具偏差变元微分方程解的振动性

该文建立了具偏差变元微分方程 ｘ’（ｔ）＋ ｐ（ｔ）ｘ（τ（ｔ））＝ ０的新的振动准则,所得定理改进了文献［１－６］中相应的结果．     

变系数函数方程解的振动性

本文给出了变系数函数方程ｘ（ｇ（ｔ））＝Ｐ（ｔ）ｘ（ｔ）＋∑Ｑｉ（ｔ）ｘ（ｇｋ＋ｉ（ｔ））的一切解均ｉ＝１为振动的充分条件,其中Ｋ≥１为正整数．     

临界状态下具渐近周期系数的一阶时滞微分方程的振动性

首先证明了在临界情形ｌｉｍｉｎｆ「ｐ（ｔ）－ｒ（ｔ）」＝０且∫ｔ－ｒｒ（ｓ）ｄｓ＝１／ｅ下一阶时滞微分方程ｘ’（ｔ）＋ｐ（ｔ）ｘ（ｔ－τ）＝０（＊）所有解振动等价于Ｒｉｃｃａｔｉ不等式ｗ（ｔ）＋ｒ（ｔ）ｗ＾２（ｔ）＋２ｅ＾２（ｐ（ｔ）＝ｒ（ｔ））≤０无最终正解,然后据此给出了方程（＊）在临界状态下两个振动及非振动准则。     

一阶中立型时滞微分方程的振动性

分别获得了中立型时滞微分方程「ｘ（ｔ）＋ｐｘ（ｔ－γ」’＋ｑ（ｔ）ｘ（ｔ－σ）＝０的振动性和非振动性的充分条件,其中ｐ〉０,ｑ（ｔ）是一个正的周期函数。     

高阶中立型非线性泛函微分方程解的渐近性

本文在∫＾∞ｔ０ｄｔｒ（ｔ）＝∞与∫＾∞ｔ０ｄｔｒ（ｔ）〈∞这两种情况下讨论了下面高阶中立型非线性方程「ｒ（ｔ）（ｘ（ｔ）－ｃｘ（ｔ－τ））′」＾（ｎ－１）＋ｆ（ｔ，ｘ（ｇ１（ｔ）），…，ｘ（ｇｍ（ｔ）））＝０（ｔ≥ｔ０）非振动解的分类，并且给出了各类非振动解存在的条件。     

临界状态下一阶时滞微分方程的线性化振动性

本文首先在临界状态下建立了一阶非线性非自治时滞微分方程ｘ＇（ｔ）＋＝１ｐｉｘ（ｔ－Ｔｉ）＋ｆ（ｔ,ｘ（ｔ－σ１（ｔ））…,ｘ（ｔ－σｎ（ｔ））＝０与一个相关的二阶常微分方程振动性等价定理,进而给出了一阶非线性自治微分方程与相应的线性方程振动性等价的充分条件,从而较好地回答了张炳根在文［２］中提出的一个公开问题．     

奇数阶中立型时滞微分方程的线性化振动性

考虑奇数阶中立型非线性微分方程ｄ＾ｎ／ｄｔ＾ｎ（ｘ（ｔ）－Ｐ（ｔ）ｇ（ｘ（ｔ－τ）））＋Ｑ（ｔ）ｈ（ｘ（ｔ－σ））＝０。本文在允许Ｐ（ｔ）－１振动的条件下给出了该方程的几个线性化振动结果。     

一类一阶中立型方程解的渐近性与振动性

讨论具有连续分布滞量的一阶中立型微分方程ｄｄｔｘ（ｔ）－∑ｍｉ＝１ｐｉ（ｔ）ｘ（ｔ－τｉ）［］＋∫ｂａｆ（ｔ,ζ,ｘ［ｇ（ｔ,ζ）］）ｄσ（ζ）＝０,（１）给出了非振动解当ｔ→∞时收敛于零的充分条件和方程（１）所有解振动的判据     

二阶NFDE零解的稳定性

本文给出了二阶中立型微分方程ｘ（ｔ）＋ｘ（ｔ－τ）＋ｂｘ（ｔ）＋ｂ１ｘ（ｔ－τ）＋ｃｘ（ｔ）＋ｃ１ｘ（ｔ－τ）＝０零解稳定的代数判据．     

变系数高阶中立型泛函数分方程的振动性与渐近性

考虑变系数高阶中立型泛函微分方程ｄ＾ｎ／ｄｔ＾ｎ（ｘ（ｔ）＋ｐ（ｔ）ｘ（ｔ－τ（ｔ））＋ｍ∑ｉ＝１Ｐｉ（ｔ）ｘ（ｔ－τｉ（ｔ）＝０，在－１＜ｐ（ｔ）≤０情形下解的振动性与渐近性，取消了Ｐｉ（ｔ）≥ｑｉ＞０的限制，改进以往的相应结果，本文结果时高阶泛函方程Ｘ＾（ｎ）（ｔ）＋ｍ∑ｉ＝１ｐｉ（ｔ）ｘ（ｔ－τｉ（ｔ））＝０也是适用的。     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.