Singular nonhomogeneous quasilinear elliptic equations with a convection term

In this work we establish existence results for a class of nonhomogeneous and singular quasilinear elliptic equations involving a convection term. The gradient term makes the problem non variational, and in addition to this difficulty we have to handle the singular term with a sign changing nonlinearity. The proof of the results are made combining the sub‐super solution method, fixed point theorem, Leray–Schauder degree theory and comparison theorems.     

Single‐crystal X‐ray diffraction and resonant X‐ray magnetic scattering at helium‐3 temperatures in high magnetic fields at beamline P09 at PETRA III

The resonant scattering and diffraction beamline P09 at PETRA III at DESY is equipped with a 14 T vertical field split‐pair magnet. A helium‐3 refrigerator is available that can be fitted inside the magnet's variable‐temperature insert. Here the results of a series of experiments aimed at determining the beam conditions permitting operations with the He‐3 insert are presented. By measuring the tetragonal‐to‐orthorhombic phase transition occurring at 2.1 K in the Jahn–Teller compound TmVO₄, it is found that the photon flux at P09 must be attenuated down to 1.5 × 10⁹ photons s^?1 for the sample to remain at temperatures below 800 mK. Despite such a reduction of the incident flux and the subsequent use of a Cu(111) analyzer, the resonant X‐ray magnetic scattering signal at the Tm L_III absorption edge associated with the spin‐density wave in TmNi₂B₂C below 1.5 K is intense enough to permit a complete study in magnetic field and at sub‐Kelvin temperatures to be carried out.     

被动线谱检测的子带分解和分方位区间融合算法

目标辐射噪声中低频线谱丰富,而且谱级比高、强度稳定,相比调制谱检测具有优越性。基于子带分解处理的现有融合方法适用在信噪比相对较高情况下,而当干扰是相干的或强宽带信号时,对线谱目标有效检测仍没很好解决。本文从子带空间谱统计特性出发,利用线谱谱级高出连续谱10-25dB;线谱频带所在方位区间的输出方位波动小,而其他分区间的输出方位波动大特点,提出了一种在信噪比低,多目标并存情况下更有效的弱线谱提取融合方法。理论仿真和海试实验数据处理结果验证该方法具有创新性、较常规方位稳定算法适用范围更广、检测效果更好,适合工程应用。     

On a multivariable extension for the extended Jacobi polynomials

The main object of this paper is to construct a systematic investigation of a multivariable extension of the extended Jacobi polynomials and give some relations for these polynomials. We derive various families of multilinear and multilateral generating functions. We also obtain relations between the polynomials extended Jacobi polynomials and some other well-known polynomials. Other miscellaneous properties of these general families of multivariable polynomials are also discussed. Furthermore, some special cases of the results are presented in this study.     

On waiting time distributions associated with compound patterns in a sequence of multi-state trials

In this article, waiting time distributions of compound patterns are considered in terms of the generating function of the numbers of occurrences of the compound patterns. Formulae for the evaluation of the generating functions of waiting time are given, which are very effective computational tools. We provide several viewpoints on waiting time problems associated with compound patterns and develop a general workable framework for the study of the corresponding distributions. The general theory is employed for the investigation of some examples in order to illustrate how the distributions of waiting time can be derived through our theoretical results. This research was partially supported by the ISM Cooperative Research Program (2006-ISM·CRP-2007).     

On the matching polynomial of subdivision graphs

Let G be a simple graph and let S(G) be the subdivision graph of G, which is obtained from G by replacing each edge of G by a path of length two. In this paper, by the Principle of Inclusion and Exclusion we express the matching polynomial and Hosoya index of S(G) in terms of the matchings of G. Particularly, if G is a regular graph or a semi-regular bipartite graph, then the closed formulae of the matching polynomial and Hosoya index of S(G) are obtained. As an application, we prove a combinatorial identity.     

Instanton partition functions and M-theory

We discuss instanton partition functions in various spacetime dimensions. These partition functions capture some information about the spectrum of the supersymmetric gauge theories and their low-energy dynamics. Some of these theories can be defined microscopically only through string theory. Remarkably, they even know about the M-theory. Our conjectures include the identities between the generalization of the MacMahon formula and the character of M-theory, compactified down to 0 + 1 dimension. This article is based on the 5th Takagi Lectures that the author delivered at the University of Tokyo on October 4 and 5, 2008.     

On a class of renewal risk model with random income

In this paper, we consider a renewal risk process with random premium income based on a Poisson process. Generating function for the discounted penalty function is obtained. We show that the discounted penalty function satisfies a defective renewal equation and the corresponding explicit expression can be obtained via a compound geometric tail. Finally, we consider the Laplace transform of the time to ruin, and derive the closed‐form expression for it when the claims have a discrete K_m distribution (i.e. the generating function of the distribution function is a ratio of two polynomials of order m∈?⁺). Copyright © 2008 John Wiley & Sons, Ltd.     

Birkhoff‐Frink representations as functors

In an earlier article we characterized, from the viewpoint of set theory, those closure operators for which the classical result of Birkhoff and Frink, stating the equivalence between algebraic closure spaces, subalgebra lattices and algebraic lattices, holds in a many‐sorted setting. In the present article we investigate, from the standpoint of category theory, the form these equivalences take when the adequate morphisms of the several different species of structures implicated in them are also taken into account. Specifically, our main aim is to provide a functorial rendering of the Birkhoff‐Frink representation theorems for both single‐sorted algebras and many‐sorted algebras, by defining the appropriate categories and functors, covariant and contravariant, involved in the process (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)