On Physically Unacceptable Numerical Solutions Yielding Strong Chaotic Signals

Physically unacceptable chaotic numerical solutions of nonlinear circuits and systems are discussed in this paper. First, as an introduction, a simple example of a wrong choice of a numerical solver to deal with a second-order linear ordinary differential equation is presented. Then, the main result follows with the analysis of an ill-designed numerical approach to solve and analyze a particular nonlinear memristive circuit. The obtained trajectory of the numerical solution is unphysical (not acceptable), as it violates the presence of an invariant plane in the continuous systems. Such a poor outcome is then turned around, as we look at the unphysical numerical solution as a source of strong chaotic sequences. The 0–1 test for chaos and bifurcation diagrams are applied to prove that the unacceptable (from the continuous system point of view) numerical solutions are, in fact, useful chaotic sequences with possible applications in cryptography and the secure transmission of data.     

一类非线性边值问题正解的存在性

本文运用锥上的不动点理论,讨论了一类与一阶导函数有关的二阶奇性混合边值问题的正解存在性．     

Monte carlo studies of phase transitions in polymer blends and block copolymer melts

Summary The unmixing transition of both symmetrical polymer blends AB (i.e. chain lengthsN _A=N _B=N) and asymmetrical ones (N _B/N _A=2,3) is studied by large-scale Monte Carlo simulations of the bond fluctuation model. Combination of semi-grand-canonical simulation techniques, ?histogram reweighting? and finitesize scaling allows an accurate location of the coexistence curve in the critical region. The variation of the critical temperature with chain length (N) is studied and compared to theoretical predictions. For the symmetrical case, use of chain lengths up toN=512 allows a rough estimation of crossover scaling functions for the crossover from Ising to mean-field exponents. The order-disorder transitions in melts of both symmetric (compositionf=N _A/(N _A+N _B)=1/2) and asymmetric (f=3/4) block copolymers is studied for very short chains (16≤N≤60). The interplay between structure and chain configuration is emphasized. Qualitative evidence for ?dumbell formation? of chains and vacancy enrichment in A-B-interfaces and near hard walls is presented. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

An extended continuous Newton method

This paper describes a numerical realization of an extended continuous Newton method defined by Diener. It traces a connected set of locally one-dimensional trajectories which contains all critical points of a smooth functionf: ⁿ . The results show that the method is effectively applicable.The authors would like to thank L. C. W. Dixon for pointing out some errors in the original version of this paper and for several suggestions of improvements.     

Indefinite preference structures and decision analysis

It always takes time for people to digest information and make judgments. The decision maker's preference is not always clear and stable when decision analysis and decision making are performed. In this paper, we introduce a generalized preference structure to cope with indefinite preferences. We describe its general properties, its implication on value function representation, its solution concepts, and methods for obtaining the solutions.This research has been partially supported by NSF Grant No. IST-84-18863. The authors are grateful to Dr. D. J. White for his helpful comments on a previous draft.     

Positive solutions of singular boundary value problem of negative exponent Emden—Fowler equation

This paper investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar to standard Emden-Fowler equation. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as well as C¹[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem.     

On Fučik Spectra and Periodic Solutions

In this paper, we continue extending the theory of boundary-value problems to ordinary differential equations and inclusions with discontinuous right-hand side. To this end, we construct a new version of the method of shifts along trajectories. We compare the results obtained by the new approach and those obtained by the method of Fuik spectra.     

Convergence Dynamics of Delayed Hopfield-Type Neural Networks Under Almost Periodic Stimuli

Convergence dynamics of Hopfield-type neural networks subjected to almost periodic external stimuli are investigated. In this article, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures. By employing Halanay inequalities, we obtain delay independent sufficient conditions for the networks to converge exponentially toward encoded patterns associated with the external stimuli. The networks are guaranteed to have exponentially hetero-associative stable encoding of the external stimuli.     

Probability Inequalities and Limit Theorems for Generalized L-Statistics

We obtain exponential upper bounds for tails of distributions of generalized L-statistics based on a sample from an exponential distribution. We prove the asymptotic normality of generalized L-statistics based on a sample from the uniform distribution on [0,1] and of L-statistics with decomposed kernels (without any restrictions on the sample distribution type).     

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators. This revised version was published online in June 2006 with corrections to the Cover Date.