This paper considers the scalar differential delay equation x（t） -μ x（t）-f（x（t-τ））, where f（x） is a decreasing continuous function. By proving that all solutions will beultimately in some interval, we give...This paper considers the scalar differential delay equation x（t） -μ x（t）-f（x（t-τ））, where f（x） is a decreasing continuous function. By proving that all solutions will beultimately in some interval, we give tile conditions under which the unique equilibrium pointof the differential delay equation is globally attractive.展开更多
We discuss a variant of restarted GMRES method that allows changes of the restarting vector at each cycle of iterations.The merit of the variant is that previously generated information can be utilized to select a new...We discuss a variant of restarted GMRES method that allows changes of the restarting vector at each cycle of iterations.The merit of the variant is that previously generated information can be utilized to select a new starting vector,such that the occurrence of stagnation be mitigated or the convergence be accelerated.The more appealing utilization of the new method is in conjunction with a harmonic Ritz vector as the starting vector,which is discussed in detail.Numerical experiments are carried out to demonstrate that the proposed procedure can effectively mitigate the occurrence of stagnation due to the presence of small eigenvalues in modulus.展开更多
In the preceding paper [Commun. Theor. Phys. 51 （2009） 321] we have recommended a convenient method for disentangling exponential operators in the form of exp{B ＋ C}, trying to find an operator A that satisfies [A,...In the preceding paper [Commun. Theor. Phys. 51 （2009） 321] we have recommended a convenient method for disentangling exponential operators in the form of exp{B ＋ C}, trying to find an operator A that satisfies [A, B] = C, and [A, [A, B]] = 0, then from the Baker-Hausdorff formula we have exp{B ＋C} ： exp（B ＋ [A, B]} = e^A e^B e^-A. After arranging e^Ae^B = e^B e^A e^W, the disentangling exp{B ＋ C} = e^B e^W is obtained. In this work we use this method to two-mode case, especially, derive the normal ordering form of exp[h（a^＋a ＋ b^＋b） ＋ ga^＋b^＋ ＋ kab] without appealing to Lie algebra method.展开更多
Geodesic forms constitute an important family of structural systems. They are efficient and appealing and are employed frequently for dome structures. Data generation for geodesic forms has always been a difficult tas...Geodesic forms constitute an important family of structural systems. They are efficient and appealing and are employed frequently for dome structures. Data generation for geodesic forms has always been a difficult task, from the days of hand data generation using tables of coefficients to today＇s specially written computer programs with many limitations and shortcomings. Formex algebra is a mathematical system which is ideally suited for data generation and configuration processing. The objective of the present paper is to introduce the concepts of formex algebra through which data generation for polyhedric and geodesic forms can be handled with ease and elegance.展开更多
In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field...In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field of research, the applications of integral inequalities have known a great development in many branches of mathematics in statistics, differential equations and numerical integration, The aim of this paper is to establish new extension of the weighted montgomery identity for double integrals then used it to establish new t^eby^evtype inequalities.展开更多
文摘This paper considers the scalar differential delay equation x（t） -μ x（t）-f（x（t-τ））, where f（x） is a decreasing continuous function. By proving that all solutions will beultimately in some interval, we give tile conditions under which the unique equilibrium pointof the differential delay equation is globally attractive.
文摘We discuss a variant of restarted GMRES method that allows changes of the restarting vector at each cycle of iterations.The merit of the variant is that previously generated information can be utilized to select a new starting vector,such that the occurrence of stagnation be mitigated or the convergence be accelerated.The more appealing utilization of the new method is in conjunction with a harmonic Ritz vector as the starting vector,which is discussed in detail.Numerical experiments are carried out to demonstrate that the proposed procedure can effectively mitigate the occurrence of stagnation due to the presence of small eigenvalues in modulus.
基金supported by the National Natural Science Foundation of China under Grant Nos.10775097 and 10874174
文摘In the preceding paper [Commun. Theor. Phys. 51 （2009） 321] we have recommended a convenient method for disentangling exponential operators in the form of exp{B ＋ C}, trying to find an operator A that satisfies [A, B] = C, and [A, [A, B]] = 0, then from the Baker-Hausdorff formula we have exp{B ＋C} ： exp（B ＋ [A, B]} = e^A e^B e^-A. After arranging e^Ae^B = e^B e^A e^W, the disentangling exp{B ＋ C} = e^B e^W is obtained. In this work we use this method to two-mode case, especially, derive the normal ordering form of exp[h（a^＋a ＋ b^＋b） ＋ ga^＋b^＋ ＋ kab] without appealing to Lie algebra method.
文摘Geodesic forms constitute an important family of structural systems. They are efficient and appealing and are employed frequently for dome structures. Data generation for geodesic forms has always been a difficult task, from the days of hand data generation using tables of coefficients to today＇s specially written computer programs with many limitations and shortcomings. Formex algebra is a mathematical system which is ideally suited for data generation and configuration processing. The objective of the present paper is to introduce the concepts of formex algebra through which data generation for polyhedric and geodesic forms can be handled with ease and elegance.
文摘In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field of research, the applications of integral inequalities have known a great development in many branches of mathematics in statistics, differential equations and numerical integration, The aim of this paper is to establish new extension of the weighted montgomery identity for double integrals then used it to establish new t^eby^evtype inequalities.
