In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function ...In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.展开更多
This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Und...This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.展开更多
We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localiz...We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localized wave solution,the N-fold generalized Darboux transformation is given.Under the condition that the characteristic equation admits a double-root,we present the expression of the first-order interactional solution.Then we graphically analyze the dynamics of the breather and rogue wave.Due to the simultaneous existence of nonlinear and self-steepening terms in the equation,different profiles in two components for the breathers are presented.展开更多
In this paper,we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrodinger equation with aμ-Laplacian term(BNLS).Such BNLS models the propagation of intense laser beams in a bu...In this paper,we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrodinger equation with aμ-Laplacian term(BNLS).Such BNLS models the propagation of intense laser beams in a bulk medium with a second-order dispersion term.Denoting by Qpthe ground state for the BNLS withμ=0,we prove that in the mass-subcritical regime p∈(1,1+8/d),there exist orbit ally stable ground state solutions for the BNLS when p∈(-λ0,∞)for someλ0=λ0(p,d,‖Qp‖L2)>0.Moreover,in the mass-critical case p=1+8/d,we prove the orbital stability on a certain mass level below‖Q*‖L2,provided thatμ∈(-λ1,0),where■and Q*=Q1+8/d.The proofs are mainly based on the profile decomposition and a sharp Gagliardo-Nirenberg type inequality.Our treatment allows us to fill the gap concerning the existence of the ground states for the BNLS when p is negative and p∈(1,1+8/d].展开更多
The metaheuristic algorithms are widely used in solving the parameters of the optimization problem.The marine predators algorithm(MPA)is a novel population-based intelligent algorithm.Although MPA has shown a talented...The metaheuristic algorithms are widely used in solving the parameters of the optimization problem.The marine predators algorithm(MPA)is a novel population-based intelligent algorithm.Although MPA has shown a talented foraging strategy,it still needs a balance of exploration and exploitation.Therefore,a multi-stage improvement of marine predators algorithm(MSMPA)is proposed in this paper.The algorithm retains the advantage of multistage search and introduces a linear flight strategy in the middle stage to enhance the interaction between predators.Predators further away from the historical optimum are required to move,increasing the exploration capability of the algorithm.In the middle and late stages,the searchmechanism of particle swarmoptimization(PSO)is inserted,which enhances the exploitation capability of the algorithm.This means that the stochasticity is decreased,that is the optimal region where predators jumping out is effectively stifled.At the same time,self-adjusting weight is used to regulate the convergence speed of the algorithm,which can balance the exploration and exploitation capability of the algorithm.The algorithm is applied to different types of CEC2017 benchmark test functions and threemultidimensional nonlinear structure design optimization problems,compared with other recent algorithms.The results show that the convergence speed and accuracy of MSMPA are significantly better than that of the comparison algorithms.展开更多
This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent ...This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.展开更多
As one of the most effective techniques for finding software vulnerabilities,fuzzing has become a hot topic in software security.It feeds potentially syntactically or semantically malformed test data to a target progr...As one of the most effective techniques for finding software vulnerabilities,fuzzing has become a hot topic in software security.It feeds potentially syntactically or semantically malformed test data to a target program to mine vulnerabilities and crash the system.In recent years,considerable efforts have been dedicated by researchers and practitioners towards improving fuzzing,so there aremore and more methods and forms,whichmake it difficult to have a comprehensive understanding of the technique.This paper conducts a thorough survey of fuzzing,focusing on its general process,classification,common application scenarios,and some state-of-the-art techniques that have been introduced to improve its performance.Finally,this paper puts forward key research challenges and proposes possible future research directions that may provide new insights for researchers.展开更多
Spatial distribution patterns of element concentrations can reflect the information of the mineralization processes. Both the Hurst exponent calculated by R/S analysis and the generalized fractal dimension calculated ...Spatial distribution patterns of element concentrations can reflect the information of the mineralization processes. Both the Hurst exponent calculated by R/S analysis and the generalized fractal dimension calculated by using the multifractal model are important parameters for describing the spatial distribution of elements. Five long drill holes, named as M1, S1, S2, S3, and S4, have been selected in the Shizishan (狮子山) skarn orefield in Tongling (铜陵), Anhui (安徽) Province, China. Marbles are well developed around M1 and skarn rocks are largely distributed along S1, S2, S3, and S4 drill holes. The drill holes were sampled evenly with an interval of 10 m and 16 trace elements have been measured. The mean of the △D(q) (the height of the generalized dimension spectrum) in the M1 drill hole is the lowest. In addition, the mean of the Hurst exponents of the 16 elements in the M1 drill hole is also much smaller than that of S1, S2, S3, S4 drill holes, which is in accordance with the analysis of the generalized dimension. It is indicated by the generalized dimension and Hurst exponent that the distribution of trace elements in the marbles is more random than that in the skarn. The result suggests that the mineralization process can change the randomness and persistence features of the element distribution.展开更多
In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy.The main techniques is the Faedo-Galerkin app...In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy.The main techniques is the Faedo-Galerkin approximation and weak compactness theory.展开更多
The application of χ state are investigated in remote state preparation(RSP). By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and thr...The application of χ state are investigated in remote state preparation(RSP). By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and three-qubit states via the χ state as the entangled resource. It is shown that the original state can be successfully prepared with the probability100% and 50% for real coefficients and complex coefficients, respectively. For the latter case, the special ensembles with unit success probability are discussed by the permutation group. It is worth mentioning that the novel measurement bases have no restrictions on the coefficients of the prepared state, which means that the proposed schemes are more applicable.展开更多
In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases.This paper derives the ...In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases.This paper derives the distributed-free optimal linear estimator of random parameters in the model by means of the credibility theory method. The estimators the authors derive can be applied in more extensive practical scenarios since they are only dependent on the first two moments of prior parameter rather than on specific prior distribution. Finally, the results are compared with some classical models and a numerical example is given to show the effectiveness of the estimators.展开更多
Diagnosability of a multiprocessor system is one important study topic. In 2012,Peng et al. proposed the g-good-neighbor diagnosability that restrains every fault-free nodeto contain at least g fault-free neighbors. T...Diagnosability of a multiprocessor system is one important study topic. In 2012,Peng et al. proposed the g-good-neighbor diagnosability that restrains every fault-free nodeto contain at least g fault-free neighbors. The locally twisted cube LTQn has many goodproperties. In this paper, we show that the 1-good-neighbor connectivity al （LTQn） =2n-2and the 1-good-neighbor diagnosability of LTQn is 2n - 1 under the PMC model for n ≥ 4and the MM model for n ≥ 5.展开更多
In this paper,we discuss the Lagrangian angle and the Kahler angle of immersed surfaces in C^2.Firstly,we provide an extension of Lagrangian angle,Maslov form and Maslov class to more general surfaces in C^2 than Lagr...In this paper,we discuss the Lagrangian angle and the Kahler angle of immersed surfaces in C^2.Firstly,we provide an extension of Lagrangian angle,Maslov form and Maslov class to more general surfaces in C^2 than Lagrangian surfaces,and then naturally extend a theorem by J.-M.Morvan to surfaces of constant Kahler angle,together with an application showing that the Maslov class of a compact self-shrinker surface with constant Kahler angle is generally non-vanishing.Secondly,we obtain two pinching results for the Kahler angle which imply rigidity theorems of self-shrinkers with Kahler angle under the condition that∫M|h|^2e^-|x|^2/2dVM<∞,where h and x denote,respectively,the second fundamental form and the position vector of the surface.展开更多
In this paper, we first employ the complex method to deritive all meromorphic solutions of an auxiliary ordinary differential equation, and then find all meromorphic exact solutions of the modified ZK equation, modifi...In this paper, we first employ the complex method to deritive all meromorphic solutions of an auxiliary ordinary differential equation, and then find all meromorphic exact solutions of the modified ZK equation, modified Kd V equation, nonlinear Klein-Gordon equation and modified BBM equation. Our work shows that there exist some classes of rational solutionswr,2(z) and simple periodic solutionsws,1(z) which are new and are not degenerated successively to by the elliptic function solutions.展开更多
We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + ...We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + λ2 p2 + λ3 p2 3 + η| < (max pj )- 1/40 (log max pj ) 4 .展开更多
Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks ...Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks share structural properties with natural transcriptional regulatory networks. Specifically, these networks can display scale-free and small-world structures. We also find that these networks have a higher probability to operate in the ordered regimen, and a lower probability to operate in the chaotic regimen. That is, the dynamics of these networks is similar to that of natural networks. The results show that the structure and dynamics inherent in natural networks may be in part due to their method of generation rather than being exclusively shaped by subsequent evolution under natural selection.展开更多
In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplic...In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplicity at least k.Suppose that for each f∈F,f(z)and f(k)(z)share the set{a,b,c}.Then F is a normal family in D.展开更多
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of th...An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
Diagnosability of a multiprocessor system G is one important measure of the reliability of interconnection networks. In 2016, Zhang et al. proposed the g-extra diagnosability of G, which restrains that every component...Diagnosability of a multiprocessor system G is one important measure of the reliability of interconnection networks. In 2016, Zhang et al. proposed the g-extra diagnosability of G, which restrains that every component of G – S has at least (g + 1) vertices. The locally twisted cube LTQn is applied widely. In this paper, we show that LTQn is tightly (4n – 9) super 3-extra connected for n ≥ 6 and the 3-extra diagnosability of LTQn under the PMC model and MM* model is 4n - 6 for n ≥ 5 and n ≥ 7, respectively.展开更多
基金supported by the NSFC(11931013)the GXNSF(2022GXNSFDA035078)。
文摘In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.
基金supported by the Natural Science Foundation of China(11801108)the Natural Science Foundation of Guangdong Province(2021A1515010314)the Science and Technology Planning Project of Guangzhou City(202201010111)。
文摘This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.
基金the National Natural Science Foundation of China(Grant Nos.11871232 and 12201578)Natural Science Foundation of Henan Province,China(Grant Nos.222300420377 and 212300410417)。
文摘We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localized wave solution,the N-fold generalized Darboux transformation is given.Under the condition that the characteristic equation admits a double-root,we present the expression of the first-order interactional solution.Then we graphically analyze the dynamics of the breather and rogue wave.Due to the simultaneous existence of nonlinear and self-steepening terms in the equation,different profiles in two components for the breathers are presented.
基金partially supported by the National Natural Science Foundation of China(11501137)partially supported by the National Natural Science Foundation of China(11501395,12071323)the Guangdong Basic and Applied Basic Research Foundation(2016A030310258,2020A1515011019)。
文摘In this paper,we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrodinger equation with aμ-Laplacian term(BNLS).Such BNLS models the propagation of intense laser beams in a bulk medium with a second-order dispersion term.Denoting by Qpthe ground state for the BNLS withμ=0,we prove that in the mass-subcritical regime p∈(1,1+8/d),there exist orbit ally stable ground state solutions for the BNLS when p∈(-λ0,∞)for someλ0=λ0(p,d,‖Qp‖L2)>0.Moreover,in the mass-critical case p=1+8/d,we prove the orbital stability on a certain mass level below‖Q*‖L2,provided thatμ∈(-λ1,0),where■and Q*=Q1+8/d.The proofs are mainly based on the profile decomposition and a sharp Gagliardo-Nirenberg type inequality.Our treatment allows us to fill the gap concerning the existence of the ground states for the BNLS when p is negative and p∈(1,1+8/d].
基金supported in part byNationalNatural Science Foundation of China(No.62066001)Natural Science Foundation of Ningxia Province(No.2021AAC03230)Program of Graduate Innovation Research of North Minzu University(No.YCX22111).
文摘The metaheuristic algorithms are widely used in solving the parameters of the optimization problem.The marine predators algorithm(MPA)is a novel population-based intelligent algorithm.Although MPA has shown a talented foraging strategy,it still needs a balance of exploration and exploitation.Therefore,a multi-stage improvement of marine predators algorithm(MSMPA)is proposed in this paper.The algorithm retains the advantage of multistage search and introduces a linear flight strategy in the middle stage to enhance the interaction between predators.Predators further away from the historical optimum are required to move,increasing the exploration capability of the algorithm.In the middle and late stages,the searchmechanism of particle swarmoptimization(PSO)is inserted,which enhances the exploitation capability of the algorithm.This means that the stochasticity is decreased,that is the optimal region where predators jumping out is effectively stifled.At the same time,self-adjusting weight is used to regulate the convergence speed of the algorithm,which can balance the exploration and exploitation capability of the algorithm.The algorithm is applied to different types of CEC2017 benchmark test functions and threemultidimensional nonlinear structure design optimization problems,compared with other recent algorithms.The results show that the convergence speed and accuracy of MSMPA are significantly better than that of the comparison algorithms.
基金supported by the National Natural Science Foundation of China(12126318,12126302).
文摘This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.
基金supported in part by the National Natural Science Foundation of China under Grants 62273272,62303375,and 61873277in part by the Key Research and Development Program of Shaanxi Province under Grant 2023-YBGY-243+1 种基金in part by the Natural Science Foundation of Shaanxi Province under Grant 2020JQ-758in part by the Youth Innovation Team of Shaanxi Universities,and in part by the Special Fund for Scientific and Technological Innovation Strategy of Guangdong Province under Grant 2022A0505030025.
文摘As one of the most effective techniques for finding software vulnerabilities,fuzzing has become a hot topic in software security.It feeds potentially syntactically or semantically malformed test data to a target program to mine vulnerabilities and crash the system.In recent years,considerable efforts have been dedicated by researchers and practitioners towards improving fuzzing,so there aremore and more methods and forms,whichmake it difficult to have a comprehensive understanding of the technique.This paper conducts a thorough survey of fuzzing,focusing on its general process,classification,common application scenarios,and some state-of-the-art techniques that have been introduced to improve its performance.Finally,this paper puts forward key research challenges and proposes possible future research directions that may provide new insights for researchers.
基金supported by the Special Plans of Science and Technology of the Ministry of Land and Resources (No. 20010103)Trans-century Training Program Foundation by the Ministry of Education, 111 Project (No. B07011)+1 种基金Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT)State Key Laboratory of Geological Processes and Mineral Resources (No. GPMR200640)
文摘Spatial distribution patterns of element concentrations can reflect the information of the mineralization processes. Both the Hurst exponent calculated by R/S analysis and the generalized fractal dimension calculated by using the multifractal model are important parameters for describing the spatial distribution of elements. Five long drill holes, named as M1, S1, S2, S3, and S4, have been selected in the Shizishan (狮子山) skarn orefield in Tongling (铜陵), Anhui (安徽) Province, China. Marbles are well developed around M1 and skarn rocks are largely distributed along S1, S2, S3, and S4 drill holes. The drill holes were sampled evenly with an interval of 10 m and 16 trace elements have been measured. The mean of the △D(q) (the height of the generalized dimension spectrum) in the M1 drill hole is the lowest. In addition, the mean of the Hurst exponents of the 16 elements in the M1 drill hole is also much smaller than that of S1, S2, S3, S4 drill holes, which is in accordance with the analysis of the generalized dimension. It is indicated by the generalized dimension and Hurst exponent that the distribution of trace elements in the marbles is more random than that in the skarn. The result suggests that the mineralization process can change the randomness and persistence features of the element distribution.
文摘In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy.The main techniques is the Faedo-Galerkin approximation and weak compactness theory.
基金supported by the National Natural Science Foundation of China(Grant Nos.61201253 and 61303039)the Fundamental Research Funds for the Central Universities of China(Grant No.2682014CX095)
文摘The application of χ state are investigated in remote state preparation(RSP). By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and three-qubit states via the χ state as the entangled resource. It is shown that the original state can be successfully prepared with the probability100% and 50% for real coefficients and complex coefficients, respectively. For the latter case, the special ensembles with unit success probability are discussed by the permutation group. It is worth mentioning that the novel measurement bases have no restrictions on the coefficients of the prepared state, which means that the proposed schemes are more applicable.
基金supported by the National Science Foundation of China under Grant Nos.71361015,71340010,71371074the Jiangxi Provincial Natural Science Foundation under Grant No.20142BAB201013+2 种基金China Postdoctoral Science Foundation under Grant No.2013M540534China Postdoctoral Fund special Project under Grant No.2014T70615Jiangxi Postdoctoral Science Foundation under Grant No.2013KY53
文摘In the hierarchical random effect linear model, the Bayes estimator of random parameter are not only dependent on specific prior distribution but also it is difficult to calculate in most cases.This paper derives the distributed-free optimal linear estimator of random parameters in the model by means of the credibility theory method. The estimators the authors derive can be applied in more extensive practical scenarios since they are only dependent on the first two moments of prior parameter rather than on specific prior distribution. Finally, the results are compared with some classical models and a numerical example is given to show the effectiveness of the estimators.
基金supported by the National Natural Science Foundation of China(61772010)
文摘Diagnosability of a multiprocessor system is one important study topic. In 2012,Peng et al. proposed the g-good-neighbor diagnosability that restrains every fault-free nodeto contain at least g fault-free neighbors. The locally twisted cube LTQn has many goodproperties. In this paper, we show that the 1-good-neighbor connectivity al （LTQn） =2n-2and the 1-good-neighbor diagnosability of LTQn is 2n - 1 under the PMC model for n ≥ 4and the MM model for n ≥ 5.
基金supported by National Natural Science Foundation of China(11671121,11871197)
文摘In this paper,we discuss the Lagrangian angle and the Kahler angle of immersed surfaces in C^2.Firstly,we provide an extension of Lagrangian angle,Maslov form and Maslov class to more general surfaces in C^2 than Lagrangian surfaces,and then naturally extend a theorem by J.-M.Morvan to surfaces of constant Kahler angle,together with an application showing that the Maslov class of a compact self-shrinker surface with constant Kahler angle is generally non-vanishing.Secondly,we obtain two pinching results for the Kahler angle which imply rigidity theorems of self-shrinkers with Kahler angle under the condition that∫M|h|^2e^-|x|^2/2dVM<∞,where h and x denote,respectively,the second fundamental form and the position vector of the surface.
基金supported by the NSFC(11271090)NSF of Guangdong(S2012010010121)
文摘In this paper, we first employ the complex method to deritive all meromorphic solutions of an auxiliary ordinary differential equation, and then find all meromorphic exact solutions of the modified ZK equation, modified Kd V equation, nonlinear Klein-Gordon equation and modified BBM equation. Our work shows that there exist some classes of rational solutionswr,2(z) and simple periodic solutionsws,1(z) which are new and are not degenerated successively to by the elliptic function solutions.
基金Supported by the NNSF of China(11071070)Supported by the Science Research Plan of Education Department of Henan Province(2011B110002)
文摘We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + λ2 p2 + λ3 p2 3 + η| < (max pj )- 1/40 (log max pj ) 4 .
文摘Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks share structural properties with natural transcriptional regulatory networks. Specifically, these networks can display scale-free and small-world structures. We also find that these networks have a higher probability to operate in the ordered regimen, and a lower probability to operate in the chaotic regimen. That is, the dynamics of these networks is similar to that of natural networks. The results show that the structure and dynamics inherent in natural networks may be in part due to their method of generation rather than being exclusively shaped by subsequent evolution under natural selection.
基金Supported by the NSF of China(10771220)Supported by the Doctorial Point Fund of National Education Ministry of China(200810780002)
文摘In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplicity at least k.Suppose that for each f∈F,f(z)and f(k)(z)share the set{a,b,c}.Then F is a normal family in D.
文摘An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
文摘Diagnosability of a multiprocessor system G is one important measure of the reliability of interconnection networks. In 2016, Zhang et al. proposed the g-extra diagnosability of G, which restrains that every component of G – S has at least (g + 1) vertices. The locally twisted cube LTQn is applied widely. In this paper, we show that LTQn is tightly (4n – 9) super 3-extra connected for n ≥ 6 and the 3-extra diagnosability of LTQn under the PMC model and MM* model is 4n - 6 for n ≥ 5 and n ≥ 7, respectively.
