Integral Representations for the Deflection and the Slope of a Plate on an Elastic Foundation

With the help of two fundamental solutions, integral representations for the deflection and the slope of polygonal shaped plates on an elastic foundation are derived. The kernel functions are evaluated in terms of zero-order Kelvin- or Thomson-functions and their derivatives, respectively. This revised version was published online in August 2006 with corrections to the Cover Date.     

Exploring correlations in the stochastic Yang–Mills vacuum

The correlation lengths of nonperturbative-nonconfining and confining stochastic background Yang–Mills fields are obtained by means of a direct analytic path-integral evaluation of the Green functions of the so-called one- and two-gluon gluelumps. Numerically, these lengths turn out to be in a good agreement with those known from the earlier, Hamiltonian, treatment of such Green functions. It is also demonstrated that the correlation function of nonperturbative-nonconfining fields decreases with the deviation of the path in this correlation function from the straight-line one.     

Algebras, Projective Geometry, Mathematical Logic, and Constructing the World: Intersections in the Philosophy of Mathematics of A. N. Whitehead

A. N. Whitehead (1861–1947) contributed notably to the foundations of pure and applied mathematics, especially from the late 1890s to the mid 1920s. An algebraist by mathematical tendency, he surveyed several algebras in his book Universal Algebra (1898). Then in the 1900s he joined Bertrand Russell in an attempt to ground many parts of mathematics in the newly developing mathematical logic. In this connection he published in 1906 a long paper on geometry, space and time, and matter. The main outcome of the collaboration was a three-volume work, Principia Mathematica (1910–1913): he was supposed to write a fourth volume on parts of geometries, but he abandoned it after much of it was done. By then his interests had switched to educational issues, and especially to space and time and relativity theory, where his earlier dependence upon logic was extended to an ontology of events and to a general notion of “process,” especially in human experience. These innovations led to somewhat revised conceptions of logic and of the philosophy of mathematics. © 2002 Elsevier Science (USA).A. N. Whitehead (1861–1947) contribuiu de forma marcante para os Fundamentos da Matemática Pura e Aplicada, especialmente entre o fim da década de 1890 e meados da década de 1920. Sendo um algebrista na sua vertente matemática, fez um levantamento de diversas álgebras no seu livro Universal Algebra (1898). Pouco depois de 1900 juntou-se a Bertrand Russell numa tentativa para basear várias partes da matemática sobre a lógica matemática, que se começava então a desenvolver. Nesse âmbito publicou em 1906 um longo artigo sobre geometria, espaço e tempo, e matéria. O principal resultado da colaboração foi um trabalho em três volumes, Principia Mathematica (1910–1913): estava previsto que Whitehead escrevesse um quarto volume sobre aspectos das geometrias, mas abandonou-o depois de uma boa parte já estar escrita. Por essa altura os seus interesses tinham-se voltado para questões educacionais; especialmente para o espaço e o tempo e para a teoria da relatividade, onde a sua anterior dependência da lógica se estendeu a uma ontologia de acontecimentos e a uma noção geral de “processo” especialmente na experiência humana. Estas inovações levaram a concepções um pouco revistas da lógica e da filosofia da matemática. © 2002 Elsevier Science (USA).MSC 1991 subject classifications: 00A30; 01A60; 03-03; 03A05.     

A new theorem of information theory

Consider a random experiment whose possible outcomes arez ₁,z ₂,...,z _n. Let the prior probabilities be p₁ ⁰, ...,p_n ⁰, and let the posterior probabilities bep ₁,...,p _n. It is shown that, subject to certain prescribed and intuitively reasonable conditions, the expressionI =k p _i In (p _i/p _i ⁰), wherek is a positive constant, is the unique expression for the information contained in a message which alters the probabilities from thep _i ⁰ to thep _i.     

A new approach for the justification of ensembles in quantum statistical mechanics — II

The results of the first paper in this series are generalized to include spin, permutation symmetry, and time dependence. In particular, the question of time invariance of localness in the Heisenberg picture is discussed and it is conjectured that an operator that is initially local will remain local over time. In order to treat macroscopic systems, it is shown that the ensemble decomposition of the previous paper can be used to coarsegrain configuration space. Finally, a physical interpretation of the ensemble decomposition in terms of redundant macroscopic information is used to give a derivation of the generalized microcanonical average.This work was supported in part by research grants from the National Science Foundation and the U.S. Public Health Service. Some of the material in this paper is contained in a doctoral dissertation submitted by the author to the University of Oregon (1969).     

Consistent Quantum Realism: A Reply to Griffiths

We call attention on the fact that we have already replied to the criticisms put forward by R. B. Griffiths to our position about decoherent histories.     

地铁隧道施工诱发桩基变形的数值仿真分析

利用数值分析软件ANSYS建立弹塑性有限元模型;考虑位于区间隧道轴线不同位置的邻近桩基及不同桩长情况,对区间隧道施工诱发邻近桩基的变形进行数值仿真试验分析,同时分析隧道开挖后土体与桩体参数等因素对邻近桩基变形的影响。数值仿真试验结果表明：地铁隧道开挖后桩体发生倾倒变形,桩端与洞轴线的相对位置及桩端土性对桩基变形有明显的影响,有桩侧隧道周围向洞内的水平位移比无桩侧的水平位移小,且随桩长增加,两者差别增大。     

基于弹塑性有限元分析土工安定性计算方法及其应用

将弹塑性有限元法与安定性分析的Melan静力型定理相结合发展了一种土工极限分析与安定性分析的数值计算方法,依此可以预测一般土工结构 极限荷载和安定荷载,利用弹塑性分析求解弹塑性应力场与弹性应力场,构造安定性分析所需的残余应力场,摆脱了传统分析方法中的大型数学规划运算,解决了计算中的维数障碍问题,残余应力场的构造与土工结构的弹塑性分析是同时进行的,而且无需对屈服面进行线性化处理,求解的精度依赖于弹缔造性分析,通过算例,验证分析方法与计算程序是可靠的,并利用此方法计算了条形地基的极限荷载与安定荷载。     

Pancharatnam phase of two Cooper-pair boxes in a dissipative cavity

The time evolution of a single Cooper pair in the presence of another Cooper pair interacting with an electromagnetic field in a dissipative cavity is presented. The strong dependence of the dynamics of two superconducting charge qubits interacting with the microcavity field on the instantaneous phase shift experienced by the second qubit is demonstrated. The Pancharatnam phase is found to be more sensitive than the population dynamics to the phase shift. This leads us to suggest a new technique for controlling the system dynamics. Furthermore, although the atom is not directly coupled to the cavity modes, its coherent properties are found to be strongly influenced by dissipation, both qualitatively and quantitatively.     

Nonrelativistic Quantum Mechanics with Spin in the Framework of a Classical Subquantum Kinetics

Recently it has been shown that the spinless one-particle quantum mechanics can be obtained in the framework of entirely classical subquantum kinetics. In the present paper we argue that, within the same scheme and without any extra assumption, it is possible to obtain both the nonrelativistic quantum mechanics with spin, in the presence of an arbitrary external electromagnetic field, as well as the nonlinear quantum mechanics.