Objective:To examine the effect of an neurokinin 3 receptor(NK3R)agonist,senktide,on neuronal nitric oxide synthase(nNOS)activation in the median eminence-arcuate nucleus(ME-ARC)and preoptic area(POA)regions of the hy...Objective:To examine the effect of an neurokinin 3 receptor(NK3R)agonist,senktide,on neuronal nitric oxide synthase(nNOS)activation in the median eminence-arcuate nucleus(ME-ARC)and preoptic area(POA)regions of the hypothalamus across proestrus,diestrus,and ovariectomized states in female rats and its correlation with luteinizing hormone(LH)secretion.Methods:Adult female Sprague-Dawley rats were examined for proestrus and diestrus phases of the estrous cycle.Female rats were categorized into proestrus and diestrus groups,and each was further divided into four subgroups(n=4).In both the diestrus and proestrus categories,Group 1 was the control group.Groups 2,3,and 4 received senktide(100μg/kg-1),NK3R antagonist SB222200(10 mg/kg-1),and SB222200 followed by senktide,respectively.To evaluate the effect of sex steroids on NK3R agonist-induced nNOS activation,female rats underwent bilateral ovariectomy and were divided into four groups(n=3).Group 1 served as the control.Group 2 received a subcutaneous injection of 17β-estradiol 3-benzoate(E2,3μg/rat).Group 3 received E2 and progesterone(30μg/rat).Group 4 was administered senktide(100μg/kg).Female rats from each group were sacrificed,blood was collected for LH ELISA,and hypothalamic tissues were collected for Western blotting.Results:Senktide increased nNOS phosphorylation in the ME-ARC during both the proestrus and diestrus phases.In the POA,senktide increased nNOS phosphorylation only during the diestrus phase.In ovariectomized rats,senktide activated nNOS independent of sex steroid levels.Senktide also increased serum LH concentration in diestrus and ovariectomized female rats.Conclusions:Senktide,an NK3R agonist,activates nNOS in the POA and ME-ARC regions of the hypothalamus in a phase dependent manner.The activation of nNOS by senktide suggests a potential mechanism by which neurokinin B triggers nNOS activation in the ARC and POA regions and regulates GnRH/LH secretion.展开更多
In this work, we apply the bifurcation method of dynamical systems to investigate the underlying complex dynamics of traveling wave solutions to a highly nonlinear Fujimoto–Watanabe equation. We identify all bifurcat...In this work, we apply the bifurcation method of dynamical systems to investigate the underlying complex dynamics of traveling wave solutions to a highly nonlinear Fujimoto–Watanabe equation. We identify all bifurcation conditions and phase portraits of the system in different regions of the three-dimensional parametric space, from which we present the sufficient conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like(antikink-like) wave solutions, and compactons. Furthermore, we obtain their exact expressions and simulations, which can help us understand the underlying physical behaviors of traveling wave solutions to the equation.展开更多
This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,a...This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,and food for the prey or vegetation.The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process.We study the problem of minimization of a given integral cost functional over solutions of the above system.The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable.Some relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.展开更多
The bilinear form of two nonlinear evolution equations are derived by using Hirota derivative. The Backlund transformation based on the Hirota bilinear method for these two equations are presented, respectively. As an...The bilinear form of two nonlinear evolution equations are derived by using Hirota derivative. The Backlund transformation based on the Hirota bilinear method for these two equations are presented, respectively. As an application, the explicit solutions including soliton and stationary rational solutions for these two equations are obtained.展开更多
Based on the multiplicity results of Benci and Fortunato [4], we consider some elliptic systems with strongly indefinite quadratic part, and establish the existence of infinitely many nontrivial solutions in a suitabl...Based on the multiplicity results of Benci and Fortunato [4], we consider some elliptic systems with strongly indefinite quadratic part, and establish the existence of infinitely many nontrivial solutions in a suitable family of products of fractional Sobolev spaces.展开更多
We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably sm...We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small.Note that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.展开更多
In this paper, we study the Cauchy problem of the inhomogeneous energy-critical Schrōdinger equation： iаtu=-△u-k（x）｜u｜4/N-2u,N≥3. Using the potential well method, we establish some new sharp criteria for blow...In this paper, we study the Cauchy problem of the inhomogeneous energy-critical Schrōdinger equation： iаtu=-△u-k（x）｜u｜4/N-2u,N≥3. Using the potential well method, we establish some new sharp criteria for blow-up of solutions in tile nonradial case. In particular, our conclusion in some sense improves on the results in [Kenig and Merle, invent. Math. 166, 645-675 （2006）], where only the radial case is considered in dimensions 3. 4. 5.展开更多
This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between,within,and across layers.Based on the Lyapunov stability met...This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between,within,and across layers.Based on the Lyapunov stability method,we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions,and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers.Interestingly,for a certain class of coupling matrices across layers,it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger,intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers.Finally,numerical simulations further verify the theoretical results.展开更多
A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries(DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissma...A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries(DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissmann box scheme,we obtain a conformal multi-symplectic scheme for multi-symplectic partial differential equations(PDEs) with added dissipation. Applying it to the DKdV equation, we construct a conformal multi-symplectic algorithm for it, which is of second order accuracy in time. Numerical experiments demonstrate that the proposed method not only preserves the dissipation rate of mass exactly with periodic boundary conditions, but also has excellent long-time numerical behavior.展开更多
We scrutinize the approximate analytical solutions by the optimal homotopy analysis method(OHAM) for the flow and mass transfer within the Marangoni boundary layer of power-law fluids over a disk with suction and inje...We scrutinize the approximate analytical solutions by the optimal homotopy analysis method(OHAM) for the flow and mass transfer within the Marangoni boundary layer of power-law fluids over a disk with suction and injection in the present paper. Concentration distribution on the surface of a disk varies in a power-law form. The non-Newtonian fluid flow is due to the surface concentration gradient without considering gravity and buoyancy. According to the conservation of mass, momentum and concentration, the governing partial differential equations are established, and the appropriate generalized Kármán transformation is found to reduce them to the nonlinear ordinary differential equations. OHAM is used to access the approximate analytical solution. The influences of Marangoni the number, suction/injection parameters and power-law exponent on the flow and mass transfer are examined.展开更多
A completely integrable Toda-like lattice equation in 2+1 dimensions is studied.Four kinds of exact solutions to this equation are derived by virtue of variable separation and the Hirota bilinear approach.The relation...A completely integrable Toda-like lattice equation in 2+1 dimensions is studied.Four kinds of exact solutions to this equation are derived by virtue of variable separation and the Hirota bilinear approach.The relations between each two solutions are also presented.展开更多
The one-and two-periodic wave solutions for the Hirota–Satsuma(HS)equation are presented by using the Hirota derivative and Riemann theta function.The rigorous proofs on asymptotic behaviors of these two solutions ar...The one-and two-periodic wave solutions for the Hirota–Satsuma(HS)equation are presented by using the Hirota derivative and Riemann theta function.The rigorous proofs on asymptotic behaviors of these two solutions are given such that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.展开更多
Let Bn be the set of all n×n Boolean Matrices; R（A） denote the row space of A∈Bn, ｜R（A）｜ denote the cardinality of R（A）, m, n, k, l, t, i, γi be positive integers, Si, λi be non negative integers. In t...Let Bn be the set of all n×n Boolean Matrices; R（A） denote the row space of A∈Bn, ｜R（A）｜ denote the cardinality of R（A）, m, n, k, l, t, i, γi be positive integers, Si, λi be non negative integers. In this paper, we prove the following two results：（1）Let n≥13,n-3≥k〉Sl,Si＋〉Si,i=1,2…,l-1.if k＋l≤n,then for any m=2^k＋2^S1-l＋…＋2^S1,there exists A∈Bn,such that ｜R（A）｜=m.（2）Let n≥13,n-3≥k〉Sn-k-1〉Sn-k-2〉…S1〉λt〉λt-1〉…〉λ1,2≤t≤n-k.If exist γi（k＋1≤γi≤n-1,i=1,2…,t-1）γi〈γi＋1 and λt-λt-1≤k-Sn-γ1,λt-i-λt-i-1≤Sn-γi-Sn-γii＋1,i=1,2…,t-2,then for any m=2^k＋2^Sn-k-1＋2^Sn-k-1＋2^Sn-k-2＋…＋2^S1＋2^λt＋2^λt-1…＋2^λ1,there exists A∈Bn,as such that ｜R（A）｜=m.展开更多
In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. B...In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.展开更多
The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approxima...The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate thenonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation beforeapproximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic modedecomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, anovel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid oferror data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.展开更多
When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Li...When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.展开更多
In this paper a modifed continuous energy law was explored to investigate transport behavior in a gas metal arc welding(GMAW)system.The energy law equality at a discrete level for the GMAW system was derived by using ...In this paper a modifed continuous energy law was explored to investigate transport behavior in a gas metal arc welding(GMAW)system.The energy law equality at a discrete level for the GMAW system was derived by using the finite element scheme.The mass conservation and current density continuous equation with the penalty scheme was applied 10 improve the stability.According to the phase-field model coupled with the energy law preserving method,the GMAW model was discretized and a metal transfer process with a pulse current was simulated.It was found that the numerical solution agrees well with the data of the metal transfer process obtained by high-speed photography.Compared with the numerical solution of the volume of fuid model,which was widely studied in the GMAW system based on the finite element method Euler scheme,the energy law preserving method can provide better accuracy in predicting the shape evolution of the droplet and with a greater computing efficiency.展开更多
There are several difficulties in generalized/extended finite element methods(GFEM/XFEM)for moving interface problems.First,the GFEM/XFEM may be unstable in a sense that condition numbers of system matrices could be m...There are several difficulties in generalized/extended finite element methods(GFEM/XFEM)for moving interface problems.First,the GFEM/XFEM may be unstable in a sense that condition numbers of system matrices could be much bigger than those of standard FEM.Second,they may not be robust in that the condition numbers increase rapidly as interface curves approach edges of meshes.Furthermore,time stepping schemes need carrying out carefully since both enrichment functions and enriched nodes in the GFEM/XFEM vary in time.This paper is devoted to proposing the stable and robust GFEM/XFEM with efficient time stepping schemes for the parabolic interface problems with moving interfaces.A so-called stable GFEM(SGFEM)developed for elliptical interface problems is extended to the parabolic interface problems for spatial discretizations;while backward difference formulae(BDF)are used for the time stepping.Numerical studies demonstrate that the SGFEM with the first and second order BDF(also known as backward Euler method and BDF2)is stable,robust,and achieves optimal convergence rates.Comparisons of the proposed SGFEM with various commonly-used GFEM/XFEM are made,which show advantages of the SGFEM over the other GFEM/XFEM in aspects of stability,robustness,and convergence.展开更多
We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the "stable set" M2 and "unstable set" M1, we show that there exists a unique gl...We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the "stable set" M2 and "unstable set" M1, we show that there exists a unique global solution provided the initial data belong to M2 and the global solution converges to zero in H^1 exponentially as time goes to infinity. Moreover, we also prove that the local regular solution must blow up at finite time provided the initial data belong to M1.展开更多
This paper investigates the impact of inter-layer coupling functions and intra-layer coupling delays on intra-layer synchronization regions and sychronizability. It is found that the inter-layer coupling functions hav...This paper investigates the impact of inter-layer coupling functions and intra-layer coupling delays on intra-layer synchronization regions and sychronizability. It is found that the inter-layer coupling functions have great influence on intra-layer synchronization regions, as well as on the intra-layer synchronizability. In particular, there exists an inter-layer coupling function such that the inter-layer coupling strength neither improves nor weakens the intra-layer synchronizability. Furthermore, no matter which one of three inter-layer coupling functions is chosen, a small intra-layer delay always keeps the intra-layer synchronized regions almost unchanged, implying that the small delay neither enhances nor suppresses the intra-layer synchronizability. At the same time the delay greatly frustrates the synchronizability in each layer when it is greater than some threshold. Our results may have potential applications for interconnected technological networks where communication delays are inevitably present.展开更多
基金supported by DST-Science and Engineering Research Board(SERB)Early carrier research grant ECR/2015/000240Core research grant CRG/2020/003257,the University Grants Commission(UGC start-up grant F.30-318/2016)the Central University of Punjab RSM grant-CUPB/CC/16/00/13.
文摘Objective:To examine the effect of an neurokinin 3 receptor(NK3R)agonist,senktide,on neuronal nitric oxide synthase(nNOS)activation in the median eminence-arcuate nucleus(ME-ARC)and preoptic area(POA)regions of the hypothalamus across proestrus,diestrus,and ovariectomized states in female rats and its correlation with luteinizing hormone(LH)secretion.Methods:Adult female Sprague-Dawley rats were examined for proestrus and diestrus phases of the estrous cycle.Female rats were categorized into proestrus and diestrus groups,and each was further divided into four subgroups(n=4).In both the diestrus and proestrus categories,Group 1 was the control group.Groups 2,3,and 4 received senktide(100μg/kg-1),NK3R antagonist SB222200(10 mg/kg-1),and SB222200 followed by senktide,respectively.To evaluate the effect of sex steroids on NK3R agonist-induced nNOS activation,female rats underwent bilateral ovariectomy and were divided into four groups(n=3).Group 1 served as the control.Group 2 received a subcutaneous injection of 17β-estradiol 3-benzoate(E2,3μg/rat).Group 3 received E2 and progesterone(30μg/rat).Group 4 was administered senktide(100μg/kg).Female rats from each group were sacrificed,blood was collected for LH ELISA,and hypothalamic tissues were collected for Western blotting.Results:Senktide increased nNOS phosphorylation in the ME-ARC during both the proestrus and diestrus phases.In the POA,senktide increased nNOS phosphorylation only during the diestrus phase.In ovariectomized rats,senktide activated nNOS independent of sex steroid levels.Senktide also increased serum LH concentration in diestrus and ovariectomized female rats.Conclusions:Senktide,an NK3R agonist,activates nNOS in the POA and ME-ARC regions of the hypothalamus in a phase dependent manner.The activation of nNOS by senktide suggests a potential mechanism by which neurokinin B triggers nNOS activation in the ARC and POA regions and regulates GnRH/LH secretion.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11701191 and 11871232)the Program for Innovative Research Team in Science and Technology in University of Fujian Province,Quanzhou High-Level Talents Support Plan(Grant No.2017ZT012)the Subsidized Project for Cultivating Postgraduates’ Innovative Ability in Scientific Research of Huaqiao University
文摘In this work, we apply the bifurcation method of dynamical systems to investigate the underlying complex dynamics of traveling wave solutions to a highly nonlinear Fujimoto–Watanabe equation. We identify all bifurcation conditions and phase portraits of the system in different regions of the three-dimensional parametric space, from which we present the sufficient conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like(antikink-like) wave solutions, and compactons. Furthermore, we obtain their exact expressions and simulations, which can help us understand the underlying physical behaviors of traveling wave solutions to the equation.
基金supported by National Natural Science Foundation of China(12071165 and 62076104)Natural Science Foundation of Fujian Province(2020J01072)+2 种基金Program for Innovative Research Team in Science and Technology in Fujian Province University,Quanzhou High-Level Talents Support Plan(2017ZT012)Scientific Research Funds of Huaqiao University(605-50Y 19017,605-50Y14040)supported by Ministry of Science and Higher Education of Russian Federation(075-15-2020-787,large scientific project"Fundamentals,methods and technologies for digital monitoring and forecasting of the environmental situation on the Baikal natural territory")。
文摘This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,and food for the prey or vegetation.The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process.We study the problem of minimization of a given integral cost functional over solutions of the above system.The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable.Some relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.
基金Project supported by the Science Research Foundation of Zhanjiang Normal University (Grant No. L0803)
文摘The bilinear form of two nonlinear evolution equations are derived by using Hirota derivative. The Backlund transformation based on the Hirota bilinear method for these two equations are presented, respectively. As an application, the explicit solutions including soliton and stationary rational solutions for these two equations are obtained.
文摘Based on the multiplicity results of Benci and Fortunato [4], we consider some elliptic systems with strongly indefinite quadratic part, and establish the existence of infinitely many nontrivial solutions in a suitable family of products of fractional Sobolev spaces.
基金supported by National Natural Science Foundation of China(11701193,11671086)Natural Science Foundation of Fujian Province(2018J05005,2017J01562)+3 种基金Program for Innovative Research Team in Science and Technology in Fujian Province University Quanzhou High-Level Talents Support Plan(2017ZT012)supported by National Natural Science Foundation of China(11901474)the Chongqing Talent Plan for Young Topnotch Talents(CQYC202005074)the Innovation Support Program for Chongqing Overseas Returnees(cx2020082).
文摘We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small.Note that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.
文摘In this paper, we study the Cauchy problem of the inhomogeneous energy-critical Schrōdinger equation： iаtu=-△u-k（x）｜u｜4/N-2u,N≥3. Using the potential well method, we establish some new sharp criteria for blow-up of solutions in tile nonradial case. In particular, our conclusion in some sense improves on the results in [Kenig and Merle, invent. Math. 166, 645-675 （2006）], where only the radial case is considered in dimensions 3. 4. 5.
基金Project supported in part by the National Natural Science Foundation of China(Grant Nos.61573004 and 11501221)the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University(Grant No.ZQN-YX301)+1 种基金the Program for New Century Excellent Talents in Fujian Province University in 2016the Project of Education and Scientific Research for Middle and Young Teachers in Fujian Province,China(Grant Nos.JAT170027 and JA15030)
文摘This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between,within,and across layers.Based on the Lyapunov stability method,we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions,and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers.Interestingly,for a certain class of coupling matrices across layers,it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger,intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers.Finally,numerical simulations further verify the theoretical results.
基金Project supported by the Program for Innovative Research Team in Science and Technology in Fujian Province University,China,the Quanzhou High Level Talents Support Plan,China(Grant No.2017ZT012)the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University,China(Grant No.ZQN-YX502)
文摘A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries(DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissmann box scheme,we obtain a conformal multi-symplectic scheme for multi-symplectic partial differential equations(PDEs) with added dissipation. Applying it to the DKdV equation, we construct a conformal multi-symplectic algorithm for it, which is of second order accuracy in time. Numerical experiments demonstrate that the proposed method not only preserves the dissipation rate of mass exactly with periodic boundary conditions, but also has excellent long-time numerical behavior.
基金supported by the National Natural Science Foundation of China (No. 11702101)the Fundamental Research Funds for the Central Universities and the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (No. ZQNPY502)+2 种基金the Natural Science Foundation of Fujian Province (No. 2019J05093)Quanzhou High-Level Talents Support Plansupported by Subsidized Project for Postgraduates’ Innovative Fund in Scientific Research of Huaqiao University。
文摘We scrutinize the approximate analytical solutions by the optimal homotopy analysis method(OHAM) for the flow and mass transfer within the Marangoni boundary layer of power-law fluids over a disk with suction and injection in the present paper. Concentration distribution on the surface of a disk varies in a power-law form. The non-Newtonian fluid flow is due to the surface concentration gradient without considering gravity and buoyancy. According to the conservation of mass, momentum and concentration, the governing partial differential equations are established, and the appropriate generalized Kármán transformation is found to reduce them to the nonlinear ordinary differential equations. OHAM is used to access the approximate analytical solution. The influences of Marangoni the number, suction/injection parameters and power-law exponent on the flow and mass transfer are examined.
基金Supported by the Science Research Foundation of Zhanjiang Normal University(L0803).
文摘A completely integrable Toda-like lattice equation in 2+1 dimensions is studied.Four kinds of exact solutions to this equation are derived by virtue of variable separation and the Hirota bilinear approach.The relations between each two solutions are also presented.
基金by the Science Research Foundation of Zhanjiang Normal University(L0803).
文摘The one-and two-periodic wave solutions for the Hirota–Satsuma(HS)equation are presented by using the Hirota derivative and Riemann theta function.The rigorous proofs on asymptotic behaviors of these two solutions are given such that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.
基金Foundation item： Supported by the Guangdong Provincial Natural Science Foundation of China（06029035）
文摘Let Bn be the set of all n×n Boolean Matrices; R（A） denote the row space of A∈Bn, ｜R（A）｜ denote the cardinality of R（A）, m, n, k, l, t, i, γi be positive integers, Si, λi be non negative integers. In this paper, we prove the following two results：（1）Let n≥13,n-3≥k〉Sl,Si＋〉Si,i=1,2…,l-1.if k＋l≤n,then for any m=2^k＋2^S1-l＋…＋2^S1,there exists A∈Bn,such that ｜R（A）｜=m.（2）Let n≥13,n-3≥k〉Sn-k-1〉Sn-k-2〉…S1〉λt〉λt-1〉…〉λ1,2≤t≤n-k.If exist γi（k＋1≤γi≤n-1,i=1,2…,t-1）γi〈γi＋1 and λt-λt-1≤k-Sn-γ1,λt-i-λt-i-1≤Sn-γi-Sn-γii＋1,i=1,2…,t-2,then for any m=2^k＋2^Sn-k-1＋2^Sn-k-1＋2^Sn-k-2＋…＋2^S1＋2^λt＋2^λt-1…＋2^λ1,there exists A∈Bn,as such that ｜R（A）｜=m.
基金supported by the Natural Science Foundation of China under Grant Nos.60804008,61174048and 11071263the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at Sun Yat-Sen University
文摘In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11871400 and 11971386)the Natural Science Foundation of Shaanxi Province,China(Grant No.2017JM1019).
文摘The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate thenonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation beforeapproximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic modedecomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, anovel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid oferror data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.
基金Supported by the National Natural Science Foundation of China(10571141,70971109,71371152)supported by the Talents Fund of Xi’an Polytechnic University(BS1320)the Mathematics Discipline Development Fund of Xi’an Ploytechnic University(107090701)
文摘When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.
基金Yanhai Lin was supported by the National Natural Science Foundation of China(Grant No.11702101)the Fundamental Research Funds for the Central Universities and the Promo-tion Program for Young and Middle aged Teacher in Science and Technology Research of Huaqiao University(Grant No.ZQN-PY502)+1 种基金the Natural Science Foundation of Fujian Province(Grant No.2019105093)Quanzhou High-Level Talents Support Plan.
文摘In this paper a modifed continuous energy law was explored to investigate transport behavior in a gas metal arc welding(GMAW)system.The energy law equality at a discrete level for the GMAW system was derived by using the finite element scheme.The mass conservation and current density continuous equation with the penalty scheme was applied 10 improve the stability.According to the phase-field model coupled with the energy law preserving method,the GMAW model was discretized and a metal transfer process with a pulse current was simulated.It was found that the numerical solution agrees well with the data of the metal transfer process obtained by high-speed photography.Compared with the numerical solution of the volume of fuid model,which was widely studied in the GMAW system based on the finite element method Euler scheme,the energy law preserving method can provide better accuracy in predicting the shape evolution of the droplet and with a greater computing efficiency.
基金supported by the Natural Science Foundation of China under grants 11471343,11628104,and Guangdong Provincial Natural Science Foundation of China under grant 2015A030306016.
文摘There are several difficulties in generalized/extended finite element methods(GFEM/XFEM)for moving interface problems.First,the GFEM/XFEM may be unstable in a sense that condition numbers of system matrices could be much bigger than those of standard FEM.Second,they may not be robust in that the condition numbers increase rapidly as interface curves approach edges of meshes.Furthermore,time stepping schemes need carrying out carefully since both enrichment functions and enriched nodes in the GFEM/XFEM vary in time.This paper is devoted to proposing the stable and robust GFEM/XFEM with efficient time stepping schemes for the parabolic interface problems with moving interfaces.A so-called stable GFEM(SGFEM)developed for elliptical interface problems is extended to the parabolic interface problems for spatial discretizations;while backward difference formulae(BDF)are used for the time stepping.Numerical studies demonstrate that the SGFEM with the first and second order BDF(also known as backward Euler method and BDF2)is stable,robust,and achieves optimal convergence rates.Comparisons of the proposed SGFEM with various commonly-used GFEM/XFEM are made,which show advantages of the SGFEM over the other GFEM/XFEM in aspects of stability,robustness,and convergence.
基金supported by National Natural Science Foundation of China(11701193,11671086)Natural Science Foundation of Fujian Province(2018J05005)+3 种基金Program for Innovative Research Team in Science and Technology in Fujian Province University Quanzhou High-Level Talents Support Plan(2017ZT012)part supported by National Natural Science Foundation of China(11271305,11531010)Jiankai Xu’s research was in part supported by National Natural Science Foundation(11671086,11871208)Natural Science Foundation of Hunan Province(2018JJ2159)
文摘We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the "stable set" M2 and "unstable set" M1, we show that there exists a unique global solution provided the initial data belong to M2 and the global solution converges to zero in H^1 exponentially as time goes to infinity. Moreover, we also prove that the local regular solution must blow up at finite time provided the initial data belong to M1.
基金supported by the National Key Research and Development Program of China (Grant No. 2016YFB0800401)the National Natural Science Foundation of China (Grant Nos. 61621003, 61532020, 61573262, 61573004)+3 种基金the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (Grant No. ZQNYX301, ZQN-PY401)the Natural Science Foundation of Fujian Province (Grant Nos. 2015J01260, 2015J01584)the Program for New Century Excellent Talents in Fujian Province University in 2016the Cultivation Program for Outstanding Young Scientific Talents of the Higher Education Institutions of Fujian Province in 2016
文摘This paper investigates the impact of inter-layer coupling functions and intra-layer coupling delays on intra-layer synchronization regions and sychronizability. It is found that the inter-layer coupling functions have great influence on intra-layer synchronization regions, as well as on the intra-layer synchronizability. In particular, there exists an inter-layer coupling function such that the inter-layer coupling strength neither improves nor weakens the intra-layer synchronizability. Furthermore, no matter which one of three inter-layer coupling functions is chosen, a small intra-layer delay always keeps the intra-layer synchronized regions almost unchanged, implying that the small delay neither enhances nor suppresses the intra-layer synchronizability. At the same time the delay greatly frustrates the synchronizability in each layer when it is greater than some threshold. Our results may have potential applications for interconnected technological networks where communication delays are inevitably present.
