Theoretical analysis of the possible ultra-low-Q-value decay branch of Cs

We have investigated the feasibility of observing an ultra-low-Q-value beta-decay branch of ¹³⁵Cs by applying the microscopic quasiparticle-phonon model with a realistic two-body nuclear interaction. This work was motivated by an earlier combined experimental and theoretical work on decays of ¹¹⁵In. The inaccuracy of the ground-state-to-ground-state Q value limits our ability to draw definite conclusions, and therefore modern precision measurements for it are called for. We present the computed partial half-lives of each channel for the most likely ranges of Q values.     

天然黄铁矿光吸收特征

以天然黄铁矿为样本,用Cary 500型紫外可见近红外分光光度计在200～2 000 nm范围内测出了样品的吸收谱和反射谱,计算出了吸收系数,并根据Tauc规则算出了样品的禁带宽度.结果表明:所测天然黄铁矿光吸收系数在105数量级;在吸收图谱中出现了明显的肩行结构,可以判断样品属于间接禁带半导体,其禁带宽度为0.64 ...     

Nonstandard second-order arithmetic and Riemannʼs mapping theorem

In this paper, we introduce systems of nonstandard second-order arithmetic which are conservative extensions of systems of second-order arithmetic. Within these systems, we do reverse mathematics for nonstandard analysis, and we can import techniques of nonstandard analysis into analysis in weak systems of second-order arithmetic. Then, we apply nonstandard techniques to a version of Riemannʼs mapping theorem, and show several different versions of Riemannʼs mapping theorem.     

A generalization of a conservativity theorem for classical versus intuitionistic arithmetic

A basic result in intuitionism is Π⁰₂‐conservativity. Take any proof p in classical arithmetic of some Π⁰₂‐statement (some arithmetical statement ?x.?y.P(x, y), with P decidable). Then we may effectively turn p in some intuitionistic proof of the same statement. In a previous paper [1], we generalized this result: any classical proof p of an arithmetical statement ?x.?y.P(x, y), with P of degree k, may be effectively turned into some proof of the same statement, using Excluded Middle only over degree k formulas. When k = 0, we get the original conservativity result as particular case. This result was a by‐product of a semantical construction. J. Avigad of Carnegie Mellon University, found a short, direct syntactical derivation of the same result, using H. Friedman's A‐translation. His proof is included here with his permission. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Restricted signed permutations counted by the Schröder numbers

Gire, West, and Kremer have found ten classes of restricted permutations counted by the large Schröder numbers, no two of which are trivially Wilf-equivalent. In this paper we enumerate eleven classes of restricted signed permutations counted by the large Schröder numbers, no two of which are trivially Wilf-equivalent. We obtain five of these enumerations by elementary methods, five by displaying isomorphisms with the classical Schröder generating tree, and one by giving an isomorphism with a new Schröder generating tree. When combined with a result of Egge and a computer search, this completes the classification of restricted signed permutations counted by the large Schröder numbers in which the set of restrictions consists of two patterns of length 2 and two of length 3.     

一个矩阵不等式和Bayes无偏估计（英）

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Existence test for solution of nonlinear systems applying affine arithmetic

A computational test is proposed for existence of solution in nonlinear systems. In this test, an interval inclusion of Newton mapping is estimated applying affine arithmetic. Numerical examples are presented to show the efficiency of this test.     

The small octagon with longest perimeter

The convex octagon with unit diameter and maximum perimeter is determined. This answers an open question dating from 1922. The proof uses geometric reasoning and an interval arithmetic based global optimization algorithm to solve a series of non-linear and non-convex programs involving trigonometric functions.