Environments with reciprocal patchiness of resources, in which the availability of two resources such as light and soil nutrients are patchily distributed in horizontal space and negatively correlated in each patch, a...Environments with reciprocal patchiness of resources, in which the availability of two resources such as light and soil nutrients are patchily distributed in horizontal space and negatively correlated in each patch, are common in many ecosystems. The strategies by which clonal plants adapt to this type of heterogeneous environment were examined in three stoloniferous herbs,Potentilla reptans L. var. sericophylla Franch., P. anserina L. and Halerpestes ruthenica (Jacq.) Qvcz., commonly inhabiting forest understories, grasslands and low saline meadows, respectively. As pairs of connected ramets were subjected to reciprocal patchiness of light and nutrients, stolon connection between the two ramets significantly enhanced biomass of both ramet growing in low light intensity but high soil nutrient condition (LH ramet) and ramet growing in high light intensity but low soil nutrient condition (HL ramet) as well as whole ramet pairs (consisting of LH ramets and HL ramets). Additionally, stolon connection greatly increased root/shoot ratio of LH ramet while significantly decreased that of HL ramet. The results indicate that a reciprocal transportation of resources between interconnected ramets and a functional specialization of ramets in uptake of abundant resources occurred. By resource sharing and functional specialization, clonal plants can efficiently acquire locally abundant resources and buffer the stress caused by reciprocal patchiness of resources.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
In this work,we investigate the thermodynamic variables of a harmonic oscillator in a conical geometry metric.Moreover,we introduce an external field in the form of a Wu-Yang magnetic monopole(WYMM)and an inverse squa...In this work,we investigate the thermodynamic variables of a harmonic oscillator in a conical geometry metric.Moreover,we introduce an external field in the form of a Wu-Yang magnetic monopole(WYMM)and an inverse square potential into the system and analyze the results.Using an analytical approach,we obtain the energy level and study the thermodynamics at finite temperature.Our findings demonstrate that thermodynamic variables,except for the specific heat and entropy,are influenced by the topological parameters,the strength of the WYMM,and the inverse square potential.展开更多
In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above ...In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above function,are obtained.Especially,we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions.Meanwhile,some interesting integral operators and derivative operators of this function,are also discussed.展开更多
In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bound...In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.展开更多
In the past decades, terahertz technology has a great development and steady improvement, which has kept discovering and developing a series of potential applications in terahertz sensing, imaging, spectroscopy, secur...In the past decades, terahertz technology has a great development and steady improvement, which has kept discovering and developing a series of potential applications in terahertz sensing, imaging, spectroscopy, security, and communication. After the recent technical breakthroughs in reliable sources and sensitive detectors, terahertz functional devices, such as waveguides, switches, filters, splitters, isolators, modulators and sensors, are indispensable for the construction of compact application systems and have become a worldwide supreme issue in research.展开更多
In our investigation,we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity,considering the Bonnor–Melvin-Lambda(BML)space-time back...In our investigation,we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity,considering the Bonnor–Melvin-Lambda(BML)space-time background.The BML solution is characterized by the magnetic field strength along the axis of the symmetry direction which is related to the cosmological constantΛand the topological parameterαof the geometry.The behavior of charge-free scalar particles described by the Klein–Gordon equation is investigated,utilizing two sets of rainbow functions:(i)f(χ)=■,h(χ)=1 and(ii)f(χ)=1,h(χ)=1+βХ/2.Here 0<(Х=■)≤1 with E representing the particle's energy,Ep is the Planck's energy,andβis the rainbow parameter.We obtain the approximate analytical solutions for the scalar particles and conduct a thorough analysis of the obtained results.Afterwards,we study the quantum dynamics of quantum oscillator fields within this BML space-time,employing the Klein–Gordon oscillator.Here also,we choose the same sets of rainbow functions and obtain the approximate eigenvalue solution for the oscillator fields.Notably,we demonstrate that the relativistic approximate energy profiles of charge-free scalar particles and oscillator fields get influenced by the topology of the geometry and the cosmological constant.Furthermore,we show that the energy profiles of scalar particles receive modifications from the rainbow parameter and the quantum oscillator fields by both the rainbow parameter and the frequency of oscillation.展开更多
The Cr^3＋：BeAl2O4 crystal, Cr^3＋：LiNbO3 crystal, and ZnO-Al2O3-SiO2 glass-ceramic were obtained by the Czochralski technique, Bridgman method, and melting processing, respectively. The optical absorption and emiss...The Cr^3＋：BeAl2O4 crystal, Cr^3＋：LiNbO3 crystal, and ZnO-Al2O3-SiO2 glass-ceramic were obtained by the Czochralski technique, Bridgman method, and melting processing, respectively. The optical absorption and emission spectra of the above Cr^3＋-incorporated solid-state materials were recorded. The technical parameters for growing high-quality Cr^3＋：BeAl2O4 and Cr^3＋：LINbO3 crystals were obtained. The results indicate that the optical absorption and fluorescence spectra of Cr^3＋ show quite a few differences in various matrixes. The sharp line emissions were observed in the Cr^3＋：BeAl2O4 and Cr^3＋：LiNbO3 crystals. The crystal-field parameters （Dq） for Cr^3＋. in different matrixes were calculated from their corresponding spectra. It is indicated that Cr^3＋：BeAl2O4 and Cr^3＋：LiNbO3 belong to the high-field site crystal, while the Cr^3＋ ZnO-Al2O3-SiO2 glass and glass-ceramic belong to the weak-field site crystal.展开更多
A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. T...A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Hermite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation （nonlinear convection- diffusion problem） and KdV equation（single solitary and 2-solitary wave problems）, where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.展开更多
Nanostructural monophase LaxBi2-xSeyTe3-y alloy was synthesized with a hydrothermal route using BiCl3, LaCl3, selenium and tellurium powders as the precursors, NaOH and disodium ethylenediaminetetraacetiate （EDTA） ...Nanostructural monophase LaxBi2-xSeyTe3-y alloy was synthesized with a hydrothermal route using BiCl3, LaCl3, selenium and tellurium powders as the precursors, NaOH and disodium ethylenediaminetetraacetiate （EDTA） as the additives. The hydrothermally synthesized powders have a petal-like morphology self-structured by the parallel side-by-side arrangement of the nano-scales. It is found that an alkaline additive is necessary for the synthesis of a monophase Bi2Te3 based alloy.展开更多
A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous bound...A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel Junctions, the equation With respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.展开更多
In this paper,we investigate the quantum dynamics of a non-relativistic particle confined by the Aharonov-Bohm quantum flux field with pseudoharmonic-type potential in the background of topological defect produced by ...In this paper,we investigate the quantum dynamics of a non-relativistic particle confined by the Aharonov-Bohm quantum flux field with pseudoharmonic-type potential in the background of topological defect produced by a point-like global monopole.We solve the radial Schrödinger equation analytically and determine the exact eigenvalue solution of the quantum system.Afterwards,we consider a Mie-type potential in the quantum system and solve the radial equation analytically and obtain the eigenvalue solution.We analyze the effects of the topological defect and the quantum flux with these potentials on the energy eigenvalue and wave function of the nonrelativistic particles.In fact,it is shown that the energy levels and wave functions are influenced by the topological defect shifted the result compared to the flat space results.In addition,the quantum flux field also shifted the eigenvalue solutions and an analogue of the Aharonov-Bohm effect for bound-states is observed.Finally,we utilize these eigenvalue solutions to some known diatomic molecular potential models and presented the energy eigenvalue and wave function.展开更多
By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable ...By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.展开更多
Under investigation is the(2+1)-dimensional breaking soliton equation. Based on a special ans?tz functions and the bilinear form, some entirely new double-periodic soliton solutions for the(2+1)-dimensional breaking s...Under investigation is the(2+1)-dimensional breaking soliton equation. Based on a special ans?tz functions and the bilinear form, some entirely new double-periodic soliton solutions for the(2+1)-dimensional breaking soliton equation are presented. With the help of symbolic computation software Mathematica, many important and interesting properties for these obtained solutions are revealed with some figures.展开更多
Anti-plane electroelastic problems are studied by the Trefftz boundary element method （BEM） in this paper. The Trefftz BEM is based on a weighted residual formulation and indirect boundary approach. In particular th...Anti-plane electroelastic problems are studied by the Trefftz boundary element method （BEM） in this paper. The Trefftz BEM is based on a weighted residual formulation and indirect boundary approach. In particular the point-collocation and Galerkin techniques, in which the basic unknowns are the retained expansion coefficients in the system of complete equations, are considered. Furthermore, special Trefftz functions and auxiliary functions which satisfy exactly the specified boundary conditions along the slit boundaries are also used to derive a special purpose element with local defects. The path-independent integral is evaluated at the tip of a crack to determine the energy release rate for a mode Ⅲ fracture problem. In final, the accuracy and efficiency of the Trefftz boundary element method are illustrated by an example and the comparison is made with other methods.展开更多
Using the coordinate transformation method, we solve the one-dimensional Schrodinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the sy...Using the coordinate transformation method, we solve the one-dimensional Schrodinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The eigenfunctions can be expressed in terms of the Jacobi, Hermite, and generalized Laguerre polynomials. All potentials for these solvable systems have an extra term Vm, which is produced from the dependence of mass on the position, compared with those for the systems of constant mass. The properties of Vm for several mass functions are discussed.展开更多
By virtue of the parabose squeezed operator, propagator of a parabose parametric amplifier, explicit forms of parabose squeezed number states and normalization factors of excitation states on a parabose squeezed vacuu...By virtue of the parabose squeezed operator, propagator of a parabose parametric amplifier, explicit forms of parabose squeezed number states and normalization factors of excitation states on a parabose squeezed vacuum state are calculated, which generalize the relevant results from ordinary Bose statistics to the parabose case.展开更多
By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-seri...By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e.,min（m,n）∑l=0^min（m,n）n!m!（-1）^l/l!（n-1）!（m-l）!/Hn-l（x）y^m-l≡ n,m（x,y）.By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators（IWOP） we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.展开更多
As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the fi...As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.展开更多
This paper contains material presented by the first authors in CIMPA School at Kathmandu University.,July 26,27,28,2010,to be included in ,and is intended for a rambling introduction to number-theoretic concepts throu...This paper contains material presented by the first authors in CIMPA School at Kathmandu University.,July 26,27,28,2010,to be included in ,and is intended for a rambling introduction to number-theoretic concepts through built-in properties of(number-theoretic) special functions.We follow roughly the historical order of events from somewhat more modern point of view.§1 deals with Euler's fundamental ideas as expounded in [6] and ,from a more advanced standpoint.§2 gives some rudiments of Bernoulli numbers and polynomials as consequences of the partial fraction expansion.§3 states sieve-theoretic treatment of the Euler product.Thus,the events in §1-§3 more or less belong to Euler's era.§4 deals with RSA cryptography as motivated by Euler's function,with its several descriptions being given.§5 contains a slight generalization of Dirichlet's test on uniform convergence of series,which is more effectively used in §6 to elucidate Riemann's posthumous Fragment II than in [1].Thus §5-§6 belong to the Dirichlet-Riemann era.§7 gives the most general modular relation which is the culmination of the Riemann-Hecke-Bochner correspondence between modular forms and zeta-functions.Appendix gives a penetrating principle of the least period that appears in various contexts.展开更多
文摘Environments with reciprocal patchiness of resources, in which the availability of two resources such as light and soil nutrients are patchily distributed in horizontal space and negatively correlated in each patch, are common in many ecosystems. The strategies by which clonal plants adapt to this type of heterogeneous environment were examined in three stoloniferous herbs,Potentilla reptans L. var. sericophylla Franch., P. anserina L. and Halerpestes ruthenica (Jacq.) Qvcz., commonly inhabiting forest understories, grasslands and low saline meadows, respectively. As pairs of connected ramets were subjected to reciprocal patchiness of light and nutrients, stolon connection between the two ramets significantly enhanced biomass of both ramet growing in low light intensity but high soil nutrient condition (LH ramet) and ramet growing in high light intensity but low soil nutrient condition (HL ramet) as well as whole ramet pairs (consisting of LH ramets and HL ramets). Additionally, stolon connection greatly increased root/shoot ratio of LH ramet while significantly decreased that of HL ramet. The results indicate that a reciprocal transportation of resources between interconnected ramets and a functional specialization of ramets in uptake of abundant resources occurred. By resource sharing and functional specialization, clonal plants can efficiently acquire locally abundant resources and buffer the stress caused by reciprocal patchiness of resources.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
文摘In this work,we investigate the thermodynamic variables of a harmonic oscillator in a conical geometry metric.Moreover,we introduce an external field in the form of a Wu-Yang magnetic monopole(WYMM)and an inverse square potential into the system and analyze the results.Using an analytical approach,we obtain the energy level and study the thermodynamics at finite temperature.Our findings demonstrate that thermodynamic variables,except for the specific heat and entropy,are influenced by the topological parameters,the strength of the WYMM,and the inverse square potential.
基金Supported by The National Undergraduate Innovation Training Program(Grant No.202310290069Z).
文摘In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above function,are obtained.Especially,we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions.Meanwhile,some interesting integral operators and derivative operators of this function,are also discussed.
基金the Doctorial Programme Foundation of EducationMinistry of of China(20030288002)the Science Foundation of Jiangsu Province(BK2006209)+1 种基金NaturalScience Foundation of Jiangsu Higher Education Bureau(07KJD110206)NNSF of China(10771181)
文摘In this article,the authors obtain an integral representation for the relaxation of the functionalF（x,u,Ω）：={∫^f（x,u（x）,εu（x））dx Ω if u∈W^1,1（Ω,R^N）, ＋∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f（x,p,ξ）satisfying weak convexity assumption.
文摘In the past decades, terahertz technology has a great development and steady improvement, which has kept discovering and developing a series of potential applications in terahertz sensing, imaging, spectroscopy, security, and communication. After the recent technical breakthroughs in reliable sources and sensitive detectors, terahertz functional devices, such as waveguides, switches, filters, splitters, isolators, modulators and sensors, are indispensable for the construction of compact application systems and have become a worldwide supreme issue in research.
文摘In our investigation,we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity,considering the Bonnor–Melvin-Lambda(BML)space-time background.The BML solution is characterized by the magnetic field strength along the axis of the symmetry direction which is related to the cosmological constantΛand the topological parameterαof the geometry.The behavior of charge-free scalar particles described by the Klein–Gordon equation is investigated,utilizing two sets of rainbow functions:(i)f(χ)=■,h(χ)=1 and(ii)f(χ)=1,h(χ)=1+βХ/2.Here 0<(Х=■)≤1 with E representing the particle's energy,Ep is the Planck's energy,andβis the rainbow parameter.We obtain the approximate analytical solutions for the scalar particles and conduct a thorough analysis of the obtained results.Afterwards,we study the quantum dynamics of quantum oscillator fields within this BML space-time,employing the Klein–Gordon oscillator.Here also,we choose the same sets of rainbow functions and obtain the approximate eigenvalue solution for the oscillator fields.Notably,we demonstrate that the relativistic approximate energy profiles of charge-free scalar particles and oscillator fields get influenced by the topology of the geometry and the cosmological constant.Furthermore,we show that the energy profiles of scalar particles receive modifications from the rainbow parameter and the quantum oscillator fields by both the rainbow parameter and the frequency of oscillation.
基金This work is financially supported by the Project of Science and Technology of Zhejiang Province (No. 011066)Project of Education Committee of Zhejiang Province (No. 20010231)the Doctoral Science Foundation of Ningbo City (No. 02J20101-12)the Personal Bureau of Ningbo City, China (No. 2002182).
文摘The Cr^3＋：BeAl2O4 crystal, Cr^3＋：LiNbO3 crystal, and ZnO-Al2O3-SiO2 glass-ceramic were obtained by the Czochralski technique, Bridgman method, and melting processing, respectively. The optical absorption and emission spectra of the above Cr^3＋-incorporated solid-state materials were recorded. The technical parameters for growing high-quality Cr^3＋：BeAl2O4 and Cr^3＋：LINbO3 crystals were obtained. The results indicate that the optical absorption and fluorescence spectra of Cr^3＋ show quite a few differences in various matrixes. The sharp line emissions were observed in the Cr^3＋：BeAl2O4 and Cr^3＋：LiNbO3 crystals. The crystal-field parameters （Dq） for Cr^3＋. in different matrixes were calculated from their corresponding spectra. It is indicated that Cr^3＋：BeAl2O4 and Cr^3＋：LiNbO3 belong to the high-field site crystal, while the Cr^3＋ ZnO-Al2O3-SiO2 glass and glass-ceramic belong to the weak-field site crystal.
基金Project supported by the National Natural Science Foundation of China (No.10272118) the Hong Kong Polytechnic University Research Grant (No.A-PE28) the Research Fund for the Doctoral Program of Ministry of Education of China (No.20020558013)
文摘A generalized finite spectral method is proposed. The method is of highorder accuracy. To attain high accuracy in time discretization, the fourth-order AdamsBashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Hermite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation （nonlinear convection- diffusion problem） and KdV equation（single solitary and 2-solitary wave problems）, where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.
文摘Nanostructural monophase LaxBi2-xSeyTe3-y alloy was synthesized with a hydrothermal route using BiCl3, LaCl3, selenium and tellurium powders as the precursors, NaOH and disodium ethylenediaminetetraacetiate （EDTA） as the additives. The hydrothermally synthesized powders have a petal-like morphology self-structured by the parallel side-by-side arrangement of the nano-scales. It is found that an alkaline additive is necessary for the synthesis of a monophase Bi2Te3 based alloy.
文摘A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel Junctions, the equation With respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.
文摘In this paper,we investigate the quantum dynamics of a non-relativistic particle confined by the Aharonov-Bohm quantum flux field with pseudoharmonic-type potential in the background of topological defect produced by a point-like global monopole.We solve the radial Schrödinger equation analytically and determine the exact eigenvalue solution of the quantum system.Afterwards,we consider a Mie-type potential in the quantum system and solve the radial equation analytically and obtain the eigenvalue solution.We analyze the effects of the topological defect and the quantum flux with these potentials on the energy eigenvalue and wave function of the nonrelativistic particles.In fact,it is shown that the energy levels and wave functions are influenced by the topological defect shifted the result compared to the flat space results.In addition,the quantum flux field also shifted the eigenvalue solutions and an analogue of the Aharonov-Bohm effect for bound-states is observed.Finally,we utilize these eigenvalue solutions to some known diatomic molecular potential models and presented the energy eigenvalue and wave function.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175113)
文摘By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.
基金Supported by National Natural Science Foundation of China under Grant No.61377067
文摘Under investigation is the(2+1)-dimensional breaking soliton equation. Based on a special ans?tz functions and the bilinear form, some entirely new double-periodic soliton solutions for the(2+1)-dimensional breaking soliton equation are presented. With the help of symbolic computation software Mathematica, many important and interesting properties for these obtained solutions are revealed with some figures.
基金Project supported by the National Natural Science Foundation of China (No. 10472086).
文摘Anti-plane electroelastic problems are studied by the Trefftz boundary element method （BEM） in this paper. The Trefftz BEM is based on a weighted residual formulation and indirect boundary approach. In particular the point-collocation and Galerkin techniques, in which the basic unknowns are the retained expansion coefficients in the system of complete equations, are considered. Furthermore, special Trefftz functions and auxiliary functions which satisfy exactly the specified boundary conditions along the slit boundaries are also used to derive a special purpose element with local defects. The path-independent integral is evaluated at the tip of a crack to determine the energy release rate for a mode Ⅲ fracture problem. In final, the accuracy and efficiency of the Trefftz boundary element method are illustrated by an example and the comparison is made with other methods.
基金The project supported by National Natural Science Foundation of China for 0utstanding Young Scientists under Grant No. 10125521, the Doctoral Fund of the Ministry of Education under Grant No. 20010284036, the State Key Basic Research Development Program of China under Grant No. G2000077400, the Chinese Academy of Sciences Knowledge Innovation Project under Grant No. KJCX2-SW-N02, and National Natural Science Foundation of China under Grant No. 60371013
文摘Using the coordinate transformation method, we solve the one-dimensional Schrodinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The eigenfunctions can be expressed in terms of the Jacobi, Hermite, and generalized Laguerre polynomials. All potentials for these solvable systems have an extra term Vm, which is produced from the dependence of mass on the position, compared with those for the systems of constant mass. The properties of Vm for several mass functions are discussed.
文摘By virtue of the parabose squeezed operator, propagator of a parabose parametric amplifier, explicit forms of parabose squeezed number states and normalization factors of excitation states on a parabose squeezed vacuum state are calculated, which generalize the relevant results from ordinary Bose statistics to the parabose case.
基金supported by the Natural Science Fund of Education Department of Anhui Province,China(Grant No.KJ2016A590)the Talent Foundation of Hefei University,China(Grant No.15RC11)the National Natural Science Foundation of China(Grant Nos.11247009 and 11574295)
文摘By virtue of the operator Hermite polynomial method [Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301] we find a new special function which is useful in quantum optics theory, whose expansion involves both power-series and Hermite polynomials, i.e.,min（m,n）∑l=0^min（m,n）n!m!（-1）^l/l!（n-1）!（m-l）!/Hn-l（x）y^m-l≡ n,m（x,y）.By virtue of the operator Hermite polynomial method and the technique of integration within ordered product of operators（IWOP） we derive its generating function. The circumstance in which this new special function appears and is applicable is considered.
基金Supported by the National Natural Science Foundation Fujian province of China(2016J01032).
文摘As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.
文摘This paper contains material presented by the first authors in CIMPA School at Kathmandu University.,July 26,27,28,2010,to be included in ,and is intended for a rambling introduction to number-theoretic concepts through built-in properties of(number-theoretic) special functions.We follow roughly the historical order of events from somewhat more modern point of view.§1 deals with Euler's fundamental ideas as expounded in [6] and ,from a more advanced standpoint.§2 gives some rudiments of Bernoulli numbers and polynomials as consequences of the partial fraction expansion.§3 states sieve-theoretic treatment of the Euler product.Thus,the events in §1-§3 more or less belong to Euler's era.§4 deals with RSA cryptography as motivated by Euler's function,with its several descriptions being given.§5 contains a slight generalization of Dirichlet's test on uniform convergence of series,which is more effectively used in §6 to elucidate Riemann's posthumous Fragment II than in [1].Thus §5-§6 belong to the Dirichlet-Riemann era.§7 gives the most general modular relation which is the culmination of the Riemann-Hecke-Bochner correspondence between modular forms and zeta-functions.Appendix gives a penetrating principle of the least period that appears in various contexts.
