Interchanges and Invariant Positions in (?)_c (R,S)

Let C=(c_(ij)) be an m×n (0,1)-matrix. Let R=(r_1,…,r_m) and S=(s_1,…,s_n) be nonnegative integral vectors. Denote by (?)_c(R,S) the set of all m×n (0, 1)-matrices A=(a_(ij)) satisfying a_(ij)≥c_(ij),a_(il)+…+a_(in)=r_i,a_(lj)+…+a_(mj)=s_j for 1≤i≤m, 1≤j≤n.     

Young’s Seminormal Form and Simple Modules for S n in Characteristic p

We realize the integral Specht modules for the symmetric group S _n as induced modules from the subalgebra of the group algebra generated by the Jucys–Murphy elements. We deduce from this that the simple modules for ${{\mathbb F}_p} S_n $ are generated by reductions modulo p of the corresponding Jucys–Murphy idempotents.     

Recurrence in the dynamical system (X,〈Ts〉s∈S) and ideals of βS

A dynamical system is a pair $(X,{〈T_s〉}_{s\in S})$, where $X$ is a compact Hausdorff space, $S$ is a semigroup, for each $s\in S$, $T_s$ is a continuous function from $X$ to $X$, and for all $s,t\in S$, $T_s°T_t=T_{st}$. Given a point $p\in \beta S$, the Stone–?ech compactification of the discrete space $S$, $T_p:X\to X$ is defined by, for $x\in X$, $T_p\left(x\right)=p?{lim}_{s\in S}{T}_s\left(x\right)$. We let $\beta S$ have the operation extending the operation of $S$ such that $\beta S$ is a right topological semigroup and multiplication on the left by any point of $S$ is continuous. Given $p,q\in \beta S$, $T_p°T_q=T_{pq}$, but $T_p$ is usually not continuous. Given a dynamical system $(X,{〈T_s〉}_{s\in S})$, and a point $x\in X$, we let $U\left(x\right)=\{p\in \beta S:T_p\left(x\right)\text{ be uniformly recurrent}\}$. We show that each $U\left(x\right)$ is a left ideal of $\beta S$ and for any semigroup we can get a dynamical system with respect to which $K\left(\beta S\right)={?}_{x\in X}U\left(x\right)$ and $c?K\left(\beta S\right)=?\{U\left(x\right):x\in X\text{and}U\left(x\right)\text{is closed}\}$. And we show that weak cancellation assumptions guarantee that each such $U\left(x\right)$ properly contains $K\left(\beta S\right)$ and has $U\left(x\right)?c?K\left(\beta S\right)\ne ?$.     

Volterra-Type Equations in S + ′

Necessary and sufficient condition for the unique solvability of Volterra integro-differential equation in $S\prime _ + $ is given.     

Cusp forms in S 6(Γ 0(23)), S 8(Γ 0(23)) and the number of representations of numbers by some quadratic forms in 12 and 16 variables

In this study we find bases of S ₆(Γ ₀(23)), S ₈(Γ ₀(23)) and obtain explicit formulae for the number of representations of numbers by some quadratic forms in 12 and 16 variables that are direct sums of binary quadratic forms $F_{1}=x_{1}^{2}+x_{1}x_{2}+6x_{2}^{2}$ and $\varPhi_{1}=2x_{1}^{2}+x_{1}x_{2}+3x_{2}^{2}$ (or its inverse) with discriminant ?23.     

Technological progress and productivity growth in the U.S. mobile telecommunications industry

The fast growing U.S. mobile wireless industry has been experiencing dramatic technological change and substantial competition. As a result of these catalysts, we argue that wireless firms have experienced significant productivity improvement and provide new evidence that technological progress almost exclusively contributed to productivity improvements in the wireless industry by significantly expanding the production possibilities set. We employ nonparametric estimation procedures based on Data Envelopment Analysis (DEA) that utilize input-output data from a representative sample of 16 firms in the mobile wireless industry to estimate productivity change, technological change, and relative efficiency change for the period spanning the years from 2000 to 2002. Our findings show that the industry experienced a significant growth of 13% in productivity, which was primarily due to an average technological progress of 9.9% in the industry. Additionally, we find that national wireless operators experienced significantly higher productivity growth and contributed more to technological progress than regional providers. Firms that were industry pioneers as evidenced by high market share at the beginning of our sample period experienced higher productivity growth and greater technological progress compared to firms with lower initial market share. Moreover, the industry experienced significantly higher productivity growth and technical progress in the later sample period between 2001 and 2002 than in the early period between 2000 and 2001.     

Similarities and differences in teachers’ questioning in German and Japanese mathematics classrooms

This study aims to capture similarities and differences in teachers’ questioning in German and Japanese mathematics classrooms, specifically focusing on the stage of introducing new mathematical content. The author analyzed consecutive mathematics classes taught by experienced teachers in Germany and Japan, who were recruited based on their locally defined “teaching competence” in the Learner’s Perspective Study. The results revealed that even questions that required students to recall previously learned content or provide the results of a calculation, which were regarded as lower cognitive questions in previous studies, played key roles at the stage of introducing new mathematical content in both German and Japanese classrooms. Further, distinctive patterns in the sequences of teachers’ questioning were identified. These differences suggest what is valued as quality mathematics teaching in each educational system.     

Geometry in Nature and Art

Nature displays an infinite array of geometric shapes from the small atom to the greatest of the spiral galaxies, crystalline solids, the honeycomb of the bee, snowflakes, the arrangement of seeds on sunflowers and pinecones, the spiral of the nautilus shell, the spider's web, and the regular polygons found in the basic shapes of many flowers are just a few of nature's geometric masterpieces.     

Presentations for S and S/ρ from a Given Presentation for ρ

We consider a congruence on a semigroup S as a subsemigroup of the direct product S × S. Then we prove that if is finitely presented then both S and S/ are finitely presented.     

Four Classes of Surfaces with Constant Mean Curvature in S 3 × R and H 3 × R

Deforming rotation surfaces with constant mean curvature in S ³ and H ³ to S ³ × R and H ³ × R respectvely, we give four classes of surfaces with mean curvature vector of constant length in S ³ × R and H ³ × R. We have complete minimal surfaces in S ³ × R and H ³ × R. Also we obtain minimal 2-tori in S ³ × S ¹, some of which are embedded.     

Elimination in Weyl Algebra and q-Identities

For the algorithmic proof of q-proper-hypergeometric identities, H.Wilf and D.Zeiberggave a theoretical frame work. In [1], they proved that q-proper-hypergeometric termssatisfy recurrence relations with polynomial coefficients and could obtain quite explicitbounds for the order of such a recurrence. But how can we find the recurrence relations?We consider single-variable q-proper-hypergeometric identities based on Zeilberg's basicidea. To find the recurrence relations, an elimination in the non-conuntative Weyl algebra     

Elimination in Weyl Algebra and Identities

In paper[1], Zeilberger presented an approach to sprcial functions identities, besdes     

Spaces which contain a copy of Sω or S2 and their applications

Let S_ω and S₂ denote the sequential fan and Arens' space, respectively. In this paper, we shall prove the following main results. (1) If Π^∞_i=1 X_i contains a copy of S_ω (S₂), then some Πⁿ_i=1 X_i contains a copy of S_ω (S_ω or S₂, respectively). (2) Let f: X → Y be a closed map such that any f^-1(y) contains no closed copy of S_ω (S₂). If X contains a closed copy of S_ω (S₂), then Y contains a closed copy of S_ω (S_ω or S₂, respectively).As applications of (1) and (2), we shall consider the Fréchet or strongly Fréchetness, or sequentiality of products of finitely or countably many spaces.     

k-Factors and Spanning Subgraph in Graphs

In this paper, we discussed k-factors and spanning subgraph, and propose a conjecture which will lead to a series of important conclusion.     

K-Factors and Hamilton Cycles in Graphs

We discuss k-factors and Hamiltonian Graphs in graph theory. We prove a general version of the conjecture by R. Haggkvist; as a result, we prove two extended versions of two well-known theorems due to O. Ore and B. Jachson, respectively.     

σ-additivity in manuals and orthoalgebras

Notions of -additivity are introduced for orthoalgebras and for manuals. It is shown that the logic of a -additive manual is a -additive orthoalgebra, and that, conversely, every -additive orthoalgebra arises as such a logic. Using this theorem, it is shown that a given orthoalgebra admits at most one reasonable extension of its orthogonal sum operation to countable jointly orthogonal sets. It is also shown that every orthoalgebra can be embedded in a sigma-orthoalgebra and every orthomodular poset, in a -OMP.     

Bifurcations and Chaos in Duffing Equation

The Duffing equation with even-odd asymmetrical nonlinear-restoring force and one external forcingis investigated.The conditions of existence of primary resonance,second-order,third-order subharmonics,m-order subharmonics and chaos are given by using the second-averaging method,the Melnikov method andbifurcation theory.Numerical simulations including bifurcation diagram,bifurcation surfaces and phase portraitsshow the consistence with the theoretical analysis.The numerical results also exhibit new dynamical behaviorsincluding onset of chaos,chaos suddenly disappearing to periodic orbit,cascades of inverse period-doublingbifurcations,period-doubling bifurcation,symmetry period-doubling bifurcations of period-3 orbit,symmetry-breaking of periodic orbits,interleaving occurrence of chaotic behaviors and period-one orbit,a great abundanceof periodic windows in transient chaotic regions with interior crises and boundary crisis and varied chaoticattractors.Our results show that many dynamical behaviors are strictly departure from the behaviors of theDuffing equation with odd-nonlinear restoring force.     

Rigidity and regularity in group actions

Some new results on the rigidity of automorphism groups and the regularity of(?)-Neumann operator in group actions are presented.     

Fekete and Szeg problem in one and higher dimensions

In this paper, we establish the Fekete and Szeg inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in C~n.