We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)d_r^m where f(r) = r~μ, r~μjJ(qr)...We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)d_r^m where f(r) = r~μ, r~μjJ(qr), V(r)corresponding to the Gaussian and the Yukawa potentials used in nuclear shell models and nuclear structure. In addition,we take into account a general integral formula of the matrix element 〈 n′ l′|f(r) d_r^(m) |n l〉 that covers all seven matrix elements obtained analytically.展开更多
The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case, of operator's square is discussed ...The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case, of operator's square is discussed in details. The two-dimensional Dirac oscillator has similar behavior to that for three-dimensional one.展开更多
Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary m...Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.展开更多
We present an analysis of a recent approach for determining the average pairing matrix elements within a specified interval of single-particle(sp)states around the Fermi level,denoted asλ.This method,known as the uni...We present an analysis of a recent approach for determining the average pairing matrix elements within a specified interval of single-particle(sp)states around the Fermi level,denoted asλ.This method,known as the uniform gap method(UGM),highlights the critical importance of the averaged sp level density.The pairing matrix elements within the UGM approach are deduced from microscopically calculated values of and gaps obtained from analytical formulae of a semi-classical nature.Two effects generally ignored in similar fits are addressed:(a)a correction for a systematic bias introduced by fitting pairing gaps corresponding to equilibrium deformation solutions,as discussed by Möller and Nix[Nucl.Phys.A 476,1(1992)],and(b)a correction for a systematic spurious enhancement of for protons in the vicinity ofλ,caused by the local Slater approximation commonly employed in treating Coulomb exchange terms(e.g.,[Phys.Rev.C 84,014310(2011)]).This approach has demonstrated significant efficiency when applied to Hartree-Fock+Bardeen-Cooper-Schrieffer(BCS)calculations(including the seniority force and self-consistent blocking for odd nuclei)of a large sample of well and rigidly deformed even-even rare-earth nuclei.The experimental moments of inertia for these nuclei were reproduced with an accuracy comparable to that achieved through direct fitting of the data[Phys.Rev.C 99,064306(2019)].In this study,we extended the evaluation of our method to the reproduction of three-point odd-even mass differences centered on odd-N or odd-Z nuclei in the same region.The agreement with experimental data was found to be comparable to that obtained through direct fitting,as reported in[Phys.Rev.C 99,064306(2019)].展开更多
The matrix elements along the reduction chain Sp(12,R)⊃SU(1,1)⊗SO(6)⊃U(1)⊗SUpn(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM)are considered.Closed analytical expressions are obtained for the matrix element...The matrix elements along the reduction chain Sp(12,R)⊃SU(1,1)⊗SO(6)⊃U(1)⊗SUpn(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM)are considered.Closed analytical expressions are obtained for the matrix elements of the basic building blocks of the PNSM and the Sp(12,R)symplectic generators,allowing the computation of matrix elements of other physical operators as well.The computational technique developed in the present study generally provides us with the required algebraic tool for performing realistic symplectic-based shell-model calculations of nuclear collective excitations.Utilizing two simple examples,we illustrate the application of the theory.展开更多
In this work,the characteristics of 2νββ decays for six nuclei(36Ar,46Ca,48Ca,50Cr,70Zn,and 136Xe)in a mass range from A=36 to A=136 are studied within the nuclear shell model(NSM)framework.Calculations are present...In this work,the characteristics of 2νββ decays for six nuclei(36Ar,46Ca,48Ca,50Cr,70Zn,and 136Xe)in a mass range from A=36 to A=136 are studied within the nuclear shell model(NSM)framework.Calculations are presented for the half-lives,nuclear matrix elements(NMEs),phase space factors(G2ν),and convergence of the NMEs.The theoretical results agree well with the experimental data.In addition,we predict the half-lives of 2νββ decays for four nuclei.We focus on the convergence of the NMEs by analyzing the number of contributing intermediate 1+states(NC)for the nuclei of interest.We assume that NC is safely determined when the accumulated NMEs saturate 99.7%of the final calculated magnitude.From the calculations of the involved nuclei,we discover a connection between NC and the total number of intermediate 1+states(NT).According to the least squares fit,we conclude that the correlation is NC=(10.8±1.2)×N(0.29±0.02)T.展开更多
We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quant...We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.展开更多
Matrix metalloproteinase-9（MMP-9） plays a beneficial role in the sub-acute phase after ischemic stroke.However,unrestrained MMP-9 may disrupt the blood-brain barrier（BBB）,which has limited its use for the treatmen...Matrix metalloproteinase-9（MMP-9） plays a beneficial role in the sub-acute phase after ischemic stroke.However,unrestrained MMP-9 may disrupt the blood-brain barrier（BBB）,which has limited its use for the treatment of brain ischemia.In the present study,we constructed lentivirus mediated hypoxiacontrolled MMP-9 expression and explored its role after stroke.Hypoxia response element（HRE）was used to confine MMP-9 expression only to the hypoxic region of mouse brain after 120-min transient middle cerebral artery occlusion.Lentiviruses were injected into the peri-infarct area on day 7 after transient ischemia.We found hyperexpression of exogenous HRE-MMP-9 under the control of hypoxia,and its expression was mainly located in neurons and astrocytes without aggravation of BBB damage compared to the CMV group.Furthermore,mice in the HRE-MMP-9 group showed the best behavioral recovery compared with the normal saline,GFP,and SB-3CT groups.Therefore,hypoxia-controlled MMP-9 hyperexpression during the sub-acute phase of ischemia may provide a novel promising approach of gene therapy for stroke.展开更多
Element stiffness equation is very important in structural analysis, and directly influences the accuracy of the results. At present, derivation method of element stiffness equation is relatively mature under ambient ...Element stiffness equation is very important in structural analysis, and directly influences the accuracy of the results. At present, derivation method of element stiffness equation is relatively mature under ambient temperature, and the elastic phrase of material stress-strain curve is generally adopted as physical equation in derivation. However, the material stress-strain relationship is very complicated at elevated temperature, and its form is not unique, which brings great difficulty to the derivation of element stiffness equation. Referring to the derivation method of element stiffness equation at ambient temperature, by using the continuous function of stress-strain-temperature at elevated temperature, and based on the principle of virtual work, the stiffness equation of space beam element and the formulas of stiffness matrix are derived in this paper, which provide basis for finite element analysis on structures at elevated temperature.展开更多
The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then...The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.展开更多
Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I ex...Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.展开更多
On the basis of concept of element node topological analysis, the normalized element node topological matrices for finite element meshes are presented in the paper, including 3-node and 6-node triangular element, 4-n...On the basis of concept of element node topological analysis, the normalized element node topological matrices for finite element meshes are presented in the paper, including 3-node and 6-node triangular element, 4-node and 8-node quadrilateral element, 8-node and 20-node hexahedral element. It is beneficial to further analyzing topological characteristics of finite element models and automatic generation of meshes展开更多
The explicit expressions of energy eigenvalues and eigenfunctions of bound states for a three-dimensional diatomic molecule oscillator with a hyperbolic potential function are obtained approximately by means of the hy...The explicit expressions of energy eigenvalues and eigenfunctions of bound states for a three-dimensional diatomic molecule oscillator with a hyperbolic potential function are obtained approximately by means of the hypergeometric series method. Then for a one-dimensional system, the rigorous solutions of bound states are solved with a similar method. The eigenfunctions of a one-dimensional diatomic molecule oscillator, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.展开更多
The wave functions,energy levels and matrix elements of Yb+ions are calculated using the relativistic configuration interaction plus core polarization(RCICP)method.The static and dynamic electric dipole polarizabiliti...The wave functions,energy levels and matrix elements of Yb+ions are calculated using the relativistic configuration interaction plus core polarization(RCICP)method.The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined.Then,the magic wavelengths of the magnetic sublevel 6s_(1/2,m=1/2)→5d_(3/2,m=±3/2,±1/2)and 6s_(1/2,m=1/2)→5_(d5/2,m=±5/2,±3/2,±1/2)transitions in the linearly,right-handed,and left-handed polarized light are further determined.The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.展开更多
The <img alt="" src="Edit_a001991b-d72d-4ec7-885a-6fd2c587397c.bmp" /> <span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;&qu...The <img alt="" src="Edit_a001991b-d72d-4ec7-885a-6fd2c587397c.bmp" /> <span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">doubly excited states of helium-like ions are investigated using a combination of the no-linear parameters of Hylleraas and the </span><i><span style="font-family:Verdana;">β</span></i><span style="font-family:Verdana;">-parameters of screening constant by unit nuclear charge. Calculations are performed for total energies of low-lying doubly excited states (</span><i><span style="font-family:Verdana;">N</span></i><span style="font-family:Verdana;"> = 2</span></span><span><span><span><span> </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span></span><span><span><span><span> </span></span></span></span><span><span><span><span><span style="font-family:Verdana;">9)</span><i> </i><span style="font-family:Verdana;">in He-like ions up to </span><i><span style="font-family:Verdana;">Z</span></i><span style="font-family:Verdana;"> = 10. The results obtained from the novel method are in good agreement with the available theoretical calculations and experimental observations.</span></span></span></span></span>展开更多
This work presents results of the different parameters which characterize the nonrelativistic Hamilton operator for the helium atoms allowing us to solve the Schrödinger equation. The total energy is decomposed i...This work presents results of the different parameters which characterize the nonrelativistic Hamilton operator for the helium atoms allowing us to solve the Schrödinger equation. The total energy is decomposed into three terms allowing to separate the kinetic energy, the electrons-nucleus interaction energy and the electron-electron interaction energy of the (2s<sup>2</sup>, 3s<sup>2</sup> and 4s<sup>2</sup>) <sup>1</sup>S<sup>e</sup>, (2p<sup>2</sup>, 3p<sup>2</sup> and 4p<sup>2</sup>) <sup>1</sup>D<sup>e</sup> and (3d<sup>2</sup> and 4d<sup>2</sup>) <sup>1</sup>G<sup>e</sup> resonance singlet states of the helium isoelectronic sequences. The states have been defined by using special forms of the Hylleraas type wave functions. The calculations have been carried out in the framework of the variational method using configuration interaction basis states with a real Hamiltonian. The agreement of the energy value of other states between the present theoretical values available in the literature is excellent. But as for the comparison of the kinetic energies, the electrons-nucleus energies interaction and the electron-electron interaction energies, we note a slight difference with the theoretical values common in literature.展开更多
For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is develo...For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.展开更多
The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical ex...The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical expressions of the matrix dements for both position and momentum operators are obtained.展开更多
A new approach applying fuzzy mathematic theorems, including the Primary Matrix Element Theorem and the Fisher Classification Method, was established to solve the optimization problem of atmospheric environmental samp...A new approach applying fuzzy mathematic theorems, including the Primary Matrix Element Theorem and the Fisher Classification Method, was established to solve the optimization problem of atmospheric environmental sampling sites. According to its basis, an application in the optimization of sampling sites in the atmospheric environmental monitoring was discussed. The method was proven to be suitable and effective. The results were admitted and applied by the Environmental Protection Bureau (EPB) of many cities of China. A set of computer software of this approach was also completely compiled and used.展开更多
In this article, we calculate the contribution from the nonfactorizable soft hadronic matrix element to the decay B^0→Xc1π^0 with the light-cone quantum chromo-dynamic （QCD） sum rules. The numerical results show t...In this article, we calculate the contribution from the nonfactorizable soft hadronic matrix element to the decay B^0→Xc1π^0 with the light-cone quantum chromo-dynamic （QCD） sum rules. The numerical results show that its contribution is rather large and should not be neglected. The total amplitudes lead to a branching fraction which is in agreement with the experimental data marginally.展开更多
文摘We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)d_r^m where f(r) = r~μ, r~μjJ(qr), V(r)corresponding to the Gaussian and the Yukawa potentials used in nuclear shell models and nuclear structure. In addition,we take into account a general integral formula of the matrix element 〈 n′ l′|f(r) d_r^(m) |n l〉 that covers all seven matrix elements obtained analytically.
基金The project supported by the Research Fund for the Doctorial Program of Higher Education of China under Grant No.20010284036+2 种基金National Natural Science Foundation of China under Grant No.10125521the 973 State Basic Key Research and Development of China under Grant No.G20000077400
文摘The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case, of operator's square is discussed in details. The two-dimensional Dirac oscillator has similar behavior to that for three-dimensional one.
基金The authors would like to thank Prof. Y.D. Zhang for selfless helps and valuable discussions.
文摘Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.
基金support by the Hue University under the Core Research Program,(NCM.DHH.2018.09)Universiti Teknologi Malaysia for its UTMShine grant(Q.J130000.2454.09G96)。
文摘We present an analysis of a recent approach for determining the average pairing matrix elements within a specified interval of single-particle(sp)states around the Fermi level,denoted asλ.This method,known as the uniform gap method(UGM),highlights the critical importance of the averaged sp level density.The pairing matrix elements within the UGM approach are deduced from microscopically calculated values of and gaps obtained from analytical formulae of a semi-classical nature.Two effects generally ignored in similar fits are addressed:(a)a correction for a systematic bias introduced by fitting pairing gaps corresponding to equilibrium deformation solutions,as discussed by Möller and Nix[Nucl.Phys.A 476,1(1992)],and(b)a correction for a systematic spurious enhancement of for protons in the vicinity ofλ,caused by the local Slater approximation commonly employed in treating Coulomb exchange terms(e.g.,[Phys.Rev.C 84,014310(2011)]).This approach has demonstrated significant efficiency when applied to Hartree-Fock+Bardeen-Cooper-Schrieffer(BCS)calculations(including the seniority force and self-consistent blocking for odd nuclei)of a large sample of well and rigidly deformed even-even rare-earth nuclei.The experimental moments of inertia for these nuclei were reproduced with an accuracy comparable to that achieved through direct fitting of the data[Phys.Rev.C 99,064306(2019)].In this study,we extended the evaluation of our method to the reproduction of three-point odd-even mass differences centered on odd-N or odd-Z nuclei in the same region.The agreement with experimental data was found to be comparable to that obtained through direct fitting,as reported in[Phys.Rev.C 99,064306(2019)].
文摘The matrix elements along the reduction chain Sp(12,R)⊃SU(1,1)⊗SO(6)⊃U(1)⊗SUpn(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM)are considered.Closed analytical expressions are obtained for the matrix elements of the basic building blocks of the PNSM and the Sp(12,R)symplectic generators,allowing the computation of matrix elements of other physical operators as well.The computational technique developed in the present study generally provides us with the required algebraic tool for performing realistic symplectic-based shell-model calculations of nuclear collective excitations.Utilizing two simple examples,we illustrate the application of the theory.
基金Supported by National Natural Science Foundation of China(11647086,11647085)Shanxi Province Science Foundation for Youths(201901D211252)+1 种基金Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(2019L0554,2019L0505)the Natural Science Research Fund of North University of China(XJJ201811)。
文摘In this work,the characteristics of 2νββ decays for six nuclei(36Ar,46Ca,48Ca,50Cr,70Zn,and 136Xe)in a mass range from A=36 to A=136 are studied within the nuclear shell model(NSM)framework.Calculations are presented for the half-lives,nuclear matrix elements(NMEs),phase space factors(G2ν),and convergence of the NMEs.The theoretical results agree well with the experimental data.In addition,we predict the half-lives of 2νββ decays for four nuclei.We focus on the convergence of the NMEs by analyzing the number of contributing intermediate 1+states(NC)for the nuclei of interest.We assume that NC is safely determined when the accumulated NMEs saturate 99.7%of the final calculated magnitude.From the calculations of the involved nuclei,we discover a connection between NC and the total number of intermediate 1+states(NT).According to the least squares fit,we conclude that the correlation is NC=(10.8±1.2)×N(0.29±0.02)T.
文摘We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.
基金supported by the grants from the National Natural Science Foundation of China (U1232205)the National Basic Research Development Program (973 Program) of China (2011CB504405)+2 种基金the Science and Technology Commission of Shanghai Municipality, China (13140903500 and 13ZR1422600)Shanghai Jiao Tong University Foundation for Technological Innovation in Major Projects (12X190030021)the KC Wong Foundation
文摘Matrix metalloproteinase-9（MMP-9） plays a beneficial role in the sub-acute phase after ischemic stroke.However,unrestrained MMP-9 may disrupt the blood-brain barrier（BBB）,which has limited its use for the treatment of brain ischemia.In the present study,we constructed lentivirus mediated hypoxiacontrolled MMP-9 expression and explored its role after stroke.Hypoxia response element（HRE）was used to confine MMP-9 expression only to the hypoxic region of mouse brain after 120-min transient middle cerebral artery occlusion.Lentiviruses were injected into the peri-infarct area on day 7 after transient ischemia.We found hyperexpression of exogenous HRE-MMP-9 under the control of hypoxia,and its expression was mainly located in neurons and astrocytes without aggravation of BBB damage compared to the CMV group.Furthermore,mice in the HRE-MMP-9 group showed the best behavioral recovery compared with the normal saline,GFP,and SB-3CT groups.Therefore,hypoxia-controlled MMP-9 hyperexpression during the sub-acute phase of ischemia may provide a novel promising approach of gene therapy for stroke.
基金the National Natural Science Foundation of China(No.50578093)
文摘Element stiffness equation is very important in structural analysis, and directly influences the accuracy of the results. At present, derivation method of element stiffness equation is relatively mature under ambient temperature, and the elastic phrase of material stress-strain curve is generally adopted as physical equation in derivation. However, the material stress-strain relationship is very complicated at elevated temperature, and its form is not unique, which brings great difficulty to the derivation of element stiffness equation. Referring to the derivation method of element stiffness equation at ambient temperature, by using the continuous function of stress-strain-temperature at elevated temperature, and based on the principle of virtual work, the stiffness equation of space beam element and the formulas of stiffness matrix are derived in this paper, which provide basis for finite element analysis on structures at elevated temperature.
文摘The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.
文摘Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.
文摘On the basis of concept of element node topological analysis, the normalized element node topological matrices for finite element meshes are presented in the paper, including 3-node and 6-node triangular element, 4-node and 8-node quadrilateral element, 8-node and 20-node hexahedral element. It is beneficial to further analyzing topological characteristics of finite element models and automatic generation of meshes
基金Project supported by the National Natural Science Foundation of China （Grant No 90403028）.
文摘The explicit expressions of energy eigenvalues and eigenfunctions of bound states for a three-dimensional diatomic molecule oscillator with a hyperbolic potential function are obtained approximately by means of the hypergeometric series method. Then for a one-dimensional system, the rigorous solutions of bound states are solved with a similar method. The eigenfunctions of a one-dimensional diatomic molecule oscillator, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.
基金the National Key Research and Development Program of China(Grant No.2022YFA1602500)the National Natural Science Foundation of China(Grant Nos.12174316 and 12174268)+2 种基金the Young Teachers Scientific Research Ability Promotion Plan of Northwest Normal University(Grant No.NWNU-LKQN2020-10)the Innovative Fundamental Research Group Project of Gansu Province,China(Grant No.20JR5RA541)the Project of the Educational Commission of Guangdong Province of China(Grant No.2020KTSCX124)。
文摘The wave functions,energy levels and matrix elements of Yb+ions are calculated using the relativistic configuration interaction plus core polarization(RCICP)method.The static and dynamic electric dipole polarizabilities of the ground state and low-lying excited states are determined.Then,the magic wavelengths of the magnetic sublevel 6s_(1/2,m=1/2)→5d_(3/2,m=±3/2,±1/2)and 6s_(1/2,m=1/2)→5_(d5/2,m=±5/2,±3/2,±1/2)transitions in the linearly,right-handed,and left-handed polarized light are further determined.The dependence of the magic wavelengths upon the angle between the direction of magnetic field and the direction of laser polarization is analyzed.
文摘The <img alt="" src="Edit_a001991b-d72d-4ec7-885a-6fd2c587397c.bmp" /> <span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">doubly excited states of helium-like ions are investigated using a combination of the no-linear parameters of Hylleraas and the </span><i><span style="font-family:Verdana;">β</span></i><span style="font-family:Verdana;">-parameters of screening constant by unit nuclear charge. Calculations are performed for total energies of low-lying doubly excited states (</span><i><span style="font-family:Verdana;">N</span></i><span style="font-family:Verdana;"> = 2</span></span><span><span><span><span> </span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span></span><span><span><span><span> </span></span></span></span><span><span><span><span><span style="font-family:Verdana;">9)</span><i> </i><span style="font-family:Verdana;">in He-like ions up to </span><i><span style="font-family:Verdana;">Z</span></i><span style="font-family:Verdana;"> = 10. The results obtained from the novel method are in good agreement with the available theoretical calculations and experimental observations.</span></span></span></span></span>
文摘This work presents results of the different parameters which characterize the nonrelativistic Hamilton operator for the helium atoms allowing us to solve the Schrödinger equation. The total energy is decomposed into three terms allowing to separate the kinetic energy, the electrons-nucleus interaction energy and the electron-electron interaction energy of the (2s<sup>2</sup>, 3s<sup>2</sup> and 4s<sup>2</sup>) <sup>1</sup>S<sup>e</sup>, (2p<sup>2</sup>, 3p<sup>2</sup> and 4p<sup>2</sup>) <sup>1</sup>D<sup>e</sup> and (3d<sup>2</sup> and 4d<sup>2</sup>) <sup>1</sup>G<sup>e</sup> resonance singlet states of the helium isoelectronic sequences. The states have been defined by using special forms of the Hylleraas type wave functions. The calculations have been carried out in the framework of the variational method using configuration interaction basis states with a real Hamiltonian. The agreement of the energy value of other states between the present theoretical values available in the literature is excellent. But as for the comparison of the kinetic energies, the electrons-nucleus energies interaction and the electron-electron interaction energies, we note a slight difference with the theoretical values common in literature.
基金financially supported by the Program for New Century Excellent Talents in University(No.NCET-13-0229,NCET-09-0396)the National Science & Technology Key Projects of Numerical Control(No.2012ZX04010-031,2012ZX0412-011)the National High Technology Research and Development Program("863"Program)of China(No.2013031003)
文摘For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.
基金National Natural Science Foundation of China under Grant Nos.10125521 and 60371013the 973 State Key Basic Research Development Project of China under Grant No.G2000077400
文摘The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical expressions of the matrix dements for both position and momentum operators are obtained.
文摘A new approach applying fuzzy mathematic theorems, including the Primary Matrix Element Theorem and the Fisher Classification Method, was established to solve the optimization problem of atmospheric environmental sampling sites. According to its basis, an application in the optimization of sampling sites in the atmospheric environmental monitoring was discussed. The method was proven to be suitable and effective. The results were admitted and applied by the Environmental Protection Bureau (EPB) of many cities of China. A set of computer software of this approach was also completely compiled and used.
基金supported by the National Natural Science Foundation of China (Grant No 10775051)the Program for New Century Excellent Talents in University of China (Grant No NCET-07-0282)
文摘In this article, we calculate the contribution from the nonfactorizable soft hadronic matrix element to the decay B^0→Xc1π^0 with the light-cone quantum chromo-dynamic （QCD） sum rules. The numerical results show that its contribution is rather large and should not be neglected. The total amplitudes lead to a branching fraction which is in agreement with the experimental data marginally.
