Bifurcation of limit cycles from a compound loop with five saddles

We concern the number of limit cycles of a polynomial system with degree nine. We prove that under different conditions, the system can have 12 and 20 limit cycles bifurcating from a compound loop with five saddles. Our method relies upon the Melnikov function method and the method of stability-changing of a double homoclinic loop proposed by the authors[J. Yang, Y. Xiong and M. Han, {\em Nonlinear Anal-Theor.}, 2014, 95, 756--773].     

Liénard型系统解的有界性与极限环的存在性

本文讨论比Lienard系统更广的一类非线性系统 x=h(y)-F(x) y=-g(x)解的有界性与极限环的存在性,得到了解正向有界的充要条件和存在极限环的充分条件,推广和改进了文[1-5]的工作.     

Optimal order of accuracy in Vasin's method for differentiation of noisy functions

We improve the order of accuracy estimate for Vasin's method for approximate differentiation. The improved estimate is shown to be the best possible.Part of this work was performed while the author was a visiting member of the Forschungsinstitut für Mathematik, ETH, Zürich, Switzerland. The support of FIM is gratefully acknowledged.     

自校整空间位移测量仪精度分析

对自校整空间位移测量仪的原理作了简要介绍，推导和计算了导向测量单元和总体的测量精度，对提高总体测量精度提出了几点建议，为该仪器的精度设计提供了理论依据。     

The influence of some fuzzy implication operators on the accuracy of a fuzzy model-Part I

The problem of the influence of fuzzy implication operators and connective also on the accuracy of a fuzzy model of a d.c. series motor is considered. Several typical fuzzy implication operators are used to construct the fuzzy model of a d.c. series motor. A root-mean-square error is adopted as the criterion of the model's adequacy to the real system. The best typical fuzzy relations are selected.     

Residual Smoothing Techniques: Do They Improve the Limiting Accuracy of Iterative Solvers?

Many iterative methods for solving linear systems, in particular the biconjugate gradient (BiCG) method and its squared version CGS (or BiCGS), produce often residuals whose norms decrease far from monotonously, but fluctuate rather strongly. Large intermediate residuals are known to reduce the ultimately attainable accuracy of the method, unless special measures are taken to counteract this effect. One measure that has been suggested is residual smoothing: by application of simple recurrences, the iterates x _n and the corresponding residuals r _n : b – Ax _n are replaced by smoothed iterates y _n and corresponding residuals s _n : b– Ay _n. We address the question whether the smoothed residuals can ultimately become markedly smaller than the primary ones. To investigate this, we present a roundoff error analysis of the smoothing algorithms. It shows that the ultimately attainable accuracy of the smoothed iterates, measured in the norm of the corresponding residuals, is, in general, not higher than that of the primary iterates. Nevertheless, smoothing can be used to produce certain residuals, most notably those of the minimum residual method, with higher attainable accuracy than by other frequently used algorithms.     

Almost sure limit points of and the number of boundary crossings related to SLLN and LIL for record times,inter-record times and the number of record values

In this paper, the almost sure limit points and the moments of the number of boundary crossings of some functions of record times, inter-record times and the frequency of record values of a sequence of independent and identically distributed continuous random variables are studied.     

Random walks in quenched i.i.d. space-time random environment are always a.s. diffusive

We consider a general model of discrete-time random walk X_t on the lattice , = 1,..., in a random environment ={(t,x):(t,x)⁺¹} with i.i.d. components (t,x). Previous results on the a.s. validity of the Central Limit Theorem for the quenched model required a small stochasticity condition. In this paper we show that the result holds provided only that an obvious non-degeneracy condition is met. The proof is based on the analysis of a suitable generating function, which allows to estimate L₂ norms by contour integrals.Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds.Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds, by R.F.F.I. grants n. 99-01-00284, 97-01-00714, and CRDF research funds N RM1-2085.Partially supported by C.N.R. (G.N.F.M.) and M.U.R.S.T. research funds.Mathematics Subject Classification (2000): 60J15, 60F05, 60G60, 82B41     

The limit of the product of the parameterized exponentials of two operators

Given two self-adjoint, positive, compact operators A,B on a separable Hilbert space, we show that there exists a self-adjoint, positive, compact operator C commuting with B such that

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Hydrodynamic limit for the Ginzburg-Landau ∇φ interface model with boundary conditions

Hydrodynamic limit for the Ginzburg-Landau interface model was established in [6] under periodic boundary conditions. This paper studies the same problem on a bounded domain imposing Dirichlet boundary conditions. A nonlinear partial differential equation of second order with boundary conditions is derived as a macroscopic equation. The main tools are H ^–1-method used in [6] and the higher integrability of gradients in [2].The author was supported by DFG project De 663/2-2 and 2/3 from April, 2001 to March, 2002, and by JSPS reserch fellowship for young scientists from April, 2002. Mathematics Subject Classification (2000): 60K35, 82C24, 35K55