在几何和参数上表示同一条曲线的两条有理NURBS曲线的权与控制顶点之间的关系

The paper discusses the relationship between weights and control vertices of two rational NURBS curves of degree two or three with all weights larger than zero when they represent the same curve parametrically and geometrically, and gives sufficient and necessary conditions for coincidence of two rational NURBS curves in non-degeneracy case.     

The lie group and integrability of the Fisher type travelling wave equation

For the Fisher-type wave equation, which has two stable states and one unstable state, it is proved that only in two particular cases, the corresponding travelling wave equation admits a double parameter Lie group, and based on a method different to the traditional one, its two independent first integrals are given. It is proved further that in the two integrable cases, the different bounded and non-trivial travelling wave solutions, which are corresponding the invariant manifolds of the corresponding equation under the Lie transformation, can be expressed with elementary functions although they cannot be obtained directly from the two independent first integrals.     

ON POLYA-SZEG INEQUALITIES

This paper gives two new inequalities, which improve two Polya-Szego 's inequlities.     

可定向曲面上两个地图的交叉数

In this paper, we discuss the crossing numbers of two one-vertex maps on orientable surfaces. By using a reductive method, we give the crossing number of two one-vertex maps with one face on an orientable surface and the crossing number of a one-vertex map with one face and a one-vertex map with two faces on an orientable surface. This provides a lower bound for the crossing number of two general maps on an orientable surface.     

ON POLYA-SZEGO INEQUALITIES

This paper gives two new inequalities, which improve two Polya-Szego ＇s inequlities.     

The Isomorphism Theorem of Regular Bisimple ω2-semigroups

In this paper we study the isomorphisms of two regular bisimple ω2- semigroups and obtain a criterion for two such semigroups to be isomorphic.     

Compressed data separation via dual frames based split-analysis with Weibull matrices

In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two diff erent general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix （not Gaussian） and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.     

Some Results on the Uniqueness of Meromorphic Mappings

The authors study the problem of uniqueness of meromorphic mappings and obtain two results which partially improve two theorems of Yah and Chen in 2006.     

The number of rooted circuit boundary maps

In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.     

Cubic Lienard Equations with Quadratic Damping (Ⅱ)

Abstract Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienardequations with quadratic damping have at most three limit cycles. This implies that the guess in which thesystem has at most two limit cycles is false. We give the sufficient conditions for the system has at most threelimit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by usingnumerical simulation.     

Spectrality of planar self-affine measures with two-element digit set

The iterated function system with two element digit set is the simplest case and the most important case in the study of self affine measures.The one dimensional case corresponds to the Bernoulli convolution whose spectral property is understandable.The higher dimensional analogue is not known,for which two conjectures about the spectrality and the non spectrality remain open.In the present paper,we consider the spectrality and non spectrality of planar self affine measures with two element digit set.We give a method to deal with the two dimensional case,and clarify the spectrality and non spectrality of a class of planar self affine measures.The result here provides some supportive evidence to the two related conjectures.     

二阶变系数椭圆型微分方程谱方法的后验误差估计

As to the posteriori error of spectral method for second order elliptic differential equation of variable coefficient,we construct two easy solvable differential equations of constant coefficient. Among the two energy norms of the solutions of two differential equations, one is larger than the energy norm of exact error ,another is smaller than the energy norm of exact error, and the two energy norms of the solutions are of same order.     

ON THE EXISTENCE,MULTIPLICITY AND UNIQUENESS OF POSITIVE SOLUTION FOR A THIRD ORDER TWO-POINT BOUNDARY VALUE PROBLEM

The existence, multiplicity and uniqueness of positive solutions of a third order two point boundary value problem are discussed with the help of two fixed point theorems in cones, respectively.     

THE EQUITYPE AND QUASI-EQUITYPE DECOMPOSITIONS OF PERMUTATIONS BY PERMUTATIONS OF ORDER 2 OR 3

In this papar,we give some conditions and methods about expressing an evenpermutation as a product of two equitype permutations of order 2 or 2; and expres-sing an odd permutation as a product of two quasi-equitype involutions.We provethat any even permutation can be expressed as a product of two equitypeinvolutions. And except one special case,any even permutation Can be expressedas a product of two equitype permutations of order 3.     

Spherical f-Tilings by Two Noncongruent Classes of Isosceles Triangles-Ⅱ

In this work,we give a complete classification of spherical dihedral f-tilings when the prototiles are two noncongruent isosceles triangles with certain adjacency pattern.As it will be shown,this class is composed by two discrete families denoted by Em,m ≥ 2,m ∈ N,Fk,k ≥ 4,k ∈ N and two sporadic tilings denoted by G and H.     

THE SOLVABILITY FOR HEAT CONDUCTIVE PROBLEM WITH BOUNDARY PERTURBATION

In this paper, the heat conductive problem with boundary perturbations is considered. Using the solvability of the problem, two eigenfunctions corresponding to two eigenvalues for the nm-th modular form are obtained.     

On Uniqueness of Meromorphic Functions That Share Two Values

A problem of meromorphic functions that share two values is discussed, and two results recently obtained respectively by Yi H. X. and Song G. D. ＆ Li N. are improved.     

REGULARITY CRITERIA FOR WEAK SOLUTION TO THE 3D MAGNETOHYDRODYNAMIC EQUATIONS＊

In this article,regularity criteria for the 3D magnetohydrodynamic equations are investigated.Some sufficient integrability conditions on two components or the gradient of two components of u + B and u...     

Nonlinear Korn Inequalities on a Hypersurface

The authors establish several estimates showing that the distance in W~(1,p),1 p ∞,between two immersions from a domain of R~n into R~(n+1) is bounded by the distance in L~p between two matrix fields defined in terms of the first two fundamental forms associated with each immersion. These estimates generalize previous estimates obtained by the authors and P. G. Ciarlet and weaken the assumptions on the fundamental forms at the expense of replacing them by two different matrix fields.