Digraphs with at most one trivial critical ideal

Critical ideals generalize the critical group, Smith group and the characteristic polynomials of the adjacency and Laplacian matrices of a graph. We give a complete characterization of the digraphs with at most one trivial critical ideal. Which implies the characterizations of the digraphs whose critical group has one invariant factor equal to one, and the digraphs whose Smith group has one invariant factor equal to one.     

Commutative Standard Table Algebras with at Most One Nontrivial Multiplicity

We classify commutative standard table algebras (STA) with at most one nontrivial multiplicity. The main result shows that there exists exactly one nontrivial multiplicity if and only if the table basis is the wreath product of a two-dimensional subalgebra and an abelian group. The theorem applies to adjacency algebras of commutative association schemes with exactly one primitive idempotent matrix of rank greater than one. A theorem of Seitz that characterizes finite groups with exactly one irreducible representation of degree greater than one is another corollary of the main theorem.     

The Advanced Australian Shuffle

The “classical” Australian under-down shuffle starts with a deck of n cards. Then one proceeds as follows: one card under the deck, one on the table, one under the deck, one on the table, etc. One continues until only one card remains. There is an explicit formula to calculate the number of the card in the original deck that survives, and this is the basis of several mathematical magic tricks.     

Two regularity criteria for the 3D MHD equations

This work establishes two regularity criteria for the 3D incompressible MHD equations. The first one is in terms of the derivative of the velocity field in one direction while the second one requires suitable boundedness of the derivative of the pressure in one direction.     

Lower bounds on the number of scattering poles under lines parallel to the axis

We provide lower bounds in slab domains on the number of scattering poles, generated by two different types of periodic non-hyperbolic rays. For the first one all eigenvalues of the corresponding Poincaré map are equal to one and for the second one two of the eigenvalues are equal to one and two are different from one. In the second case we find also the closest to the real axis “line of poles”     

Rank one preservers between spaces of Boolean matrices

In this paper, we characterize (i) linear transformations from one space of Boolean matrices to another that send pairs of distinct rank one elements to pairs of distinct rank one elements and (ii) surjective mappings from one space of Boolean matrices to another that send rank one matrices to rank one matrices and preserve order relation in both directions. Both results are proved in a more general setting of tensor products of two Boolean vector spaces of arbitrary dimension.     

Bifurcation of rough heteroclinic loop with orbit and inclination flips

In this paper, we are concerned with the heteroclinic loop bifurcations accompanied by one orbit flip and one inclination flip under some roughness conditions. The existence of one 1-periodic orbit, one 1-homoclinic orbit, two 1-periodic orbits, one double 1-periodic orbit is obtained, respectively, approximate expressions of the corresponding bifurcation curves (or surfaces) and the corresponding bifurcation graphs under nontwisted or twisted conditions are also given.     

About one - an inquiry about the meanings and uses of the number one

The story of the number one is told. The long struggle to recognize one as a number is described. The role of the number one in philosophy, religion, mathematics and science is briefly discussed. Finally, the relationship between one and some other numbers is presented.     

对主成分分析法三个问题的剖析

从主成分分析法的基本原理入手,针对教学过程中学生对主成分分析法感到费解的三个问题进行了逐一剖析:1.为什么主成分系数是经标准差标准化后原始变量的协方差矩阵的特征向量?2.特征向量正负号如何选取?对进一步的研究如计算综合得分和聚类分析有何影响?3.主成分载荷值是如何得来的?同时指出有些教材在计算主成分得分时混淆了主成分载荷和特征向量的概念,以致造成错误的结果.     

Genus one knots which admit (1,1)-decompositions

We determine the knot types of genus one knots which admit genus one, one bridge decompositions.

     

迹稳定秩一的C~*-代数

本文引入了一类迹稳定秩一的C*-代数,证明了迹稳定秩一的C*-代数与AF-代数的张量积是迹稳定秩一的,得到了一个可分的单的有单位元的迹稳定秩一的,并且具有SP性质的C*-代数是稳定秩一的.同时,还讨论了迹稳定秩一的C*-代数的K-群的某些性质.     

Prime Ideals in Near-Rings

An ideal I of a near-ring R is a type one prime ideal if whenever a Rb ? I, then a ∈ I or b ∈ I. This paper considers the interconnections between prime ideals and type one prime ideals in near-rings. It also develops properties of type one prime ideals, gives several examples illustrating where prime and type one prime are not equivalent, and investigates the properties of the type one prime radical. Several different types of conditions are given which guarantee that a prime ideal is type one. The class of all near-rings for which each prime ideal is type one is investigated and many examples of such near-rings are exhibited. Various localized distributivity conditions are found which are useful in establishing when prime ideals will be type one prime.     

Nonlinear equations of a variable type

In the paper one gives a survey of the investigations regarding, basically one-dimensional, model equations of the Navier-Stokes type with a variable nonlinear viscosity, including sign-changing viscosity. For concrete dependences of the viscosity on the velocity gradient, one establishes a priori estimates, one carries out a numerical investigation and one formulates results regarding the uniqueness of the solution.     

A survey of game-theoretic models of cooperative advertising

The paper surveys the literature on cooperative advertising in marketing channels (supply chains) using game theoretic methods. During the last decade, in particular, this literature has expanded considerably and has studied static as well as dynamic settings. The survey is divided into two main parts. The first one deals with simple marketing channels having one supplier and one reseller only. The second one covers marketing channels of a more complex structure, having more than one supplier and/or reseller.     

On unequal powers of primes and powers of 2

We consider Linnik’s type of the Waring–Goldbach problem with unequal powers of primes. In particular, it is proved that every sufficiently large even integer can be represented as a sum of one prime, one square of prime, one cube of prime, one fourth power of prime and 18 powers of 2.     

Bifurcations of heterodimensional cycles with two saddle points

The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.     

下层独立的一主多从双层随机线性规划问题研究

Herminia I.Calvete等研究了一主多从双层确定性线性规划问题,证明了这类问题等价于一类常规的双层线性规划问题.本文在此基础上,推广确定型的问题到随机型优化情况,考虑了一类下层优化相互独立的一主多从双层随机优化问题(SLBMFP).在特定的随机变量分布条件下,理论上证明了该类问题可以转化为一主一从双层确定性优化问题.本文的研究对于求解一主多从双层随机优化模型,解决此类模型在实际应用中的问题具有一定的意义.     

On the point spectrum of periodic Jacobi matrices with matrix entries: elementary approach

This work consists of two parts. The first one contains a characterization (localization) of the point spectrum of one sided, infinite and periodic Jacobi matrices with scalar entries. The second one deals with the same questions about one sided, infinite periodic Jacobi matrices with matrix entries. In particular, an example illustrating the difference between the above localization property in scalar and matrix entries cases is given.     

Reports: Vanderbilt's New Change School

Abstract

In my experience, students of all races are hungering to be heard, to listen to others, and to have honest conversations about race and racism. I recently taught one course that brought out particularly clearly the challenges of teaching racially volatile material, of integrating personal experience and academic learning, and of negotiating the minefields of identity politics. It taught me the satisfactions of helping students cross racial barriers and of learning from one another.

The class—“Race and Racism”— met once a week. A master's-level course with a few doctoral students, it raised pedagogical issues similar to those I'd found teaching undergraduates. The class consisted of nine black students, of whom one was African (from Ethiopia), one Jamaican (but had spent most of her life in the United States), the rest African American; in addition, it included one Cuban American, one Filipino American, one Russian Jewish immigrant (seven years in this country), and one Japanese student who had only recently arrived in the United States. The remaining 13 students were white and non-Hispanic.     

On a quasilinear elliptic eigenvalue problem with constraint

Via construction of pseudo gradient vector field and descending flow argument, we prove the existence of one positive, one negative and one sign-changing solutions for a quasilinear elliptic eigenvalue problem with constraint.