Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet ...Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.展开更多
In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal ste...In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.展开更多
Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continu...Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.展开更多
We present photometric observations in Sloan filters g′, i′of the eclipsing W UMa stars USNOA2.0 1350-17365531, V471 Cas, V479 Lac and V560 Lac. The sinusoidal-like O-C diagram of V471 Cas indicates the presence of ...We present photometric observations in Sloan filters g′, i′of the eclipsing W UMa stars USNOA2.0 1350-17365531, V471 Cas, V479 Lac and V560 Lac. The sinusoidal-like O-C diagram of V471 Cas indicates the presence of a third body with mass 0.12 M_⊙(a red dwarf) at distance 897 R_⊙. The O-C diagram of V479 Lac reveals a period decrease of d P/dt =-1.69 × 10-6d yr-1. The results of the light curve solutions are:(i) the targets are overcontact binaries with small fill-out factors;(ii) their components are F–K stars, comparable in size, whose temperature differences are below 80 K;(iii) all targets undergo partial eclipses and to limit the possible mass ratios we carried out two-step q-search analysis. The target global parameters(luminosities, radii, masses) were obtained on the basis of their Gaia distances and the results of our light curve solutions. The obtained total mass of V560 Lac turns out to be smaller than the lower mass limit for presently known W UMa binaries of 1.0-1.2 M_⊙, i.e. this target is a peculiar overcontact system.展开更多
Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classic...Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.展开更多
基金the National Natural Science Foundation of China (Nos.11571238,11601332,91130014,11471312 and 91430216).
文摘Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.
基金The research is supported by the National Natural Science Foundation of China(No.11671081)the Fundamental Research Funds for the Central Universities(No.242017K41044).
文摘In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.
基金Project supported by D.G.E.S. Pb 96-1338-CO 2-01 and the Junta de Andalucia
文摘Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.
基金supported partly by project DN08/20 of the Scientific Foundation of the Bulgarian Ministry of Education and Scienceby project RD 08-142 of Shumen University+1 种基金the support of the private IRIDA Observatory operated remotely(www.iridaobservatory.org)Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement
文摘We present photometric observations in Sloan filters g′, i′of the eclipsing W UMa stars USNOA2.0 1350-17365531, V471 Cas, V479 Lac and V560 Lac. The sinusoidal-like O-C diagram of V471 Cas indicates the presence of a third body with mass 0.12 M_⊙(a red dwarf) at distance 897 R_⊙. The O-C diagram of V479 Lac reveals a period decrease of d P/dt =-1.69 × 10-6d yr-1. The results of the light curve solutions are:(i) the targets are overcontact binaries with small fill-out factors;(ii) their components are F–K stars, comparable in size, whose temperature differences are below 80 K;(iii) all targets undergo partial eclipses and to limit the possible mass ratios we carried out two-step q-search analysis. The target global parameters(luminosities, radii, masses) were obtained on the basis of their Gaia distances and the results of our light curve solutions. The obtained total mass of V560 Lac turns out to be smaller than the lower mass limit for presently known W UMa binaries of 1.0-1.2 M_⊙, i.e. this target is a peculiar overcontact system.
文摘Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.
