In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another consideration concerns the entropy production across the shocks. The latter is natural from the physical point of view, but is not sufficient in its straightforward formulation, if the system is not genuinely nonlinear. In this paper we propose the principles of increasing entropy production and that of the superposition of shocks. These principles are shown to be equivalent to the admissibility criterion.
In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another consideration concerns the entropy production across the shocks. The latter is natural from the physical point of view, but is not sufficient in its straightforward formulation, if the system is not genuinely nonlinear. In this paper we propose the principles of increasing entropy production and that of the superposition of shocks. These principles are shown to be equivalent to the admissibility criterion.
Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the dispersion matrix can be singular. Our results show that any one of both estimates cannot be always superior to the other. Some sufficient criteria for any one of them to be better than the other are established. Some interesting relations between these two estimates are also given.
Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the dispersion matrix can be singular. Our results show that any one of both estimates cannot be always superior to the other. Some sufficient criteria for any one of them to be better than the other are established. Some interesting relations between these two estimates are also given.
In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the convexity assumption on objective function, the global convergence of the Broyden's class is proved.
In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the convexity assumption on objective function, the global convergence of the Broyden's class is proved.
A finite element method is proposed for the singularly perturbed reaction-diffusion problem. An optimal error bound is derived, independent of the perturbation parameter.
A finite element method is proposed for the singularly perturbed reaction-diffusion problem. An optimal error bound is derived, independent of the perturbation parameter.
This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are given to illustrate the efficiency of the method.
This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are given to illustrate the efficiency of the method.
An ordered circular permutation S of u's and v' s is called an ordered circular sequence of u' s and v' s. A kernel of a digraph G=(V,A) is an independent subset of V, say K, such that for any vertex vi in V\K there is an arc from v_i to a vertex v_j in K. G is said to be kernel-perfect (KP) if every induced subgraph of G has a kernel. G is said to be kernel-perfect-critical (KPC) if G has no kernel but every proper induced subgraph of G has a kernel. The digraph G = (V,A) = C_n(j_1,j_x,…,j_k) is defined by: V(G) = {0,1,…,n-1}, A(G) = {uv | v-u≡j_i (mod n) for 1 ≤ i ≤ k}. In an earlier work, we investigated the digraph G = C_n (1,±δd,±2d,±3d,…,±sd), denoted by G(n,d,r,s), where δ = 1 for d > 1 or δ = 0 for d = 1, and n,d,r,s are positive integers with (n,d) = r and n = mr, and gave some necessary and sufficient conditions for G(n,d,r,s) with r ≥ 3 and s = 1 to be KP or KPC. In this paper, we prove a combinatorial theorem on ordered circular sequences of n_1 u's and n_2 v's. By using the theorem, we prove that, if (n,d) = r ≥ 2 and s ≥ 2, then G(n,d,r,s) is a KP graph.
An ordered circular permutation S of u's and v' s is called an ordered circular sequence of u' s and v' s. A kernel of a digraph G=(V,A) is an independent subset of V, say K, such that for any vertex vi in V\K there is an arc from v_i to a vertex v_j in K. G is said to be kernel-perfect (KP) if every induced subgraph of G has a kernel. G is said to be kernel-perfect-critical (KPC) if G has no kernel but every proper induced subgraph of G has a kernel. The digraph G = (V,A) = C_n(j_1,j_x,…,j_k) is defined by: V(G) = {0,1,…,n-1}, A(G) = {uv | v-u≡j_i (mod n) for 1 ≤ i ≤ k}. In an earlier work, we investigated the digraph G = C_n (1,±δd,±2d,±3d,…,±sd), denoted by G(n,d,r,s), where δ = 1 for d > 1 or δ = 0 for d = 1, and n,d,r,s are positive integers with (n,d) = r and n = mr, and gave some necessary and sufficient conditions for G(n,d,r,s) with r ≥ 3 and s = 1 to be KP or KPC. In this paper, we prove a combinatorial theorem on ordered circular sequences of n_1 u's and n_2 v's. By using the theorem, we prove that, if (n,d) = r ≥ 2 and s ≥ 2, then G(n,d,r,s) is a KP graph.
Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied. The methods are based on the first-second order backward difference methods. The memory term is approximated by the convolution quadrature and the interpolant quadrature. Discretization of the spatial partial differential operators by the finite element method is also considered
Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied. The methods are based on the first-second order backward difference methods. The memory term is approximated by the convolution quadrature and the interpolant quadrature. Discretization of the spatial partial differential operators by the finite element method is also considered
In this paper we consider the risk process that is described by a piecewise deterministic Markov processes (PDMP). We first present the construction of the risk process and then discuss some ruin problems for this new kind of risk model.
In this paper we consider the risk process that is described by a piecewise deterministic Markov processes (PDMP). We first present the construction of the risk process and then discuss some ruin problems for this new kind of risk model.
In this paper, the author studies the global existence, singularities and life span of smooth solutions of the Cauchy problem for a class of quasilinear hyperbolic systems with higher order dissipative terms and gives their applications to nonlinear wave equations with higher order dissipative terms
In this paper, the author studies the global existence, singularities and life span of smooth solutions of the Cauchy problem for a class of quasilinear hyperbolic systems with higher order dissipative terms and gives their applications to nonlinear wave equations with higher order dissipative terms
Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p~k (k ≥ 1), and let A be the full automorphism group of X. In this paper, we prove that the stabilizer Av of a vertex v in A is a 2-group if p ≠ 5, or a {2,3}-group if p = 5. Furthermore, if p = 5 |A_v| is not divisible by 3~2. As a result, we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p~k (k ≥ 1) is at most 1-arc-transitive for p ≠ 5 and 2-arc-transitive for p = 5.
Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p~k (k ≥ 1), and let A be the full automorphism group of X. In this paper, we prove that the stabilizer Av of a vertex v in A is a 2-group if p ≠ 5, or a {2,3}-group if p = 5. Furthermore, if p = 5 |A_v| is not divisible by 3~2. As a result, we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p~k (k ≥ 1) is at most 1-arc-transitive for p ≠ 5 and 2-arc-transitive for p = 5.
In this paper a reversible Markov process as a chemical polymers reaction of two types of monomers is defined. By analyzing the partition functions of the process we obtain three different distributions of the average molecular weight, depending on the value of strength of the fragmentation reaction, and prove that a gelation of the process will occur in the thermodynamic limit.
In this paper a reversible Markov process as a chemical polymers reaction of two types of monomers is defined. By analyzing the partition functions of the process we obtain three different distributions of the average molecular weight, depending on the value of strength of the fragmentation reaction, and prove that a gelation of the process will occur in the thermodynamic limit.
A graph g is k-ordered Hamiltonian, 2 ≤ k ≤ n, if for every ordered sequence S of k distinct vertices of G, there exists a Hamiltonian cycle that encounters S in the given order. In this article, we prove that if G is a graph on n vertices with degree sum of nonadjacent vertices at least n + 3k-9/2, then G is k-ordered Hamiltonian for k=3,4,…[n/19]. We also show that the degree sum bound can be reduced to n + 2 [k/2]-2 if k(G) ≥ 3k-1/2 or δ(G) ≥ 5k-4. Several known results are generalized.
A graph g is k-ordered Hamiltonian, 2 ≤ k ≤ n, if for every ordered sequence S of k distinct vertices of G, there exists a Hamiltonian cycle that encounters S in the given order. In this article, we prove that if G is a graph on n vertices with degree sum of nonadjacent vertices at least n + 3k-9/2, then G is k-ordered Hamiltonian for k=3,4,…[n/19]. We also show that the degree sum bound can be reduced to n + 2 [k/2]-2 if k(G) ≥ 3k-1/2 or δ(G) ≥ 5k-4. Several known results are generalized.
Let Ω is contained in R~m (m ≥ 1) be a bounded domain with piecewise smooth boundary partial derivΩ. Let t and r be positive integers with t > r + 1. We consider the eigenvalue problems (1.1) and (1.2), and obtain Theorem 1 and Theorem 2, which generalize the results in [1,2,5].
Let Ω is contained in R~m (m ≥ 1) be a bounded domain with piecewise smooth boundary partial derivΩ. Let t and r be positive integers with t > r + 1. We consider the eigenvalue problems (1.1) and (1.2), and obtain Theorem 1 and Theorem 2, which generalize the results in [1,2,5].
The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.
The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.
This paper gives new sufficient conditions for the existence of periodic solutions of a second order non-autonomous differential system by using Mawhin's coincidence degree theory and Brousk's theorem. These results substantially extend and improve the corresponding results in the literatures [1,6,7].
This paper gives new sufficient conditions for the existence of periodic solutions of a second order non-autonomous differential system by using Mawhin's coincidence degree theory and Brousk's theorem. These results substantially extend and improve the corresponding results in the literatures [1,6,7].
A geometric reduction procedure for volume-preserving flows with a volume-preserving symmetry on an n-dimensional manifold is obtained. Instead of the coordinate-dependent theory and the concrete coordinate transformation, we show that a volume-preserving flow with a one-parameter volume-preserving symmetry on an n-dimensional manifold can be reduced to a volume-preserving flow on the corresponding (n-1)-dimensional quotient space. More generally, if it admits an r-parameter volume-preserving commutable symmetry, then the reduced flow preserves the corresponding (n - r)-dimensional volume form.
A geometric reduction procedure for volume-preserving flows with a volume-preserving symmetry on an n-dimensional manifold is obtained. Instead of the coordinate-dependent theory and the concrete coordinate transformation, we show that a volume-preserving flow with a one-parameter volume-preserving symmetry on an n-dimensional manifold can be reduced to a volume-preserving flow on the corresponding (n-1)-dimensional quotient space. More generally, if it admits an r-parameter volume-preserving commutable symmetry, then the reduced flow preserves the corresponding (n - r)-dimensional volume form.
Let F(x) be a distribution function supported on [0,∞), with an equilibrium distribution function F_e(x). In this paper we shall study the function r_e(x) = (-ln F-bar e(x))' = F-bar(x)/∫_x~∞ F-bar (u) du, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.
Let F(x) be a distribution function supported on [0,∞), with an equilibrium distribution function F_e(x). In this paper we shall study the function r_e(x) = (-ln F-bar e(x))' = F-bar(x)/∫_x~∞ F-bar (u) du, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.
This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions. For the heat diffusion case, the necessary and sufficient conditions on the global existence of all positive solutions are obtained. For the general fast diffusion case, we get some conditions on the global existence and nonexistence of positive solutions. The results of this paper fill the same gaps which were left in this field.
This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions. For the heat diffusion case, the necessary and sufficient conditions on the global existence of all positive solutions are obtained. For the general fast diffusion case, we get some conditions on the global existence and nonexistence of positive solutions. The results of this paper fill the same gaps which were left in this field.
In this paper, a liminf behavior is studied of a two-parameter Gaussian process which is a generalization of a two-parameter Wiener process. The results improve on the liminfs in [7].
In this paper, a liminf behavior is studied of a two-parameter Gaussian process which is a generalization of a two-parameter Wiener process. The results improve on the liminfs in [7].
An SIS model with periodic maximum infectious force, recruitment rate and the removal rate of the infectives has been investigated in this article. Sufficient conditions for the permanence and extinction of the disease are obtained. Furthermore, the existence and global stability of positive periodic solution are established. Finally, we present a procedure by which one can control the parameters of the model to keep the infectives stay eventually in a desired set.
An SIS model with periodic maximum infectious force, recruitment rate and the removal rate of the infectives has been investigated in this article. Sufficient conditions for the permanence and extinction of the disease are obtained. Furthermore, the existence and global stability of positive periodic solution are established. Finally, we present a procedure by which one can control the parameters of the model to keep the infectives stay eventually in a desired set.