For a graph G and two positive integers j and k an m-L j k -edge-labeling of G is an assignment from the set 0 1 … m-to the edges such that adjacent edges receive labels that differ by at least j and edges at distanc...For a graph G and two positive integers j and k an m-L j k -edge-labeling of G is an assignment from the set 0 1 … m-to the edges such that adjacent edges receive labels that differ by at least j and edges at distance two receive labels that differ by at least k.Theλ′j k-number of G denoted byλ′j k G is the minimum integer m overall m-L j k -edge-labeling of G.The necklace is a specific type of Halin graph.The L 1 2 -edge-labeling of necklaces is studied and the lower and upper bounds on λ′1 2-number for necklaces are given.Also both the lower and upper bounds are attainable.展开更多
Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.
Using the resolution of unity composed of bosonic creation operator＇s eigenkets and annihilation operator＇s un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we de...Using the resolution of unity composed of bosonic creation operator＇s eigenkets and annihilation operator＇s un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we derive new contour integration expression of associated Laguerre polynomials L^ρm （｜z｜^2） and its generalized generating function formula. A series of recursive relations regarding to L^ρm （｜z｜^2） are also deduced in the context of the Fock representation by algebraic method.展开更多
Global long-term emission reduction targets need well defined options for equitable allocation of greenhouse gas emissions. Scholars from developing countries put forward the concept of equitable per capita cumulative...Global long-term emission reduction targets need well defined options for equitable allocation of greenhouse gas emissions. Scholars from developing countries put forward the concept of equitable per capita cumulative emission rights. There are four possible operational definitions resulting from this concept. These potential options for allocation of emission rights are expressed with mathematical equations. Through simple simulation, this paper reveals the advantages, disadvantages and characteristics of each option.展开更多
In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smoo...In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.展开更多
We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state ＂related to Laughlin wave function＂. The entangled state representatio...We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state ＂related to Laughlin wave function＂. The entangled state representation for describing electrons in uniform magnetic field is used.展开更多
In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it...In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals with same and different screening parameters mentioned as finite sums of Gegenbauer, Gaunt, binomial coefficients, and STOs.展开更多
基金The National Natural Science Foundation of China(No.10971025,10901035)
文摘For a graph G and two positive integers j and k an m-L j k -edge-labeling of G is an assignment from the set 0 1 … m-to the edges such that adjacent edges receive labels that differ by at least j and edges at distance two receive labels that differ by at least k.Theλ′j k-number of G denoted byλ′j k G is the minimum integer m overall m-L j k -edge-labeling of G.The necklace is a specific type of Halin graph.The L 1 2 -edge-labeling of necklaces is studied and the lower and upper bounds on λ′1 2-number for necklaces are given.Also both the lower and upper bounds are attainable.
文摘Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.
基金supported by the Specialized Research Fund for the Doctorial Progress of Higher Education of China under Grant No.20070358009
文摘Using the resolution of unity composed of bosonic creation operator＇s eigenkets and annihilation operator＇s un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we derive new contour integration expression of associated Laguerre polynomials L^ρm （｜z｜^2） and its generalized generating function formula. A series of recursive relations regarding to L^ρm （｜z｜^2） are also deduced in the context of the Fock representation by algebraic method.
基金supported by the 2009 special study project employing basic scientific research fund of the Academy of Macroeconomic Research of NDRC
文摘Global long-term emission reduction targets need well defined options for equitable allocation of greenhouse gas emissions. Scholars from developing countries put forward the concept of equitable per capita cumulative emission rights. There are four possible operational definitions resulting from this concept. These potential options for allocation of emission rights are expressed with mathematical equations. Through simple simulation, this paper reveals the advantages, disadvantages and characteristics of each option.
文摘In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056
文摘We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state ＂related to Laughlin wave function＂. The entangled state representation for describing electrons in uniform magnetic field is used.
文摘In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals with same and different screening parameters mentioned as finite sums of Gegenbauer, Gaunt, binomial coefficients, and STOs.
