The semigroup generated by a unitary orbit of a singular matrix

We investigate the structure of the multiplicative semigroup generated by the set of matrices that are unitarily equivalent to a given singular matrix A. In particular, we give necessary and sufficient conditions, in terms of the singular values of A, for such a semigroup to consist of all matrices of rank not exceeding the rank of A.     

Spectrum-Generating Symmetries for the Superpotentials Acot θ and Btanh y

The hierarchy of supersymmetric partner Schrödinger equations for the superpotentials Acot?θ and Btanh?y with A and B as half-integer and negative integer numbers are solved. The number of bound states for given trigonometric and hyperbolic potentials are infinite and finite, respectively. In addition to the spectrum-generating corresponding to the standard supersymmetry which is based on shifting potential parameter, there exist three other different methods for generating the spectrum. The first method is based on supersymmetrizing two given models via infinite and finite number of their bound states. This is realized by the ladder operators which shift only quantum numbers. The second and third methods are based on supersymmetrizing any of the models via all bound states corresponding to hierarchy of their partner potentials. They are respectively realized via simultaneous increasing or decreasing of quantum number and the potential parameter, and also, increasing one of them while decreasing the other. Any of the second and third methods leads to introducing two different classes of the algebraic solutions for both models.     

Characterizations of modalities and lex modalities

A reflective subuniverse in homotopy type theory is an internal version of the notion of a localization in topology or in the theory of ∞-categories. Working in homotopy type theory, we give new characterizations of the following conditions on a reflective subuniverse L: (1) the associated subuniverse $L^{\prime }$ of L-separated types is a modality; (2) L is a modality; (3) L is a lex modality; and (4) L is a cotopological modality. In each case, we give several necessary and sufficient conditions. Our characterizations involve various families of maps associated to L, such as the L-étale maps, the L-equivalences, the L-local maps, the L-connected maps, the unit maps ${\eta }_X$, and their left and/or right orthogonal complements. More generally, our main theorem gives an overview of how all of these classes related to each other. We also give examples that show that all of the inclusions we describe between these classes of maps can be strict.     

Primitive permutation groups with a regular subgroup

This paper starts the classification of the primitive permutation groups (G,Ω) such that G contains a regular subgroup X. We determine all the triples (G,Ω,X) with soc(G) an alternating, or a sporadic or an exceptional group of Lie type. Further, we construct all the examples (G,Ω,X) with G a classical group which are known to us. Our particular interest is in the 8-dimensional orthogonal groups of Witt index 4. We determine all the triples (G,Ω,X) with . In order to obtain all these triples, we also study the almost simple groups G with GPΩ_2n+1(q). The case GU_n(q) is started in this paper and finished in [B. Baumeister, Primitive permutation groups of unitary type with a regular subgroup, Bull. Belg. Math. Soc. 112 (5) (2006) 657–673]. A group X is called a Burnside-group (or short a B-group) if each primitive permutation group which contains a regular subgroup isomorphic to X is necessarily 2-transitive. In the end of the paper we discuss B-groups.     

Factoring an infinite abelian group by lacunary cyclic subsets

It was proved in Corrádi and Szabó (Math Pannonica 5:275–280, 1994) that if a finite abelian group of odd order is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper extends this result for certain infinite torsion groups.      

求分块鳞状因子循环矩阵逆矩阵的一种快速算法

给出了一种计算分块鳞状因子循环矩阵逆矩阵的快速算法,该算法主要利用了离散傅立叶变换和对角块矩阵求逆的递归算法,与标准的利用LU分解法求逆的算法相比,在计算复杂性上有很大的优势.     

Source Apportionment Research of Fine Particulate Matter in the Atmosphere by PAHs

Haze weather frequently occurs in many cities in China. Polycyclic aromatic hydrocarbons(PAHs) in fine particulate matter(PM_2.5) can adversely affect the environment and human health. In this paper, PM_2.5 samples were collected at nine sites in a city in northeastern China from September 2013 to October 2014. Sixteen USEPA(US Evironment Protection Agency) priority PAHs in PM_2.5 were analyzed to determine their spatial and temporal distribution characteristics. The source apportionment of PAHs was conducted with the Positive Matrix Factorization(PMF) model. The results indicate that the concentrations of total PAHs(T-PAHs) in PM_2.5 are within the range of 0.26 to 72.48 ng/m³. The seasonal variation of T-PAHs is winter >spring >autumn >summer, and the space distribution of PAHs is JZP >DP >BFH >LP >EESA >IPT >CP >HZMC >JYP. In all types of PAHs, three-ring and five-ring PAHs are significantly prominent(62%) in the heating period due to petrogenic sources and traffic emissions. Middle- and high-ring PAHs in the non-heating period are caused by coal combustion and vehicle exhaust, which accounts for 77% of the total emissions. The source apportionment results obtained by the diagnostic ratio of PAHs reflect that coal burning, traffic and other sources have a distinct influence on PAH emissions in this city. Six factors are defined by PMF v5.0, namely, coke oven emissions(7.7%), biomass burning(44.3%), petrogenic sources(10.7%), coal combustion(10.4%), gasoline engine emissions(16.7%), and diesel engine emissions(10.3%). The results indicate that the PAHs in PM_2.5 in the city are primarily caused by combustion processes and vehicle exhaust.     

Block ILU Preconditioners for a Nonsymmetric Block-Tridiagonal M-Matrix

We propose block ILU (incomplete LU) factorization preconditioners for a nonsymmetric block-tridiagonal M-matrix whose computation can be done in parallel based on matrix blocks. Some theoretical properties for these block ILU factorization preconditioners are studied and then we describe how to construct them effectively for a special type of matrix. We also discuss a parallelization of the preconditioner solver step used in nonstationary iterative methods with the block ILU preconditioners. Numerical results of the right preconditioned BiCGSTAB method using the block ILU preconditioners are compared with those of the right preconditioned BiCGSTAB using a standard ILU factorization preconditioner to see how effective the block ILU preconditioners are.     

绕旋转圆柱流动涡尾流结构和临界状态特性

采用作者提出的基于区域分解，有限差分法与涡法杂交的数值方法，结合高阶隐式差分格式，和以修正的不完全ＬＵ分解为预处理器的共轭梯度法作求解器，系统地研究了雷诺数Ｒｅ＝１０００，旋转速度比α∈（０．５，３．２５）范围内，绕旋转圆柱从突然起到充分发展，长时间内尾流旋涡结构和阻力，升力系数的变化规律，计算所得流动图案与实验流场显示符合很好。数值试验证帝了临界状态的存在，并首次给出了临界状态时的旋涡结构特性。