We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential p...We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential polynomials of entire functions sharing a common value.展开更多
We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functions. The represen...We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functions. The representation of semigroup of Cauchy problem solutions for considered functional differential equation is given by the Feynman formulas.展开更多
In this paper we extend the theory of Grbner bases to difference-differential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module eq...In this paper we extend the theory of Grbner 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 Grbner bases counterparts. To this aim we introduce the concept of "generalized term order" on Nm ×Zn and on difference-differential modules. Using Grbner 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.展开更多
Insa and Pauer presented a basic theory of Grbner bases for differential operators with coefficients in a commutative ring and an improved version of this result was given by Ma et al.In this paper,we present an algor...Insa and Pauer presented a basic theory of Grbner bases for differential operators with coefficients in a commutative ring and an improved version of this result was given by Ma et al.In this paper,we present an algorithmic approach for computing Grbner bases in difference-differential modules with coefficients in a commutative ring.We combine the generalized term order method of Zhou and Winkler with SPoly method of Insa and Pauer to deal with the problem.Our result is a generalization of theories of Insa and Pauer,Ma et al.,Zhou and Winkler and includes them as special cases.展开更多
In this paper, a bivariate stochastic process with Poisson postulates has been considered to model the incomings, outgoings and mutual transfers of investments between and within the portfolios during an epoch of time...In this paper, a bivariate stochastic process with Poisson postulates has been considered to model the incomings, outgoings and mutual transfers of investments between and within the portfolios during an epoch of time “t”. Stochastic differential equations were obtained from the simple differential difference equations during the epoch of time “Δt”. The notion of bivariate linear birth, death and migration process has been utilized for measuring various statistical characteristics among the investments of Long and Short terms. All possible fluctuations in the investment flow have been considered to explore more meaningful assumptions with contemporary marketing environments. Mathematical relations for proposed statistical measures such as average sizes and variances of short term and long-term investments along with the correlation coefficient between them are derived after obtaining the related differential equations. Numerical illustrations were provided for better understanding of the developed models with practitioner’s point of view.展开更多
The objective of the paper is to derive new simple criteria for the stability of alinear non-autonomous delay system by using a difference-differential inequality.
We introduce the concept of difference-differential degree compatibility on generalized term orders. Then we prove that in the process of the algorithm the polynomials with higher and higher degree would not be produc...We introduce the concept of difference-differential degree compatibility on generalized term orders. Then we prove that in the process of the algorithm the polynomials with higher and higher degree would not be produced, if the term orders ＇ and ＇ ＇ are difference-differential degree compatibility. So we present a condition on the generalized orders and prove that under the condition the algorithm for computing relative GrSbner bases will terminate. Also the relative Gr6bner bases exist under the condition. Finally, we prove the algorithm for computation of the bivariate dimension polynomials in difference-differential modules terminates.展开更多
基金supported by the NSFC(11026110,11101201)the NSF of Jiangxi(2010GQS0144)
文摘We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions. We also investigate the uniqueness problems of difference-differential polynomials of entire functions sharing a common value.
文摘We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functions. The representation of semigroup of Cauchy problem solutions for considered functional differential equation is given by the Feynman formulas.
基金supported by the National Natural Science Foundation of China (Grant No. 60473019)the KLMM (Grant No. 0705)
文摘In this paper we extend the theory of Grbner 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 Grbner bases counterparts. To this aim we introduce the concept of "generalized term order" on Nm ×Zn and on difference-differential modules. Using Grbner 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.
基金supported by National Natural Science Foundation of China (Grant No.10871017)Natural Science Foundation of Beijing (Grant No. 1102026)
文摘Insa and Pauer presented a basic theory of Grbner bases for differential operators with coefficients in a commutative ring and an improved version of this result was given by Ma et al.In this paper,we present an algorithmic approach for computing Grbner bases in difference-differential modules with coefficients in a commutative ring.We combine the generalized term order method of Zhou and Winkler with SPoly method of Insa and Pauer to deal with the problem.Our result is a generalization of theories of Insa and Pauer,Ma et al.,Zhou and Winkler and includes them as special cases.
文摘In this paper, a bivariate stochastic process with Poisson postulates has been considered to model the incomings, outgoings and mutual transfers of investments between and within the portfolios during an epoch of time “t”. Stochastic differential equations were obtained from the simple differential difference equations during the epoch of time “Δt”. The notion of bivariate linear birth, death and migration process has been utilized for measuring various statistical characteristics among the investments of Long and Short terms. All possible fluctuations in the investment flow have been considered to explore more meaningful assumptions with contemporary marketing environments. Mathematical relations for proposed statistical measures such as average sizes and variances of short term and long-term investments along with the correlation coefficient between them are derived after obtaining the related differential equations. Numerical illustrations were provided for better understanding of the developed models with practitioner’s point of view.
文摘The objective of the paper is to derive new simple criteria for the stability of alinear non-autonomous delay system by using a difference-differential inequality.
基金Acknowledgements The authors thank the anonymous referees for their constructive comments and suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11271040）.
文摘We introduce the concept of difference-differential degree compatibility on generalized term orders. Then we prove that in the process of the algorithm the polynomials with higher and higher degree would not be produced, if the term orders ＇ and ＇ ＇ are difference-differential degree compatibility. So we present a condition on the generalized orders and prove that under the condition the algorithm for computing relative GrSbner bases will terminate. Also the relative Gr6bner bases exist under the condition. Finally, we prove the algorithm for computation of the bivariate dimension polynomials in difference-differential modules terminates.
