This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals ...This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.展开更多
Electrocatalysis is undergoing a renaissance due to its central importance for a sustainable energy economy,relying on green(electro-)chemical processes to harvest,convert,and store energy.Theoretical considerations b...Electrocatalysis is undergoing a renaissance due to its central importance for a sustainable energy economy,relying on green(electro-)chemical processes to harvest,convert,and store energy.Theoretical considerations by electronic structure methods are key to identify potential material motifs for electrocatalytic processes at the solid/liquid interface.Most commonly,heuristic concepts in the realm of materials screening by the compilation of volcano plots are used,which rely on a plethora of simplifications and approximations of the complex electrochemical interface.While the investigation of the catalytic processes at the solid/liquid interface mainly relies on descriptor-based approaches,in the present future article it is discussed that the inclusion of the liquid part of the interface by mean-field models is crucial to elevate screening approaches to the next level.展开更多
In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The firs...In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.展开更多
Self-normalizing neural networks(SNN)regulate the activation and gradient flows through activation functions with the self-normalization property.As SNNs do not rely on norms computed from minibatches,they are more fr...Self-normalizing neural networks(SNN)regulate the activation and gradient flows through activation functions with the self-normalization property.As SNNs do not rely on norms computed from minibatches,they are more friendly to data parallelism,kernel fusion,and emerging architectures such as ReRAM-based accelerators.However,existing SNNs have mainly demonstrated their effectiveness on toy datasets and fall short in accuracy when dealing with large-scale tasks like ImageNet.They lack the strong normalization,regularization,and expression power required for wider,deeper models and larger-scale tasks.To enhance the normalization strength,this paper introduces a comprehensive and practical definition of the self-normalization property in terms of the stability and attractiveness of the statistical fixed points.It is comprehensive as it jointly considers all the fixed points used by existing studies:the first and second moment of forward activation and the expected Frobenius norm of backward gradient.The practicality comes from the analytical equations provided by our paper to assess the stability and attractiveness of each fixed point,which are derived from theoretical analysis of the forward and backward signals.The proposed definition is applied to a meta activation function inspired by prior research,leading to a stronger self-normalizing activation function named‘‘bi-scaled exponential linear unit with backward standardized’’(bSELU-BSTD).We provide both theoretical and empirical evidence to show that it is superior to existing studies.To enhance the regularization and expression power,we further propose scaled-Mixup and channel-wise scale&shift.With these three techniques,our approach achieves 75.23%top-1 accuracy on the ImageNet with Conv MobileNet V1,surpassing the performance of existing self-normalizing activation functions.To the best of our knowledge,this is the first SNN that achieves comparable accuracy to batch normalization on ImageNet.展开更多
The potential energy surfaces are calculated for neutron-deficient At isotopes from A - 190 to 207 in an axially deformed relativistic mean-field approach, using a quadratic constraint scheme for the first time. We fi...The potential energy surfaces are calculated for neutron-deficient At isotopes from A - 190 to 207 in an axially deformed relativistic mean-field approach, using a quadratic constraint scheme for the first time. We find several minima in the potential energy surface for each nucleus, shape-coexistence, and quadratic deform are discussed.展开更多
By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensionalspin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-compone...By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensionalspin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-components of the spins.The thermodynamic quantities,such as Helmholtz free energy,the internal energy,the specificheat,and the isothermal susceptibility,are obtained.Under degenerating condition,our results agree with numericalresults of the other literatures.展开更多
In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers (n = 2, 3, 4, 5, 6, and bulk (∞) by means of a me...In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers (n = 2, 3, 4, 5, 6, and bulk (∞) by means of a mean-field and high temperature series expansion (HTSE) combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff (mean), ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk (∞).展开更多
In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the s...In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.展开更多
This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information avail...This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.展开更多
Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated inthe framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvab...Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated inthe framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvable.It is shown that, although the input radio frequency field is in an ordinary Glauber coherent state, the output matterwave will periodically exhibit quadrature squeezing effects purely originated from the nonlinear atom-atom collisions.展开更多
By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we ...By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we show that the emission from the microcavity manifests periodic oscillation behaviour and the oscillation can be suppressed under a certain condition.展开更多
Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gros...Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N|k|, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.展开更多
Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relat...Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativisticmean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. Theresonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 1 14Sn, 1 16Sn, 1 18Sn,and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determiningenergies and widths of resonant states.展开更多
The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromag- netic system with different anisotropies are studied by means of mean-field theory (MFT). The dependence of th...The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromag- netic system with different anisotropies are studied by means of mean-field theory (MFT). The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and trieritical line.展开更多
The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation result...The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.展开更多
We calculate the binding energies of Ni, Cu, Xe, Cs, Pt, Au, Np, Pu isotope chains using two interaction parameter sets NL-3 and NL-Z, and compared the relative errors of the even-even nuclei with those of odd-even nu...We calculate the binding energies of Ni, Cu, Xe, Cs, Pt, Au, Np, Pu isotope chains using two interaction parameter sets NL-3 and NL-Z, and compared the relative errors of the even-even nuclei with those of odd-even nuclei and odd-odd nuclei. We find that the errors of binding energy of odd-even and odd-odd nuclei are not bigger than the one of even-even nuclei. The result shows that comparing with even-even nuclei, there is no systematic error and approximation in the calculations of the binding energy of odd-even and odd-odd nuclei with relativistic mean-field theory. In addition, the result is explained theoretically.展开更多
We study contributions of the pion meson and spatial component of the omega meson in the odd-A carbon isotopes. The pion and spatial omega provide small attractions in odd-A nuclei, giving rise to considerable influen...We study contributions of the pion meson and spatial component of the omega meson in the odd-A carbon isotopes. The pion and spatial omega provide small attractions in odd-A nuclei, giving rise to considerable influences on the single-particle energies rather than the bulk properties such as total binding energies, and root-mean-square (rms) radii. The ±? (spin) splittings, arising from the spatial omega, are large in <SUP>11</SUP>C and <SUP>13</SUP>C and drop as the isospin rises in odd-A carbon isotopes. As an isovector, the pion can shift slightly the relative potential depth of neutron and proton, contrary to the role of the rho meson. There is a general trend that both the pion and spatial omega fields reduce with the rise of isospin in the isotopic chain. From the normal nucleus to halo nucleus, an abnormal drop of the pion or spatial omega field may occur, as can be seen in <SUP>19</SUP>C, <SUP>15</SUP>C, and <SUP>21</SUP>C.展开更多
Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to ...Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to explore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus Transport Networks (BTNs) evolution model with random overlapping clique structure, which gives a possible explanation for the observed exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-field theory, we analyze the BTNs model and prove that this model has the character of exponential distribution of the connectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with the statistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponential distribution of the connectivities, and their exponents have same order of magnitude, which show the availability of the analytical result of this paper.展开更多
In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first...In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions.With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth,and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.展开更多
基金supported by the National Key Research and Development Program of China(2022YFA1006103,2023YFA1009203)the National Natural Science Foundation of China(61925306,61821004,11831010,61977043,12001320)+2 种基金the Natural Science Foundation of Shandong Province(ZR2019ZD42,ZR2020ZD24)the Taishan Scholars Young Program of Shandong(TSQN202211032)the Young Scholars Program of Shandong University。
文摘This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.
基金funding by the Ministry of Culture and Science of the Federal State of North Rhine-Westphalia(NRW Return Grant)funded by the CRC/TRR247:“Heterogeneous Oxidation Catalysis in the Liquid Phase”(Project number 388390466-TRR 247)+2 种基金the RESOLV Cluster of Excellence,funded by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy–EXC 2033–390677874–RESOLVthe Center for Nanointegration(CENIDE)supported by COST(European Cooperation in Science and Technology)。
文摘Electrocatalysis is undergoing a renaissance due to its central importance for a sustainable energy economy,relying on green(electro-)chemical processes to harvest,convert,and store energy.Theoretical considerations by electronic structure methods are key to identify potential material motifs for electrocatalytic processes at the solid/liquid interface.Most commonly,heuristic concepts in the realm of materials screening by the compilation of volcano plots are used,which rely on a plethora of simplifications and approximations of the complex electrochemical interface.While the investigation of the catalytic processes at the solid/liquid interface mainly relies on descriptor-based approaches,in the present future article it is discussed that the inclusion of the liquid part of the interface by mean-field models is crucial to elevate screening approaches to the next level.
基金supported in part by theNSFC(11871037)Shandong Province(JQ201202)+3 种基金NSFC-RS(11661130148NA150344)111 Project(B12023)supported by the Qingdao Postdoctoral Application Research Project(QDBSH20220202092)。
文摘In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner.
基金National Key R&D Program of China(2018AAA0102600)National Natural Science Foundation of China(No.61876215,62106119)+1 种基金Beijing Academy of Artificial Intelligence(BAAI),ChinaChinese Institute for Brain Research,Beijing,and the Science and Technology Major Project of Guangzhou,China(202007030006).
文摘Self-normalizing neural networks(SNN)regulate the activation and gradient flows through activation functions with the self-normalization property.As SNNs do not rely on norms computed from minibatches,they are more friendly to data parallelism,kernel fusion,and emerging architectures such as ReRAM-based accelerators.However,existing SNNs have mainly demonstrated their effectiveness on toy datasets and fall short in accuracy when dealing with large-scale tasks like ImageNet.They lack the strong normalization,regularization,and expression power required for wider,deeper models and larger-scale tasks.To enhance the normalization strength,this paper introduces a comprehensive and practical definition of the self-normalization property in terms of the stability and attractiveness of the statistical fixed points.It is comprehensive as it jointly considers all the fixed points used by existing studies:the first and second moment of forward activation and the expected Frobenius norm of backward gradient.The practicality comes from the analytical equations provided by our paper to assess the stability and attractiveness of each fixed point,which are derived from theoretical analysis of the forward and backward signals.The proposed definition is applied to a meta activation function inspired by prior research,leading to a stronger self-normalizing activation function named‘‘bi-scaled exponential linear unit with backward standardized’’(bSELU-BSTD).We provide both theoretical and empirical evidence to show that it is superior to existing studies.To enhance the regularization and expression power,we further propose scaled-Mixup and channel-wise scale&shift.With these three techniques,our approach achieves 75.23%top-1 accuracy on the ImageNet with Conv MobileNet V1,surpassing the performance of existing self-normalizing activation functions.To the best of our knowledge,this is the first SNN that achieves comparable accuracy to batch normalization on ImageNet.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475116, 10535010, and 10235030, and Asia-Europe Link in Nuclear Physics and Astrophysics under Grant No. CN/ASIA-LINK/008 (094-791) and by Major State Basic Research Development Program of China under Grant No. 2007CB815000
文摘The potential energy surfaces are calculated for neutron-deficient At isotopes from A - 190 to 207 in an axially deformed relativistic mean-field approach, using a quadratic constraint scheme for the first time. We find several minima in the potential energy surface for each nucleus, shape-coexistence, and quadratic deform are discussed.
基金the Open Fund of Jiangsu Laboratory of Advanced Functional Materials under Grant No.06KFJJ004
文摘By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensionalspin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-components of the spins.The thermodynamic quantities,such as Helmholtz free energy,the internal energy,the specificheat,and the isothermal susceptibility,are obtained.Under degenerating condition,our results agree with numericalresults of the other literatures.
文摘In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers (n = 2, 3, 4, 5, 6, and bulk (∞) by means of a mean-field and high temperature series expansion (HTSE) combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff (mean), ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk (∞).
基金supported in part by the NSFC(11222110,11871037)Shandong Province(JQ201202)+1 种基金NSFC-RS(11661130148,NA150344)111 Project(B12023)。
文摘In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.
文摘This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.
文摘Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated inthe framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvable.It is shown that, although the input radio frequency field is in an ordinary Glauber coherent state, the output matterwave will periodically exhibit quadrature squeezing effects purely originated from the nonlinear atom-atom collisions.
基金Project supported in part by the Natural Science Foundation of China (Grant Nos. 10575040,90503010,10634060 and 10874050)by National Basic Research Program of China (Grant No. 2005CB724508)+1 种基金the Foundation from the ministry of the National Education of China (Grant No. 200804870051)the Science Innovation Foundation of Huazhong University of Science and Technology (Grant No. HF-06-010-08-012)
文摘By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we show that the emission from the microcavity manifests periodic oscillation behaviour and the oscillation can be suppressed under a certain condition.
基金supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry of China,National Center for Mathematics and Interdisciplinary Sciences in China
文摘Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N|k|, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10075080, 19847002, 19835010 and Major State Basic Research Development Program under Grant No. G20000774
文摘Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativisticmean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. Theresonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 1 14Sn, 1 16Sn, 1 18Sn,and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determiningenergies and widths of resonant states.
文摘The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromag- netic system with different anisotropies are studied by means of mean-field theory (MFT). The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and trieritical line.
文摘The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475026 (2004)
文摘We calculate the binding energies of Ni, Cu, Xe, Cs, Pt, Au, Np, Pu isotope chains using two interaction parameter sets NL-3 and NL-Z, and compared the relative errors of the even-even nuclei with those of odd-even nuclei and odd-odd nuclei. We find that the errors of binding energy of odd-even and odd-odd nuclei are not bigger than the one of even-even nuclei. The result shows that comparing with even-even nuclei, there is no systematic error and approximation in the calculations of the binding energy of odd-even and odd-odd nuclei with relativistic mean-field theory. In addition, the result is explained theoretically.
文摘We study contributions of the pion meson and spatial component of the omega meson in the odd-A carbon isotopes. The pion and spatial omega provide small attractions in odd-A nuclei, giving rise to considerable influences on the single-particle energies rather than the bulk properties such as total binding energies, and root-mean-square (rms) radii. The ±? (spin) splittings, arising from the spatial omega, are large in <SUP>11</SUP>C and <SUP>13</SUP>C and drop as the isospin rises in odd-A carbon isotopes. As an isovector, the pion can shift slightly the relative potential depth of neutron and proton, contrary to the role of the rho meson. There is a general trend that both the pion and spatial omega fields reduce with the rise of isospin in the isotopic chain. From the normal nucleus to halo nucleus, an abnormal drop of the pion or spatial omega field may occur, as can be seen in <SUP>19</SUP>C, <SUP>15</SUP>C, and <SUP>21</SUP>C.
基金Supported by National Natural Science Foundation of China under Grant Nos. 60874080 and 60504027China Postdoctoral Science Foundation Funded Project under Grant No. 20060401037
文摘Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to explore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus Transport Networks (BTNs) evolution model with random overlapping clique structure, which gives a possible explanation for the observed exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-field theory, we analyze the BTNs model and prove that this model has the character of exponential distribution of the connectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with the statistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponential distribution of the connectivities, and their exponents have same order of magnitude, which show the availability of the analytical result of this paper.
基金supported in part by the NSF of P.R.China(11871037,11222110)Shandong Province(JQ201202)+1 种基金NSFC-RS(11661130148,NA150344)111 Project(B12023)。
文摘In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions.With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth,and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.