On computing Grbner bases in rings of differential operators

Insa and Pauer presented a basic theory of Grbner basis for differential operators with coeffcients in a commutative ring in 1998,and a criterion was proposed to determine if a set of differential operators is a Gro¨bner basis.In this paper,we will give a new criterion such that Insa and Pauer's criterion could be concluded as a special case and one could compute the Grbner basis more effciently by this new criterion.     

本刊英文版2011年54卷第6期摘要

On computing Grbner bases in rings of differential operators MA Xiao Dong,SUN Yao&WANG Ding Kang Abstract Insa and Pauer presented a basic theory of Gr¨obner basis for     

Grbner bases in difference-differential modules and difference-differential dimension polynomials

In this paper we extend the theory of Grbner bases to difference-differential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural filtration. We present and verify algorithms for construct-ing these Grbner bases counterparts. To this aim we introduce the concept of "generalized term order" on Nm ×Zn and on difference-differential modules. Using Grbner bases on difference-differential mod-ules we present a direct and algorithmic approach to computing the difference-differential dimension polynomials of a difference-differential module and of a system of linear partial difference-differential equations.     

Invariant G2V algorithm for computing SAGBI-Gröbner bases

Faugère and Rahmany have presented the invariant F5 algorithm to compute SAGBI-Grbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 algorithm to use F5 criterion to remove a part of useless reductions. Although this algorithm is more efficient than the Buchberger-like algorithm, however it does not use all the existing criteria (for an incremental structure) to detect superfluous reductions. In this paper, we consider a new algorithm, namely, invariant G2V algorithm, to compute SAGBI-Grbner bases of ideals of invariant rings using more criteria. This algorithm has a new structure and it is based on the G2V algorithm; a variant of the F5 algorithm to compute Grbner bases. We have implemented our new algorithm in Maple , and we give experimental comparison, via some examples, of performance of this algorithm with the invariant F5 algorithm.     

Optimal Control Problem Governed by Semilinear Parabolic Equation and its Algorithm

In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.     

Best Proximity Point Theorems for p-Proximalα-η-β-Quasi Contractions in Metric Spaces with w0-Distance

In this paper,we propose a new class of non-self mappings called p-proximalα-η-β-quasi contraction,and introduce the concepts ofα-proximal admissible mapping with respect toηand(α,d)regular mapping with respect toη.Based on these new notions,we study the existence and uniqueness of best proximity point for this kind of new contractions in metric spaces with w;-distance and obtain a new theorem,which generalize and complement the results in[Ayari,M.I.et al.Fixed Point Theory Appl.,2017,2017:16]and[Ayari,M.I.et al.Fixed Point Theory Appl.,2019,2019:7].We give an example to show the validity of our main result.Moreover,we obtain several consequences concerning about best proximity point and common fixed point results for two mappings,and we present an application of a corollary to discuss the solutions to a class of systems of Volterra type integral equations.     

CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION

In this article,by applying the super-solution and sub-solution methods,instead of energy estimate methods,the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlocal source and an absorption term,and give a classification of the exponents and coefficients for the solutions to vanish in finite time or not,which improve one of our results(Applicable Analysis,92(2013),636-650) and the results of Zheng et al(Math.Meth.Appl.Sci.,36(2013),730-743).     

A TRIANGULAR FINITE VOLUME ELEMENT METHOD FOR A SEMILINEAR ELLIPTIC EQUATION

In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. We then derive convergence estimate in Hi-norm, L2-norm and L∞-norm, respectively. Finally an example is given to illustrate the effectiveness of the proposed method.     

LIE IDEALS, MORITA CONTEXT AND GENERALIZED （α β）-DERIVATIONS

A classical problem in ring theory is to study conditions under which a ring is forced to become commutative. Stimulated from Jacobson＇s famous result, several tech- niques are developed to achieve this goal. In the present note, we use a pair of rings, which are the ingredients of a Morita context, and obtain that if one of the ring is prime with the generalized （α β）-derivations that satisfy certain conditions on the trace ideal of the ring, which by default is a Lie ideal, and the other ring is reduced, then the trace ideal of the reduced ring is contained in the center of the ring. As an outcome, in case of a semi-projective Morita context, the reduced ring becomes commutative.     

Rings with Maximal Finite Subrings

In[1 ] and[2 ] ,itwas proved thata ring with a finite maximal subring mustbe finite.Special cases of this result had been shown for commutative ring(see[3 ] ) and for PI-rings (see [4 ] ) . Lanski[5] extends the result to the ring with a finite maximal invariantsubring with respect to certain automorphism.In this paper,we shall consider ringswith maximal finite subrings. Such a ring,of course,is not necessarily finite. Becauseevery finite ring has maximal finite subrings,we shall be interest…     

<Emphasis Type="Italic">k</Emphasis>-factors in regular graphs

Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular （2n ＋ 1）-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and （or） excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik＇s result and the results obtained by Liu et al. in 1998, and improve Katerinis＇ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.     

The Commutator of the Kato Square Root for Second Order Elliptic Operators on R~n

Let L=-div(A?) be a second order divergence form elliptic operator,and A be an accretive,n×n matrix with bounded measurable complex coefficients in R~n.We obtain the L~p bounds for the commutator generated by the Kato square root L~(1/2) and a Lipschitz function,which recovers a previous result of Calderón,by a different method.In this work,we develop a new theory for the commutators associated to elliptic operators with Lipschitz function.The theory of the commutator with Lipschitz function is distinguished from the analogous elliptic operator theory.     

Shrinking Projection Methods for a Family of Quasi-φ-Strict Asymptotically Pseudo-Contractions in Banach Spaces

The purpose of this article is to propose a shrinking projection method and prove a strong convergence theorem for a family of quasi-φ-strict asymptotically pseudo-contractions. Its results hold in reflexive, strictly convex, smooth Banach spaces with the property (K). The results of this paper improve and extend the results of Matsushita and Takahashi, Marino and Xu, Zhou and Gao and others.     

高阶抛物不等式组的Liouville型定理及其应用

In this paper, we establish a Liouville-type theorem for a system of higher-order parabolic inequalities by using the method of test functions and an integral estimate. As an application, we observe the Fujita blow-up phenomena for the corresponding parabolic system, which in particular fills up the gap in the recent result of Pang et. al. （Existence and nonexistence of global solutions for a higher-order semilinear parabolic system, Indiana Univ. Math. J., 55（2006）, 1113-1134）. Moreover, the importance of this observation is that we do not impose any regularity assumption on the initial data.     

Properties of Solutions of BSDEs with Integrable Parameters

The main result of this study is to obtain,using the localization method in Briand et al.Levi,Fatou and Lebesgue type theorems for the solutions of certain one-dimensional backward stochastic differentialequation(BSDEs)with integrable parameters with respect to the terminal condition.     

REFLECTION/TRANSMISSION CHARACTERISTICS OF A DISCONTINUOUS GALERKIN METHOD FOR MAXWELL＇S EQUATIONS IN DISPERSIVE INHOMOGENEOUS MEDIA

In this paper, we analyze the transmission and reflection properties of a high order discontinuous Galerkin method for dispersive Maxwell＇s equations, originally proposed by Lu et al. [J. Comput. Phys. 200 （2004）, pp. 549-580]. We study the reflection and transmission properties of the numerical method for up to second-order polynomial elements for one- and two-dimensional Maxwell＇s equations with rectangular meshes. High order accuracy has been shown for reflection and transmission coefficients near material interfaces.     

对于金融资产波动率估计的双域组合方法

Time- and state-domain methods are two common approaches for nonparametrically estimating the volatility of financial assets. Economic conditions vary over time in real financial market. It is reasonable to expect that volatility depends on both time and price level for a given state variable. Recently, Fan, et al （2007） proposed the idea of dynamically integrated method in both time-and state domain. This idea has become an interesting topic in the estimation of volatility. In this paper, our purpose is to discuss the integrated method in the estimation of volatility. Simulations are conducted to demonstrate that the newly integrated method outperforms some old ones, and the results of simulations demonstrate this fact. Furthermore, we establish its asymptotic properties.     

MUSIC ALGORITHM FOR LOCATING POINT-LIKE SCATTERERS CONTAINED IN A SAMPLE ON FLAT SUBSTRATE

In this paper, we consider a MUSIC algorithm for locating point-like scatterers contained in a sample on flat substrate. Based on an asymptotic expansion of the scattering amplitude proposed by Ammari et al., the reconstruction problem can be reduced to a calculation of Green function corresponding to the background medium. In addition, we use an explicit formulation of Green function in the MUSIC algorithm to simplify the calculation when the cross-section of sample is a half-disc. Numerical experiments are included to demonstrate the feasibility of this method.     

Computing polynomial univariate representations of zero-dimensional ideals by Grbner basis

Rational Univariate Representation(RUR) of zero-dimensional ideals is used to describe the zeros of zero-dimensional ideals and RUR has been studied extensively.In 1999,Roullier proposed an efficient algorithm to compute RUR of zero-dimensional ideals.In this paper,we will present a new algorithm to compute Polynomial Univariate Representation(PUR) of zero-dimensional ideals.The new algorithm is based on some interesting properties of Grbner basis.The new algorithm also provides a method for testing separating elements.