A GUIDED TOUR THROUGH ORIENTED MATROID AXIOMS

Oriented Matroids arise as a natural combinatorial abstraction of linear algebra and geometry.Some of the topics were foreseen by Rockafellar.Later,oriented matroids were independently discovered by Bland,Dress and Las Vergnas.As with matroids oriented matroids can be developed from many different axiom systems.In this survey we shall concentrate on some of the more important ones and show how one system can be     

最佳逼近的正交化算法

In the present paper,we shall give a new algorithm of the best approximation in Hilbert spaces by using Gram-Schmidt orthogonalization and give some examples to show that the new method is simple and convenient.And we also point out that the best approximation have a wonderful superposition property by using orthogonal method.     

A MODIFIED CONJUGATE DIRECTION METHOD FOR COMPUTING THE PSEUDOINVERSF

In this paper we are concerned with the modified conjugate direction method for computing the pseudoinverse by using an orthogonal basis of the range space of A. Numerical results show that the new method retains some main advantages in terms of efficiency and accuracy.     

A REMARK FOR “ASYMPTOTIC BEHAVIOR OF DELAY 2-D DISCRETE LOGISTIC SYSTEMS”

In this remark,we shall show some counter examples for the main results of the recent paper "Asymptotic Behavior of Delay 2-D Discrete Logistic Systems" (IEEE Trans.Circuits Systems,49(2002),1677-1682.)     

ASYMPTOTICS OF THE SOLUTIONS TO STOCHASTIC WAVE EQUATIONS DRIVEN BY A NON-GAUSSIAN LéVY PROCESS

In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Lévy process. We shall prove that under some appropriate conditions, the exponential stability of the solutions holds. Finally, we give two examples to illustrate our results.     

Approximation of conic section by quartic Bzier curve with endpoints continuity condition

A new method for approximation of conic section by quartic B′ezier curve is presented, based on the quartic B′ezier approximation of circular arcs. Here we give an upper bound of the Hausdorff distance between the conic section and the approximation curve, and show that the error bounds have the approximation order of eight. Furthermore, our method yields quartic G2 continuous spline approximation of conic section when using the subdivision scheme,and the effectiveness of this method is demonstrated by some numerical examples.     

Some Properties of Bounded Linear Operator Over L_p Space

<正> We shall extend the concepts of the kernel and the image of the homomorphism φ in Abstract Algebra to the bounded linear operator of L_p space. We can obtain some results. Definition 1 let A be a L_p space, B(?)A. If B is a L_p space by the operation and the norm in A, then the subset B of A is called a L_p subspace of A.     

ON A CLASS OF BESICOVITCHFUNCTIONS TO HAVE EXACT BOX DIMENSION： A NECESSARY AND SUFFICIENT CONDITION

This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given byB(t) := ∞∑k=1 λs-2k sin(λkt),where 1 ＜ s ＜ 2, λk ＞ 0 tends to infinity as k →∞ and λk satisfies λk 1/λk ≥λ＞ 1. The results show thatlimk→∞ log λk 1/log λk = 1is a necessary and sufficient condition for Graph(B(t)) to have same upper and lower box dimensions.For the fractional Riemann-Liouville differential operator Du and the fractional integral operator D-v,the results show that if λ is sufficiently large, then a necessary and sufficient condition for box dimension of Graph(D-v(B)),0 ＜ v ＜ s - 1, to be s - v and box dimension of Graph(Du(B)),0 ＜ u ＜ 2 - s, to be s uis also lim k→∞logλk 1/log λk = 1.     

两类拟序列鞅的结构与比较

There are several important generalizations of martingales such as games fairer with time, quasi-mils and sequential martingales in the limit. In the note, we shall consider all possible structures of a probability space (Ω, A, (An), P) associated with a stochastic basis(An) of subσ-fields of A with An↑A. Then, we shall apply them to establish some comparison results for the aforementioned generalizations of martingales.     

Topology and topological sequence entropy

Let X be a compact metric space and T:X-→X be continuous.Let h*(T)be the supremum of topological sequence entropies of T over all the subsequences of Z+and S(X)be the set of the values h*(T)for all the continuous maps T on X.It is known that{0}■S(X)■{0,log 2,log 3,...}∪{∞}.Only three possibilities for S(X)have been observed so far,namely S(X)={0},S(X)={0,log 2,∞}and S(X)={0,log 2,log 3,...}∪{∞}.In this paper we completely solve the problem of finding all possibilities for S(X)by showing that in fact for every set{0}?A?{0,log 2,log 3,...}∪{∞}there exists a one-dimensional continuum XAwith S(XA)=A.In the construction of XAwe use Cook continua.This is apparently the first application of these very rigid continua in dynamics.We further show that the same result is true if one considers only homeomorphisms rather than continuous maps.The problem for group actions is also addressed.For some class of group actions(by homeomorphisms)we provide an analogous result,but in full generality this problem remains open.     

Multiplication formulas for Kubert functions

The aim of this paper is two folds. First, we shall prove a general reduction theorem to the Spannenintegral of products of （generalized） Kubert functions. Second, we apply the special case of Carlitz＇s theorem to the elaboration of earlier results on the mean values of the product of Dirichlet L-functions at integer arguments. Carlitz＇s theorem is a generalization of a classical result of Nielsen in 1923. Regarding the reduction theorem, we shall unify both the results of Carlitz （for sums） and Mordell （for integrals）, both of which are generalizations of preceding results by Frasnel, Landau, Mikolas, and Romanoff et al. These not only generalize earlier results but also cover some recent results. For example, Beck＇s lamma is the same as Carlitz＇s result, while some results of Maier may be deduced from those of Romanoff. To this end, we shall consider the Stiletjes integral which incorporates both sums and integrals. Now, we have an expansion of the sum of products of Bernoulli polynomials that we may apply it to elaborate on the results of afore-mentioned papers and can supplement them by related results.     

Hybrid fixed point result for lipschitz homomorphisms on quasi-Banach algebras

We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.     

Strong solution of Itô type set-valued stochastic differential equation

In this paper, we shall firstly illustrate why we should introduce an It5 type set-valued stochastic differential equation and why we should notice the almost everywhere problem. Secondly we shall give a clear definition of Aumann type Lebesgue integral and prove the measurability of the Lebesgue integral of set-valued stochastic processes with respect to time t. Then we shall present some new properties, especially prove an important inequality of set-valued Lebesgue integrals. Finally we shall prove the existence and the uniqueness of a strong solution to the It5 type set-valued stochastic differential equation.     

Angular distribution in complex oscillation theory

Let f_1 and f_2 be two linearly independent solutions of the differential equationf″ Af=0,where A is an entire function.Set E=f_1f_2.In this paper,we shall studythe angular distribution of E and establish a relation between zero accumulation rays andBorel directions of E.Consequently we can obtain some results in the complex differentialequation by using known results in angular distribution theory of meromorphic functions.     

Some Remarks on the Restriction Theorems for the Maximal Operators on Rd

The aim of this paper is to give a simple proof of the restriction theorem for the maximal operators on the d-dimensional Euclidean space Rd, whose theorem was proved by Carro-Rodriguez in 2012.Moreover, we shall give some remarks of the restriction theorem for the linear and the multilinear operators by Carro-Rodriguez and Rodriguez, too.     

Verified Computation of Eigenpairs in the Generalized Eigenvalue Problem for Nonsquare Matrix Pencils

Consider an optimization problem arising from the generalized eigenvalue problem Ax=λBx,where A,B∈Cm×n and m>n.Ito et al.showed that the optimization problem can be solved by utilizing right singular vectors of C:=[B,A].In this paper,we focus on computing intervals containing the solution.When some singular values of C are multiple or nearly multiple,we can enclose bases of corresponding invariant subspaces of CHC,where CH denotes the conjugate transpose of C,but cannot enclose the corresponding right singular vectors.The purpose of this paper is to prove that the solution can be obtained even when we utilize the bases instead of the right singular vectors.Based on the proved result,we propose an algorithm for computing the intervals.Numerical results show property of the algorithm.     

Global Generalizations of the Birkhoff-Kellogg Theorem on Set-Contraction Operators

The purpose of this paper is to give some global generalizations of the Birkhoff—Kellogg theorem on set-contraction operators.In this paper,we 8uppose that X is an infinite-dimensional Banach space and A:x→X is a κ-set-contraction operator,0≤κ< ∞.we shall denote by E the Banach space R~1×X with norm ‖(λ,χ)‖=(λ~2 ‖χ‖~2)~1/2.The c1losure of the set of nonZero solutions of the equation χ=λAχ will be denoted by L,i.e.,     

ABSOLUTE RETRACTIVITY OF SOME SETS TO TWO-VARIABLES MULTIFUNCTIONS

In this paper,by providing some different conditions respect to another works,we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F:X × X → P b,cl (X),on complete metric spaces.     

On Hom-groups and Hom-group Actions

A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map.In this paper,we give some new examples of Hom-groups,and show the first,second and third isomorphism theorems of Hom-groups.We also introduce the notion of Hom-group action,and as an application,we prove the first Sylow theorem for Hom-groups along the line of group actions.