A general formula for phonon-assisted n-photon absorption in solids is obtained by （n ＋ 1）-th order perturbation technique. The complicated calculation process for transition element of n-photon absorption is simpl...A general formula for phonon-assisted n-photon absorption in solids is obtained by （n ＋ 1）-th order perturbation technique. The complicated calculation process for transition element of n-photon absorption is simply demonstrated by a diagram approach that is proposed in this work. We find that the transition element for the n-photon absorption has a simple form, i.e., it is just the first term of the n-th order fist kind Bessel function.展开更多
This note concerns the motion of relativistic strings in the Minkowski space R^(1+n).We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is differen...This note concerns the motion of relativistic strings in the Minkowski space R^(1+n).We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is different completelyfrom others.展开更多
General interpolation formulae for barycentric interpolation and barycen- tric rational Hermite interpolation are established by introducing multiple parameters, which include many kinds of barycentric interpolation a...General interpolation formulae for barycentric interpolation and barycen- tric rational Hermite interpolation are established by introducing multiple parameters, which include many kinds of barycentric interpolation and barycentric rational Her- mite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method.展开更多
In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of ho...In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices. It provides a concrete and applicable model to solve the relevant problem with computer.展开更多
It is very difficult, sometimes impossible, to get a formula solution of recurrence relation, even for the case of homogeneous recurrence with one indite. In this paper, according to the principle of soluting algebrai...It is very difficult, sometimes impossible, to get a formula solution of recurrence relation, even for the case of homogeneous recurrence with one indite. In this paper, according to the principle of soluting algebraic equation, we present the formula of solution for a class of recurrnce relations with two indices by appling iteration and induction. It provides a concrete model to solve the concerning problems with modern computing tools.展开更多
Methods for the analysis of heat exchangers with various flow arrangements modeling,design,and performance are essential for heat transfer system modeling and its integration with other energy system models.This paper...Methods for the analysis of heat exchangers with various flow arrangements modeling,design,and performance are essential for heat transfer system modeling and its integration with other energy system models.This paper proposes the use of the linear-transfer law for the heat exchanger design and performance analysis as a function of the thermal resistance related to the ratio of a linear temperature difference to the total heat transfer rate.Additionally,we derived a correction factor that represents the influence of the flow arrangement on the heat transfer performance by the effective thermal conductance,as a function of correction factor,heat transfer coefficient,and surface area.Based on the effective thermal conductance,we propose the hot-end NTU and cold-end NTU for deriving a standardized and general thermal resistance formula for different types of heat exchangers by the combination of the correction factor with linear-transfer law.Moreover,for parallel-flow,cross-flow,and 1-2 Tubular Exchanger Manufacturers Association(TEMA)E shell-and-tube heat exchangers,we derived and obtained alternative correction factor expressions without introducing any temperatures.Two cases about heat exchanger design and performance analysis show that the calculation processes using the correction factor-based general thermal resistance are straightforward without any iteration and the calculation results are accurate.Finally,the experimental validation shows that the general thermal resistance formula is appropriate for analyzing the heat transfer performance.That is,the correction factor-based general thermal resistance formula provides a standardized model for heat exchanger analysis and heat transfer/integrated energy system modeling using the heat current method.展开更多
By combining geographic information system (GIS), a new conception of “group” in which covers the complex connected region is introduced in the paper. Based on the conception of group, a generalized Euler formula an...By combining geographic information system (GIS), a new conception of “group” in which covers the complex connected region is introduced in the paper. Based on the conception of group, a generalized Euler formula and its properties are deduced and proved. The paper also describes the mathematical principles of generating topological information of polygon in GIS maps and the methods for checking up the veracity of topological relations of the map with Euler formula and general Euler formula. We have also obtained the quantitative relations among real nodes, chains, islands and groups with the formulas. At the same time, the paper introduces Whole Sphere Stereographic (WSS) projection into the GIS, and defines a new conception of “sea”. The deduction of general Euler formula and the introduction of WSS projection to GIS have developed new ways of delineating GIS topological models from plane to sphere and even constructing three dimensional (3-D) topological models.展开更多
In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions. It provides a con...In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions. It provides a concrete model to solve the concerned prob-lems with modern computing tools.展开更多
In this paper, we present the explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices by applying iteration and induction. It provides a concrete ...In this paper, we present the explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices by applying iteration and induction. It provides a concrete and applicable model to solve the relevant problem with computer.展开更多
基金National Natural Science Foundation of China under Grant Nos.10371070 and 10671121the Foundation of Shanghai Education Committee for Shanghai Prospective Excellent Young Teachers,the Youth Foundation of Shanghai Education Committee,and Magnolia Grant of Shanghai Sciences and Technology Committee
文摘Some general formulas in the Sato theory related to the nonisospectral KP and mKP hierarchies are derived for simplifying calculations.
基金Project supported by the National High Technology Research and Development Program of China (863 Program) (Grant Nos. 2007AA804233 and 2008AA804050)the Fundamental Research Funds for the Central Universities (Grant Nos. ZYGX2009J046 and ZYGX2009X007)
文摘A general formula for phonon-assisted n-photon absorption in solids is obtained by （n ＋ 1）-th order perturbation technique. The complicated calculation process for transition element of n-photon absorption is simply demonstrated by a diagram approach that is proposed in this work. We find that the transition element for the n-photon absorption has a simple form, i.e., it is just the first term of the n-th order fist kind Bessel function.
基金Supported in part by the NSF of China under Grant No.10671124the NCET of China under Grant No.-05-0390
文摘This note concerns the motion of relativistic strings in the Minkowski space R^(1+n).We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is different completelyfrom others.
基金supported by the grant of Key Scientific Research Foundation of Education Department of Anhui Province, No. KJ2014A210
文摘General interpolation formulae for barycentric interpolation and barycen- tric rational Hermite interpolation are established by introducing multiple parameters, which include many kinds of barycentric interpolation and barycentric rational Her- mite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method.
文摘In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices. It provides a concrete and applicable model to solve the relevant problem with computer.
基金Supported by the National Natural Science Foun-dation of China (10071059)
文摘It is very difficult, sometimes impossible, to get a formula solution of recurrence relation, even for the case of homogeneous recurrence with one indite. In this paper, according to the principle of soluting algebraic equation, we present the formula of solution for a class of recurrnce relations with two indices by appling iteration and induction. It provides a concrete model to solve the concerning problems with modern computing tools.
基金the National Natural Science Foundation of China(Grant Nos.51806119 and 51836004)the Fundamental Research Funds for the Central Universities(2020MS010)。
文摘Methods for the analysis of heat exchangers with various flow arrangements modeling,design,and performance are essential for heat transfer system modeling and its integration with other energy system models.This paper proposes the use of the linear-transfer law for the heat exchanger design and performance analysis as a function of the thermal resistance related to the ratio of a linear temperature difference to the total heat transfer rate.Additionally,we derived a correction factor that represents the influence of the flow arrangement on the heat transfer performance by the effective thermal conductance,as a function of correction factor,heat transfer coefficient,and surface area.Based on the effective thermal conductance,we propose the hot-end NTU and cold-end NTU for deriving a standardized and general thermal resistance formula for different types of heat exchangers by the combination of the correction factor with linear-transfer law.Moreover,for parallel-flow,cross-flow,and 1-2 Tubular Exchanger Manufacturers Association(TEMA)E shell-and-tube heat exchangers,we derived and obtained alternative correction factor expressions without introducing any temperatures.Two cases about heat exchanger design and performance analysis show that the calculation processes using the correction factor-based general thermal resistance are straightforward without any iteration and the calculation results are accurate.Finally,the experimental validation shows that the general thermal resistance formula is appropriate for analyzing the heat transfer performance.That is,the correction factor-based general thermal resistance formula provides a standardized model for heat exchanger analysis and heat transfer/integrated energy system modeling using the heat current method.
文摘By combining geographic information system (GIS), a new conception of “group” in which covers the complex connected region is introduced in the paper. Based on the conception of group, a generalized Euler formula and its properties are deduced and proved. The paper also describes the mathematical principles of generating topological information of polygon in GIS maps and the methods for checking up the veracity of topological relations of the map with Euler formula and general Euler formula. We have also obtained the quantitative relations among real nodes, chains, islands and groups with the formulas. At the same time, the paper introduces Whole Sphere Stereographic (WSS) projection into the GIS, and defines a new conception of “sea”. The deduction of general Euler formula and the introduction of WSS projection to GIS have developed new ways of delineating GIS topological models from plane to sphere and even constructing three dimensional (3-D) topological models.
基金Supported by the National Natural Science Foundation of China (70871094)
文摘In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions. It provides a concrete model to solve the concerned prob-lems with modern computing tools.
基金Supported by the National Natural Science Foundation of China (70871094)
文摘In this paper, we present the explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices by applying iteration and induction. It provides a concrete and applicable model to solve the relevant problem with computer.
