NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of ...     

Banach Upper Density Recurrent Points of C~0-flows

Let X denote a compact metric space with distance d and F:X×R→X or F_t :X→X denote a C~0-flow.From the point of view of ergodic theory,all important dynamical behaviors take place on a full measure set.The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C~0-flow.Moreover,we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points,and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.     

Generalized multiresolution structures in reducing subspaces of L 2(ℝ d )

In this paper, we introduce the notion of generalized multiresolution structure (GMS) in the set-ting of reducing subspaces of L2(Rd). For a general expansive matrix, we obtain a necessary and sufficient condition for GMS, and prove the existence of GMS in a reducing subspace. Using GMS, we obtain a pyramid decomposition and a frame-like expansion for signals in reducing subspaces.     

The Picard Theorem on S-metric spaces

Recently, the notion of an S-metric space is defined and extensively studied as a generalization of a metric space. In this paper, we define the notion of the S∞-space and prove its completeness. We obtain a new generalization of the classical "Picard Theorem".     

Topological Structure of Non-wandering Set of a Graph Map

Let G be a graph （i.e., a finite one-dimensional polyhedron） and f ： G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non-wandering point; every accumulation point of the set of non-wandering points of f with infinite orbit is a two-order accumulation point of the set of recurrent points of f; the derived set of an ω-limit set of f is equal to the derived set of an the set of recurrent points of f; and the two-order derived set of non-wandering set of f is equal to the two-order derived set of the set of recurrent points of f.     

On the Construction of d—Continuous Modules

In this paper we introduce: and study the notion of dual Gontinuous (d-Contmuous) modnles, A decomposrtion thcorem for a d-continuous modules proved, this generahzes all known decompositron theorems for quasi-projective modules.     

The Stable Limit Cycles of a Generalized Lienard Equation

In this paper we give a series of sufficient conditions for the existence of autonomous systems with three singular points.     

How big are the Csrg"非汉字符号"-Révész increments of two-parameter Wiener processes?

In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.     

Time-periodic solutions of the Einstein’s field equations Ⅲ:physical singularities

In this paper we construct a new time-periodic solution of the vacuum Einstein’s field equations, this solution possesses physical singularities, i.e., the norm of the solution’s Riemann curvature tensor takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the time-periodic physical singularity. By calculating the Weyl scalars of this solution, we investigate new physical phenomena and analyze new singularities for this univ...     

APPROXIMATION FOR CONTINUOUS PERIODIC FUNCTIONS OF SEVERAL VARIABLES AND ITS CONJUGATE FUNCTIONS BY RIESZ MEANS ON A SET OF TOTAL MEASURE

Let Q be the k—dimensional fundamental cube,f be an integrable periodicfunction on Q.Calderon and Zygmund,using their singular integral theory,de-finded the notion of conjugate multiple Fourier series.In this paper we shall dealwith a special class of Calderon—Zygmund kernels in denfining conjugate series,namely the spherical harmonic kernels.Let P(x)be a homogeneous harmonic poly-nomial of degree p,we call K(x) a spherical harmonic kernel if K(x)=P(x)|x|~(-k-p)(x≠0).Let Z~k be the set of lattice points in R~k.Define     

一类退化抛物方程的边值问题

In this paper, we study the boundary value problem (BVP) for a degenerate parabolic equation. By introducing a proper notion of weak solutions, we prove the uniqueness and existence of weak solutions of the problem. The localization of weak solutions is also discussed, which plays a key role in the proof of the uniqueness.     

LIPSCHITZ-ERGODIC TRANSFORMATION

In 1977 Easton introduced the notion of Lipschitz-ergodic transformation on a compact space. In this paper we consider the Lipschitz-ergodic transformation on a measure space.     

Lie-Yamaguti着色代数的导子与形变

In this paper,we introduce the representation and cohomology theory of Lie-Yamaguti color algebras.Furthermore,we introduce the notions of generalized derivations of Lie-Yamaguti color algebras and present some properties.Finally,we study linear deformations of LieYamaguti color algebras,and introduce the notion of a Nijenhuis operator on a Lie-Yamaguti color algebra,which can generate a trivial deformation.     

On the Integrability of Strictly Convex Billiard Tables with Boundaries Close to Ellipses with Small Eccentricities

In this paper,we introduce a new notion of integrability for billiard tables,namely,integrability away from the boundary.One key feature of our notion is that the integrable region could be disjoint from the boundary with a positive distance.We prove that if a strictly convex billiard table,whose boundary is a small perturbation of an ellipse with small eccentricity,is integrable in this sense,then its boundary must be itself an ellipse.     

A General Existence Principle for Fixed Point Theorems in One Parameter Case of Soft $D_{a}$-Metric Space

In this paper, we take the case of soft points into consideration and propose a new metric structure called soft D_a-metric space for a specific orbit defined with soft points. In order to establish fixed point results in the modified metric space, we modify a few existing definitions in the sense of soft points.     

ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson's extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson's extrapolation.     

关于$\omega$-Smash余积Hopf代数的$(f,\omega)$相容对$(B,,H)$

In this paper we introduce the notion of （f,ω）-compatible pair （B,H）, by which we construct a Hopf algebra in the category HHYD of Yetter-Drinfeld H-modules by twisting the comultiplication of B. We also study the property of ω-smash coproduct Hopf algebras Bω H.     

Maurer-Cartan characterizations and cohomologies of compatible Lie algebras

In this paper, we give Maurer-Cartan characterizations as well as a cohomology theory for compatible Lie algebras. Explicitly, we first introduce the notion of a bidifferential graded Lie algebra and thus give Maurer-Cartan characterizations of compatible Lie algebras. Then we introduce a cohomology theory of compatible Lie algebras and use it to classify infinitesimal deformations and abelian extensions of compatible Lie algebras. In particular, we introduce the reduced cohomology of a compatib...     

A new look at some basic concepts in arbitrage pricing theory

The notion of No Free Lunch with Vanishing Risk (or NFLVR in short) w.r.t. admissible strategies depends on the choice of numeraire. Yan introduced the notion of allowable strategy and showed that condition of NFLVR w.r.t. allowable strategies is independent of the choice of numeraire and is equivalent to the existence of an equivalent martingale measure for the deflated price process. In this paper we establish a version of the Kramkov's optional decomposition theorem in the setting of equivalent martingale measures. Based on this theorem, we have a new look at some basic concepts in arbitrage pricing theory: superhedging, fair price, attainable contingent claims, complete markets and etc.