Polynomial growth and identities of superalgebras and star-algebras

We study associative algebras with 1 endowed with an automorphism or antiautomorphism φ of order 2, i.e., superalgebras and algebras with involution. For any fixed k≥1, we construct associative φ-algebras whose φ-codimension sequence is given asymptotically by a polynomial of degree k whose leading coefficient is the largest or smallest possible.     

Random and Exhaustive Generation of Permutations and Cycles

In 1986 Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well known. We consider both methods in a unified way, and discuss their relation with exhaustive generation methods. We analyse several random variables associated with the algorithms and find their grand probability generating functions, which gives easy access to moments and limit laws.      

Cremona transformations and the conundrum of dimensionality and signature of macro-spacetime

The issue of dimensionality and signature of the observed universe is analysed. Neither of the two properties follows from first principles of physics, save for a remarkably fruitful Cantorian fractal spacetime approach pursued by El Naschie, Nottale and Ord. In the present paper, the author's theory of pencil-generated spacetime(s) is invoked to provide a clue. This theory identifies spatial coordinates with pencils of lines and the time dimension with a specific pencil of conics. Already its primitive form, where all pencils lie in one and the same projective plane, implies an intricate connection between the observed multiplicity of spatial coordinates and the (very) existence of the arrow of time. A qualitatively new insight into the matter is acquired, if these pencils are not constrained to be coplanar and are identified with the pencils of fundamental elements of a Cremona transformation in a projective space. The correct dimensionality of space (3) and time (1) is found to be uniquely tied to the so-called quadro-cubic Cremona transformations – the simplest non-trivial, non-symmetrical Cremona transformations in a projective space of three dimensions. Moreover, these transformations also uniquely specify the type of a pencil of fundamental conics, i.e. the global structure of the time dimension. Some physical and psychological implications of these findings are mentioned, and a relationship with the Cantorian model is briefly discussed.     

One-point suspensions and wreath products of polytopes and spheres

It is known that the suspension of a simplicial complex can be realized with only one additional point. Suitable iterations of this construction generate highly symmetric simplicial complexes with various interesting combinatorial and topological properties. In particular, infinitely many non-PL spheres as well as contractible simplicial complexes with a vertex-transitive group of automorphisms can be obtained in this way.     

Exponent and p-rank of finite p-groups and applications

We bound the order of a finite p-group in terms of its exponent and p-rank. Here the p-rank is the maximal rank of an abelian subgroup. These results are applied to defect groups of p-blocks of finite groups with given Loewy length. Doing so, we improve results in a recent paper by Koshitani, Külshammer, and Sambale. In particular, we determine possible defect groups for blocks with Loewy length 4.     

Non-Archimedean Analogues of Orthogonal and Symmetric Operators and p-adic Quantization

We study orthogonal and symmetric operators in non-Archimedean Hilbert spaces in the connection with p-adic quantization. This quantization describes measurements with finite precision. Symmetric (bounded) operators in the p-adic Hilbert spaces represent physical observables. We study spectral properties of one of the most important quantum operators, namely, the operator of the position (which is represented in the p-adic Hilbert L₂-space with respect to the p-adic Gaussian measure). Orthogonal isometric isomorphisms of p-adic Hilbert spaces preserve precisions of measurements. We study properties of orthogonal operators. It is proved that each orthogonal operator in the non-Archimedean Hilbert space is continuous. However, there exist discontinuous operators with the dense domain of definition which preserve the inner product. There also exist nonisometric orthogonal operators. We describe some classes of orthogonal isometric operators and we study some general questions of the theory of non-Archimedean Hilbert spaces (in particular, general connections between topology, norm and inner product).     

Approximation and optimization of higher order discrete and differential inclusions

This paper is mainly concerned with the necessary and sufficient conditions of optimality for Cauchy problem of higher order discrete and differential inclusions. Applying optimality conditions of problems with geometric constraints, for arbitrary higher order (say s-order) discrete inclusions optimality conditions are formulated. Also some special transversality conditions, which are peculiar to problems including third order derivatives are formulated. Formulation of sufficient conditions both for convex and non-convex discrete and differential inclusions are based on the apparatus of locally adjoint mappings. Furthermore, an application of these results is demonstrated by solving the problems with third order linear discrete and differential inclusions.     

Singular integrals and weighted Triebel-Lizorkin and Besov spaces of arbitrary number of parameters

Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderón's identity. This is inspired by the work of discrete Littlewood-Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe's covering lemma in multiparameter setting.     

Dirichlet函数与Riemann函数的性质及应用

探讨Dirichlet函数和Riemann函数的连续性、可导性和可积性,并由此分别构造出在一点连续、多点连续、一点可导、多点可导的函数.     

Anticoloring and separation of graphs

An anticoloring of a graph is a coloring of some of the vertices, such that no two adjacent vertices are colored in distinct colors. The anticoloring problem seeks, roughly speaking, such colorings with many vertices colored in each color. We deal with the anticoloring problem for planar graphs and, using Lipton and Tarjan’s separation algorithm, provide an algorithm with some bound on the error. We also show that, to solve the anticoloring problem for general graphs, it suffices to solve it for connected graphs.     

Validation and generalization of DEA and its uses

Summary Rapidly expanding uses of DEA have been accompanied by developments which have enhanced its power and enlarged its utility for additional applications. Developments covered in the present paper include simulation studies comparing DEA with competing forms of statistical regressions. Other studies covered show how these two approaches can be combined in complementary fashion. Another part of this paper deals with Chance Constrained Programming formulations which incorporate probabilistic elements into DEA. Included also are discussions of statistical characterizations with accompanying tests of statistical significance for DEA efficiency evaluations. This paper concludes with uses of DEA in “discovery processes”-processes that need strengthening (and encouragemnt) in contemporary social science and management science research. Suggestions are made for additional research on further developments which extend to uses of DEA to provide new approaches in economics (including econometrics), management and psychology and an Appendix introduces new or recently developed efficiency measures for use in DEA. Invited by J. T. Pastor     

Coverings of Graphs and Maps, Orthogonality, and Eigenvectors

Lifts of graph and map automorphisms can be described in terms of voltage assignments that are, in a sense, compatible with the automorphisms. We show that compatibility of ordinary voltage assignments in Abelian groups is related to orthogonality in certain -modules. For cyclic groups, compatibility turns out to be equivalent with the existence of eigenvectors of certain matrices that are naturally associated with graph automorphisms. This allows for a great simplification in characterizing compatible voltage assignments and has applications in constructions of highly symmetric graphs and maps.     

模糊数的相等、同一与等式限定运算

讨论了在模糊数运算中相等与同一的区别,在Klir的模糊数限定运算基础上提出了模糊数的等式限定运算以及等式限定运算的结构元表示方法,解决了传统模糊数运算的不可逆问题.通过模糊数的结构元表示方法,将其等式限定运算转换为两个同序单调函数的运算,这不仅仅给出等式限定运算的可操作形式,同时对于求解模糊数方程也给出了具体的计算方法.     

Stability and bifurcation of an SIVS epidemic model with treatment and age of vaccination

In this paper, we consider a two-dimensional SIS model with vaccination. It is assumed that vaccinated individuals become susceptible again when vaccine loses its protective properties with time. Here the rate at which vaccinated individual move to susceptible class again, depends upon vaccine age and hence it is assumed to be a variable. This SIVS model with treatment exhibits backward bifurcation under certain conditions on treatment which complicate the criteria for the success of the treatment by making it possible to have stable endemic states. We also show how the infectivity and the recovery function affect the existence of backward bifurcation.     

Liapunov functions and boundedness and global existence of solutions

In this paper the properties of a Liapunov function and its derivatives are combined in obtaining sufficient conditions for the boundedness and global existence of solutions of the system of differential equations

x=f(t,x) (1)

where f: [0,∞)XRⁿ→ Rⁿ is continuous. The following terms are introduced: (i) a scalar function which is mildly unbounded relative to a subset of Rⁿ,(ii) a scalar function which is radially unbounded relative to a set, (iii) a Liapunov function with mildly negative definite derivative in a set, (iv) a Liapunov function with strongly negative definite derivative in a set, and (v) a set which is unbounded-departing with respect to system (1). As a special case the autonomous system of differential equations which corresponds to (1) is considered and the semi-invariance property of the positive limiting set of a solution is used in the results     

青年科技人才绩效评价系统的设计与实现

基于青年科技人才的发展需要与成长特点,设计绩效评价指标与系统模型,并通过几个主要功能模块的分工与流程,结合系统软件的参数设置与运算,实现青年科技人才公正、全面、合理的绩效评价,以执行相对公平的绩效考核、职位晋升与薪酬发放,激励青年科技人才潜心、高效、创造性地投身科研工作,从而内发性、长效性地为企业的自主创新与蓬勃发展提供充足的动力。     

Probabilistic modeling and simulation of multiple surface crack propagation and coalescence

In the low cycle fatigue (LCF) regime, fatigue failure of metallic materials with high strength and less impurities generally dominates by multiple surface crack propagation and coalescence, in which its final failure shows a stochastic nature on crack initiation, propagation and coalescence under cyclic loadings. According to this, the competing failure modes of multiple surface cracks and interior cracks are studied through coupling numerical simulations with fracture mechanics methods. In particular, a probabilistic procedure for modeling multiple surface crack propagation and coalescence is established by incorporating Monte Carlo simulation with experimental evidences, including surface crack density and crack length distributions measured from LCF replica tests of 30NiCrMoV12 steel. In addition, it calculates the probability of coalescence of neighboring cracks with allowance for their interactions and local plastic deformation at the crack tips. Finally, it estimates the remaining usage lives of specimens from initial state to critical cracks by propagation and coalescence of dispersed cracks.     

城市创新能力评价及时空格局演化研究

采用熵值法、基尼系数、探索性空间统计分析等方法从时间、空间两个维度对2007-2016年中国35个大中城市创新能力的评价、时空格局与演化规律进行了可视化分析。结果表明:(1)从时间维度看,大中城市创新能力在先期提升明显,末期有所回落,但仍呈现出整体上的提升;知识创新能力>政府支持与服务>创新基础环境>技术创新能力,技术短板突出;城市间创新能力的差异有向优化均衡方向发展的趋势,但创新基础环境的空间失衡加剧;G2> G1、G4> G3,城市之间创新能力的差异主要集中在技术创新能力上。(2)从空间维度看,莫兰检验显示样本期内城市创新能力存在显著的空间自相关性;与先期相比,2016年创新能力高水平城市数量增加,且表现出了更强的空间"集群化"特征,总体上呈现出"东高西低"的空间格局,具有明显的经济依赖性;样本期内大中城市创新能力的局部集聚模式变化不大,体现出一定的时空惯性,且高高集聚模式的城市具有较强的经济依赖特征;创新冷热点总体上呈"东热西冷"的空间分布格局。     

On the Existence and Uniqueness of Solution of MRE and Applications

In this paper, we study the existence and uniqueness of the solution for Markov renewal equation (MRE) of a semi-Markov process with countable state space. This method and its proof are based on an iterative scheme. A numerical solution is also given as well as a case study on system reliability assessment.     

Symmetry and nonexistence of positive solutions of elliptic equations and systems with Hardy terms

We prove some symmetry property for equations with Hardy terms in cones, without any assumption at infinity. We also show symmetry property and nonexistence of entire solutions of some elliptic systems with Hardy weights.