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1981年, 第1卷, 第2期　刊出日期：1981-06-26 上一期    下一期

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关于抽象空间中的随机不动点定理 陈绍仲, 刘作述 数学物理学报. 1981 (2):  133-144.  摘要 ( 51 )   RICH HTML PDF(605KB) ( 26 )   收藏 In the present paper, we studied the random fixed point theorems in the abstract metric space X, which is metricized by the elements of the partially ordered set G. In §3, we also studied some fundamental properties of the abstract topological measure space X,. In §4, we generalized the classical random fixed point theorems. 相关文章 | 计量指标

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模糊映射 楼世博, 程里春 数学物理学报. 1981 (2):  145-155.  摘要 ( 64 )   RICH HTML PDF(479KB) ( 74 )   收藏 模糊控制器可以看做描述观测量的语言变量集到描述控制量的语言变量集的模糊映射,因而,对模糊映射的研究,在理论和应用上均有重要意义。 从本文所给的模糊映射的定义出发,可以推导得Zodeh作为定义给出的扩张原理. 本文还定义了模糊映射的α水平关系,在α水平集和α水平关系的基础上给出了三个分解定理. 对任给模糊映射T:X→Y,和Y中某个模糊集B,在什么条件下能找到X中的模糊集A,使T(A)=B呢?本文给出的两个充要条件回答了这个问题. 相关文章 | 计量指标

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非线性高阶广义Schrödinger型方程组的周期边界问题 周毓麟, 符鸿源 数学物理学报. 1981 (2):  156-164.  摘要 ( 54 )   RICH HTML PDF(445KB) ( 18 )   收藏 It is the purpose of this paper to consider some semilinear evolution systems of partial differential equations, which are found in physics, chemical reactions and biology. The existence, uniqueness and regularity of solutions for periodic boundary problems in global are proved for following degenerate parabolic and hyperbolic systems of higher order ∂u/∂t=Σm-1M(-1)m+1Am(x)∂2mu/∂x2m+Στ=0RBτ(t)∂2r+1u/∂x2r+1+f(u), where the matrices A(t), m=1,…, M are nonnegative definite and the matrices B(t), r=1.., M are symmetric. One can show that the nonlinear Schrödinger equation or system, which may be treated as a real degenerate parabolic system, the Sine-Gordon equation, Klein-Gordon equation, some simultaneous equations of Schrödinger equation and wave equation etc. may be changed into the above type. 相关文章 | 计量指标

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赫姆霍兹方程在聚焦面旁的渐近解 李志深 数学物理学报. 1981 (2):  165-176.  摘要 ( 53 )   RICH HTML PDF(619KB) ( 54 )   收藏 本文用短波近似法求得赫姆霍兹方程(3)在光滑凸聚焦面近旁的渐近解,并讨论了有关问题的物理意义。 相关文章 | 计量指标

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最小二乘辨识的一致性 陈翰馥 数学物理学报. 1981 (2):  177-183.  摘要 ( 58 )   RICH HTML PDF(334KB) ( 274 )   收藏 In this paper the least squares identification (LSI) of unknown coefficient matrices in the multi-dimensional dynamic system with uncorrelated noise is considered. Various conditions guaranteeing strong consistency of the LSI are put into comparison and the conditions proposed here and weaker than the previous one's are verified to be sufficient for the consistency of the LSI for which the asymptotic behaviors are also shown in the present paper. The main result is proved for the discrete-time system and its continuous-time analogue is also demonstrated. 相关文章 | 计量指标

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关于非线性方程的分歧问题 冯德兴, 刘嘉荃 数学物理学报. 1981 (2):  184-194.  摘要 ( 49 )   RICH HTML PDF(564KB) ( 20 )   收藏 本文讨论非线性方程的分歧问题,给出了分歧点的一个充分条件,并研究分歧解的线性化稳定性。 相关文章 | 计量指标

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THE STATIONARY DISTRIBUTIONS AND THE STEADY PROBABILITY CURRENTS OF ONEDIMENSIONAL DIFFUSION PROCESSES UNDER NON-LOCAL BOUNDARY CONDITIONS 吴承训, 郭懋正 数学物理学报. 1981 (2):  195-206.  摘要 ( 42 )   RICH HTML PDF(625KB) ( 21 )   收藏 In the present paper we study the limit distributions of one-dimensional diffusion processes under non-local boundary conditions. We obtain the existence conditions for the non-trivial stationary distributions, get their concrete formulas in all cases according to boundary classification, and give the results of some probability explanations. One-dimensional diffusion processes, which provide a simple mathematical model for studying irreversible steady systems, show that the basic characteristic of an irreversible stationary state is the occurrence of the probability current, i. e. the circulation phenomenon. 相关文章 | 计量指标

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弹性板的弯曲问题 周焕文 数学物理学报. 1981 (2):  207-217.  摘要 ( 40 )   RICH HTML PDF(548KB) ( 34 )   收藏 In this paper, a mathematical model for the problems of bending of elastic of elastic plates is established. In this mathematical model. we presented three arbitrary functions to express the bending couples、twisting couple、shear forces and angular rotation and transuerse deflection etc. mechanical quantities which satisfied equiliber ium equations. For example, considered Reissner model. If let the sign A. ψ and R to note above three arbitrary functions respectively, then functions A, ψ and R need to satisfy the following equations: △△A=q/D, △ψ-10/h2ψ=0, and △R=-(1-2μ)/10μ q/D, and where μ is Poisson's ratio. The above first two equations are known, while the third is new. 相关文章 | 计量指标

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不分明凸集的几个性质 刘应明 数学物理学报. 1981 (2):  218-226.  摘要 ( 51 )   RICH HTML PDF(523KB) ( 43 )   收藏 Let E be an n-dimensioal Euclidean space, T the induced fuzzy topology for E[8], and λ and μ fuzzy sets in E. In[10], where L. Zadeh introduced the notion of the shadow of fuzzy set λ on a hyperplane H (denoted by SH(λ)), the following statement was given:If λ and μ be fuzzy convex sets E and SH(λ)=SH(μ) for all hyperplanes H, then λ=μ. 相关文章 | 计量指标

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空间Bp,q(r)与差分法 罗佩珠, 丁夏畦 数学物理学报. 1981 (2):  227-239.  摘要 ( 43 )   RICH HTML PDF(539KB) ( 16 )   收藏 In we introduced spaces Lρ (φ), Eρ(φ). In this paper we shall take the Lρ(φ)-norm in stead of Lρ-norm in the Spaces Bp,q(r), then we get the spaces Bp,q(r)(φ). we prove a trace theorem of the spaces Bp,q(r)(φ) and we can apply this method to the estimate of difference method of the initial problem. 相关文章 | 计量指标

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INFORMATION FLOW OF TREE (1) Tree Flow Theorems 李传湘 数学物理学报. 1981 (2):  240-256.  摘要 ( 41 )   RICH HTML PDF(782KB) ( 13 )   收藏 This paper is divided into two parts, where the general regularities of information flow in the tree graph are discussed. In the first part we discuss the equivalent theorems of the tree flow, the main sections are as follows:1. fundamental definitions; 2. equivalent mapping structure; 3. equivalent partition of vector set F*; 4. theorems of tree flow. And in the second part we put stress on the establishment of tree flow equations. 相关文章 | 计量指标

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GAUGE THEORY AND FUNCTIONAL HARMONIC MAPPING 郭汉英 数学物理学报. 1981 (2):  257-259.  摘要 ( 43 )   RICH HTML PDF(171KB) ( 29 )   收藏 It is shown that the loop integral phase factors in the gauge theory (i. e. the elements of holonomy group of the gauge potentials) as the functional mappings from loops passing a given point in the space-time to the holonomy group HG of the gauge group G can be regarded as a harmonic mapping in the functional sense. The corresponding functional harmonic equations are equivalent to the sourceless Yang-Mills equatios. 相关文章 | 计量指标