The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process ...The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process functionals are presented, the following conclusions are obtained： the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent increments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Markov process being still a Markov process are given.展开更多
Given a simple graph G and a positive integer k, the induced matching k-partition problem asks whether there exists a k-partition (V 1, V 2, ..., V k) of V(G) such that for each i(1≤i≤k), G[V i] is 1-regular. This p...Given a simple graph G and a positive integer k, the induced matching k-partition problem asks whether there exists a k-partition (V 1, V 2, ..., V k) of V(G) such that for each i(1≤i≤k), G[V i] is 1-regular. This paper studies the computational complexity of this problem for graphs with small diameters. The main results are as follows: Induced matching 2-partition problem of graphs with diameter 6 and induced matching 3-partition problem of graphs with diameter 2 are NP-complete; induced matching 2-partition problem of graphs with diameter 2 is polynomially solvable.展开更多
In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly sm...In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.展开更多
The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new i...The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued （∈,∈ ∨q）-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investigated. In particular, the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.展开更多
The D-η-proper prequasi invexity of vector-valued functions is characterized by means of （weak） nearly convexity and density of sets. Under weaker assumptions, some equivalent conditions for D-η-proper prequasi-in...The D-η-proper prequasi invexity of vector-valued functions is characterized by means of （weak） nearly convexity and density of sets. Under weaker assumptions, some equivalent conditions for D-η-proper prequasi-invexity are derived.展开更多
This paper is concerned with the heteroscedastic regression model Y i=g(x i)+σ iei(1?i?n) under correlated errors e i, where it is assumed that σ i Emphasis>/2 =f(u i), the design points (x i, ui) are known and n...This paper is concerned with the heteroscedastic regression model Y i=g(x i)+σ iei(1?i?n) under correlated errors e i, where it is assumed that σ i Emphasis>/2 =f(u i), the design points (x i, ui) are known and nonrandom, and g and f are unknown functions. Assuming that unobserved disturbances e i are martingale differences. The strong uniform convergence rates and r-th moment uniform convergence rates of wavelet estimator of g are investigated. Also, the strong uniform convergence rates are discussed for wavelet estimator of f. MR Subject Classification 62G05 Keywords regression function - martingale difference error - wavelet estimator - uniform convergence rate Partially supported by the National Natural Science Foundation of China (10171079).展开更多
The problem of equilibrium of non-linear dynamic system for microorganism in continuous culture is considered in this paper. The existence of equilibrium point is proved. The conclusion that the equilibrium is the con...The problem of equilibrium of non-linear dynamic system for microorganism in continuous culture is considered in this paper. The existence of equilibrium point is proved. The conclusion that the equilibrium is the continuous function of the dilution rate and substrate concentration in medium in a certain range is concluded. And the stability criterion of equilibrium is obtained. In theory, it explains the multiplicity shown in laboratory.展开更多
Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual ...Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.展开更多
The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown f...The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.展开更多
The regularity for a class of X-elliptic equations with lower order termLu＋vu=-∑i,j=1 mXj^＊（aij（x）Xiu）＋vu=μis studied, where X = {X1,..., Xm} is a family of locally Lipschitz continuous vector fields, v is in...The regularity for a class of X-elliptic equations with lower order termLu＋vu=-∑i,j=1 mXj^＊（aij（x）Xiu）＋vu=μis studied, where X = {X1,..., Xm} is a family of locally Lipschitz continuous vector fields, v is in certain Morrey type space and μ a nonnegative Radon measure. The HSlder continuity of the solution is proved when μ satisfies suitable growth condition, and a converse result on the estimate of μ is obtained when u is in certain HSlder class.展开更多
In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact ...In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution （xs（t）, O, zs（t）） is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period T the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.展开更多
The global existence of the heat flow for harmonic maps from noncompact manifolds is considered. When L^m norm of the gradient of initial data is small, the existence of a global solution is proved.
The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it ...The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it is shown that the global weak attractor is actually the global strong attractor in Hper^k.展开更多
Let fs,t（m, n） be the number of （0, 1） - matrices of size m × n such that each row has exactly s ones and each column has exactly t ones （sm = nt）. How to determine fs,t（m,n）？ As R. P. Stanley has obser...Let fs,t（m, n） be the number of （0, 1） - matrices of size m × n such that each row has exactly s ones and each column has exactly t ones （sm = nt）. How to determine fs,t（m,n）？ As R. P. Stanley has observed （Enumerative Combinatorics I （1997）, Example 1.1.3）, the determination of fs,t（m, n） is an unsolved problem, except for very small s, t. In this paper the closed formulas for f2,2（n, n）, f3,2（m, n）, f4,2（m, n） are given. And recursion formulas and generating functions are discussed.展开更多
If the vertically-mixing time is comparable with the period of oscillatory current, the contaminant contraction may occur, then the coefficient of shear dispersion will be negative (singularity). According to the two-...If the vertically-mixing time is comparable with the period of oscillatory current, the contaminant contraction may occur, then the coefficient of shear dispersion will be negative (singularity). According to the two-dimensional delay-diffusion equation derived by Liu in another paper, The equations for X(t), Y(t), central displacement as well as dispersion tensor were derived. Generally speaking, δDij/δτ is positive when τ is small; but when τ is large, the memory functions may be negative. The analytical expressions for Dij and X,Y were also given.展开更多
Let H(n,m) be the number of rooted non-isomorphic bipartite planar maps with m edges and the valency of the rooted face being 2n. This note provides the following results: [GRAPHICS] for n greater-than-or-equal-to 2, ...Let H(n,m) be the number of rooted non-isomorphic bipartite planar maps with m edges and the valency of the rooted face being 2n. This note provides the following results: [GRAPHICS] for n greater-than-or-equal-to 2, where \DELTA(i)\m = (2i - 2)! divided-by (i - 1)!i! {(4i - 2)alpha(i + 1, m - i) + alpha(i, m - i) - i-alpha(i, m - i + 1) + (i + 1)beta(i, m - i)}, m > i, (2i - 2)! divided-by (i - 1) !i! (4i - 1 - i2), m = i;0, m < i. [GRAPHICS] Meanwhile, the combinatorial identity [GRAPHICS] is also found. In what mentioned above, alpha(s, t) and beta(s, t) are expressed by the following finite sums with all the terms positive:(~)[GRAPHICS]展开更多
The ill-posedness of the two-phase flow problems is explicitly related to the Kelvin-Helmholtz instability of two compressible fluid Layers. A long wavelength formulation of the Kelvin-Helmholtz problem is derived. Va...The ill-posedness of the two-phase flow problems is explicitly related to the Kelvin-Helmholtz instability of two compressible fluid Layers. A long wavelength formulation of the Kelvin-Helmholtz problem is derived. Various features of this formulation are explored briefly.展开更多
基金Supported by the National Natural Science Foundation of China (10671197)
文摘The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process functionals are presented, the following conclusions are obtained： the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent increments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Markov process being still a Markov process are given.
基金Supported by the National Natural Science Foundation of China( 1 0 371 1 1 2 ) and the Natural ScienceFoundation of Henan( 0 4 1 1 0 1 1 2 0 0 )
文摘Given a simple graph G and a positive integer k, the induced matching k-partition problem asks whether there exists a k-partition (V 1, V 2, ..., V k) of V(G) such that for each i(1≤i≤k), G[V i] is 1-regular. This paper studies the computational complexity of this problem for graphs with small diameters. The main results are as follows: Induced matching 2-partition problem of graphs with diameter 6 and induced matching 3-partition problem of graphs with diameter 2 are NP-complete; induced matching 2-partition problem of graphs with diameter 2 is polynomially solvable.
基金the National Natural Science Foundation of China (10771050)
文摘In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.
基金Supported by the National Natural Science Foundation of China(60474022)a grant of the Key Science Foundation of Education Committee of Hubei Province(D200729003)
文摘The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued （∈,∈ ∨q）-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investigated. In particular, the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.
文摘The D-η-proper prequasi invexity of vector-valued functions is characterized by means of （weak） nearly convexity and density of sets. Under weaker assumptions, some equivalent conditions for D-η-proper prequasi-invexity are derived.
基金Partially supported by the National Natural Science Foundation of China( 1 0 1 71 0 79)
文摘This paper is concerned with the heteroscedastic regression model Y i=g(x i)+σ iei(1?i?n) under correlated errors e i, where it is assumed that σ i Emphasis>/2 =f(u i), the design points (x i, ui) are known and nonrandom, and g and f are unknown functions. Assuming that unobserved disturbances e i are martingale differences. The strong uniform convergence rates and r-th moment uniform convergence rates of wavelet estimator of g are investigated. Also, the strong uniform convergence rates are discussed for wavelet estimator of f. MR Subject Classification 62G05 Keywords regression function - martingale difference error - wavelet estimator - uniform convergence rate Partially supported by the National Natural Science Foundation of China (10171079).
文摘The problem of equilibrium of non-linear dynamic system for microorganism in continuous culture is considered in this paper. The existence of equilibrium point is proved. The conclusion that the equilibrium is the continuous function of the dilution rate and substrate concentration in medium in a certain range is concluded. And the stability criterion of equilibrium is obtained. In theory, it explains the multiplicity shown in laboratory.
文摘Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.
基金Partially supported by the National Natural Science Foundation of China(10571136)
文摘The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.
基金Supported by the China State Scholarship (2003833095)Department of Education of Zhejiang Province(20051495)
文摘The regularity for a class of X-elliptic equations with lower order termLu＋vu=-∑i,j=1 mXj^＊（aij（x）Xiu）＋vu=μis studied, where X = {X1,..., Xm} is a family of locally Lipschitz continuous vector fields, v is in certain Morrey type space and μ a nonnegative Radon measure. The HSlder continuity of the solution is proved when μ satisfies suitable growth condition, and a converse result on the estimate of μ is obtained when u is in certain HSlder class.
基金Supported-by the National Natural Science Foundation of China(10471117)the Henan Innovation Project for University Prominent Research Talents(2005KYCX017)the Scientific Research Foundation of Education Ministry for the Returned Overseas Chinese Scholars
文摘In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution （xs（t）, O, zs（t）） is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period T the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.
基金Supported by the National Natural Science Foundation of China (1057115610671079+1 种基金10701064)the Zijin Project of Zhejiang University
文摘The global existence of the heat flow for harmonic maps from noncompact manifolds is considered. When L^m norm of the gradient of initial data is small, the existence of a global solution is proved.
基金Supported by the Natural science Foundation of Henan Education Department(2007110004)the Natural Science Foundation of Henan University(06YBZR027)
文摘The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it is shown that the global weak attractor is actually the global strong attractor in Hper^k.
文摘Let fs,t（m, n） be the number of （0, 1） - matrices of size m × n such that each row has exactly s ones and each column has exactly t ones （sm = nt）. How to determine fs,t（m,n）？ As R. P. Stanley has observed （Enumerative Combinatorics I （1997）, Example 1.1.3）, the determination of fs,t（m, n） is an unsolved problem, except for very small s, t. In this paper the closed formulas for f2,2（n, n）, f3,2（m, n）, f4,2（m, n） are given. And recursion formulas and generating functions are discussed.
基金Project supported by National Natural Science Fundation of China
文摘If the vertically-mixing time is comparable with the period of oscillatory current, the contaminant contraction may occur, then the coefficient of shear dispersion will be negative (singularity). According to the two-dimensional delay-diffusion equation derived by Liu in another paper, The equations for X(t), Y(t), central displacement as well as dispersion tensor were derived. Generally speaking, δDij/δτ is positive when τ is small; but when τ is large, the memory functions may be negative. The analytical expressions for Dij and X,Y were also given.
文摘Let H(n,m) be the number of rooted non-isomorphic bipartite planar maps with m edges and the valency of the rooted face being 2n. This note provides the following results: [GRAPHICS] for n greater-than-or-equal-to 2, where \DELTA(i)\m = (2i - 2)! divided-by (i - 1)!i! {(4i - 2)alpha(i + 1, m - i) + alpha(i, m - i) - i-alpha(i, m - i + 1) + (i + 1)beta(i, m - i)}, m > i, (2i - 2)! divided-by (i - 1) !i! (4i - 1 - i2), m = i;0, m < i. [GRAPHICS] Meanwhile, the combinatorial identity [GRAPHICS] is also found. In what mentioned above, alpha(s, t) and beta(s, t) are expressed by the following finite sums with all the terms positive:(~)[GRAPHICS]
文摘The ill-posedness of the two-phase flow problems is explicitly related to the Kelvin-Helmholtz instability of two compressible fluid Layers. A long wavelength formulation of the Kelvin-Helmholtz problem is derived. Various features of this formulation are explored briefly.
