Dunham型联合Chebyshev逼近理论

本文在不假定 G 在紧集 X 上满足 Haar 条件的情形,建立了 Dunham 型联合最佳逼近的 Chebyshev 理论,包括特征定理(定理5、定理6和推论2),唯一性与强唯一性定理(定理9和推论3)以及连续性定理,同时我们也得到了“削皮”定理与联合最佳逼近的量的对偶形式。(定理7)。     

最佳混合范数逼近

本文研究了两变量函数 f(x,y)用单变量函数 g(x)作混合范数逼近问题,即求g~*(x)∈G,G 是一 Haar 子空间,使(?)integral from Y|f(x,y)-g~*(x)|dμ=(?)integral from Y|f((?),y)-g(x)|dμ我们建立了包括交错定理、de la Vallee Poussin 定理、唯一性定理和强唯一性定理在内的 Chebyshev 逼近理论。     

置换空间中的最佳逼近存在性与唯一性定理

得到了置换空间PXXn中的最佳逼近存在性与唯一性定理.     

取值为Banach空间的集值映射的非线性逼近

本文研究了取值为Ｂａｎａｃｈ空间中的集的集值映射的非线性逼近问题．给出集值映射的最佳逼近的特征和唯一性定理，并刻划了使其特征定理成立的非线性类的特征．     

拟凸函数与切比晓夫逼近

木文第一节给出拟凸函数和显拟凸函数(explicitly quasiconvex functions)的一个新的特征;同时引进一种新的凸性——我们称它为强伪凸性,并给出它的若干重要性质.第二节讨论第一节的结果在最佳一致逼近中的应用,建立了交错定理、唯一性定理和强唯一性定理.     

二阶混合单调型脉冲微分方程的初值问题

利用混合单调凝聚算子的耦合不动点定理,给出了二阶混合单调型脉冲微分方程的初值问题的解的存在唯一性及迭代逼近定理。     

分数阶R-L微分方程初值问题解的存在唯一性

研究了R-L导数定义下的分数维微分方程初值问题解的存在性及其唯一性,给出了方程的Peano存在定理和不等式定理,基于逐次逼近的方法,利用对分数阶R-L微夯方程构造的Tonelli序列和Ascoli引理证明分数阶R-L微分方程解的存在性,根据分数阶不等式定理证明了分数阶R-L微分方程解的唯一性.     

复赋范空间中的同时太阳集的最佳逼近

研究了复赋范空间中的同时太阳集对无穷序列的最佳逼近问题，得到了特征及唯一性定理．     

任意权函数的最佳逼近

本文对非对称的任意权函数(可以取值∞的非负不连续函数)的最佳逼近建立切比晓夫理论,包括存在性、唯一性、交错定理和其他定理,从而拓广了经典的切比晓夫理论.     

有约束单向豪斯道夫最佳逼近的唯一性

本文研究单向豪斯道夫度量下的带约束条件的多项式最佳逼近问题，得到唯一性定理。     

受迫Li\''{e}nard方程周期解的存在唯一性

本文利用整体反函数理论证明了受迫Li\'{e}nard方程$x'+f(x)x'+g(t,x)=e(t)$周期解的存在唯一性，推广和改进了现有的结果.     

p-ADIC亚纯函数在截断重级下的一个定理

本文研究p-adic亚纯函数在截断重级下分担两个公共值集的唯一性问题，得到了一个相应的定理．定理的证明主要利用p-adic亚纯函数论中的两个基本定理和一个辅助函数．     

Deformations of hypersurfaces in equiaffine differential geometry

We study infinitesimal normal deformations in equiaffine hypersurface theory and prove local and global rigidity results. Main tool are uniqueness theorems for certain p.d.e. of second order.     

Bruck猜想的一类微分和差分方程

运用值分布以及Wiman-Valiron理论研究了整函数与它的k阶导数分担某些小函数问题,得到了一些涉及到Bruck猜想的唯一性结果.     

非正规情形下代数Hermite-Pade逼近的存在性与唯一性

本文研究了非正规情形下一局部解析函数ｆ（ｚ）的代数Ｈｅｒｍｉｔｅ－Ｐａｄé逼近,并在一般条件下证明了它的存在性与唯一性     

Uniqueness of entire functions sharing an entire function of smaller order with their derivatives

In this paper, we prove some uniqueness theorems of entire functions and their derivatives that share an entire of function whose order is less than their order. The results in this paper improve those given by G. G. Gundersen and L. Z. Yang, J. P. Wang, J. M. Chang, and Y. Z. Zhu, X. M. Li and H. X. Yi, and others. Some examples are provided to show that the results in this paper are the best possible.     

Teoremi di unicità della magnetoidrodinamica in domini illimitati

Riassunto In questa nota si stabiliscono due teoremi di unicità della soluzione per il problema del moto di un fluido omogenco, incomprimibile, perfetto, elettricamente conduttore attorno ad un ostacolo fisso, anch'esso elettricamente conduttore. Nelprimo teorema viene trascurata la corrente di spostamento, mentre nel secondo si tiene conto anche di quest'ultima. Per la dimostrazione si utilizza il “metodo della funzione peso” usato da G. P. Galdi e S. Rionero in un analogo teorema di unicità per magnetofluidi viscosi.

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Summary The Author establishes two solution uniqueness theorems for the problem of homogeneous, incompressible, perfect, electrically conducting fluid motion around a fixed, electrically conducting solid body. In the first theorem displacemt current is disregarded, in the other one this current is considered. The proof is obtained by using the “weight function method” adopted by G. P. Galdi and S. Rionero in an analogous uniqueness theorem for viscous magnetofluids.

     

Solvability of a boundary value problem for a mixed-type equation with a partial Riemann-Liouville fractional derivative

We prove existence and uniqueness theorems for the solution of a nonlocal problem for a partial differential equation with a Riemann-Liouville fractional derivative in which the boundary condition contains a generalized fractional differentiation operator with the Gauss hypergeometric function in the kernel. We present a closed-form solution of the problem.     

Asymptotic Properties of the Markov Branching Process with Immigration

We consider the Markov branching process with immigration allowing the possibility of infinite numbers of offspring and/or immigrants. Our focus is on the construction and uniqueness of the minimal transition function and on its asymptotic behavior. Conditional limit theorems for the population size are given in cases for which the transition function is dishonest.     

New proofs and generalisations of theorems of existence and uniqueness for the goursat problem

Abstract theorems of existence and uniqueness are proved for a differential equation whose solution takes its values in a sequence of Banach spaces called a Banach filtration (a notion introduced by F. Treves). The abstract theorems are then applied to obtain existence and uniqueness theorems of a classical nature bearing on that generalization of the Cauchy problem of partial differential equations known as the Goursat problem. All the results so obtained remain true in the case when the equations involve more general operators than partial differential operators (e.g., pseudo-differential operators)