In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentiall...In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.展开更多
A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. ...A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. It spans simultaneously wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to solve different problems and compared with analytical and published results. The comparison exhibits the strengths and accuracy of the presented basis set.展开更多
In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded...In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α-times Integrated Cosine Function by the approximation theorem of n-times integrated semigroups. If the semigroups are equicontinuous at each point ? , we give different methods to prove the theorem.展开更多
Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GET...Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.展开更多
We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ i...We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.展开更多
A new exponential bidirectional associative memory model is introduced. It offers an even better recall performance than the modified exponential bidirectional associative memory (MEBAM). Only a little complexity of r...A new exponential bidirectional associative memory model is introduced. It offers an even better recall performance than the modified exponential bidirectional associative memory (MEBAM). Only a little complexity of realization is spent for the improvement.展开更多
We establish the exponential stability of global solutions and C0-semigroup for the compressible Navier.Stokes equations of a viscous polytropic ideal gas in both bounded domain in R^1 and bounded annular domains in R...We establish the exponential stability of global solutions and C0-semigroup for the compressible Navier.Stokes equations of a viscous polytropic ideal gas in both bounded domain in R^1 and bounded annular domains in R^n （n=2,3）.展开更多
The capability of neurons to discriminate between intensity of external stimulus is measured by its dynamic range.A larger dynamic range indicates a greater probability of neuronal survival.In this study,the potential...The capability of neurons to discriminate between intensity of external stimulus is measured by its dynamic range.A larger dynamic range indicates a greater probability of neuronal survival.In this study,the potential roles of adaptation mechanisms（ion currents） in modulating neuronal dynamic range were numerically investigated.Based on the adaptive exponential integrate-and-fire model,which includes two different adaptation mechanisms,i.e.subthreshold and suprathreshold（spike-triggered） adaptation,our results reveal that the two adaptation mechanisms exhibit rather different roles in regulating neuronal dynamic range.Specifically,subthreshold adaptation acts as a negative factor that observably decreases the neuronal dynamic range,while suprathreshold adaptation has little influence on the neuronal dynamic range.Moreover,when stochastic noise was introduced into the adaptation mechanisms,the dynamic range was apparently enhanced,regardless of what state the neuron was in,e.g.adaptive or non-adaptive.Our model results suggested that the neuronal dynamic range can be differentially modulated by different adaptation mechanisms.Additionally,noise was a non-ignorable factor,which could effectively modulate the neuronal dynamic range.展开更多
Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive an...Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.展开更多
The authors consider two discrete-time insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest f...The authors consider two discrete-time insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by the martingale method.展开更多
Let (X;‖ ‖) be a Banach space. By B(X) we denote the set of all bounded linear operators in X. Let C∈B(X) be injective.A strongly continuous family of bounded operators {S(t); t≥0} is called an exponentially bound...Let (X;‖ ‖) be a Banach space. By B(X) we denote the set of all bounded linear operators in X. Let C∈B(X) be injective.A strongly continuous family of bounded operators {S(t); t≥0} is called an exponentially bounded C-semigroup (hereinafter abbrevi-展开更多
The Peng-Robison equation of state,one of the most extensively applied equations of state in the petroleum industry and chemical engineering,has an excel-lent appearance in predicting the thermodynamic properties of a...The Peng-Robison equation of state,one of the most extensively applied equations of state in the petroleum industry and chemical engineering,has an excel-lent appearance in predicting the thermodynamic properties of a wide variety of ma-terials.It has been a great challenge on how to design numerical schemes with preser-vation of mass conservation and energy dissipation law.Based on the exponential time difference combined with the stabilizing technique and added Lagrange multi-plier enforcing the mass conservation,we develop the efficientfirst-and second-order numerical schemes with preservation of maximum bound principle(MBP)to solve the single-component two-phase diffuse interface model with Peng-Robison equation of state.Convergence analyses as well as energy stability are also proven.Several two-dimensional and three-dimensional experiments are performed to verify these theo-retical results.展开更多
基金This project is supported by the National Science Foundation of China.
文摘In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.
文摘A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. It spans simultaneously wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to solve different problems and compared with analytical and published results. The comparison exhibits the strengths and accuracy of the presented basis set.
文摘In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α-times Integrated Cosine Function by the approximation theorem of n-times integrated semigroups. If the semigroups are equicontinuous at each point ? , we give different methods to prove the theorem.
文摘Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.
文摘We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.
基金Supported by Climbing Program-National Key Project for Fundamental Research in China
文摘A new exponential bidirectional associative memory model is introduced. It offers an even better recall performance than the modified exponential bidirectional associative memory (MEBAM). Only a little complexity of realization is spent for the improvement.
基金Foundation item: Supported by the NSF of ChinaSupported by the Prominent Youth from Henan Province(0412000100)
文摘We establish the exponential stability of global solutions and C0-semigroup for the compressible Navier.Stokes equations of a viscous polytropic ideal gas in both bounded domain in R^1 and bounded annular domains in R^n （n=2,3）.
基金supported by a grant from Beijing Municipal Commission of Science and Technology of China,No.Z151100000915070
文摘The capability of neurons to discriminate between intensity of external stimulus is measured by its dynamic range.A larger dynamic range indicates a greater probability of neuronal survival.In this study,the potential roles of adaptation mechanisms（ion currents） in modulating neuronal dynamic range were numerically investigated.Based on the adaptive exponential integrate-and-fire model,which includes two different adaptation mechanisms,i.e.subthreshold and suprathreshold（spike-triggered） adaptation,our results reveal that the two adaptation mechanisms exhibit rather different roles in regulating neuronal dynamic range.Specifically,subthreshold adaptation acts as a negative factor that observably decreases the neuronal dynamic range,while suprathreshold adaptation has little influence on the neuronal dynamic range.Moreover,when stochastic noise was introduced into the adaptation mechanisms,the dynamic range was apparently enhanced,regardless of what state the neuron was in,e.g.adaptive or non-adaptive.Our model results suggested that the neuronal dynamic range can be differentially modulated by different adaptation mechanisms.Additionally,noise was a non-ignorable factor,which could effectively modulate the neuronal dynamic range.
基金Project supported by the Major State Basic Research Development Program of China(Grant No.2012CB215202)the National Natural Science Foundation of China(Grant Nos.61104080 and 61134001)the Fundamental Research Funds for the Central Universities(Grant No.CDJZR13 175501)
文摘Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.
基金a grant from National Natural Science Foundation of China,Grant No.10671072Doctoral Program Foundation of the Ministry of Education of China,Grant No.20060269016+1 种基金"Shu Guang"project of Shanghai Municipal Education Commission and Shanghai Education Development Foundation,Grant No.04SG27the National Basic Research Program of China (973 Program),Grant No.2007CB814904
文摘The authors consider two discrete-time insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by the martingale method.
基金Project supported by the National Natural Science Foundation of China.
文摘Let (X;‖ ‖) be a Banach space. By B(X) we denote the set of all bounded linear operators in X. Let C∈B(X) be injective.A strongly continuous family of bounded operators {S(t); t≥0} is called an exponentially bounded C-semigroup (hereinafter abbrevi-
基金supported by National Natural Science Foundation of China under grant number No.11971047supported by National Natural Science Foundation of China under grant number No.61962056.
文摘The Peng-Robison equation of state,one of the most extensively applied equations of state in the petroleum industry and chemical engineering,has an excel-lent appearance in predicting the thermodynamic properties of a wide variety of ma-terials.It has been a great challenge on how to design numerical schemes with preser-vation of mass conservation and energy dissipation law.Based on the exponential time difference combined with the stabilizing technique and added Lagrange multi-plier enforcing the mass conservation,we develop the efficientfirst-and second-order numerical schemes with preservation of maximum bound principle(MBP)to solve the single-component two-phase diffuse interface model with Peng-Robison equation of state.Convergence analyses as well as energy stability are also proven.Several two-dimensional and three-dimensional experiments are performed to verify these theo-retical results.
