一类非线性混合型方程的Tricomi问题

本文考虑非线性混合型方程 k(x,y)u_xx+u_yy+α(x,y)u_x+β(x,y)u_y+γ(x,y)u-|u|^ρu=f(x,y)的Tricomi 问题.利用能量积分和不动点原理,在很弱的条件下证明了H¹强解的存在性.     

一个方程组的解及相关边值问题

该文考虑方程组 t(u_x - v_y - w_t ) + w = 0 (H) u_y = -v_x, u_t = -w_x, v_t = w_y 的解f = u + iv + jt ∈C²,找到(H)可解的一个充要条件,并讨论相关边值问题解的存在性和积分表示,推广了1992年H. Leutwiler［1］的结果.     

五维空间中半线性波动方程整体解的存在性定理

本文研究五维空间中半线性波动方程u_tt-△u=G（u）整体解的存在性,其中G（u）～|u|^p并且p>（3+(17)^1/2)/4.利用经典的迭代方法证明了:如果初始值很小并且紧支的,径向对称方程有一个经典整体解.     

Stability of Rotation Relations of Three Unitaries with the Flip Action in C*-Algebras*

The authors show that if Θ = (θ_jk) is a 3 × 3 totally irrational real skewsymmetric matrix, where θ_jk ∈ [0, 1) for j, k = 1, 2, 3, then for any ε > 0, there exists δ > 0 satisfying the following: For any unital C^*-algebra A with the cancellation property,strict comparison and nonempty tracial state space, any four unitaries u₁, u₂, u₃, w ∈ A such that (1) u_ku_j - e^{2πiθjk ujukk} < δ, wu_jw^-1 = u^-1_j, w² = 1_A for j, k = 1, 2, 3; (2)τ (aw) = 0 and τ ((u_ku_ju_k^*u_j^* )ⁿ ) = e^2πinθjk for all n ∈ N, all a ∈ C^*(u₁, u₂, u₃), j, k = 1, 2, 3 and all tracial states τ on A, where C^*(u₁, u₂, u₃) is the C^*-subalgebra generated by u₁, u₂ and u₃, there exists a 4-tuple of unitaries u₁, u₂, u₃, w in A such that u_ku_j = e^2πinθjk u_ku_j, w u_j w^-1 = u^-1 _j, w² = 1A and k u_j - u_jk < ε, k w - wk < ε for j, k = 1, 2, 3. The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions.     

非线性四阶周期边值问题的最优正解

该文使用锥不动点定理研究了四阶周期边值问题u⁽⁴)-m⁴u+F(t, u(τ(t)))=0, 0 < t < 2π, u⁽ⁱ⁾(0)=u⁽ⁱ⁾(2π),~ i=0,1, 2, 3, 这里 F: [0,2π ]×R⁺→R⁺ 和τ: [0, 2π]→[0, 2π] 是连续的, 0-7.     

拟线性抛物方程组第一边界问题的有限差分法

本文利用有限差分法来作出拟线性抛物方程组u_t=(-1)^M+1A(x,t,u…,u_x^M-1)u_x^2M+F(x,t,u,…,u_x^2M-1) (1)具有齐次边界条件u_xk(0,t)=u_xk(l,t)=0 (k=0,1,…,M-1) (2)与初始条件u(x,0)=φ(x) (3)在矩形区域Q_T={0≤x≤l,0≤t≤T}上的解,其中u=(u₁,…,u_m),φ(x)与F为m维向量值函数,A为m×m正定矩阵。证明了问题(1),(2)与(3)的一类相当广泛的有限差分格式的解的收敛性。所得向量值极限函数u(x,t)∈W₂^2M,1(Q_T)是问题(1),(2),(3)的唯一广义整体解。     

拟线性抛物方程组第一边界问题的有限差分法 ——Ⅲ.稳定性

讨论如下拟线性抛物组第一边值问题的显式、弱隐式和强隐式差分解u_t=(-1)^M+1A(x,t,u,…,u_x^M-1)u_x^2M+f(x,t,u,…,u_x^2M-1(x,t)∈Q_T={O<x<l,0<t≤T.}，u_x^k(0，t)=u_x^k(l，t)=0 (k=0，1，…，M -1)，0<t≤T，u(x，0)=φ(x)，0≤x≤l，其中u，φ和f是m维向量值函数，A是m×m正定矩阵，u_t=∂u/∂t，u_x^k=∂^ku/∂x^k.在以下意义下证明了该问题的一般有限差分格式的稳定性：即离散向量解在W₂^(2M，M)(Q_T)中的离散范数是连续地依赖于初始数据的H^M离散范数，以及矩阵A与自由项f的相应的离散范数.     

更新序列对于圈乘运算的封闭性

本文的主要结果有二:ⅰ)用纯分析且初等方法证明了:若u=(u₀,u₁,…)和u=(u₀,u₁,…)是两个更新序列,则u和u的圈积uu=(u₀u₀,u₁u₁,…)也是一个更新序列;ⅱ)分别用概率和分析方法给出了两个更新序列的圈积的f-序列的明显表达式。     

关于集值系统x∈F(x,y),y∈G(x,y)解的存在性

Let (E, ‖·‖) be a uniformly convex Banach space, X a nonempty compact and convex subset of E. Let F be a closed mapping of X×X into 2^X, G a mapping of X×X into C(X). It is shown that if for any f∈C(X), x∈X, F(x,f(x)) is a closed and convex subset of X, and G(x,f(x)) is a continuous function and for any x,y₁,y₂∈X,H(x,G(x,y₁),G(x,y₂))≤‖y₁-y₂‖ then there exist X₀,y₀∈X such that X₀∈F(x₀,y₀) and y₀∈G(x₀, y₀).     

交换群上Hopf路余代数的结构分类

设G是群, kG是域k上的群代数. 对任意Hopf箭向Q=(G, r), 利用右kZ_u(C) -模的直积范畴∏_C∈K(G) MkZ_u(C)与kG-Hopf双模范畴^kG_kG M^kG_kG之间的同构, 可由^u(C)(kQ₁)¹上的右kZ_u(C) -模结构导出在箭向余模kQ₁上的kG-Hopf双模结构. 该文讨论在群G分别是2阶循环群与克莱茵四元群时的Hopf路余代数kQ^c的同构分类及其子Hopf代数kG[kQ₁]结构.     

COMMON FIXED POINTS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS

For a subset K of a metric space (X , d) and x ∈ X ,P K (x) ={y ∈ K : d(x, y) = d(x, K) ≡ inf { d(x, k) : k ∈ K }}is called the set of best K-approximant to x. An element g。∈ K is said to be a best simultaneous approximation of the pair y 1 , y 2 ∈ X if max{d(y 1 , g。), d(y 2 , g。) } = inf g ∈ K max { d(y 1 , g), d(y 2 , g)}.In this paper, some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved. For self mappings T and S on K, results are proved on both T - and S- invariant points for a set of best simultaneous approximation. Some results on best K-approximant are also deduced. The results proved generalize and extend some results of I. Beg and M. Abbas [1] , S. Chandok and T.D. Narang [2] , T.D. Narang and S. Chandok [11] , S.A. Sahab, M.S. Khan and S. Sessa [14] , P. Vijayaraju [20] and P. Vijayaraju and M. Marudai [21] .     

多目标最优化问题相依导数的灵敏性与稳定性(英)

设Y（u）是可行域在目标空间的像，W（u）＝minpY（u）是有效集和N（u）＝W－minDDY是弱有效集．在适当条件下，本文证明了DNW－minpY和W－minDDY＝DW＝DN．本文也讨论了边缘映射导数的连续性．     

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM, FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS, AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article,we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems,the set of common fixed point for a family of infinite...     

SOME NEW TYPE OF DIFFERENCE SEQUENCE SPACES DEFINED BY MODULUS FUNCTION AND STATISTICAL CONVERGENCE

In this article we introduce the difference sequence spaces W 0 [f,Δm ],W 1 [f,Δm ],W∞[f,Δm ] and S[f,Δm ],defined by a modulus function f.We obtain a relation between W 1 [f,Δm ] ∩l∞[f,Δm ] and S[f,Δm ] ∩l∞[f,Δm ] and prove some inclusion results.     

Nonlinear Degenerate Oblique Boundary Value Problems for Second Order Fully Nonlinear Elliptic Equations

In this paper we study the existence theorem for solution of the nonlinear degenerate oblique boundary value problems for second order fully nonlinear elliptic equations F(x, u, Du, D²u) = 0 \quad x ∈ Ω, G(x, u, D, u) = 0, \qquad x ∈ ∂Ω where F (x, z, p, r) satisfies the natural structure conditions, G (x, z, q) satisfies G_q ≥ 0, G_x ≤ - G_0 < 0 and some structure conditions, vector τ is nowhere tangential to ∂Ω. This result extends the works of Lieberman G. M., Trudinger N. S. [2], Zhu Rujln [1] and Wang Feng [6].     

Halin-图的邻强边染色

图G(V,E)的正常κ-边染色f叫做图G(V,E)的κ-邻强边染色当且仅当任意uv∈E(G)满足f[u]≠f[v],其中,f[u]={f(uw)|uw∈E(G)},称f是G的κ-临强边染色,简记为κ-ASEC.并且x′_as(G)=min{k|κ-ASEC of G}叫做G(V,E)的邻强边色数.本文研究了△(G)≥5的Halin-图的邻强边色数.     

Approximation of fixed points of nonexpansive mapping in Banach spaces

In this paper, some iterative schemes are given to approximate a fixed point of the nonexpansive non-self-mapping and nonexpansive self-mapping. Furthermore, the strong convergence of the scheme to a fixed point is shown in a Banach space with uniformly Gâteaux differentiable norm. The theorems extend and improve some corresponding results of Matsushita and Takahashi [S. Matsushita, W. Takahashi, Strong convergence theorems for nonexpansive nonself-mappings without boundary conditions, Nonlinear Anal. 68 (2008) 412–419], Chang et al. [S.S. Chang, H.W. Joseph Lee, C.K. Chan, On Reich’s strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal. 66 (2007) 2364–2374], Chidume and Chidume [C.E. Chidume, C.O. Chidume, Iterative approximation of fixed points of nonexpansive mappings, J. Math. Anal. Appl. 318 (2006) 288–295] and Suzuki [T. Suzuki, A sufficient and necessary condition for Halpern-type strong convergence to fixed point of nonexpansive mappings, Proc. Amer. Math. Society 135 (1) (2007) 99–106].     

Kirchhoff方程单峰解的局部唯一性

该文主要证明了以下非线Kirchhoff问题的单峰解的局部唯一性-(∈^2a+∈b∫R^3|▽u|^2dx)△u+u=K(x)|u|^p-1u,u> 0,x∈R^3,其中∈>0任意小,a,b> 0,1相似文献   

ON THE WEIGHTED VARIABLE EXPONENT AMALGAM SPACE W（L^p（x）, Lm^q）

In [4], a new family W（L^p（x）, Lm^q） of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space L^p（x） （R） and the global component is a weighted Lebesgue space Lm^q （R）. This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W （L^p（x）, Lm^q） = L^q （R）. Later we give some characterization of Wiener amalgam space W （L^p（x）, Lm^q）.In Section 3 we define the Wiener amalgam space W （FL^p（x）, Lm^q） and investigate some properties of this space, where FL^p（x） is the image of L^p（x） under the Fourier transform. In Section 4, we discuss boundedness of the Hardy- Littlewood maximal operator between some Wiener amalgam spaces.     

Hypervarieties of a given type

In this paper we consider the notions of hyperidentities and hypervarieties of a given type , without nullary operations, originated by J. Aczel [1], V. D. Belousov [2], W. D. Neumann [12] and W. Taylor [21]. Solid varieties are defined. Their equations correspond to hyperidentities and they form a complete sublattice of the lattice L() of all varieties of type . A completeness theorem for hyperidentities is formulated in analogue to G. Birkhoff [3]. The technique of weak isomorphisms, introduced by E. Marczewski and A. Goetz [7] assists us in partially answering a problem of W. Taylor (Problem 4, [21]).Presented by Ivo Rosenberg.This work was done while the first author was visiting the University of Kaiserslautern, under the auspices of the Alexander von Humboldt Foundation.As a part of this paper was done during the second author's visit to La Trobe University, the financial assistance by ARGS grant B 85154851 and by the DFG is gratefully acknowledged.