In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequal...In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality.展开更多
This article studies one dimensional viscous Camassa-Holm equation with a periodic boundary condition. The existence of the almost periodic solution is investigated by using the Galerkin method.
Global classical solutions near Maxwellians are constructed for the Boltzmann equation in a periodic box with angular soft cutoff, that is, -3 〈 γ 〈 0. The construction of global solution is based on an energy meth...Global classical solutions near Maxwellians are constructed for the Boltzmann equation in a periodic box with angular soft cutoff, that is, -3 〈 γ 〈 0. The construction of global solution is based on an energy method used in [9].展开更多
This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protoc...This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary (?) y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.展开更多
We consider the geometric global quantum discord (GGQD) of two-qubit systems. By analyzing the symmetry of geometric global quantum discord we give an approach for deriving analytical formulae of the extremum proble...We consider the geometric global quantum discord (GGQD) of two-qubit systems. By analyzing the symmetry of geometric global quantum discord we give an approach for deriving analytical formulae of the extremum problem which lies at the core of computing the GGQD for arbitrary two-qubit states. Furthermore, formulae of GGQD of arbitrary two-qubit states and some concrete examples are presented.展开更多
The multifractal formalism is shown to hold for a class of Moran measures supported on the Moran fractals associated with the sequences of which the frequency of the letter exists.
This article deals with the problem-△pu=λ|u|p/-2|x|pIn^p R/|x|+f(x,u),x∈Ω;u=0,x∈δΩ,where n = p. The authors prove that a Hardy inequality and the constant (p/p-1)^p is optimal. They also prove the ex...This article deals with the problem-△pu=λ|u|p/-2|x|pIn^p R/|x|+f(x,u),x∈Ω;u=0,x∈δΩ,where n = p. The authors prove that a Hardy inequality and the constant (p/p-1)^p is optimal. They also prove the existence of a nontrivial solution of the above mentioned problem by using the Mountain Pass Lemma.展开更多
This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing an...This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.展开更多
Some embedding inequalities in Hardy-Sobolev space are proved. Furthermore, by the improved inequalities and the linking theorem, in a new k-order SobolevHardy space, we obtain the existence of sign-changing solutions...Some embedding inequalities in Hardy-Sobolev space are proved. Furthermore, by the improved inequalities and the linking theorem, in a new k-order SobolevHardy space, we obtain the existence of sign-changing solutions for the nonlinear elliptic equation {-△(k)u:=-△u-(N-2)2/4u/|x|2-1/4k-1∑im1u/|x|2(ln(i)R/|x|2=f(x,u),x∈Ω,u=0,x∈Ω,where 0∈ΩBa(0)RN,n≥3,ln)i)=6jm1ln(j),and R=ae(k-1),where e(0)=1,e(j)=ee(j=1)for j≥1,ln(1)=ln,ln(j)=lnln(j-1)for j≥2.Besides,positive and negative solutions are obtained by a variant mountain pass theorem.展开更多
The Hardy-Sobolev inequality with general weights is established, and it is shown that the constant is optimal. The two weights in this inequality are determined by a Bernoulli equation. In addition, the authors obtai...The Hardy-Sobolev inequality with general weights is established, and it is shown that the constant is optimal. The two weights in this inequality are determined by a Bernoulli equation. In addition, the authors obtain the Hardy-Sobolev inequality with general weights and remainder terms. By choosing special weights, it turns to be many versions of the Hardy-Sobolev inequality and the Caffarelli-Kohn-Nirenberg inequality with remainder terms in the literature.展开更多
In this paper, we propose two kinds of modifications in speaker recognition. First, the correlations between frequency channels are of prime importance for speaker recognition. Some of these correlations are lost when...In this paper, we propose two kinds of modifications in speaker recognition. First, the correlations between frequency channels are of prime importance for speaker recognition. Some of these correlations are lost when the frequency domain is divided into sub-bands. Consequently we propose a particularly redundant parallel architecture for which most of the correlations are kept. Second, generally a log transformation used to modify the power spectrum is done after the filter-bank in the classical spectrum calculation. We will see that performing this transformation before the filter bank is more interesting in our case. In the processing of recognition, the Gaussian mixture model (GMM) recognition arithmetic is adopted. Experiments on speech corrupted by noise show a better adaptability of this approach in noisy environments, comoared with a conventional device, esoeciallv when oruning of some recognizers is performed.展开更多
In this paper,we study the convergence rate of an Embedded exponential-type low-regularity integrator(ELRI)for the Korteweg-de Vries equation.We develop some new harmonic analysis techniques to handle the"stabili...In this paper,we study the convergence rate of an Embedded exponential-type low-regularity integrator(ELRI)for the Korteweg-de Vries equation.We develop some new harmonic analysis techniques to handle the"stability"issue.In particular,we use a new stability estimate which allows us to avoid the use of the fractional Leibniz inequality,|<J^(γ)δx(fg),J^(γ)f>|■||f||H^(γ)^(2)||g||H^(γ+1),and replace f regularity.Based on these techniques,we prove that the ELRI scheme proposed in[41]provides 1/2-order convergence accuracy in H^(γ)for any initial data belonging to H^(γ)with γ>3/2,which does not require any additional derivative assumptions.展开更多
This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrodinger equations with homogeneous Dirichlet boundary condition.The authors prove the existence of compact ...This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrodinger equations with homogeneous Dirichlet boundary condition.The authors prove the existence of compact kernel sections for the associated process by using a suitable decomposition of the equations.展开更多
We provide a Faddeev–Reshetikhin–Takhtajan’sRTT approach to the quantum group Fun(GLr,s(n))and the quantum enveloping algebra Ur,s(gln)corresponding to the two-parameter R-matrix.We prove that the quantum determina...We provide a Faddeev–Reshetikhin–Takhtajan’sRTT approach to the quantum group Fun(GLr,s(n))and the quantum enveloping algebra Ur,s(gln)corresponding to the two-parameter R-matrix.We prove that the quantum determinant detr,sT is a quasi-central element in Fun(GLr,s(n))generalizing earlier results of Dipper–Donkin and Du–Parshall–Wang.The explicit formulation provides an interpretation of the deforming parameters,and the quantized algebra Ur,s(R)is identified to Ur,s(gln)as the dual algebra.We then construct n−1 quasi-central elements in Ur,s(R)which are analogs of higher Casimir elements in Uq(gln).展开更多
To the problem that it is hard to determine the clustering number and the abnormal points by using the clustering validity function, an effective clustering partition model based on the genetic algorithm is built in t...To the problem that it is hard to determine the clustering number and the abnormal points by using the clustering validity function, an effective clustering partition model based on the genetic algorithm is built in this paper. The solution to the problem is formed by the combination of the clustering partition and the encoding samples, and the fitness function is defined by the distances among and within clusters. The clustering number and the samples in each cluster are determined and the abnormal points are distinguished by implementing the triple random crossover operator and the mutation. Based on the known sample data, the results of the novel method and the clustering validity function are compared. Numerical experiments are given and the results show that the novel method is more effective.展开更多
We present some conditions for the existence and uniqueness of almost automorphic solutions of third order neutral delay-differential equations with piecewise constant of the form(X(t) +px(t - 1))″′, = a0x(...We present some conditions for the existence and uniqueness of almost automorphic solutions of third order neutral delay-differential equations with piecewise constant of the form(X(t) +px(t - 1))″′, = a0x([t]) + a1x([t - 1]) + f(t),where [.] is the greatest integer function, p, a0 and al are nonzero constants, and f(t) is almost automorphic.展开更多
This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties....This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties. The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties. By constructing an appropriate Lyapunov-Krasvskii functional, a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality. From the derived criterion, the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically. A simulation example is given to illustrate the effectiveness of the proposed design method,展开更多
Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorousl...Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.展开更多
In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The co...In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.展开更多
基金Supported by NSFC(10471047)NSF Guangdong Province(05300159).
文摘In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality.
基金Supported by Natural Science Foundation of China (10471047)Natural Science Foundation of Guangdong Province (05300162)
文摘This article studies one dimensional viscous Camassa-Holm equation with a periodic boundary condition. The existence of the almost periodic solution is investigated by using the Galerkin method.
文摘Global classical solutions near Maxwellians are constructed for the Boltzmann equation in a periodic box with angular soft cutoff, that is, -3 〈 γ 〈 0. The construction of global solution is based on an energy method used in [9].
基金The project is supported by National Natural Science Foundation of China(10371045)Guangdong Provincial Natural Science Foundation of China(000671)National Natural Science Foundation of China(10426015).
文摘This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary (?) y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11275131,11305105,and 11271138)Simons Foundation(Grant No.198129)
文摘We consider the geometric global quantum discord (GGQD) of two-qubit systems. By analyzing the symmetry of geometric global quantum discord we give an approach for deriving analytical formulae of the extremum problem which lies at the core of computing the GGQD for arbitrary two-qubit states. Furthermore, formulae of GGQD of arbitrary two-qubit states and some concrete examples are presented.
基金supported by the National Natural Science Foundation of China(Grant No.10171028)the Special for Major State Basic Research Projects of China.
文摘The multifractal formalism is shown to hold for a class of Moran measures supported on the Moran fractals associated with the sequences of which the frequency of the letter exists.
基金Supported by NSFC(10471047)NSF Guangdong Province(04020077)
文摘This article deals with the problem-△pu=λ|u|p/-2|x|pIn^p R/|x|+f(x,u),x∈Ω;u=0,x∈δΩ,where n = p. The authors prove that a Hardy inequality and the constant (p/p-1)^p is optimal. They also prove the existence of a nontrivial solution of the above mentioned problem by using the Mountain Pass Lemma.
基金Sponsored by the National NSF (10901121, 10826091,10771074, and 10771139)NSF for Postdoctors in China (20090460952)+3 种基金NSF of Zhejiang Province (Y6080077)NSF of Guangdong Province (004020077)NSF of Wenzhou University (2008YYLQ01)Zhejiang youthteacher training project and Wenzhou 551 project
文摘This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.
基金supported by the National Science Foundation of China (10471047)the Natural Science Foundation of Guangdong Province (04020077)
文摘Some embedding inequalities in Hardy-Sobolev space are proved. Furthermore, by the improved inequalities and the linking theorem, in a new k-order SobolevHardy space, we obtain the existence of sign-changing solutions for the nonlinear elliptic equation {-△(k)u:=-△u-(N-2)2/4u/|x|2-1/4k-1∑im1u/|x|2(ln(i)R/|x|2=f(x,u),x∈Ω,u=0,x∈Ω,where 0∈ΩBa(0)RN,n≥3,ln)i)=6jm1ln(j),and R=ae(k-1),where e(0)=1,e(j)=ee(j=1)for j≥1,ln(1)=ln,ln(j)=lnln(j-1)for j≥2.Besides,positive and negative solutions are obtained by a variant mountain pass theorem.
基金the National Natural Science Foundation of China(10771074,10726060)the Natural Science Foundation of Guangdong Province(04020077)
文摘The Hardy-Sobolev inequality with general weights is established, and it is shown that the constant is optimal. The two weights in this inequality are determined by a Bernoulli equation. In addition, the authors obtain the Hardy-Sobolev inequality with general weights and remainder terms. By choosing special weights, it turns to be many versions of the Hardy-Sobolev inequality and the Caffarelli-Kohn-Nirenberg inequality with remainder terms in the literature.
基金the National Natural Science Foundation of China (No. 60171043, 60371046)
文摘In this paper, we propose two kinds of modifications in speaker recognition. First, the correlations between frequency channels are of prime importance for speaker recognition. Some of these correlations are lost when the frequency domain is divided into sub-bands. Consequently we propose a particularly redundant parallel architecture for which most of the correlations are kept. Second, generally a log transformation used to modify the power spectrum is done after the filter-bank in the classical spectrum calculation. We will see that performing this transformation before the filter bank is more interesting in our case. In the processing of recognition, the Gaussian mixture model (GMM) recognition arithmetic is adopted. Experiments on speech corrupted by noise show a better adaptability of this approach in noisy environments, comoared with a conventional device, esoeciallv when oruning of some recognizers is performed.
文摘In this paper,we study the convergence rate of an Embedded exponential-type low-regularity integrator(ELRI)for the Korteweg-de Vries equation.We develop some new harmonic analysis techniques to handle the"stability"issue.In particular,we use a new stability estimate which allows us to avoid the use of the fractional Leibniz inequality,|<J^(γ)δx(fg),J^(γ)f>|■||f||H^(γ)^(2)||g||H^(γ+1),and replace f regularity.Based on these techniques,we prove that the ELRI scheme proposed in[41]provides 1/2-order convergence accuracy in H^(γ)for any initial data belonging to H^(γ)with γ>3/2,which does not require any additional derivative assumptions.
基金the NNSFC(10771139 and 10771074)NSF of Wenzhou University(2007L024)NSF of Guangdong Province(004020077)
文摘This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrodinger equations with homogeneous Dirichlet boundary condition.The authors prove the existence of compact kernel sections for the associated process by using a suitable decomposition of the equations.
基金Naihuan Jing gratefully acknowledges the support of Humboldt Foundation,MPILeipzig,Simons Foundation grant 198129and NSFC grant 11271138 during this work.Ming Liu thanks the support of NSFC grant 11271238.
文摘We provide a Faddeev–Reshetikhin–Takhtajan’sRTT approach to the quantum group Fun(GLr,s(n))and the quantum enveloping algebra Ur,s(gln)corresponding to the two-parameter R-matrix.We prove that the quantum determinant detr,sT is a quasi-central element in Fun(GLr,s(n))generalizing earlier results of Dipper–Donkin and Du–Parshall–Wang.The explicit formulation provides an interpretation of the deforming parameters,and the quantized algebra Ur,s(R)is identified to Ur,s(gln)as the dual algebra.We then construct n−1 quasi-central elements in Ur,s(R)which are analogs of higher Casimir elements in Uq(gln).
文摘To the problem that it is hard to determine the clustering number and the abnormal points by using the clustering validity function, an effective clustering partition model based on the genetic algorithm is built in this paper. The solution to the problem is formed by the combination of the clustering partition and the encoding samples, and the fitness function is defined by the distances among and within clusters. The clustering number and the samples in each cluster are determined and the abnormal points are distinguished by implementing the triple random crossover operator and the mutation. Based on the known sample data, the results of the novel method and the clustering validity function are compared. Numerical experiments are given and the results show that the novel method is more effective.
基金supported by National Natural Science Foundation of China(Grant Nos.11271380,11501238)Natural Science Foundation of Guangdong Province(Grant Nos.2014A030313641,2016A030313119,S2013010013212)the Major Project Foundation of Guangdong Province Education Department(No.2014KZDXM070)
文摘We present some conditions for the existence and uniqueness of almost automorphic solutions of third order neutral delay-differential equations with piecewise constant of the form(X(t) +px(t - 1))″′, = a0x([t]) + a1x([t - 1]) + f(t),where [.] is the greatest integer function, p, a0 and al are nonzero constants, and f(t) is almost automorphic.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61104138)the Guangdong Natural Science Foundation,China (Grant No. S2011040001704)the Foundation for Distinguished Young Talents in Higher Education of Guangdong,China (Grant No. LYM10074)
文摘This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties. The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties. By constructing an appropriate Lyapunov-Krasvskii functional, a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality. From the derived criterion, the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically. A simulation example is given to illustrate the effectiveness of the proposed design method,
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10871074 and 10572011)the Natural Science Foundation of Guangxi Province,China (Grant No 0832244)
文摘Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10572011, 100461002, and 10661005)the Natural Science Foundation of Guangxi Province, China (Grant Nos 0575092 and 0832244)
文摘In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.