On the Ascending Subgraph Decompositions Problem

Inthispaper,weconsideronlysimpleundirectedgraphsandfollowBondyandMurtyl7]forterminologyandnotationnotdefinedhere.Y.Alaviandothershavegiventhedefinitionoftheascendingsubgraphdecomposionin[1].LetGbeagraphofqedgessatisfy(" 1)5q<(" ,).ThenGissaidtohavean...     

On the Problem of Heilbron Type

ＯｎｔｈｅＰｒｏｂｌｅｍｏｆＨｅｉｌｂｒｏｎＴｙｐｅ￥ＴｉａｎＺｈｅｎｇｐｉｎｇ（田正平）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＲｏｙａｌＨｏｌｌｏｗａｙａｎｄＢｅｄｆｏｒｄＮｅｗＣｏｌｅｇｅ，ＵｎｉｖｅｒｓｉｔｙｏｆＬｏｎｄｏｎ，Ｅｇｈ...     

On the Pal‘s Problem

The correct answer of Pal‘s interpolation polynomial problem has been given is this paper,espe-cially,the explict form of this polynomial has been obtained.     

On the Waring Problem for Infinite Matrices

ＯｎｔｈｅＷａｒｉｎｇＰｒｏｂｌｅｍｆｏｒＩｎｆｉｎｉｔｅＭａｔｒｉｃｅｓＷａｎｇＸｉａｏｈｏｎｇ（王晓红）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣａｐｉｔａｌＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１０００３７）Ａｂｓｔｒａｃ...     

A Carleson Problem for the Boussinesq Operator

In this paper,we show that the Boussinesq operator B_tf converges pointwise to its initial data.f ∈ H^s(R) as t→0 provided s≥1/4-more precisely-on one hand,by constructing a counterexample in R we discover that the optimal convergence index s_c,1=1/4;on the other hand,we find that the Hausdorff dimension of the divergence set for B_tf is■Moreover,a higher dimensional lift was also obtained for f being radial.     

A Problem on the Spherical Maximal Functions

The classical Lebesgue’s theorem shows that for any locally integrable functionf defined on R~n where B(x;ε)are n-dimensional balls with center x and radius ε. A extendedproblem of the above is,does     

On the Syskin Problem of Finite Groups

In 1980, at the Seventh All-Union Symposium on Group Theory, ProfessorS.A .Syskin raised the following well-known problem: In a finite group G, supposeany two elemeuts of the same order are conjugate. Is |G|≤6? It is quite easy to     

Adaptive Wavelet Solution to the Stokes Problem

This paper deals with the design and analysis of adaptive wavelet method for the Stokes problem. First, the limitation of Richardson iteration is explained and the multiplied matrix M0 in the paper of Bramble and Pasciak is proved to be the simplest possible in an appropiate sense. Similar to the divergence operator, an exact application of its dual is shown; Second, based on these above observations, an adaptive wavelet algorithm for the Stokes problem is designed. Error analysis and computational complexity are given; Finally, since our algorithm is mainly to deal with an elliptic and positive definite operator equation, the last section is devoted to the Galerkin solution of an elliptic and positive definite equation. It turns out that the upper bound for error estimation may be improved.     

RESEARCH ANNOUNCEMENTS Morrey Regularity of the Solutionto the Dirichlet Problem

To study the local regularity of solutions to second order elliptic partial differential equations, Morrey in [1] introduced some function spaces, which are called the Morrey spaces todaySince then, many mathematicians have studied regularities of solutions to some kinds of secondorder elliptic equations in Morrey spaces.We give the deceptions of Morrey space and weak Morrey space first.Definition 1 Let TheThesubset of those functions of Lp for which will be called the Morrey space LpDefi…     

The Monge Problem of “Piles and Holes” on the Torus and the Problem of Small Denominators

We discuss the problem of existence of a smooth endomorphism of a closed n-dimensional manifold carrying a differential n-form into a prescribed volume form. Of course, we assume that the integrals of these forms over the whole manifold are equal. The solution of this problem for the n-dimensional torus reduces to the problem of small denominators well known in analysis.     

On the Equation and the Number of Solution of Znam's Problem

§1. In 1972,St.Znam posed the problem whether for every s>1 thereexist integers x_i>1,i=1,…,s such that x_i is a proper divisor of the numberx_1…x_(i-1)x_(i 1)…x_s 1 for i=1,…, s.Without loss of generality, we may assume1相似文献   

Suslov Problem with the Clebsch–Tisserand Potential

In this paper, we study a nonholonomic mechanical system, namely, the Suslov problem with the Clebsch–Tisserand potential. We analyze the topology of the level sets defined by the integrals in two ways: using an explicit construction and as a consequence of the Poincaré–Hopf theorem. We describe the flow on such manifolds.     

The Initial-Boundary Value Problem for the Boussinesq Equations

ＴｈｅＩｎｉｔｉａｌ－ＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｆｏｒｔｈｅＢｏｕｓｓｉｎｅｓｑＥｑｕａｔｉｏｎｓｗｉｔｈＤａｔａｉｎＬ￣ＰＧｕｏＢｏｌｉｎｇ（郭柏灵），ＹｕａｎＧｕａｎｇｗｅｉ（袁光伟）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉ...     

Instability Paths in the Kirchhoff–Plateau Problem

The Kirchhoff–Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a soap film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. Adopting a variational approach, we define an energy associated with shape deformations of the system and then derive general equilibrium and (linear) stability conditions by considering the first and second variations of the energy functional. We analyze in detail the transition to instability of flat circular configurations, which are ground states for the system in the absence of surface tension, when the latter is progressively increased. Such a theoretical study is particularly useful here, since the many different perturbations that can lead to instability make it challenging to perform an exhaustive experimental investigation. We generalize previous results, since we allow the filament to possess a curved intrinsic shape and also to display anisotropic flexural properties (as happens when the cross section of the filament is noncircular). This is accomplished by using a rod energy which is familiar from the modeling of DNA filaments. We find that the presence of intrinsic curvature is necessary to obtain a first buckling mode which is not purely tangent to the spanning surface. We also elucidate the role of twisting buckling modes, which become relevant in the presence of flexural anisotropy.     

ADirect Method for the Problem of the Solid Cylinder in Elasticity

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅＳａｉｎｔＶｅｎａｎｔｐｒｏｐｏｓｅｄｔｈｅｆａｍｏｕｓｓｅｍｉ－ｉｎｖｅｒｓｅｓｏｌｕｔｉｏｎｍｅｔｈｏｄ［１］，ｔｈａｔｓｏｍｅａｐｐｒｏ－ｐｒｉａｔｅａｓｓｕｍｐｔｉｏｎｓｔｏｔｈｅｄｅｆｏｒｍａｔｉｏｎｓｈｏｕｌｄｂｅｍａｄｅｂｅｆｏｒｅｈａｎｄｔｏｆｉｎｄｔｈｅｓｏｌｕｔｉｏｎ，ａｆｔｅｒ－ｗａｒｄｓｃｈｅｃｋｉｎｇｔｈｅａｓｓｕｍｐｔｉｏｎｓｂｅｉｎｇｖａｌｉｄ．Ｔｈｅｒｅａｆｔｅｒ，ｔｈｅｓｅｍｉ－ｉｎｖｅｒｓｅｓｏｌｕｔｉｏｎｂｅｃｏｍｅｓｔ…     

Extremum Problem for the Wiener–Hopf Equation

The extremum problem for the Wiener–Hopf equation obtained by replacing the condition u(x) = 0, x < 0, by the condition of the minimum of the quadratic functional of the function u(x)exp(–x), – < x < , is solved in closed form.     

On the Suitable Weak Solutions for the Cauchy Problem of the Boussinesq Equations

ＯｎｔｈｅＳｕｉｔａｂｌｅＷｅａｋＳｏｌｕｔｉｏｎｓｆｏｒｔｈｅＣａｕｃｈｙＰｒｏｂｌｅｍｏｆｔｈｅＢｏｕｓｓｉｎｅｓｑＥｑｕａｔｉｏｎｓＧｕｏＢｏｌｉｎｇ（郭柏灵），ＹｕａｎＧｕａｎｇｗｅｉ（袁光伟）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｇｓｉ...     

A Simple Approach to the Inverse Scattering Problem Via the Gauge Transformations

Since the found of the Inverse Scattering Transform the investigation of the inverse scattering problem (ISP) associated with the spectral problem has become one of the most attractive topics in mathematical physics. It is well known that even for the following simple AKNS-ZS spectral problem     

On the Strong Solutions and the Structural Stability of the g-Bénard Problem

In this paper, we study a type of modified Boussinesq equations which is called g-Bénard problem. We show the existence and uniqueness of strong solutions of the problem in two dimensions, and then, we investigate the continuous dependence of the solutions on the viscosity parameter.