This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.
This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.
In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy spaces H~1(R~n) into the Lebesgue space L~1 (R~n).
In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy spaces H~1(R~n) into the Lebesgue space L~1 (R~n).
In this paper a canonicalneural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.
In this paper a canonicalneural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.
Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of three dimensional nonlinear partial differential equations with initial-boundary value problems. In this paper, according to the actual conditions of molecular and three-dimensional characteristics of the problem, we construct the characteristic finite element alternating-direction schemes which can be divided into three continuous one-dimensional problems. By making use of tensor product algorithm, and priori estimation theory and techniques, the optimal order estimates in H~1 norm are derived for the error in the approximate solution.
Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of three dimensional nonlinear partial differential equations with initial-boundary value problems. In this paper, according to the actual conditions of molecular and three-dimensional characteristics of the problem, we construct the characteristic finite element alternating-direction schemes which can be divided into three continuous one-dimensional problems. By making use of tensor product algorithm, and priori estimation theory and techniques, the optimal order estimates in H~1 norm are derived for the error in the approximate solution.
An isospectral problem with four potential is discussed. The corresponding hierarchy of Lax integrable evolution equations is derived. For the hierarchy, it is shown that there exist other new reductions except those presented by Tu, Meng and Ma. For each reduction case the relevant Hamiltonian structure is established by means of trace identity.
An isospectral problem with four potential is discussed. The corresponding hierarchy of Lax integrable evolution equations is derived. For the hierarchy, it is shown that there exist other new reductions except those presented by Tu, Meng and Ma. For each reduction case the relevant Hamiltonian structure is established by means of trace identity.
In this paper some easily verifiable sufficient conditions on the permanence of solutions for general nonautonomous two-species predator-prey model are established. These new criteria improve and extend the results given by Ma, Wang, Teng and Ten, Yu
In this paper some easily verifiable sufficient conditions on the permanence of solutions for general nonautonomous two-species predator-prey model are established. These new criteria improve and extend the results given by Ma, Wang, Teng and Ten, Yu
The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.
The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.
In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile, the H?lder continuity of such functions is also discussed.
In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile, the H?lder continuity of such functions is also discussed.
The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown
The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown
Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.
Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.
In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equations mdiv Ap (x, u) + ap (x, u) = f (x) in space W (/, p)(Q), which is bigger than W(/, p)(Q). Next, using revise reverse H?lder inequality we prove that if Pc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ] U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.
In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equations mdiv Ap (x, u) + ap (x, u) = f (x) in space W (/, p)(Q), which is bigger than W(/, p)(Q). Next, using revise reverse H?lder inequality we prove that if Pc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ] U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.
A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs.
A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs.
A (k;g)-graph is a k-regular graph with girth g. A (k;g)-cage is a (k;g)-graph with the least possible number of vertices. Let f (k;g) denote the number of vertices in a (k;g)-cage. The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. A k-regular graph with girth pair (g,h) is called a (k;g,h)-graph. A (k;g,h)-cage is a (k;g,h)-graph with the least possible number of vertices. Let f(k;g,h) denote the number of vertices in a (k;g,h)-cage. In this paper, we prove the following strict inequality f (k;h-1,h)
A (k;g)-graph is a k-regular graph with girth g. A (k;g)-cage is a (k;g)-graph with the least possible number of vertices. Let f (k;g) denote the number of vertices in a (k;g)-cage. The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. A k-regular graph with girth pair (g,h) is called a (k;g,h)-graph. A (k;g,h)-cage is a (k;g,h)-graph with the least possible number of vertices. Let f(k;g,h) denote the number of vertices in a (k;g,h)-cage. In this paper, we prove the following strict inequality f (k;h-1,h)
This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximation to function exp(q). The algorithms fall into the catalogue of implicit formula, which involves sth order derivative and s+1 free parameters. The order of the algorithms satisfies s+1hph2s+2. The stability of the methods is also studied, necessary and sufficient conditions for A-stability and L-stability are given. In addition, some examples are also given to demonstrate the method presented.
This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximation to function exp(q). The algorithms fall into the catalogue of implicit formula, which involves sth order derivative and s+1 free parameters. The order of the algorithms satisfies s+1hph2s+2. The stability of the methods is also studied, necessary and sufficient conditions for A-stability and L-stability are given. In addition, some examples are also given to demonstrate the method presented.
Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integer-valued functions defined on V(G) such that 2k m 2 h f(x) for all x ] V(G). Let H be a subgraph of G with mk edges. In this paper it is proved that every (mg + m m 1,mf m m + 1)-graph G has (g,f)-factorizations randomly k-orthogonal to H and shown that the result is best possible.
Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integer-valued functions defined on V(G) such that 2k m 2 h f(x) for all x ] V(G). Let H be a subgraph of G with mk edges. In this paper it is proved that every (mg + m m 1,mf m m + 1)-graph G has (g,f)-factorizations randomly k-orthogonal to H and shown that the result is best possible.
The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas. We investigate the properties of p-bounded integrable random set. Based on this we endow it with Δ~p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to Δ~p metric. Moreover we also can establish analogous theorem for other integral type operator in Δ~p space.
The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas. We investigate the properties of p-bounded integrable random set. Based on this we endow it with Δ~p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to Δ~p metric. Moreover we also can establish analogous theorem for other integral type operator in Δ~p space.
In this paper the dynamics of a weakly nonlinear system subjected to combined parametric and external excitation are discussed. The existence of transversal homoclinic orbits resulting in chaotic dynamics and bifurcation are established by using the averaging method and Melnikov method. Numerical simulations are also provided to demonstrate the theoretical analysis.
In this paper the dynamics of a weakly nonlinear system subjected to combined parametric and external excitation are discussed. The existence of transversal homoclinic orbits resulting in chaotic dynamics and bifurcation are established by using the averaging method and Melnikov method. Numerical simulations are also provided to demonstrate the theoretical analysis.
In this paper we study a class of semi-positone singular boundary value problem. With prior bounds estimate and topology degree method, some existence results of nonnegative solution will be shown.
In this paper we study a class of semi-positone singular boundary value problem. With prior bounds estimate and topology degree method, some existence results of nonnegative solution will be shown.