Why Matter Occupies so Large a Volume？

The paper represents a rigorous treatment of the underlying quantum theory, not just in words but providing the underlying technical details, as to why matter occupies so large a volume and its intimate connection with the Pauli exclusion principle, as more and more matter is put together, as well as of the contraction or shrinkage of ＂bosonic matter＂, upon collapse, for which the Panli exclusion is abolished. From the derived explicit bounds of integrals of powers of the particle number densities, explicit bounds on probabilities of the occurrences of the events just described are extracted. These probabilities lead one to infer the change of the ＂size＂ or extension of such matter, upon expansion or contraction, respectively, as their content is increased.     

超导体/正常金属/半导体/正常金属/超导体结的研究

在约瑟夫逊效应的理论研究中,大体上有微观和宏观两种方法。采用的是宏观的方法。利用推广的Ja-cobson方法,讨论了超导体/正常金属/半导体/正常金属/超导体结的约瑟夫逊效应,并在小电流假设下,推导出了该结的电流密度与位相之间的关系。     

Wolfe Duality for Interval-Valued Optimization

Weak and strong duality theorems in interval-valued optimization problem based on the formulation of the Wolfe primal and dual problems are derived. The solution concepts of the primal and dual problems are based on the concept of nondominated solution employed in vector optimization problems. The concepts of no duality gap in the weak and strong sense are also introduced, and strong duality theorems in the weak and strong sense are then derived.     

Gâteaux differentiability of the dual gap function of a variational inequality

In terms of the mapping involved in a variational inequality, we characterize the Gâteaux differentiability of the dual gap function G and present several sufficient conditions for its directional derivative expression, including one weaker than that of Danskin [J.M. Danskin, The theory of max–min, with applications, SIAM Journal on Applied Mathematics 14 (1966) 641–664]. When the solution set of a variational inequality problem is contained in that of its dual problem, the Gâteaux differentiability of G on the latter turns out to be equivalent to the conditions appearing in the authors’ recent results about the weakly sharp solutions of the variational inequality problem.     

Detection of copper(II) sulfate’s uniformity and its thermal behavior in flammability of cotton fabric

Blue vitriol (copper(II) sulfate pentahydrate), CuSO₄·5H₂O has been chosen and investigated for its effectiveness as a flame-retardant, when impregnated into cotton fabric (cotton with a plain structure; woven 180 g m⁻², with 22 numbers of yarns per 10 mm). Using the vertical flame test, the extent of resistance to burning of the specimens has been determined. The impregnation was accomplished via dipping and stirring of bone-dried, weighed fabrics into the individual and suitable concentrations of the salt at room temperature. Afterwards the samples were squeeze rolled and dried horizontally at 110°C for 30 min in an oven and cooled in a desiccator and reweighed with an analytical precision. They were then kept under ordinary conditions overnight prior the fulfillment of the vertical flame test. The efficient quantities of the aforesaid salt expressed in g per 100 g dry fabric have been determined in an average figure of 12.75%. Estimation of uniformity in a selected sample was carried out via a spectrophotometer and results are in favor of the heterogeneous distribution of the salt in the fabric’s middle sectors. However initial and final parts of specimen showed to be rather uniformed. Thermogravimetric analysis of the pure cotton and the treated ones with insufficient and effective amounts of the salt were fulfilled and their thermograms were compared and commented. The results obtained for the effect of copper(II) sulfate comply with ‘The Dust or Wall Effect Theory’. This action is also assigned to the condensed phase retardation.     

Radical of weakly ordered semigroup algebras

We define the notion of weakly ordered semigroups. For this class of semigroups, we compute the radical of the semigroup algebras. This generalizes some results on left regular bands and on 0- Hecke algebras.     

弱双曲流形的逼近

弱双曲流形是一类包含中心流形作为其特例的不变流形.本文讨论了它的逼近问题,不仅给出了计算其逼近的方法,还估计了使得这一逼近有效的它的局部性半径. 同时给出了一个具体实例来展示这些计算和估计.     

A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions

We provide sufficient conditions for the convergence of the Newton-like methods in the assumption that the derivative satisfies some kind of weak Lipschitz conditions. Consequently, some important convergence theorems follow from our main result in this paper.     

A convergence result in the study of bone remodeling contact problems

We consider the approximation of a bone remodeling model with the Signorini contact conditions by a contact problem with normal compliant obstacle, when the obstacle's deformability coefficient converges to zero (that is, the obstacle's stiffness tends to infinity). The variational problem is a coupled system composed of a nonlinear variational equation (in the case of normal compliance contact conditions) or a variational inequality (for the case of Signorini's contact conditions), for the mechanical displacement field, and a first-order ordinary differential equation for the bone remodeling function. A theoretical result, which states the convergence of the contact problem with normal compliance contact law to the Signorini problem, is then proved. Finally, some numerical simulations, involving examples in one and two dimensions, are reported to show this convergence behaviour.     

WEAK CONVERGENCE OF SOME DIRICHLET SERIES

1 Besicovitch Inner ProductIll this paper, we consider Dirichlet serie8where an, tL = 1, 2,' ', are complex nunlbers. They are Besicovitch almost periodic functionsWe see the 8ystenl {e.(t); e.(t) = e--it Iog 1l, 71 = l, 2,' .} fOrnis a1l orthollor11la1 systelll witl1respect to tI1e BesicovitcI1 iIl1ler productThell we call fOrm the gelleralized trigouolnetrical polynolIlialsAccording to tl1e idea developed il1 [l],[2], auy Dirichlet seriesis weakly convergent over K witll respect to …