The Binding Number of a Graph

The binding number of a graph is an important characteristic quantity of agraph.In1973 Woodall first introduced the concept of the binding number ofa graph and then gave the binding number of some special graphs in[1].In1981 Kane,Mohanty and Hales gave the binding number of some product graphsin[2].Wang Jianfang,Tian Songlin,Liu Ziuqiang(1983-1987)gave the bin-ding number of some multi-product graphs,and it is the limit character.Up to     

The Meta-Grothendieck Group of a Ring

ＴｈｅＭｅｔａ┐ＧｒｏｔｈｅｎｄｉｅｃｋＧｒｏｕｐｏｆａＲｉｎｇ＊）ＦｅｎｇＬｉａｎｇｇｕｉ（冯良贵）（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｔｈｅｍａｔｉｃｓ，ＮＵＤＴ，Ｃｈａｎｇｓｈａ，４１００７３）ＡｂｓｔｒａｃｔＷｅｉｎｔｒｏｄｕｃｅｔｈｅｍｅｔａ－Ｇ...     

The Bandwidth of a Class of Line Graphs

本文给出了一类线图的带宽,并给出了它的最佳编号.     

The structure of a class of Z-local rings

A local ring R is called Z-local if J(R) = Z(R) and J(R)2 = 0. In this paper the structure of a class of Z-local rings is determined.     

The Global Bifurcation of a Cubic System

In this paper,we study the perturbation of certain of cubic system.By using the method of multi-parameter perturbation theory and qualitative analysis,we infer that the system under consideration can havefive limit cycles.     

The minimal polynomial of a matrix ∗

Let Rbe a finite dimensional central simple algebra over a field F A be any n× n matrix over R. By using the method of matrix representation, this paper obtains the structure formula of the minimal polynomial q_A (λ) of A over F. By using q_A (λ), this paper discusses the structure of right (left) eigenvalues set of A, and obtains the necessary and sufficient condition that a matrix over a finite dimensional central division algebra is similar to a diagonal matrix.     

The ℱ-Limit of a Sequence of Prime Ideals

In this article, we introduce new topologies on the prime spectrum of a commutative ring by using the ?-limit of a sequence of prime ideals where ? is a nonprincipal ultrafilter on the natural numbers ?. These topologies are strictly finer than the Zariski's Topology, countably compact and Hausdorff. We construct 2^𝔠 new topologies on Spec(?^?) which are pairwise non-homeomorphic.     

The Degree Theory of a New Operator

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｔｈｅｄｅｇｒｅｅｔｈｅｏｒｙｆｏｒａｋ－ｓｅｔ－ｃｏｎｔｒａｃｔｏｐｅｒａｔｏｒｈａｓｍａｎｙａｐｐｌｉｃａｔｉｏｎｓｏｎｔｈｅｅｘｉｓｔｅｎｃｅｏｆｔｈｅｓｏｌｕｔｉｏｎｓｏｆｓｏｍｅｅｑｕａｔｉｏｎｓ（ｓｅｅ［１］，［２］，［３］）．Ｈｏｗｅｖｅｒ，ｓｏｍｅｏｐｅｒａ－ｔｏｒｓａｒｅｎｏｔｋ－ｓｅｔ－ｃｏｎｔｒａｃｔｏｐｅｒａｔｏｒｓ．Ｉｔｉｓａｎｅｗｐｒｏｂｌｅｍｔｈａｔｗｅｅｓｔａｂｌｉｓｈａｄｅｇｒｅｅｔｈｅｏｒｙｆｏ…     

The Fractional Derivatives of a Fractal Function

The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Weierstrass function.     

The non-gap sequence of a subcode of a generalized Reed–Solomon code

This paper addresses the question how often the square code of an arbitrary l-dimensional subcode of the code GRS _k (a, b) is exactly the code GRS_2k-1(a, b * b). To answer this question we first introduce the notion of gaps of a code which allows us to characterize such subcodes easily. This property was first used and stated by Wieschebrink where he applied the Sidelnikov–Shestakov attack to break the Berger–Loidreau cryptosystem.     

The Blow-up Rate of Positive Solution of a Parabolic System

This paper deals with the blow-up properties of solutions to a system of semilinear heat equations with the boundary conditions u(x,t)=v(x,t)=0 on SR×[0,T).The exact estimates on blow-up rate of solutions are established.     

The Closeness of the τ-Standard Part of a Set

In this paper,the closeness of the τ-standard part of a set is discussed.Some related propositions of the τ-neighborhood system of a set are given.And then some related conclusions of the τ-monad of a set and the τ-standard part of a set are presented.And based on it,the necessary and sufficient conditions of the enlarged model and the saturated model are showed.Finally,some sufficient conditions that the τ-standard part of a set is closed are proved in the enlarged model and the saturated model.     

The Spectral Characterizations of Some Minimal Submanifolds of a Sphere

ＴｈｅＳｐｅｃｔｒａｌＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｏｆＳｏｍｅＭｉｎｉｍａｌＳｕｂｍａｎｉｆｏｌｄｓｏｆａＳｐｈｅｒｅＺｈｏｕＺｈｅｎｒｏｎｇ（周振荣）（ＢａｓｉｃＣｏｕｒｓｅＤｅｐａｒｔｍｅｎｔ，ＷｕｈａｎＦｏｏｄＩｎｄｕｓｔｒｙＣｏｌｌｅｇ...     

The attractor of a parabolic–elliptic system

Following Coclite, Holden and Karlsen [G.M. Coclite, H. Holden and K.H. Karlsen, Well-posedness for a parabolic-elliptic system, Discrete Contin. Dyn. Syst. 13 (3) (2005) 659–682] and Tian and Fan [Lixin Tian, Jinling Fan, The attractor on viscosity Degasperis-Procesi equation, Nonlinear Analysis: Real World Applications, 2007], we study the dynamical behaviors of the parabolic–elliptic system

_ut+_(f(t,x,u))x+g(t,x,u)+_Px−ε_uxx=0$u_t+{\left(f(t,x,u)\right)}_x+g(t,x,u)+P_x-\epsilon u_{xx}=0$

The Proof of a Theorem in DC Problem

ＴｈｅＰｒｏｏｆｏｆａＴｈｅｏｒｅｍｉｎＤＣＰｒｏｂｌｅｍＸｉａＺｈｏｎｇｈａｎｇＸｉａＺｕｎｑｕａｎ（ＤｅｐｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＤａｌｉａｎＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ，１１６０２４）ＴｈｅＰｒｏｏｆｏｆａＴ...     

The Quotient Category of a Graded Morita-Takeuchi Context

In this paper, we offer a graded equivalence between the quotient categories defined by any graded Morita-Takeuchi context via certain modifications of the graded cotensor functors. As a consequence, we show a commutative diagram that establish the relation between the closed objects of the categories gr^c and M^C, where C is a graded coalgebra.     

The Cauchy Problem of a Shallow Water Equation

We consider the Cauchy problem of a shallow water equation and its local wellposedness.     

The Isometry of Riemannian Manifold to a Sphere

ＴｈｅＩｓｏｍｅｔｒｙｏｆＲｉｅｍａｎｎｉａｎＭａｎｉｆｏｌｄｔｏａＳｐｈｅｒｅＺｈａｏＰｅｉｂｉａｏ（赵培标）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＡｎｈｕｉＩｎｓｔｉｔｕｔｅｏｆＦｉｎａｎｃｅ＆Ｔｒａｄｅ，２３３０４１）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐ...     

The Upper Central Chain of a Radical Ring

Ｔｈｒｏｕｇｈｏｕｔ,ＲｉｓａＪａｃｏｂｓｏｎｒａｄｉｃａｌｒｉｎｇ,ａｎｄｄｅｆｉｎｅａ ｂ =ａ +ｂ -ａｂａｎｄ [ａ ,ｂ] =ａｂ-ｂａｆｏｒａｎｙａ ,ｂ∈Ｒ .Ｔｈｅｎ (Ｒ , )ｉｓａｇｒｏｕｐｗｉｔｈｉｄｅｎｔｉｔｙ 0 ,ｃａｌｌｅｄｔｈｅａｄｊｏｉｎｔｏｒｃｉｒｃｌｅｇｒｏｕｐｏｆＲ ,ａｎｄ (Ｒ ,+,[,] )ｉｓａＬｉｅｒｉｎｇ ,ｃａｌｌｅｄｔｈｅａｓｓｏｃｉａｔｅｄＬｉｅｒｉｎｇｏｆＲ .ＩｔｗａｓｐｒｏｖｅｄｂｙＪｅｎｎｉｎｇｓ[1]ｔｈａｔ(Ｒ , )ｉｓａｎｉｌｐｏｔｅｎｔｇｒｏｕｐｉｆａｎｄｏｎｌｙｉｆ (…     

The ?ojasiewicz exponent of a set of weighted homogeneous ideals

We give an expression for the ?ojasiewicz exponent of a set of ideals which are pieces of a weighted homogeneous filtration. We also study the application of this formula to the computation of the ?ojasiewicz exponent of the gradient of a semi-weighted homogeneous function (Cⁿ,0)→(C,0) with an isolated singularity at the origin.