In this paper, the capability of neural networks and some approximation problens in system identification with neural networks are investigated. Some results are given: (i) For any function g ∈Llocp (R1) ∩S’ (R1) t...In this paper, the capability of neural networks and some approximation problens in system identification with neural networks are investigated. Some results are given: (i) For any function g ∈Llocp (R1) ∩S’ (R1) to be an Lp-Tauber-Wiener function, it is necessary and sufficient that g is not apolynomial; (ii) If g∈(Lp TW), then the set of is dense in Lp(K)’ (iii) It is proved that bycompositions of some functions of one variable, one can approximate continuous functional defined on compact Lp(K) and continuous operators from compact Lp1(K1) to LP2(K2). These results confirm the capability of neural networks in identifying dynamic systems.展开更多
In this paper,adaptive dynamic surface control(DSC) is developed for a class of nonlinear systems with unknown discrete and distributed time-varying delays and unknown dead-zone.Fuzzy logic systems are used to approxi...In this paper,adaptive dynamic surface control(DSC) is developed for a class of nonlinear systems with unknown discrete and distributed time-varying delays and unknown dead-zone.Fuzzy logic systems are used to approximate the unknown nonlinear functions.Then,by combining the backstepping technique and the appropriate Lyapunov-Krasovskii functionals with the dynamic surface control approach,the adaptive fuzzy tracking controller is designed.Our development is able to eliminate the problem of 'explosion of complexity' inherent in the existing backstepping-based methods.The main advantages of our approach include:1) for the n-th-order nonlinear systems,only one parameter needs to be adjusted online in the controller design procedure,which reduces the computation burden greatly.Moreover,the input of the dead-zone with only one adjusted parameter is much simpler than the ones in the existing results;2) the proposed control scheme does not need to know the time delays and their upper bounds.It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound,Finally,simulation results demonstrate the effectiveness of the proposed approach.展开更多
A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and...A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.展开更多
A new result on the stability of delay difference equations is established, in which a kind of weighted norm for x is adopted in order to estimate the upper bound of Liapunov functional.
Strong shock may induce complex processes in porous materials. We use the newly developed materialpoint-method to simulate such processes in an HMX-like material. To pick out relevant information, morphological charac...Strong shock may induce complex processes in porous materials. We use the newly developed materialpoint-method to simulate such processes in an HMX-like material. To pick out relevant information, morphological characterization is used to treat with the temperature map. Via the Minkowski funetional analysis the dynamics and thermodynamics of the shock wave reaction on porous HMX-like material are studied. The geometrical and topological properties of the ＂hot-spots＂ are revealed. Numerical results indicate that, shocks in porous materials are not simple jump states as classically viewed, but rather are a complex sequence of compressions and rarefactions. They cover a broad spectrum of states. We can use coarse-grained description to the wave series. A threshold value of temperature presents a Turing pattern dynamical procedure. A higher porosity is generally preferred when the energetic material needs a higher temperature for initiation. The technique of data analysis can be used to other physical quantities, for example, density, particle velocity, some specific stress, etc. From a series of studies along the line, one may get a large quantity of information for desiring the fabrication of material and choosing shock strength according to what needed is scattered or connected ＂hot-spots＂. PACS numbers： 05.70.Ln, 05 Key words： porous material 70.-a, 05.40.-a, 62.50.Ef shock wave, Minkowski functionals展开更多
Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theor...Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.展开更多
We conducted a large-scale density-functional theory study on the influence of the exchange-correlation functional in the calculation of electronic band gaps of solids.First,we use the large materials data set that we...We conducted a large-scale density-functional theory study on the influence of the exchange-correlation functional in the calculation of electronic band gaps of solids.First,we use the large materials data set that we have recently proposed to benchmark 21 different functionals,with a particular focus on approximations of the meta-generalized-gradient family.Combining these data with the results for 12 functionals in our previous work,we can analyze in detail the characteristics of each approximation and identify its strong and/or weak points.Beside confirming that mBJ,HLE16 and HSE06 are the most accurate functionals for band gap calculations,we reveal several other interesting functionals,chief among which are the local Slater potential approximation,the GGA AK13LDA,and the meta-GGAs HLE17 and TASK.We also compare the computational efficiency of these different approximations.Relying on these data,we investigate the potential for improvement of a promising subset of functionals by varying their internal parameters.The identified optimal parameters yield a family of functionals fitted for the calculation of band gaps.Finally,we demonstrate how to train machine learning models for accurate band gap prediction,using as input structural and composition data,as well as approximate band gaps obtained from density-functional theory.展开更多
In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate coercivity whose prototype is$ - {\rm div}\left( {a\left( {x,u} \right)Du} \right) = f$...In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate coercivity whose prototype is$ - {\rm div}\left( {a\left( {x,u} \right)Du} \right) = f$ in $D^' \left( \Omega \right),\,\,f \in L^r \left( \Omega \right),\,\,r > 1$where for example, a(x,u)=(1+|u|)^m/ with / ] (0,1). We study the same problem for minima of functionals closely related to the previous equation.展开更多
To investigate the impact of the fixed latent periods in the human and vector populations on the disease transmission in heterogenous environment,we formulate a nonlocal and time-delayed reaction-diffusion(NLTD-RD)sys...To investigate the impact of the fixed latent periods in the human and vector populations on the disease transmission in heterogenous environment,we formulate a nonlocal and time-delayed reaction-diffusion(NLTD-RD)system.By appealing to the next generation operator(NGO),we define the basic reproduction number(BRN)Ro,and prove it as a threshold parameter for indicating whether disease persists or not.Specifically,if o<1,the disease-free equilibrium is globally asymptotically stable,while if Ro>1,the disease is shown to be uniformly persistent.In the homogeneous case that all parameters are assumed to be constants,the explicit expression of o is obtained.We further achieved the global attractivity of the constant equilibria by utilizing Lyapunov functionals.Numerical simulations are performed to verify the theoretical results and the effects of the diffusion rate on disease transmission.展开更多
In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the ...In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion展开更多
Banach space-valued generalized functionals of white noise form an important part of vector-valued generalized functionals of white noise. In this paper, we discuss the differential of abstract function valued in B-va...Banach space-valued generalized functionals of white noise form an important part of vector-valued generalized functionals of white noise. In this paper, we discuss the differential of abstract function valued in B-valued generalized functional space. A characterized theorem is obtained by using their S-transform.展开更多
Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are ...Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.展开更多
At the Second International Conference of Mathematics, Hilbert raised 23 problems, which promoted the development of mathematics in the 20th century. Among them, the 13th problem can be described as follows: Can the s...At the Second International Conference of Mathematics, Hilbert raised 23 problems, which promoted the development of mathematics in the 20th century. Among them, the 13th problem can be described as follows: Can the solution of any algebraic equation be expressed by superpositions of some functions of one variable? Hilbert conjectured that the solution of the equation x^7+ax^3 +bx^2+cx+1=0, viewed as a function of a, b, c,展开更多
The robust stability of uncertain neutral systems with mixed time-varying delays is investigated in this paper. The uncertainties under consideration are norm-bounded and time-varying. Based on the Lyapunov stability ...The robust stability of uncertain neutral systems with mixed time-varying delays is investigated in this paper. The uncertainties under consideration are norm-bounded and time-varying. Based on the Lyapunov stability theory, a delay-dependent stability criterion is derived and given in the form of a linear matrix inequality （LMI）. Finally, a numerical example is given to illustrate significant improvement over some existing results.展开更多
In this work,we systematically evaluate the accuracy in band gap prediction of range-separated hybrid functionals on a large set of semiconducting and insulating materials and carry out comparisons with the performanc...In this work,we systematically evaluate the accuracy in band gap prediction of range-separated hybrid functionals on a large set of semiconducting and insulating materials and carry out comparisons with the performance of their global counterparts.We observe that all the range-separated hybrid functionals that correctly describe the long-range dielectric screening significantly improve upon standard hybrid functionals such as PBE0 and HSE06.The choice of the short-range Fock exchange fraction and the screening length can further reduce the predicted error.We then propose a universal expression for the selection of the inverse screening parameter as a function of the short-range and long-range Fock exchange fractions,which results in a mean absolute error as small as 0.15 eV for band gap prediction.展开更多
This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solution...This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.展开更多
We first prove various kinds of expressions for modulus of random convexity by using an L^0（F, R）-valued function＇s intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random...We first prove various kinds of expressions for modulus of random convexity by using an L^0（F, R）-valued function＇s intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals, then establish some basic properties including continuity for modulus of random convexity. In particular, we express the modulus of random convexity of a special random normed module L^0（F, X） derived from a normed space X by the classical modulus of convexity of X.展开更多
Two Minkowski functionals were tested in the capacity of morphological descriptors to quantitatively compare the arrays of vertically-aligned graphene flakes grown on smooth and nanoporous alumina and silica surfaces....Two Minkowski functionals were tested in the capacity of morphological descriptors to quantitatively compare the arrays of vertically-aligned graphene flakes grown on smooth and nanoporous alumina and silica surfaces. Specifically, the Euler-Poincaré characteristic and fractal dimension graphs were used to characterize the degree of connectivity and order in the systems, i.e. in the graphene flake patterns of petal-like and tree-like morphologies on solid substrates, and meshlike patterns (networks) grown on nanoporous alumina treated in low-temperature inductivelycoupled plasma. It was found that the Minkowski functionals return higher connectivity and fractal dimension numbers for the graphene flakepatterns with more complex morphologies, and indeed can be used as morphological descriptors to differentiate among various configurations of vertically-aligned graphene flakes grown on surfaces.展开更多
基金Project supported by the Climbing Programme-National Key Project for Fundamental Research in China, Grant NSC 92092 and NSF 19371022
文摘In this paper, the capability of neural networks and some approximation problens in system identification with neural networks are investigated. Some results are given: (i) For any function g ∈Llocp (R1) ∩S’ (R1) to be an Lp-Tauber-Wiener function, it is necessary and sufficient that g is not apolynomial; (ii) If g∈(Lp TW), then the set of is dense in Lp(K)’ (iii) It is proved that bycompositions of some functions of one variable, one can approximate continuous functional defined on compact Lp(K) and continuous operators from compact Lp1(K1) to LP2(K2). These results confirm the capability of neural networks in identifying dynamic systems.
基金supported by National Natural Science Foundation of China (Nos. 60974139 and 60804021)Fundamental Research Funds for the Central Universities (No. 72103676)
文摘In this paper,adaptive dynamic surface control(DSC) is developed for a class of nonlinear systems with unknown discrete and distributed time-varying delays and unknown dead-zone.Fuzzy logic systems are used to approximate the unknown nonlinear functions.Then,by combining the backstepping technique and the appropriate Lyapunov-Krasovskii functionals with the dynamic surface control approach,the adaptive fuzzy tracking controller is designed.Our development is able to eliminate the problem of 'explosion of complexity' inherent in the existing backstepping-based methods.The main advantages of our approach include:1) for the n-th-order nonlinear systems,only one parameter needs to be adjusted online in the controller design procedure,which reduces the computation burden greatly.Moreover,the input of the dead-zone with only one adjusted parameter is much simpler than the ones in the existing results;2) the proposed control scheme does not need to know the time delays and their upper bounds.It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound,Finally,simulation results demonstrate the effectiveness of the proposed approach.
文摘A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.
文摘A new result on the stability of delay difference equations is established, in which a kind of weighted norm for x is adopted in order to estimate the upper bound of Liapunov functional.
基金Supported by Science Foundations of Laboratory of Computational Physics and China Academy of Engineering Physics under Grant Nos.2009A0102005 and 2009B0101012National Science Foundation of China under Grant Nos.10702010,10775018,and 10604010
文摘Strong shock may induce complex processes in porous materials. We use the newly developed materialpoint-method to simulate such processes in an HMX-like material. To pick out relevant information, morphological characterization is used to treat with the temperature map. Via the Minkowski funetional analysis the dynamics and thermodynamics of the shock wave reaction on porous HMX-like material are studied. The geometrical and topological properties of the ＂hot-spots＂ are revealed. Numerical results indicate that, shocks in porous materials are not simple jump states as classically viewed, but rather are a complex sequence of compressions and rarefactions. They cover a broad spectrum of states. We can use coarse-grained description to the wave series. A threshold value of temperature presents a Turing pattern dynamical procedure. A higher porosity is generally preferred when the energetic material needs a higher temperature for initiation. The technique of data analysis can be used to other physical quantities, for example, density, particle velocity, some specific stress, etc. From a series of studies along the line, one may get a large quantity of information for desiring the fabrication of material and choosing shock strength according to what needed is scattered or connected ＂hot-spots＂. PACS numbers： 05.70.Ln, 05 Key words： porous material 70.-a, 05.40.-a, 62.50.Ef shock wave, Minkowski functionals
文摘Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.
基金M.A.L.M.and S.B.acknowledge partial support from the DFG through the projects TRR 227,SFB 1375,FOR 2857,BO 4280/8-1,and MA 6787/9-1.
文摘We conducted a large-scale density-functional theory study on the influence of the exchange-correlation functional in the calculation of electronic band gaps of solids.First,we use the large materials data set that we have recently proposed to benchmark 21 different functionals,with a particular focus on approximations of the meta-generalized-gradient family.Combining these data with the results for 12 functionals in our previous work,we can analyze in detail the characteristics of each approximation and identify its strong and/or weak points.Beside confirming that mBJ,HLE16 and HSE06 are the most accurate functionals for band gap calculations,we reveal several other interesting functionals,chief among which are the local Slater potential approximation,the GGA AK13LDA,and the meta-GGAs HLE17 and TASK.We also compare the computational efficiency of these different approximations.Relying on these data,we investigate the potential for improvement of a promising subset of functionals by varying their internal parameters.The identified optimal parameters yield a family of functionals fitted for the calculation of band gaps.Finally,we demonstrate how to train machine learning models for accurate band gap prediction,using as input structural and composition data,as well as approximate band gaps obtained from density-functional theory.
文摘In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate coercivity whose prototype is$ - {\rm div}\left( {a\left( {x,u} \right)Du} \right) = f$ in $D^' \left( \Omega \right),\,\,f \in L^r \left( \Omega \right),\,\,r > 1$where for example, a(x,u)=(1+|u|)^m/ with / ] (0,1). We study the same problem for minima of functionals closely related to the previous equation.
基金supported by National Natural Science Foundation of China(Nos.12071115 and 11871179)Fundamental Research Funds for the Universities in Heilongjiang Province(No.2021-KYYWF-0017)Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems.
文摘To investigate the impact of the fixed latent periods in the human and vector populations on the disease transmission in heterogenous environment,we formulate a nonlocal and time-delayed reaction-diffusion(NLTD-RD)system.By appealing to the next generation operator(NGO),we define the basic reproduction number(BRN)Ro,and prove it as a threshold parameter for indicating whether disease persists or not.Specifically,if o<1,the disease-free equilibrium is globally asymptotically stable,while if Ro>1,the disease is shown to be uniformly persistent.In the homogeneous case that all parameters are assumed to be constants,the explicit expression of o is obtained.We further achieved the global attractivity of the constant equilibria by utilizing Lyapunov functionals.Numerical simulations are performed to verify the theoretical results and the effects of the diffusion rate on disease transmission.
基金supported by the National Natural Science Fundation of China(71561017)the Science and Technology Plan of Gansu Province(1606RJZA041)+1 种基金the Youth Plan of Academic Talent of Lanzhou University of Finance and Economicssupported by the Fundamental Research Funds for the Central Universities(HUST2015QT005)
文摘In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion
文摘Banach space-valued generalized functionals of white noise form an important part of vector-valued generalized functionals of white noise. In this paper, we discuss the differential of abstract function valued in B-valued generalized functional space. A characterized theorem is obtained by using their S-transform.
基金partially supported by Grant No.DFNI I-02/9 of the Bulgarian Science Fund
文摘Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.
文摘At the Second International Conference of Mathematics, Hilbert raised 23 problems, which promoted the development of mathematics in the 20th century. Among them, the 13th problem can be described as follows: Can the solution of any algebraic equation be expressed by superpositions of some functions of one variable? Hilbert conjectured that the solution of the equation x^7+ax^3 +bx^2+cx+1=0, viewed as a function of a, b, c,
文摘The robust stability of uncertain neutral systems with mixed time-varying delays is investigated in this paper. The uncertainties under consideration are norm-bounded and time-varying. Based on the Lyapunov stability theory, a delay-dependent stability criterion is derived and given in the form of a linear matrix inequality （LMI）. Finally, a numerical example is given to illustrate significant improvement over some existing results.
基金This work is supported by Grant No.200020-152799 of the Swiss National Science Foundation(SNSF)The calculations were performed at the Swiss National Super-computing Center(CSCS)under project s1122 and at SCITAS-EPFL.
文摘In this work,we systematically evaluate the accuracy in band gap prediction of range-separated hybrid functionals on a large set of semiconducting and insulating materials and carry out comparisons with the performance of their global counterparts.We observe that all the range-separated hybrid functionals that correctly describe the long-range dielectric screening significantly improve upon standard hybrid functionals such as PBE0 and HSE06.The choice of the short-range Fock exchange fraction and the screening length can further reduce the predicted error.We then propose a universal expression for the selection of the inverse screening parameter as a function of the short-range and long-range Fock exchange fractions,which results in a mean absolute error as small as 0.15 eV for band gap prediction.
基金supported by the Hunan Provincial Innovation Foundation for Postgraduate(CX2013A003)the NNSF(11171351,11361078)SRFDP(20120162110021)of China
文摘This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.
基金Supported by National Natural Science Foundation of China(Grant No.11171015)Science Foundation of Chongqing Education Board(Grant No.KJ120732)
文摘We first prove various kinds of expressions for modulus of random convexity by using an L^0（F, R）-valued function＇s intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals, then establish some basic properties including continuity for modulus of random convexity. In particular, we express the modulus of random convexity of a special random normed module L^0（F, X） derived from a normed space X by the classical modulus of convexity of X.
文摘Two Minkowski functionals were tested in the capacity of morphological descriptors to quantitatively compare the arrays of vertically-aligned graphene flakes grown on smooth and nanoporous alumina and silica surfaces. Specifically, the Euler-Poincaré characteristic and fractal dimension graphs were used to characterize the degree of connectivity and order in the systems, i.e. in the graphene flake patterns of petal-like and tree-like morphologies on solid substrates, and meshlike patterns (networks) grown on nanoporous alumina treated in low-temperature inductivelycoupled plasma. It was found that the Minkowski functionals return higher connectivity and fractal dimension numbers for the graphene flakepatterns with more complex morphologies, and indeed can be used as morphological descriptors to differentiate among various configurations of vertically-aligned graphene flakes grown on surfaces.
