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1982年, 第2卷, 第2期　刊出日期：1982-06-26 上一期    下一期

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走向几何的机械化——评Hilbert的名著《几何原理》 吴文俊 数学物理学报. 1982 (2):  125-135.  摘要 ( 99 )   RICH HTML PDF(629KB) ( 116 )   收藏 1899年出版的Hilbert的名著《几何原理》(Grundlagen der Geometrie)的巨大功绩是普遍公认的,它是数学公理化的代表作,特别是奠定了Euclid几何的严密基础。然而,这一名著的另一巨大功绩(在作者看来,这后一功绩也许还更大些!)似乎直到现在还没有引起注意。 相关文章 | 计量指标

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人口算子的谱特性与人口半群的渐近性质 宋健, 于景元, 王彦祖, 胡顺菊, 赵忠信, 刘嘉荃, 冯德兴, 朱广田 数学物理学报. 1982 (2):  137-144.  摘要 ( 50 )   RICH HTML PDF(421KB) ( 171 )   收藏 本文讨论人口算子的谱特性,证明了人口算子只有一个实本征值γ0,γ0是实部最大的本征值,找到了妇女临界生育率βcr与γ0的对应关系。本文还论述了人口系统半群的存在性和渐近特性,由此给出了人口系统稳定性问题的结论,从理论上证明了,在临界生育率条件下存在稳态人口状态。这些都是定量人口理论的新结果。 *)三个单位同志同时得出本文主要结论,因此联名发表。 相关文章 | 计量指标

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INVARIANT SURROGATION IN SCIENTIFIC DIALOGUE P. D. Finch 数学物理学报. 1982 (2):  145-174.  摘要 ( 47 )   RICH HTML PDF(1657KB) ( 20 )   收藏 The term surrogation is used instead of approximation, estimation etc, to separate rol playing from how well a role is Played. To obtain a surrogate for an actual but unknown object one needs an algorithm to compute it from input data giving what is known about that object. Invariance arguments are used to show that surrogates must be fixed points of certain mappings associated with the mathematical structure characterizing practical context. The corresponding surrogation algorithms are said to he macroinvariant. Some special cases where there is essentially only one such algorithm are then considered. These results are derived without reference to proximity to actuality, that is to how good the surrogate is. Finally it is shown that if one does not use macroinvariant surrogation, then he could, in principle, do better, in any given metric sense, by means of such an invariant procedure. 相关文章 | 计量指标

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SYMMETRIES OF EQUATIONS qtt=g(q,qx,qxx,…) AND THE FORMAL COMPLETELY INTEGRABILITY OF BOUSSINESQ EQUATION 屠规彰 数学物理学报. 1982 (2):  175-182.  摘要 ( 45 )   RICH HTML PDF(434KB) ( 46 )   收藏 In this paper the symmetries of equations qtt=g(q,q1, q2,…) are discussed, where q=q(x,t) and qi=∂iq/∂xi. It is shown that if g=aqs+ḡ(q,…,qr), a=const, s-r ≥ 2, then any symmetry of the equation wilt be linear with respect to the term of highest order Furthermore, if the equation can be reduced to a Hamiltonian equation, then pairs of its conserved densities are in involution. As an application of this result, the Boussinesq equation qtt=q4+6q1q2 is shown to be a formal completely integrable Hamiltonian equation. 相关文章 | 计量指标

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PROBABILITY DISTRIBUTIONS OF ENERGY OF ONE-DIMENSIONAL PARTICLES OF TWO KINDS IN THE ENERGY EIGENSTATES 陶宗英, 丁立峰, 胡蓓华 数学物理学报. 1982 (2):  183-192.  摘要 ( 45 )   RICH HTML PDF(544KB) ( 17 )   收藏 Starting from Voe Neumann's axiomatic system of quantum mechanics, this paper calculates the probability distributions of the kinetic and potential energy of the one-dimensional harmonic oscillator and the particle in one-dimensional infinitely deep square potential well. The results are compared with the classical cases, and it is shown that their relation conforms to Bohr's correspondence principle. Then we put forward a new viewpoint:it seems that the concept of the total energy of the particle in quantum mechanics should be deliberated again; the two basic hypotheses in quantum mechanics-"Bohr's probabilistic interpretation" and "the postulate that the particle's energy eguals the eigenvalue in the energy eigenstate" ars not logically harmonious. At the same time, the limitation of von Neumann's axiomatic system is pointed out. 相关文章 | 计量指标

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THE CONVERGENCE THEORY FOR DISCRETE-ORDINATE APPROXIMATIONS IN HIGHER SPATIAL DIMENSIONS 阳名珠, 朱广田 数学物理学报. 1982 (2):  193-206.  摘要 ( 43 )   RICH HTML PDF(723KB) ( 45 )   收藏 In this paper the approximation theory of p-order quasi-collectively compact operators established by Ref. is applied to proving that the critical parameter and critical flux,and that the fundamental mode decay constant and fundamental mode computed by discrete-ordinate do converge to the corresponding quantities for the undiscretized, three-dimensional transport equation. 相关文章 | 计量指标

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ON SINGULAR INTEGRALS WITH SINGULARITIES OF HIGH FRACTIONAL ORDER AND THEIR APPLICATIONS 路见可 数学物理学报. 1982 (2):  207-224.  摘要 ( 39 )   RICH HTML PDF(865KB) ( 150 )   收藏 Singular integrals of high order in complex integration were lifts introduced in[1] and investigated in[2,3,4]. Using this concept, the classical residue theorem was extended to such cases and was applied to solving certain class of singular integral equations. 相关文章 | 计量指标

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A METHOD OF THE RECURSIVE ESTIMATION WITHOUT INITIAL VALUE 汪咬元 数学物理学报. 1982 (2):  225-240.  摘要 ( 34 )   RICH HTML PDF(728KB) ( 16 )   收藏 In Kalman filtering the initial values X0, P0 should be known, but they are usually unknown. In[1] the recursive estimation problem without initial value is discussed when the state noise is white noise. 相关文章 | 计量指标