Class Of Differential Systems Research Articles

Convergence and periodicity of solutions for a class of difference systems

A class of difference systems of artificial neural network with two neurons is considered. Using iterative technique, the sufficient conditions for convergence and periodicity of solutions are obtained in several cases.

NULL SURFACES AND CONTACT GEOMETRY

We give a self-contained and geometric account of a recent approach to the Einstein field equations of general relativity, based on families of null foliations of space–time. We then use exterior differential systems to make explicit the correspondence between conformal Lorentzian geometry in dimensions three and four and the contact geometry of special classes of differential systems.

Convergence of a class of discrete-time semiflows with applications to difference systems

In this paper, by employing comparison technique and invariance properties of a positively limited set, we investigate the convergence of precompact orbits of a class of discrete-time semiflows. In particular, we consider the convergence of precompact orbits of discrete-time semiflows generated by some monotone mapping. We then apply these abstract results to a class of difference systems to obtain the large-time behavior of solutions. Our results improve and extend some existing ones.

A Physicist’s View of Stellar Dynamics: Dynamical Instability of Stellar Systems

AbstractI argue that the widely adopted framework of stellar dynamics survived since 1940s, is not fitting the current knowledge on non-linear systems. Borrowed from plasma physics when several fundamental features of perturbed non-linear systems were unknown, that framework ignores the difference in the role of perturbations in two different classes of systems, in plasma with Debye screening and gravitating systems with no screening. Now, when the revolutionary role of chaotic effects is revealed even in planetary dynamics i.e. for nearly integrable systems, one would expect that for stellar systems, i.e. non-integrable systems, their role have to be far more crucial. Indeed, ergodic theory tools already enabled to prove that spherical stellar systems are exponentially instable due to N-body interactions, while the two-body encounters, contrary to existing belief, are not the dominating mechanism of their relaxation. Chaotic effects distinguish morphological and other properties of galaxies. Using the Ricci curvature criterion, one can also show that a central massive object (nucleus) makes the N-body gravitating system more instable (chaotic), while systems with double nuclei are even more instable than those with a single one.

Behavior of solutions for a class of difference systems

In this paper, the discrete-time neural network model of two neurons with piecewise constant argument is considered. Some sufficient conditions under which every solution is either periodic or convergent are obtained.

Social Security Strategies and Redistributive Effects in European Social Transfer Systems

This paper evaluates the linkage between social security strategies and redistributive effects in EU social transfer systems. It is argued that the various European systems produce different patterns of redistribution that may be explained by the adoption of different mixes of social security strategies. In support of this argument, several idealtypical strategies are characterized and a classification of European social transfer systems is introduced. Subsequently, the redistributive effects of the systems are assessed and the relationship to their class assignment is investigated. We conclude that the redistributive effects differ markedly between systems of different classes, indicating that redistributive patterns are heavily influenced by the adopted strategy mix.

Social Security Strategies and Redistributive Effects in European Social Transfer Systems

This paper evaluates the linkage between social security strategies and redistributive effects in EU social transfer systems. It is argued that the various European systems produce different patterns of redistribution that may be explained by the adoption of different mixes of social security strategies. In support of this argument, several ideal‐typical strategies are characterized and a classification of European social transfer systems is introduced. Subsequently, the redistributive effects of the systems are assessed and the relationship to their class assignment is investigated. We conclude that the redistributive effects differ markedly between systems of different classes, indicating that redistributive patterns are heavily influenced by the adopted strategy mix.

Concepts for modeling impacts without friction

There are three basic equations in mechanics for treating collisions: the law of impact, kinematic compatibility, and energetic consistency. In this paper, the conditions are examined under which a natural extension of the dynamics at an impact is possible without taking additional impact laws, and which additional assumptions have to be made to solve the impact for different classes of systems. It will be shown that Newton’s law of impact for two colliding point masses can be derived from the concept of energy conservation and the principle of maximum dissipation, and has therefore not to be regarded as an independent equation. Moreover, it can be assigned to single-contact impacts in multibody systems as soon as the classical definition of perfect constraints is being extended to impulsive dynamics and unilateral contacts. It will further be shown that the principle of maximum dissipation leads to a unique post-impact velocity in the case of multi-contact collisions. In all other cases, however, the velocities remain undetermined, and laws of impact have to be postulated as additional and independent equations, whereas the classic definition of the restitution coefficient as a dissipation parameter can still be kept.

A hard X-ray survey of the Galactic-Center region with the IBIS telescope of the INTEGRAL observatory: A catalog of sources

From August 23 through September 24, 2003, the INTEGRAL Observatory conducted a deep survey of the Galactic-Center region with a record-breaking sensitivity at energies above 20 keV. We have analyzed the images of the Galactic-Center region obtained with the ISGRI detector of the IBIS telescope (15–200 keV) and give a catalog of detected sources. We detected a total of 60 sources with fluxes above 1.5 mCrab, 44 and 3 of which were previously identified as binary systems of different classes in our Galaxy and as extragalactic objects, respectively. We discovered one new source.

On the decomposition method for system of linear equations and system of linear Volterra integral equations

In this paper, we will study the application of the Adomian decomposition method for two different classes of systems: The system of linear equations and the system of linear Volterra integral equations. For a system of linear equations we show that the Adomian decomposition method is equivalent to the classical Jacobi iterative method. Then the equivalence of the Adomian decomposition method for a system of linear Volterra integral equations and the successive approximations method, so called Picard’s method, are discussed. Finally, numerical examples are prepared to illustrate these considerations.

Liapunov Functions and Stability in Control Theory. Lecture Notes in Control and Information Sciences 267

Liapunov Functions and Stability in Control Theory. Lecture Notes in Control and Information Sciences 267

Convergence and periodicity of solutions for a discrete-time network model of two neurons

Considered is a class of difference systems with McCulloch-Pitts nonlinearity, which includes the discrete version of an artificial neural network of two neurons with piecewise constant argument. Some interesting results are obtained for the convergence and periodicity of solutions of the systems. Most importantly, multiple periodic solutions exist. Our results have potential applications in neural networks.

NECESSARY CONDITIONS FOR LOCAL SOLVABILITY FOR A CLASS OF DIFFERENTIAL SYSTEMS

ABSTRACT We prove some necessary conditions for local solvability of a class of differential systems with multiple characteristics.

DYNAMICAL SYSTEMS OF DIFFERENT CLASSES AS MODELS OF THE KICKED NONLINEAR OSCILLATOR

Using the nonlinear dissipative kicked oscillator as an example, the correspondence between the descriptions provided by model dynamical systems of different classes is discussed. A detailed study of the approximate 1D map is undertaken: the period doubling is examined and the possibility of non-Feigenbaum period doubling is shown. Illustrations in the form of bifurcation diagrams and sets of iteration diagrams are given, the scaling properties are demonstrated, and the tricritical points (the terminal points of the Feigenbaum critical curves) in parameter space are found. The congruity with the properties of the corresponding 2D map, the Ikeda map, is studied. A description in terms of tricritical dynamics is found to be adequate only in particular areas of parameter space.

Influence of surfactant addition on the rheological properties of aqueous Welan matrices

In the present work the effects produced by the presence of two different surfactants (Abil B 8842 and Triton N 101) on the rheological properties of aqueous welan matrices are studied, both in steady and in oscillatory shear conditions. Welan is an acidic microbial polysaccharide having high thermal, pH, and salt stability. At sufficiently low concentrations it forms aqueous weak gel matrices which can be profitably used to regulate the rheological properties of disperse systems and improve their stability. Different systems are examined, having the same polysaccharide concentration (0.25 wt%) and different surfactant concentrations (up to 40 wt%, far beyond the range of practical interest for emulsion preparation). All the systems exhibit marked shear-thinning properties which can be described quite satisfactorily by the Cross equation. The concentration dependence of the zero-shear-rate viscosity as well as the mechanical spectra confirm that, in the concentration range considered, the aqueous welan systems are typically weakly structured fluids. The influence of both surfactants is examined in detail by comparing the behavior of the different classes of systems. Both surfactants reduce the polymer contribution at low shear, whereas an opposite action is exerted at high concentration and shear. These contrasting effects are ascribed to the different structural features of the polymer matrix under low stresses and high shear conditions, respectively.

Dynamical systems of different classes as models of the kicked non-linear oscillator

Correspondence between the models as dynamical systems of different classes is discussed by the example of nonlinear dissipative kicked oscillator. 1D map is investigated in details: Feigenbaum’s period doubling is studied and the possibility of non—Feigenbaum’s period doubling is shown, corresponding illustration in the form of bifurcation diagrams and set of iteration diagrams are given, tricritical points (terminal points of the Feigenbaum’s critical curves) are found in parameter space. The correlation with the properties of 2D map, the phenomenon of tricritically dynamics was demonstrated to take place only on definite areas of the parameter space.

On optimal truncation of divergent series solutions of nonlinear differential systems

We prove that for divergent series solutions of nonlinear (or linear) differential systems near a generic irregular singularity, the common prescription of summation to the least term is, if properly interpreted, meaningful and correct, and we extend this method to transseries solutions. In every direction in the complex plane at the singularity (Stokes directions {\em not} excepted) there exists a nonempty set of solutions whose difference from the ``optimally'' (i.e., near the least term) truncated asymptotic series is of the same (exponentially small) order of magnitude as the least term of the series. There is a family of generalized Borel summation formulas $\mathcal{B}$ which commute with the usual algebraic and analytic operations (addition, multiplication, differentiation, etc). We show that there is exactly one of them, $\mathcal{B}_0$, such that for any formal series solution $\tilde{f}$, $\mathcal{B}_0(\tilde{f})$ differs from the optimal truncation of $\tilde{f}$ by at most the order of the least term of $\tilde{f}$. We show in addition that the Berry (1989) smoothing phenomenon is universal within this class of differential systems. Whenever the terms ``beyond all orders'' {\em change} in crossing a Stokes line, these terms vary smoothly on the Berry scale $\arg(x)\sim |x|^{-1/2}$ and the transition is always given by the error function; under the same conditions we show that Dingle's rule of signs for Stokes transitions holds.

Random integral manifolds of systems of differential equations with unbounded operator in a Banach space

We establish existence conditions for a random integral manifold of a certain class of differential systems with unbounded sectorial operator and random right-hand side in a Banach space.

Misfit strain and misfit dislocations in lattice mismatched epitaxial layers and other systems

Abstract Heterostructures in the form of thin layers of one material grown on a substrate have been the subject of intense study for several years. In the case of semiconductor systems the aim is to grow epitaxial layers of, for example, Si1-xGex on Si, and devices based on such structures are already in use. Much is known, as is summarized in this review, about the stability of such systems against the insertion of dislocations, and about the critical thicknesses up to which strained layer structures are stable. The effects of dislocation nucleation and the dynamics of dislocation motion which lead to strain relaxation in metastable systems are also reviewed. The present state of theoretical understanding is compared with what is known experimentally. For metallic systems, which often exhibit magnetic properties, the underlying problems of lattice mismatch and strain relief are similar, but much of the interest has been concentrated on the commensurate-incommensurate transition in both structurally and magnetically modulated materials. The theory of this transition is reviewed, both for metallic systems and for epitaxial layers on graphite. In bringing together these different classes of systems within one review, it has been possible to demonstrate the parallels between them. It is hoped that, as a result, transfers of ideas between the fields will be promoted.

Analysis of capacity-rate data for lithium batteries using simplified models of the discharge process

Simplified models based on porous electrode theory are used to describe the discharge of rechargeable lithium batteries and derive analytic expressions for the specific capacity against discharge rate in terms of the relevant system parameters. The resulting theoretical expressions are useful for design and optimization purposes and can also be used as a tool for the identification of system limitations from experimental data. Three major cases are considered that are expected to hold for different classes of systems being developed in the lithium battery industry. The first example is a cell with solution phase diffusion limitations for the two extreme cases of a uniform and a completely nonuniform reaction rate distribution in the porous electrode. Next, a discharge dominated by solid phase diffusion limitations inside the insertion electrode particles is analysed. Last, we consider an ohmically-limited cell with no concentration gradients and having an insertion reaction whose open-circuit potential depends linearly on state of charge. The results are applied to a cell of the form Li|solid polymer electrolyte|LiyMn2O4 in order to illustrate their utility.