The existence of periodic solutions for periodic reaction-diffusion systems with time delay by the periodic upper-lower solution method is investigated.Some methods for proving the uniqueness and the stability of the periodic solution are also given.Two examples are used to show how to use our methods.
The existence of periodic solutions for periodic reaction-diffusion systems with time delay by the periodic upper-lower solution method is investigated.Some methods for proving the uniqueness and the stability of the periodic solution are also given.Two examples are used to show how to use our methods.
An upper bound and a lower bound for α_0 are given such that αI+B∈M~(-1) for α>α_0 and αI+BM~(-1) for α<α_0,where B is a nonnegative matrix and satisfies that for any positive constant β,βI+B is a power invariant zero pattern matrix.
An upper bound and a lower bound for α_0 are given such that αI+B∈M~(-1) for α>α_0 and αI+BM~(-1) for α<α_0,where B is a nonnegative matrix and satisfies that for any positive constant β,βI+B is a power invariant zero pattern matrix.
In this paper,we present a modified decomposition algorithm and its bundle style variant for convex programming problems with separable structure.We prove that these methods are globally and linearly convergent and discuss the application of the bundle variant in parallel computations
In this paper,we present a modified decomposition algorithm and its bundle style variant for convex programming problems with separable structure.We prove that these methods are globally and linearly convergent and discuss the application of the bundle variant in parallel computations
This paper provides the parametric expressions satisfied by the enumerating functions for rooted nearly cubic C-nets with the size and/or the root-vertex valency of the maps as the parameters via nonseparable neraly cubic maps.On this basis,two explicit expressions of the functions can be derived by employing Lagrangian inversion.
This paper provides the parametric expressions satisfied by the enumerating functions for rooted nearly cubic C-nets with the size and/or the root-vertex valency of the maps as the parameters via nonseparable neraly cubic maps.On this basis,two explicit expressions of the functions can be derived by employing Lagrangian inversion.
Two fundametal convergence theorems are given for nonlinear conjugate gradient methods only under the descent condition.As a result,methods related to the Fletcher-Reeves algorithm still converge for parameters in a slightly wider range,in particular,for a parameter in its upper bound.For methods related to the Polak-Ribiere algorithm,it is shown that some negative values of the conjugate parameter do not prevent convergence.If the objective function is convex,some convergence results hold for the Hestenes-Stiefel algorithm.
Two fundametal convergence theorems are given for nonlinear conjugate gradient methods only under the descent condition.As a result,methods related to the Fletcher-Reeves algorithm still converge for parameters in a slightly wider range,in particular,for a parameter in its upper bound.For methods related to the Polak-Ribiere algorithm,it is shown that some negative values of the conjugate parameter do not prevent convergence.If the objective function is convex,some convergence results hold for the Hestenes-Stiefel algorithm.
In this paper,we consider the existence of solution for the following equations:-Δu+u=(|u|)~2*1/|x|)u+g(x),x∈R~3,where g(x)≥0,g(x)0,and g(x)∈H~(-1)(R~3).We prove that there exists a constant C,if ‖g(x)‖_(H~(-1))≤C,there are at least two solutions of the equation.
In this paper,we consider the existence of solution for the following equations:-Δu+u=(|u|)~2*1/|x|)u+g(x),x∈R~3,where g(x)≥0,g(x)0,and g(x)∈H~(-1)(R~3).We prove that there exists a constant C,if ‖g(x)‖_(H~(-1))≤C,there are at least two solutions of the equation.
Let J be the zero set of the gradient f_x of a function f:R~n→R.Under fairly general conditions the stochastic approximation algorithm ensures d(f(x_k),f(J))→0,as k→∞.First of all,the paper considers this problem:Under what conditions the convergence d(f(x_k),f(J))→〖DD(X〗k→∞〖DD)〗0 implies d(x_k,J)→〖DD(X〗k→∞〖DD)〗0.It is shown that such implication takes place if f_x is continuous and f(J) is nowhere dense.Secondly,an intensified version of Sard's theorem has been proved,which itself is interesting.As a particular case,it provides two independent sufficient conditions as answers to the previous question:If f is a C~1 function and either i)J is a compact set or ii) for any bounded set B,f~(-1)(B) is bounded,then f(J) is nowhere dense.Finally,some tools in algebraic geometry are used to prove that f(J) is a finite set if f is a polynomial.Hence f(J) is nowhere dense in the polynomial case.
Let J be the zero set of the gradient f_x of a function f:R~n→R.Under fairly general conditions the stochastic approximation algorithm ensures d(f(x_k),f(J))→0,as k→∞.First of all,the paper considers this problem:Under what conditions the convergence d(f(x_k),f(J))→〖DD(X〗k→∞〖DD)〗0 implies d(x_k,J)→〖DD(X〗k→∞〖DD)〗0.It is shown that such implication takes place if f_x is continuous and f(J) is nowhere dense.Secondly,an intensified version of Sard's theorem has been proved,which itself is interesting.As a particular case,it provides two independent sufficient conditions as answers to the previous question:If f is a C~1 function and either i)J is a compact set or ii) for any bounded set B,f~(-1)(B) is bounded,then f(J) is nowhere dense.Finally,some tools in algebraic geometry are used to prove that f(J) is a finite set if f is a polynomial.Hence f(J) is nowhere dense in the polynomial case.
In this paper,a mathematical model of competition between plasmid-bearing and plasmidfree organisms in a chemostat with an inhibitor is investigated.The model is in the form of a system of nonlinear differential equations.By using qualitative methods,the conditions for the existence and local stability of the equilibria are obtained.The existence and stability of periodic solutions of the Hopf type are studied.Numerical simulations about the Hopf bifurcation value and Hopf limit cycle are also given.
In this paper,a mathematical model of competition between plasmid-bearing and plasmidfree organisms in a chemostat with an inhibitor is investigated.The model is in the form of a system of nonlinear differential equations.By using qualitative methods,the conditions for the existence and local stability of the equilibria are obtained.The existence and stability of periodic solutions of the Hopf type are studied.Numerical simulations about the Hopf bifurcation value and Hopf limit cycle are also given.
In this paper,by introducing a new concept of absolute stability for a certain argument,necessary and sufficient conditions for absolute stability of general Lurie indirect control systems are obtained,and some practical sufficient conditions are also given
In this paper,by introducing a new concept of absolute stability for a certain argument,necessary and sufficient conditions for absolute stability of general Lurie indirect control systems are obtained,and some practical sufficient conditions are also given
In the present paper we study the long time behavior of solutions to the Davey-Stewartson system possesses a compact global attractor A_p in L~p(Ω).Furthermore,one show that the attractor is in fact independent of p and prove the attractor has finite Hausdorff and fractal dimensions.
In the present paper we study the long time behavior of solutions to the Davey-Stewartson system possesses a compact global attractor A_p in L~p(Ω).Furthermore,one show that the attractor is in fact independent of p and prove the attractor has finite Hausdorff and fractal dimensions.
We discuss the convergence rates in the law of logarithm for partial sums and randomly indexed partial sums of independent random variables in Banach space,and find the necessary and sufficient conditions on the convergence rates.The results of [1-3] for sums of i.i.d. real valued r.v.'s are extended;Yang's result is generalized and the necessity part of Yang's result is also discussed;a conjecture for the i.i.d. real-valued r.v.'s of [5] is answered in Banach space.
We discuss the convergence rates in the law of logarithm for partial sums and randomly indexed partial sums of independent random variables in Banach space,and find the necessary and sufficient conditions on the convergence rates.The results of [1-3] for sums of i.i.d. real valued r.v.'s are extended;Yang's result is generalized and the necessity part of Yang's result is also discussed;a conjecture for the i.i.d. real-valued r.v.'s of [5] is answered in Banach space.
This paper investigates several different semi-on-line two-machine scheduling problems for maximizing the minimum machine completion time.For each problem,we propose a best possible algorithm.
This paper investigates several different semi-on-line two-machine scheduling problems for maximizing the minimum machine completion time.For each problem,we propose a best possible algorithm.
This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace,on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A~((2))_(T,S) and give some of their applications.
This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace,on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A~((2))_(T,S) and give some of their applications.
In this paper,we study a class of simple and easy-to-construct shop schedules,known as dense schedules.We present tight bounds on the maximum deviation in makespan of dense flow-shop and job-shop schedules from their optimal ones.For dense open-shop schedules,we do the same for the special case of four machines and thus add a stronger supporting case for proving a standing conjecture.
In this paper,we study a class of simple and easy-to-construct shop schedules,known as dense schedules.We present tight bounds on the maximum deviation in makespan of dense flow-shop and job-shop schedules from their optimal ones.For dense open-shop schedules,we do the same for the special case of four machines and thus add a stronger supporting case for proving a standing conjecture.
Decision tree complexity is an important measure of computational complexity.A graph property is a set of graphs such that if some graph G is in the set then each isomorphic graph to G is also in the set.Let P be a graph property on n vertices,if every decision tree algorithm recognizing P must examine at least k pairs of vertices in the worst case,then it is said that the decision tree complexity of P is k.If every decision tree algorithm recognizing P must examine all n(n-1)/2 pairs of vertices in the worst case,then P is said to be elusive.Karp conjectured that every nontrivial monotone graph property is elusive.This paper concerns the elusiveness of Hamiltonian property.It is proved that if n=p+1,pq or pq+1,(where p,q are distinct primes),then Hamiltonian property on n vertices is elusive.
Decision tree complexity is an important measure of computational complexity.A graph property is a set of graphs such that if some graph G is in the set then each isomorphic graph to G is also in the set.Let P be a graph property on n vertices,if every decision tree algorithm recognizing P must examine at least k pairs of vertices in the worst case,then it is said that the decision tree complexity of P is k.If every decision tree algorithm recognizing P must examine all n(n-1)/2 pairs of vertices in the worst case,then P is said to be elusive.Karp conjectured that every nontrivial monotone graph property is elusive.This paper concerns the elusiveness of Hamiltonian property.It is proved that if n=p+1,pq or pq+1,(where p,q are distinct primes),then Hamiltonian property on n vertices is elusive.