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MULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONSWITH LIPSCHITZIAN CONDITIONMULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION

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Chinese Annals of mathematics,Series B 2000年第4期21卷 479-488页

作者： wang ZAIHONG (department of mathematics, Capital normal {4., Beijing 100037, china.) department of mathematics Capital Normal University Beijing 100037 China

This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.

关键词： Periodic solution Time mapping Poincare-Birkhoff twist theorem

Uniform blow-up profiles and boundary layer for a parabolic system with localized nonlinear reaction terms

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Science china mathematics 2005年第2期48卷 185-197页

作者： LI Huiling & wang Mingxin department of mathematics, Southeast {4., Nanjing 210018, china department of mathematics, Xuzhou normal {4., Xuzhou 221116, china 1. department of mathematics Southeast University 210018 Nanjing China 2. department of mathematics Xuzhou Normal University 221116 Xuzhou China

This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.

关键词： parabolic system, localized nonlinear reaction terms, blow-up profiles, boundary layer size.

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Science china mathematics 2004年第5期47卷 659-674页

作者： SHI Peihu & wang Mingxindepartment of mathematics, Southeast {4., Nanjing 210018, china department of mathematics, Xuzhou normal {4., Xuzhou 221116, china 1. department of mathematics Southeast University 210018 Nanjing China 2. department of mathematics Xuzhou Normal University 221116 Xuzhou China

This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1, it is shown that the very singular self-similar solution exists if and only ifnq + (n +1)p 1, it is shown that very singular self-similar solutions exist if and only if 1

关键词： quasilinear parabolic equations, self-similar solutions, very singular solution, classification.

The best quadrature based on given Hermite information for the Sobolev class KW^r[a,b]

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Science china mathematics 2006年第8期49卷 1146-1152页

作者： wang Xinghua & YANG Shijun department of mathematics, Zhejiang university, Hangzhou 310028, {4. department of mathematics, Hangzhou normal College, Hangzhou 310036, {4. department of mathematics Zhejiang University Hangzhou 310028 China department of mathematics Hangzhou Normal College Hangzhou 310036 China

As usual, denote by KWr[a,b] the Sobolev class consisting of every function whose (r-1)th derivative is absolutely continuous on the interval [a,b] and rth derivative is bounded by K a.e. In [a,b]. For a function f ∈ KWr[a,b], its values and derivatives up to r-1 order at a set of nodes x are known. These values are said to be the given Hermite *** work reports the results on the best quadrature based on the given Hermite information for the class KWr[a,b]. Existence and concrete construction issue of the best quadrature are settled down by a perfect spline interpolation. It turns out that the best quadrature depends on a system of algebraic equations satisfied by a set of free nodes of the interpolation perfect spline. From our another new result, it is shown that the system can be converted in a closed form to two single-variable polynomial equations, each being of degree approximately r/2. As a by-product,the best interpolation formula for the class KWr[a,b] is also obtained.

关键词： Sobolev class, Hermite information, perfect spline, optimal recovery, best quadrature.

Multi-parameter infinite-dimensional(r,δ)-OU process

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Chinese Science Bulletin 1999年第5期44卷 418-423页

作者： wang ZikunInstitute of mathematics, Shantou university, Shantou 515063, china {4. of mathematics, Beijing normal university, Beijing 100875, china Institute of mathematics Shantou University Shantou China department of mathematics Beijing Normal University Beijing China

The definition of n-parameter infinite-dimensional (r, δ) -Ornstein-Uhlenbeck process {X_t (·)}((r,δ)-OUP_n~∞ for short) is given. The absolute continuity of distribution μ_t of X_t(·) and the limit of X_t(·) w... 详细信息

关键词： multi-parameter (r δ)-OUPn∞ absolute continuity in hierarchy.

On solving equations of algebraic sum of equal powers

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Science china mathematics 2006年第9期49卷 1153-1157页

It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics,it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.

关键词： algebraic sum of equal powers, Newton's identities, system of equations,roots of a polynomial.

Smoothness for the collision local times of bifractional Brownian motions

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Science china mathematics 2011年第9期54卷 1859-1873页

作者： SHEN GuangJun 1,2,& YAN LiTan 3 1 department of mathematics,east china {4. of Science and Technology,Shanghai 200237,china 2 department of mathematics,Anhui normal {4.,Wuhu 24.000,china 3 department of mathematics,Donghua {4.,Shanghai 201620,china 1. department of mathematics East China University of Science and Technology Shanghai 200237 China2. Department of Mathematics Anhui Normal University Wuhu 241000 China3. Department of Mathematics Donghua University Shanghai 201620 China

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.

关键词： bifractional Brownian motion collision local time intersection local time chaos expansion

The Goldbach 3-primes property for polynomial rings over certain infinite fields

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Chinese Science Bulletin 1998年第15期43卷 1256-1260页

作者： wang Shiqiang department of mathematics, Beijing normal {4., Beijing 100875, china department of mathematics Beijing Normal University Beijing China

On the basis of Effinger and Hayes’ theorem about the Goldbach 3_primes property of polynomial rings F over finite fields F , by model_theoretic method it is proved that for each characteristic k (including 0), there... 详细信息

关键词： model theory polynomial 3 primes property.

Optimal value functions of generalized semi-infinite min-max programming on a noncompact set

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Science china mathematics 2005年第2期48卷 261-276页

作者： wang Changyu, YANG Xiaoqi & YANG Xinmin Institute oi Operations Research, Qufu normal university, Qufu 273165, china {4. of Applied mathematics, Dalian university of Technology, Dalian 116024. china {4. of Applied mathematics, The Hong Kong Polytechnic university, Hong Kong, china {4. of mathematics, Chongqing normal university, Chongqing 4.004., china 1. Institute of Operations Research Qufu Normal University 273165 Qufu China 2. department of Applied mathematics Dalian University of Technology 116024 Dalian China 3. department of Applied mathematics The Hong Kong Polytechnic University Hong Kong China 4. department of mathematics Chongqing Normal University 400047 Chongqing China

In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subdifferential characterizations of optimal value functions are given. Using these properties,we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.

关键词： optimal value function, directional derivative, subdifferential, semi-infinite programming, first order optimality condition.