G is Cohen-Macaulay. We prove the following converse: ifG is a reductive group andK[V] G is Cohen-Macaulay for every moduleV, thenG is linearly reductive.

Notes: Abstract We express the vanishing conditions satisfied by the correlation functions of Drinfeld currents of quantum affine algebras, imposed by the quantum Serre relations. We discuss the relation of these vanishing conditions with a shuffle algebra description of the algebra of Drinfeld currents.

Notes: Abstract The first part of this paper describes the construction of pseudo-Riemannian homogeneous spaces with special curvature properties such as Einstein spaces, using corresponding known compact Riemannian ones. This construction is based on the notion of a certain duality between compact and non-compact homogeneous spaces. In the second part we apply this method to obtain pseudo-Riemannian homogeneous manifolds with real Killing spinors. We will prove that under a certain additional condition a dual pseudo-Riemannian space (G′/H′, g′) of a compact Riemannian homogeneous space (G/H, g) with homogeneousSpin-structure admits a homogeneousSpin +-structure and theG_invariant Killing spinors on (G/H, g) correspond toG′-invariant Killing spinors on (G′/H′, g′). We can ensure that in most cases the hypothesis onG-invariance is satisfied.

Notes: Abstract For each compact Lie algebra g and each real representationV of g we construct a two-step nilpotent Lie groupN(g, V), endowed with a natural left-invariant riemannian metric. The main goal of this paper is to show that this construction produces many new Gelfand pairs associated with nilpotent Lie groups. Indeed, we will give a full classification of the manifoldsN(g, V) which are commutative spaces, using a characterization in terms of multiplicity-free actions.

Notes: Abstract A geometric construction of the modified quantum algebra ofgln was given in [BLM]. It was then observed independentely by Lusztig and Ginzburg-Vasserot (see [L1], [GV]) that this construction admits an affine analogue in terms of periodic flags of lattices. However the compatibility of the canonical base of the modified algebra and of the geometric base given by intersection cohomology sheaves on the affine flag variety was never proved. The aim of the paper is to prove this compatibility. As a consequence we prove a recent conjecture of Lusztig (see [L1]). Of course, our proof would work also in the finite type case.

Notes: Abstract We show that the algebras of semi-invariants of a finite connected quiverQ are complete intersections if and only ifQ is of Dynkin or Euclidean type. Moreover, we give a uniform description of the algebras of semi-invariants of Euclidean quivers.

Notes: Abstract In this paper we introduce LS algebras. We study their general properties and apply these results to Schubert varieties. Our main achievement is that any Schubert variety admits a flat deformation to a union of normal toric varieties. A new proof of Cohen-Macaulayness (and thus normality) for Schubert varieties is also obtained.

Notes: Abstract We introduce and study the notion of essential dimension for linear algebraic groups defined over an algebraically closed fields of characteristic zero. The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type. For example, if our groupG isS n , these objects are field extensions; ifG=O n , they are quadratic forms; ifG=PGL n , they are division algebras (all of degreen); ifG=G 2, they are octonion algebras; ifG=F 4, they are exceptional Jordan algebras. We develop a general theory, then compute or estimate the essential dimension for a number of specific groups, including all of the above-mentioned examples. In the last section we give an exposition of results, communicated to us by J.-P. Serre, relating essential dimension to Galois cohomology.

Notes: Abstract We present synthetic aperture radar (SAR) target feature extraction and imaging techniques with angle divesity. We first establish a flexible data model that describes each target scatterer as a two-dimensional (2D) complex sequence with arbitrary amplitude and constant phase in range and cross-range. A new algorithm, referred to as the QUasiparametric ALgorithm for target feature Extraction (QUALE), is then presented for SAR target feature extraction via data fusion through angle diversity based on the flexible data model. QUALE first estimates the model parameters, which include, for each scatterer, a 2D arbitrary real-valued amplitude sequence, a constant phase, and scatterer locations in range and cross-reange. QUALE then averages the estimated 2D real-valued amplitude sequence over range by making the assumption that the scatterer radar cross section is approximately consant. QUALE next models the so-obtained 1D sequence with a simple sinc function by assuming that the scatterer is approximately a dihedral (a trihedral is approximated as a very short dihedral) and estimates the relevant sinc function parameters by minimizing a nonlinear least-squares fitting function. Finally, the approximate 2D SAR image is reconstructed by using the estimated features. Numerical examples are given to demonstrate the perfomance of the proposed algorithm.

Notes: Abstract To solve the problem of detecting and displaying the changes in the spectra of nonstationary signals, there are two possible approaches. Either one uses the same estimators as for the stationary signals, but one approach uses shorter-length data blocks during which the signal is assumed to be stationary, and the other one uses the same length data and applies a time-varying spectrum estimator that accounts for the nonstationarity. A time-varying spectrum estimator called a time-varying correlogram (TVC) is a well-known estimator of the time-frequency spectrum of a nonstationary signal. In this paper, a high performance VLSI architecture for computing TVC is proposed.

Notes: Abstract We consider a possible evaluation of frame-based nonstationary pattern recognition methods by using the upper bound trajectories of the Bayes error based on the Bhattacharrya distance. The experimental part of the work is based on natural speech processing, using isolated spoken Serbian vowels and digits as examples of nonstationary signals. The results obtained justify the use of the upper bound trajectories of the Bayes error expressed by the Bhattacharyya distance as a possible evaluation tool for the class of frame-based nonstationary pattern recognition systems.

Notes: Abstract Often the information available for a state equation description in the form $$\dot x = Ax + Bu$$ ,y=Cx+Du is via a transfer function matrixH(s) obtained by measurements or complicated computations for frequenciess=jω. ThusH(s) is nonrational or rational of high order. Its state equation approximation means obtainingA, B, C, D in the rational transfer matrixC(sI-A) −1 B+D≈H(s). This approximation problem is difficult because it is nonlinear and often ill conditioned. This paper describes a methodology for fitting the columnsh(s) ofH(s) by two linear procedures. First θ(s)h(s) is fitted with a set of prescribed poles, where θ(s) is an unknown rational function with the same poles as θ(s)h(s). Then the poles forh(s) are calculated as the zeros of θ(s). With the poles known, the unknown residues and constant terms are calculated forh(s). If necessary, the procedure is repeated with the new poles taken as prescribed poles. The procedure is accurate and robust, and uses only standard numerical linear algebra computations. Illustrative examples for the application of vector fitting are given for a power transformer, a transmission line, and a network of transmission lines.

Notes: Abstract A comparative study of the beats of circular polarization generated by anisotropic atomic collisions is carried out on the basis of theoretical calculations for the states J=1, 3/2, and 2 of neon atoms and ions excited by monochromatic laser radiation in xenon atmosphere. Contributions made by ordinary alignment and higher polarization moments (octupole orientation and dodecapole alignment) in the collisional generation of orientation and the signal of beatings of circular polarization are compared.

Notes: Abstract Relations for the calculation of the limiting resolvable spatial frequency of a speckle image of a line mira used as a test object in the determination of the optical power of optical systems are presented. The influence of the speckle structure on the extraction of information about the shape of the object observed from the image recorded is taken into account by using the equivalent modulation transfer characteristic of the optical system than determines the transfer of spatial frequencies of the envelope of the speckle image and the threshold characteristic of speckle noise conditioned by fluctuations of the amplitudes of individual speckles. Conditions, in which the prevailing influence on the quality of the image recorded is exerted by the speckle structure, atmospheric phase distortions, and discretization noise, are determined.

Notes: Abstract UBV observations of the X-ray binary system A0535+26/V725 Tau at the Crimean Station of the Sternberg Astronomical Institute in 1980–1998 are presented. Based on our and published data, we analyze the photometric history of the star from 1898. Over a period of 100 years, the star apparently showed all three activity phases (B, Be, Be-shell) of Be stars. We conclude that the X-ray activity of the object is attributable to the 1970–1997 outburst of the Be star due to envelope ejection. The star's colors during the minimum light of 1998 and its 1953–1956 colors (before the outburst) correspond to the spectral type B0–B1 at the color excesses E B-V = 0.74 and E U-B = 0.48, in agreement with the current spectral type O9.7. The minimum light of 1998 and the color excesses are used to determine the colors of the additional radiation, analyze their evolution during the 1973–1997 outburst, and refine the distance to the object (3 kpc). The colors of the additional radiation at maximum light of the star (1973–1980) match the colors of a hydrogen plasma with T e = 1.5 × 104 K which is optically thick in the Balmer continuum. The brightness decline corresponds to a decrease in the optical depth of the plasma; at $$V \simeq 9_.^m 1$$ , it becomes optically thin in the Balmer continuum with T e = 104 K and N e = 1010 − 1012 cm−3. This conclusion is consistent with the model of a circumstellar envelope but is inconsistent with the existence of an accretion disk around the neutron star. All the additional radiation responsible for the optical variability is produced by a single source. The intensity of the Hα emission line at maximum light (1975–1980) is triple its intensity in 1987–1997, when quasi-periodic light fluctuations with P ≈ 1400d were observed [1]. At this time, the line intensity correlated with brightness. The Hα line was in absorption at the minimum of 1998, and, at present, the star's active phase appears to have ended.

Notes: Abstract We present the results of our study of the H2O maser emission from the source W75N, which is associated with a star-forming region, between November 1994 and March 1999. The observations were carried out with the RT-22 radio telescope of the Pushchino Radio Astronomy Observatory (Lebedev Physical Institute). The maser emission in 1994–1999 can be represented as a superposition of flares of separate components with a duration from two to six months, which occurred mainly in the radial-velocity range 8–17.5 km s−1. We detected a regular drift of the velocity centroid from 13 to 9 km s−1 and an abrupt change in its velocity from 9 to 5 km s−1, which took place at the initial stage of maser activity. Based on the variability of the total H2O flux in all years of our observations of W75N (from December 1979 through March 1999), we conclude that the long-period variability of the water-vapor maser emission has a period of ∼11.5 years. We give arguments that this variability is mainly associated with the most compact group of maser spots, whose positions coincide with the position of the continuum source VLA 2.

Notes: Abstract The Zeeman splitting of the fine-structure levels of the 1s2p and 1s4p configurations of neutral helium in a magnetic field is calculated. The strengths of fields of intersection of magnetic sublevels are determined, and the field regions are found in which a constant energy gap between some sublevels is observed. The results are compared with the experimental data available in the literature.

Notes: Abstract The structure of the energy level diagram for 30 ions of the thallium isoelectronic sequence is studied on the basis of the relativistic Dirac-Fock self-consistent field method with the configuration interaction taken into account. It is discovered that the ground-state configuration and the lowest term change along the thallium isoelectronic sequence: At the beginning of the sequence, the ground-state configuration is 6s 26p, and it becomes 6s 26f beginning from the Cf17+ ion. On the basis of theoretical calculations, the ground-state ionization potentials are determined for each ion. The influence of interaction of the 6s6p 2 configuration with the 6s 26d configuration on the 2 D 3/2, 5/2 levels of the latter was also studied, and values of the fine-structure splitting of the 6s 26p 2 P 0 and 6s 26d 2 D levels were determined for the Tl-like ions considered.

Notes: Abstract We study the radio galaxy RC J0105+0501 by using observations with RATAN-600, VLA, and 6-m Special Astrophysical Observatory telescope. The radio source has a structure resembling the FRII type and the spectral index α=1.23; it is identified with a faint galaxy of $$22\mathop .\limits^m 8$$ in R c . The optical object is $$1\mathop .\limits^m 5$$ brighter in V than it is in B and has an extended structure, which we interpret as intense Lyα line emission with redshift z≈3.5 and a continuum depression in the adjacent short-wavelength region. Based on BVR c I c photometry, we also estimated the age of the stellar population of the radio galaxy.

Notes: Abstract Updated proper motions for 328 probable members of the Praesepe are used to determine the distance to this open cluster by Hertzsprung's geometric method. The cluster distance was found to be r=171±15 pc, which corresponds to the distance modulus $$V_0 - M_V = 6\mathop .\limits^m 16 \pm 0.19$$ . The distance scale for open clusters is discussed.

Notes: Abstract The excited states and absorption and fluorescence spectra of styrene and β-d 2-styrene are calculated by the parametric method. It is shown that parametric models of these molecules in the excited states adequately describe their real structure and predict the fine structure of their electronic spectra at the quantitative level, which is sufficient for its detailed interpretation and the refinement of parameters of the molecular model by solving inverse problems. In a second approximation (using only one additional parameter), the method provides a more exact calculation of angular deformations of the molecule upon excitation and, in particular, describes characteristic differences in the intensities of low-frequency spectral components in a series of diphenylpolyene-stilbene-styrene. The number of parameters for molecular fragments is small (2 and 3 in the first and second approximations, respectively), and they are the same for a series of related compounds. Compared to direct ab initio calculations, the parametric method yields substantially better results already in the first approximation, and it is more efficient for modeling molecules in excited states and description of their vibronic spectra.

Notes: Abstract We investigate the effect of microlensing on parameters of the images of distant sources seen near the critical curves of complex gravitational lenses, which are represented as a sum of compact structures—microlenses (stars, star-like or planet-like bodies) and diffusely distributed matter (dust and gas clouds etc.). The observation of merging, cross-shaped, annular, or arc-shaped source images is an indication that the images are close to the critical curves of gravitational lenses. Our analysis and numerical solution have allowed us to determine the structures of the critical curves and caustics formed by macro-and microlenses, as well as to estimate the characteristic perturbations introduced by microlenses at their various positions relative to the critical curve of a regular gravitational lens. We show that, the closer are the microlenses to the critical curve, the larger is the discrepancy between our results and those obtained previously with standard (linearized) allowance for the effect of a regular gravitational lens.

Notes: Abstract We show that hydrostatically equilibrium models for the thin photospheres of helium stars based on new opacities κR (OPAL and OP) can be constructed only for masses M〈5M ⊙. The parameter Г=κL/4πGMc, defined as the ratio of light pressure to gravity, exceeds a critical value of 1.0 for larger masses, which must result in mass outflow under light pressure. This mass limit matches the observed lower limit for the masses of Wolf-Rayet stars (M WR〉5M ⊙)), which is an additional argument that the Wolf-Rayet stellar cores are actually helium stars. By solving the equation of radiative transfer in extended atmospheres, we construct a semiempirical model for a WN5 star (M WN5=10M ⊙)) with a helium core and an expanding envelope, whose physical and geometric parameters are known mainly from light-curve solution for the eclipsing binary V444 Cyg (WN5+06): outflow rate $$\dot M \approx 1.0 \times 10^{ - 5} M_ \odot yr^{ - 1} $$ , terminal velocity V ∞≈2000 km s−1, and expanding-envelope optical depth τenv≈25. The temperature at the outer boundary of the photosphere of a helium star surrounded by such an envelope is approximately 130 kK higher than that in the absence of an envelope, being T ph≈240 kK. Because of the high temperatures, the absorption coefficients at the corresponding photospheric levels are smaller than those in models with no envelope; therefore, the photosphere turns out to be in hydrostatic equilibrium and stable against light pressure (Гmax≈0.9). As a way out of this conflicting situation (an expanding envelope together with a hydrostatically equilibrium photosphere), we propose a model of discrete mass outflow, which is also supported by the observed cloudy structure of the envelopes in this type of stars. To quantitatively estimate parameters of the nonuniform outflow model requires detailed gas-dynamical calculations.

Notes: Abstract We have computed a combined spectroscopic-interferometric orbit for the nearby binary Gliese 600 discovered by us. The orbital period is 2.78 years, and the semimajor axis is 100 mas (0.1″). Its M0 V components are almost identical and have a mass of 0.5M ⊙. The mass ratio is uncertain because of the low radialvelocity semiamplitude (7 km s−1) associated with the low orbital inclination (37°). The orbital parallax of the binary (52±11 mas) matches its dynamical and photometric parallaxes but differs significantly from the Hipparcos parallax (44.3±1.6) mas; the latter was probably distorted by the orbital motion that was not taken into account.

Notes: Abstract We apply isotropy tests to our new uniform catalog of cosmic gamma-ray bursts (GRBs) (Stern and Tikhomirova 1999). The catalog contains trigger and nontrigger bursts found in 1024-ms BATSE records over seven years. Based on this catalog, we confirm isotropy of the GRB spatial distribution for a sample that surpasses previous samples in size (2934 bursts) and in achieved threshold (fluxes down to 0.1 phot. cm−2 s−1, which is a factor of ∼2 lower than the BATSE trigger threshold). We also confirm that there is no excess of bursts toward the galaxy M 31.

Notes: Abstract A study was made of spectral and luminescent properties of a squarilic dye on the basis of 1,3,3-trimethyl-3H-indoline in comparison with the cationic polymethine dye representing a derivative of the same heterocycle. The squarilic dye was introduced into polymer films of poly-N-epoxypropylcarbazole, which is capable of bearing photoproduced charges, and polystyrene, which lacks this ability. Luminescence spectra of films with different dye concentrations at temperatures of 4.2 and 300 K were studied. Spectral and luminescent properties of squarain in both types of polymers were found to be determined by the dye tendency to aggregation. For poly-N-epoxypropylcarbazole, this tendency is less pronounced than for polystyrene, which is associated with the enhancement of specific solvation of a bipolar squarain molecule by polar groups of poly-N-epoxypropylcarbazole. The structure with an angle between chromophore directions of 180° is shown to be the most likely spatial structure of associates. The advantage of this structure is that it is stabilized at both ends of bipolar molecules by electrostatic attractive forces between opposite charges.

Notes: Abstract A strong orientation effect is theoretically predicted in a suggested modified experiment on anomalous elastic scattering of linearly polarized X-rays by free oriented in space HF and HCl molecules near the ionization threshold of the 1s molecular orbital. The analytic expression for the form factor of a linear molecule is determined for the case of one-center nonrelativistic representation of the wave functions of molecular orbitals.

Notes: Abstract Propagation of a pulse of self-induced transparency in a resonance medium is discussed for the case when it is necessary to take into account the direct electric dipole-dipole interaction between atoms. An equation for the envelope of a wave packet—the sine-Gordon equation—is obtained for the case of durations short compared to ω 0 −1 (ω0 is the transition frequency). The dependence of the velocity and the amplitude of the soliton on the magnitude of the dipole-dipole interaction of atoms is examined in the adiabatic approximation.

Notes: Abstract A microscopic analysis is made of the gyrotropy of molecular crystals with vacancies. For impurity-free systems with a primitive lattice, the concentration dependence of rotatability in two frequency regions is studied.

Notes: Abstract Scattering of laser radiation by structured biotissues—histological mounts of bony and muscular tissues and skin, are studied.

Notes: Abstract A problem of light scattering by multilayer confocal ellipsoids is solved in the Rayleigh approximation. The electric field of a light wave is assumed constant and a set of Laplace equations with the corresponding boundary conditions is considered. The final expression for the polarizability of a particle is represented in the matrix form (2×2 matrices) in terms of parameters of a nucleus and subsequent layers. Numerical calculations of the scattering and absorption efficiencies of small multilayer spheres obtained using the exact (the generalization of the Mie theory) and approximate solutions well agree with each other.

Notes: Abstract The possibility of manufacturing interference filters with the transmission coefficient no less than 90% in fixed UV, visible or near IR spectral regions and completely opaque at longer wavelengths is shown. The operation of the filter is based on the method of residual rays. Angular dependences of the filter transmission bandshape on the parameters of multilayer coating, such as the thickness, refractive indices, and the number of the layers, are analyzed.

Notes: Abstract The perturbation of the Ba atom by radiation from a color center laser in the range between 8400 and 8700 cm−1 is experimentally studied. The study was performed by the method of resonance ionization spectroscopy by simultaneously irradiating a beam of Ba atoms by a color center laser and a dye laser at 17735 cm−1. The dynamic polarizabilities of the 5d6p 1 F 0 3 and 6p 2 1 D 2 levels are measured.

Notes: Abstract The three-dimensional emission tomography of a plasma partially absorbing intrinsic emission is studied. The distribution of local absorption coefficients is assumed to be known. To determine the distribution of local emission coefficients under the given conditions, the use of algebraic algorithms inverting the projection matrix constructed taking into account absorption is proposed. NDAT and NDFBP algorithms are developed, which are based on the expansion of the product of the operator of energy transport in an absorbing medium and the operator of the solution of the problem of emission tomography of a transparent plasma in a Neumann series. A numerical simulation is made, which shows that the emission field can be reconstructed with a reasonable accuracy for an optical thickness as high as 6–8.

Notes: Abstract The fluorescence spectrum of a two-level atom excited by the field, whose state represents a superposition of the coherent states, is investigated. It is shown that to each mode of the quantum-statistical distribution of the incident field, a spectral mode of the scattered radiation corresponds, and one can determine the number of statistical modes of the incident field from the number of spectral modes of the scattered field. This result is a consequence of the fact that in the quasi-classical limit, statistical modes of the superimposed state interact with the atom independently of one another.

Notes: Abstract A simplified version of the coupled dipole method (CDM) is proposed which allows one to reduce the initial system of 3N×3N equations to a simpler system of N×N equations. The method neglects depolarization effects in the interaction of dipoles but, unlike the mean field approximation, it takes into account local fluctuations of the scalar amplitudes of the excited dipole moments. Simple analytic solutions are obtained for integrated cross sections averaged over aggregate orientations. It is shown by the example of ballistic fractal aggregates that this method provides the accuracy close to that of a standard CDM, being substantially less time-consuming. In the case of biospheres, the approximate method is compared with the exact results of the multipole expansion.

Notes: Abstract Light scattering by a two-layer “soft” sphere is studied. The analysis is made by the method of expansion in the spatial spectrum in Kotel’nikov-Shannon choice functions. In the case where changes of relative refractive indices of the first (Δn 1 and the second ((Δn 2) layers have the same sign, the scattering indicatrices are found to be close to the indicatrices for a homogeneous sphere with averaged effective parameters, and the integrated cross sections should be close as well. However, in the case where Δn 1 and Δn 2 have opposite signs, changes in the indicatrix are stronger. The major lobe becomes weaker and, in certain cases, even vanishes, whereas the side lobes and backward scattering increase in intensity. The physical interpretation of the results that can be used for the analysis of experimental data is given.

Notes: Abstract Results of a detailed study of statistical characteristics of photon trajectories in a strongly scattering medium near an object surface are presented. The properties found in the study may be useful for developing an algorithm of reconstruction in real time for the optical tomography of strongly scattering (biological) object.

Notes: Abstract Observations of the X-ray pulsar Vela X-1 with the ART-P telescope onboard the Granat Observatory are presented. Variability on a time scale of several thousand seconds was detected; intensity variations are shown to be accompanied by changes in the source’s spectrum. The hardness was also found to be highly variable on a scale of one pulsation period. The source’s spectrum exhibits an absorption feature at energy ∼7 keV, which is apparently attributable to cyclotron scattering/absorption in the neutron-star magnetic field. Weak persistent emission was detected during an X-ray eclipse, which probably resulted from the scattering of pulsar emission in the stellar wind from an optical star.

Notes: Abstract The total energy E of a star as a function of its angular momentum J and mass M in the Newtonian theory, E=E(J, M) [in general relativity, the gravitational mass of a star as a function of its angular momentum J and rest mass m, M=M(J, m)], is used to determine the remaining parameters (angular velocity, chemical potential, etc.) in the case of rigid rotation. Expressions are derived for the energy release during accretion onto a cool (with constant entropy), rapidly rotating neutron star (NS) in the Newtonian theory and in general relativity. A separate analysis is performed for the cases where the NS equatorial radius is larger and smaller than the radius of the marginally stable orbit in the disk plane. An approximate formula is proposed for the NS equatorial radius for an arbitrary equation of state, which matches the exact equation of state at J=0.

Notes: Abstract The Spin-X wide-field X-ray monitor of the Spectrum-X-Gamma astrophysical observatory, which is based on the principle of a coded-aperture telescope, is designed to detect and localize cosmic gammaray-burst (GRB) sources; to survey large areas of the sky in search of new transients; and to carry out long-term observations of bright Galactic sources, including X-ray bursters. The monitor consists of two noncoaxial identical modules, Spin-X1 and Spin-X2, which together cover 6.8% of the sky. The high-apogee, four-day orbit of the Spectrum-XG satellite allows the instrument to be in observing mode more than 50% of the time. Having simulated the rate of GRB detection by Spin-X, we show that extrapolating BATSE 50–300-keV average data on the number of GRBs, their duration, and their mean energy spectrum to the X-ray energy band leads to disagreement with the observed detection rate of GRBs in the X-ray band. The number of GRBs that can be detected and localized with an accuracy r≤3′ (3σ) (the error-circle radius) by Spin-X is estimated to be ten bursts per year. We present data on the Spin-X sensitivity achievable during long-term observations of persistent and transient sources and on its sensitivity to X-ray bursts from Galactic sources in the 2–30-keV energy band.

Notes: Abstract The possibility for determining the degree of polarization of synchrotron radiation by measuring linear dichroism in stepwise ionization of an autoionization state of an atom with a known total momentum is considered.

Notes: Abstract Light absorption and scattering by weakly absorbing layers of close-packed fine-grained silver halide particles was studied. Absorption characteristics of an elementary volume and a photolayer were found to have a nonlinear and nonmonotonic dependence on the concentration. Qualitative specific features of this dependence in the range of medium values of volume concentrations from 0.4 to 0.8 were expressed by an empirical formula. The average cosine of the depth brightness diagram and the probability of photon survival Λ in a concentrated photolayer were calculated. The analysis of changes in Λ in a close-packed medium in a more general case, irrespective of the size and the degree of absorption of particles, was carried out. A conclusion was made concerning the character of changes in the scattering indicatrix of a photolayer caused by an increase of its density.

Notes: Abstract VUV spectra of a barrier discharge in a krypton-xenon mixture at the pressure P=400 hPa were experimentally studied. The xenon addition was varied in a range of 0.01–1%. The supply voltage frequency was 20 kHz. The form of spectra and their evolution at different xenon impurity concentrations were analyzed by solving the system of nonlinear differential equations simulating the main processes taking place in the active phase of a discharge and in the afterglow. The analysis supports the results obtained earlier and qualitatively describes the experimental spectra.

Notes: Abstract The spectrum of Bi VI in a wavelength region of 177–431 Å was studied. The transitions from the levels of the interacting configurations 5d 86s6p+5d 97p+5d 95f+5d 96f to the levels of the 5d 10 and 5d 96s configurations were analyzed. 174 spectral lines were identified, and 79 new levels of high-lying odd configurations of Bi VI were found.

Notes: Abstract Direct observability of polarization moments of a higher order—octupole orientation of atomic angular momenta (κ=3) and their hexadecapole alignment (κ=4)—from polarization of quadrupole radiation is discussed. The case when atoms are excited through dipole absorption of light producing orientation or alignment of angular momenta with κ=1 or 2 and higher polarization moments are induced by collisions with a beam of particles is considered. It is shown that differences in the laws of transformation of polarization moments of various ranks κ in rotations of coordinate axes allow us to select the pure contribution of the higher polarization moment under study from the signal of polarization of quadrupole emission by excluding the contribution of orientation or alignment with κ=1 or 2. Optimum systems of coordinate axes for the observation of octupole orientation from circular polarization of light and for the observation of hexadecapole alignment from linear polarization of light, in which the pure contribution of the higher polarization moment under study to polarization of quadrupole emission reaches its maximum, are calculated.

Notes: Abstract The probabilities of spontaneous transitions in v″ progressions of the G 1Σ g + →B 1Σ u + bands of the H2 molecule (the 3D→2B electronic transition in notations of G.H. Dieke) are, for the first time, experimentally studied. The line strength ratios were measured for 78 G 1Σ g + , v′, J′→B 1Σ u + , v″, J″ electronic-vibrational-rotational spectral lines having a common upper level but belonging to different bands of v″ progressions (the vibrational branching coefficients). For this purpose, the intensities of lines of the P and R branches, emitted by a low-pressure plasma and corresponding to different values of the rotational (J′=0–11) and vibrational (v′=0–3 and v″=0–7) quantum numbers, were used. It was found that the changes in the vibrational branching coefficients with variation of v′ and v″ are significant (up to a factor of 20). For most bands studied, the dependences of the vibrational branching coefficients on the rotational quantum number J′ of an upper level are rather weak and do not exceed 30%. It was established that the difference between the experimental values of ratios of the vibronic transition probabilities (summed over J″) and the results of calculation in the adiabatic approximation strongly depends on v′, reaching a factor of 25 for a transition from the v′=2 level. At the same time, the discrepancy between the experimental data and the results of nonadiabatic ab initio calculations lies between 1.0 and 2.3.

Notes: Abstract The experimental data on the structure and vibrational spectrum of the MnF3 molecule are analyzed. The vibrational modes are calculated and the vibrational spectrum of MnF3 is interpreted. A model of the electronic structure of trifluorides of transition metals is suggested which explains the observation of the strong Jahn-Teller effect in MnF3, and the influence of this effect on the molecular spectrum is discussed.

Notes: Abstract The study of luminescence of high-purity multicomponent silicate glasses excited by radiation of a N2 laser (λ=337 nm, P≈12kW) showed darkening of a sample and a monotone decrease in luminescence intensity and the transmitted radiation intensity from pulse to pulse. Additional illumination with radiation of an Ar+ laser (λ=514.5 nm) caused an increase in luminescence intensity. An increase in absorption and a decrease in luminescence intensity were found to be caused by two-photon absorption and electron-hole pair production.

Notes: Abstract Spectral luminescent properties of eight organic dyes are studied upon excitation by focused radiation from the XeCl* laser at the pump power up to 200 MW/cm2. The transmission of pump radiation by dyes is investigated as a function of the pump power. It is shown that variations in the energy, spectral, and temporal parameters of radiation of organic dyes upon high-power excitation are explained by the development of superluminescence (amplified spontaneous emission).

Notes: Abstract It is shown that the radiative losses due to parametric emission of X-rays are two times larger in the case of three-wave diffraction than in the case of two-wave diffraction. The frequency ranges are determined in which the emission is prohibited within the entire cone with the exception of two symmetrically located points. This leads to a reduction of the radiation spectral density at the Bragg frequency and makes the spectral and angular distributions asymmetric in a way that does not contradict the existing experimental data.

Notes: Abstract Maxwell’s equations in the Majorana form are extended to the case of a orthogonal curvilinear system of coordinates. The optical Magnus effect is considered as an example. The results obtained are extended to massless spin particles with half-integer spins.

Notes: Abstract A phase binary ring diffraction optical element (DOE) with a radius of 3.5 mm and microrelief height of 1.06 μm was calculated and fabricated. The element focuses a Gaussian beam of a He-Ne laser with radius of 1.5 mm to a 1.7 mm long axial segment, which ranges from 51.9 to 53.6 mm, with a focal spot diameter of about 30 μm.

Notes: Abstract Multiphoton resonant ionization in the case of a doubly degenerate intermediate bound state is studied. In the Keldysh-Feisal-Reiss approach, expressions for the energy and angular photoelectron distributions and the quasi-classical formula for the total rate of resonant ionization are obtained. It is shown that the ionization rate may be both higher and lower than the ionization rate in the usual case depending on the relationship between parameters. A situation with a strongly suppressed probability of resonant ionization is possible. In the near-threshold region, the angular dependence of the probability of photoelectron escape is shown to be weaker in comparison with the case of ionization via a nondegenerate level.

Notes: Abstract Ceramics of the Ca2CuO3 cuprate with a purely chain copper-oxygen structure is synthesized. The Raman spectra of ceramic samples are recorded upon excitation in a broad spectral range from the blue-green to near-IR region. The intensities of a number of lines and bands of different scattering orders are estimated using the internal reference method. The results are compared with physical and chemical models of the process.

Notes: Abstract Conditions for the existence of completely localized three-dimensional dissipative laser solitons—“laser bullets” in a medium with nonlinear amplification and absorption and frequency dispersion are studied. Solitons with different profiles are considered and the regions of their stable existence are found. The stability of spherical solitons is studied as a function of frequency mismatch of amplification and absorption lines by the method of direct numerical simulation.