In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery p...In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.展开更多
In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^...In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^(∞) weak-entropy solution converges to the nonlinear diffusion wave of the generalized porous media equation(GPME)in L^(2)(R).As λ∈(1/7,1),we prove that the L^(∞) weak-entropy solution converges to an expansion around the nonlinear diffusion wave in L^(2)(R),which is the best asymptotic profile.The proof is based on intensive entropy analysis and an energy method.展开更多
In this paper,the median formula of n-simplex in n-Euclidean space En is proved,and using this formula,we obtain serveral inequalities related the median lines in n-simplex.
Entanglement,quantum steering and Bell nonlocality can be used to describe the distinct quantum correlations of quantum systems.Because of their different characteristics and application fields,how to divide them quan...Entanglement,quantum steering and Bell nonlocality can be used to describe the distinct quantum correlations of quantum systems.Because of their different characteristics and application fields,how to divide them quantitatively and accurately becomes particularly important.Based on the sufficient and necessary criterion for quantum steering of an arbitrary two-qubit T-state,we derive the inequality relations between quantum steering and entanglement as well as between quantum steering and Bell nonlocality for the T-state.Additionally,we have verified those relations experimentally.展开更多
AN INEQUALITY RELATING THE ORDER, MAXIMUM DEGREE, DIAMETER AND CONNECTIVITY OF A STRONGLY CONNECTED DIGRAPH We prove that if there is a strongly connected digraph of order n, maximum degree d,diameter k and connectivi...AN INEQUALITY RELATING THE ORDER, MAXIMUM DEGREE, DIAMETER AND CONNECTIVITY OF A STRONGLY CONNECTED DIGRAPH We prove that if there is a strongly connected digraph of order n, maximum degree d,diameter k and connectivity C, then n≤c(d_k-d)/(d-1)M+d+1. It improves the previous knownresults, and it, in fact, is the best possible for several interesting cases. A similar result for arcconnectivity is also established.展开更多
基金Supported by the National Fund of Natural Sciences.
文摘In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.
基金S.Geng's research was supported in part by the National Natural Science Foundation of China(12071397)Excellent Youth Project of Hunan Education Department(21B0165)+1 种基金F.Huang's research was supported in part by the National Key R&D Program of China 2021YFA1000800the National Natural Science Foundation of China(12288201).
文摘In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^(∞) weak-entropy solution converges to the nonlinear diffusion wave of the generalized porous media equation(GPME)in L^(2)(R).As λ∈(1/7,1),we prove that the L^(∞) weak-entropy solution converges to an expansion around the nonlinear diffusion wave in L^(2)(R),which is the best asymptotic profile.The proof is based on intensive entropy analysis and an energy method.
文摘In this paper,the median formula of n-simplex in n-Euclidean space En is proved,and using this formula,we obtain serveral inequalities related the median lines in n-simplex.
基金the National Natural Science Foundation of China(Grant Nos.12175001 and 12075001).
文摘Entanglement,quantum steering and Bell nonlocality can be used to describe the distinct quantum correlations of quantum systems.Because of their different characteristics and application fields,how to divide them quantitatively and accurately becomes particularly important.Based on the sufficient and necessary criterion for quantum steering of an arbitrary two-qubit T-state,we derive the inequality relations between quantum steering and entanglement as well as between quantum steering and Bell nonlocality for the T-state.Additionally,we have verified those relations experimentally.
基金This project is supported by the National Natural Science Foundation of China
文摘AN INEQUALITY RELATING THE ORDER, MAXIMUM DEGREE, DIAMETER AND CONNECTIVITY OF A STRONGLY CONNECTED DIGRAPH We prove that if there is a strongly connected digraph of order n, maximum degree d,diameter k and connectivity C, then n≤c(d_k-d)/(d-1)M+d+1. It improves the previous knownresults, and it, in fact, is the best possible for several interesting cases. A similar result for arcconnectivity is also established.
