The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler...The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.展开更多
Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky （KS） equation. The approximate symm...Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky （KS） equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here.展开更多
The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains a...The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.展开更多
Let M1, M2 be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2 and dimM1/M2 = k < '. If M2 is an AF-cosubmodule, then the codimension dimM1/M2 of M2 in M1 equals the cardinality of zeros of ...Let M1, M2 be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2 and dimM1/M2 = k < '. If M2 is an AF-cosubmodule, then the codimension dimM1/M2 of M2 in M1 equals the cardinality of zeros of M2 related to MI by counting multiplicities. The codimension formula has some interesting applications. In particular, the author calculates out the dimension of Rudin quotient module, which is raised in [14].展开更多
The paper presents a simplified numerical model of evaporation processes inside vertical tubes.In this model only the temperature fields in the fluid domain(the liquid or two-phase mixture) and solid domain(a tube wal...The paper presents a simplified numerical model of evaporation processes inside vertical tubes.In this model only the temperature fields in the fluid domain(the liquid or two-phase mixture) and solid domain(a tube wall) are determined.Therefore its performance and efficiency is high.The analytical formulas,which allow calculating the pressure drop and the distribution of heat transfer coefficient along the tube length,are used in this model.The energy equation for the fluid domain is solved with the Control Volume Method and for the solid domain with the Finite Element Method in order to determine the temperature field for the fluid and solid domains.展开更多
The Nagumo equation ut = △u+ bu(u-a)(1-u), t＞0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and...The Nagumo equation ut = △u+ bu(u-a)(1-u), t＞0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the 'pathological' property of the fractal. However, it is shown that a global Holder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl's formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.展开更多
基金Supported by the NNSF of China(10001016) SF for the Prominent Youth of Henan Province
文摘The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.
基金The project supported by National Natural Science Foundations of China under Grant Nos. 10735030, 10475055, and 90503006； the Natural Science Research Plan in Shaanxi Province under Grant No. SJ08A09； the Research Fund of Postdoctoral of China under Grant No. 20070410727；the Research Found of Shaanxi Normal University
文摘Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky （KS） equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here.
基金Project supported by the Spanish Ministry of Science and Technology Grants MTM2005-O8689-G02-02 and MTM 2004-06015-C02-01.
文摘The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.
基金National Natural Science Foundation of China(No.10171019)Shuguan Project Shanghai and the Young Teacher Fund of Higher School of the Ministry of Education of China
文摘Let M1, M2 be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2 and dimM1/M2 = k < '. If M2 is an AF-cosubmodule, then the codimension dimM1/M2 of M2 in M1 equals the cardinality of zeros of M2 related to MI by counting multiplicities. The codimension formula has some interesting applications. In particular, the author calculates out the dimension of Rudin quotient module, which is raised in [14].
文摘The paper presents a simplified numerical model of evaporation processes inside vertical tubes.In this model only the temperature fields in the fluid domain(the liquid or two-phase mixture) and solid domain(a tube wall) are determined.Therefore its performance and efficiency is high.The analytical formulas,which allow calculating the pressure drop and the distribution of heat transfer coefficient along the tube length,are used in this model.The energy equation for the fluid domain is solved with the Control Volume Method and for the solid domain with the Finite Element Method in order to determine the temperature field for the fluid and solid domains.
文摘The Nagumo equation ut = △u+ bu(u-a)(1-u), t＞0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the 'pathological' property of the fractal. However, it is shown that a global Holder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl's formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.
