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
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
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
A class of constrained semi-infinite minimax problem is transformed into a simple constrained problem,by means of discretization decomposition and maximum entropy method,making use of surrogate constraint.The paper de...A class of constrained semi-infinite minimax problem is transformed into a simple constrained problem,by means of discretization decomposition and maximum entropy method,making use of surrogate constraint.The paper deals with the convergence of this asymptotic approach method.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
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.
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
In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o...In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.展开更多
Let Z/（p^e） be the integer residue ring modulo p^e with p an odd prime and integer e ≥ 3. For a sequence a over Z/（p^e）, there is a unique p-adic decomposition a- = a-0 ＋a-1 .p ＋… ＋ a-e-l .p^e-1 where each a-...Let Z/（p^e） be the integer residue ring modulo p^e with p an odd prime and integer e ≥ 3. For a sequence a over Z/（p^e）, there is a unique p-adic decomposition a- = a-0 ＋a-1 .p ＋… ＋ a-e-l .p^e-1 where each a-i can be regarded as a sequence over Z/（p）, 0 ≤ i ≤ e - 1. Let f（x） be a primitive polynomial over Z/（p^e） and G＇（f（x）,p^e） the set of all primitive sequences generated by f（x） over Z/（p^e）. For μ（x） ∈ Z/（p）[x] with deg（μ（x）） ≥ 2 and gad（1 ＋ deg（μ（x））,p- 1） = 1, setφe-1 （x0, x1,… , xe-1） = xe-1. [μ（xe-2） ＋ ηe-3（x0, X1,…, xe-3）] ＋ ηe-2（x0, X1,…, xe-2） which is a function of e variables over Z/（p）. Then the compressing mapφe-1 ： G＇（f（x）,p^e） → （Z/（p））^∞ ,a-→φe-1（a-0,a-1, … ,a-e-1） is injective. That is, for a-,b-∈ G＇（f（x）,p^e）, a- = b- if and only if φe-1 （a-0,a-1, … ,a-e-1） = φe-1（b-0, b-1,… ,b-e-1）. As for the case of e = 2, similar result is also given. Furthermore, if functions φe-1 and ψe-1 over Z/（p） are both of the above form and satisfy φe-1（a-0,a-1,…,a-e-1）=ψe-1（b-0, b-1,… ,b-e-1） for a-,b-∈G＇（f（x）,p^e）, the relations between a- and b-, φe-1 and ψe-1 are discussed展开更多
Bin-objective shape optimization of arch dam based on linear programming model is discussed to minimize both dam volume and maximal tensile stress.The importance of weight coefficient of the above two objectives is ch...Bin-objective shape optimization of arch dam based on linear programming model is discussed to minimize both dam volume and maximal tensile stress.The importance of weight coefficient of the above two objectives is chosen according to the value of importance ratio.The influence of weight coefficient to the optimization result is discussed in detail and the numerical example shows that both the model and method proposed is doable.展开更多
Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)...Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)=Ann(M/N).展开更多
. The expression of cyclotomic polynomial Фpq （x） is concerned for a long time. A simple and explicit expression of Фpq （x） in Z[x] has been showed. The form of the factors of Фpq （x） over F2 and the upper, l.... The expression of cyclotomic polynomial Фpq （x） is concerned for a long time. A simple and explicit expression of Фpq （x） in Z[x] has been showed. The form of the factors of Фpq （x） over F2 and the upper, lower bounds of their Hamming weight are provided.展开更多
Some new properties of polarizable Carnot group are given.By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed.Thus the mult...Some new properties of polarizable Carnot group are given.By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed.Thus the multi-solution property of corresponding non-homogeneous Dirichlet problem is proved and the best possible of LQ norm in the famous Alexandrov-Bakelman-Pucci type estimate is discussed.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.
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A class of constrained semi-infinite minimax problem is transformed into a simple constrained problem,by means of discretization decomposition and maximum entropy method,making use of surrogate constraint.The paper deals with the convergence of this asymptotic approach method.
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.
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.
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.
文摘In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.
基金Supported by the National Natural Science Foundation of China(60673081)863 Program(2006AA01Z417)
文摘Let Z/（p^e） be the integer residue ring modulo p^e with p an odd prime and integer e ≥ 3. For a sequence a over Z/（p^e）, there is a unique p-adic decomposition a- = a-0 ＋a-1 .p ＋… ＋ a-e-l .p^e-1 where each a-i can be regarded as a sequence over Z/（p）, 0 ≤ i ≤ e - 1. Let f（x） be a primitive polynomial over Z/（p^e） and G＇（f（x）,p^e） the set of all primitive sequences generated by f（x） over Z/（p^e）. For μ（x） ∈ Z/（p）[x] with deg（μ（x）） ≥ 2 and gad（1 ＋ deg（μ（x））,p- 1） = 1, setφe-1 （x0, x1,… , xe-1） = xe-1. [μ（xe-2） ＋ ηe-3（x0, X1,…, xe-3）] ＋ ηe-2（x0, X1,…, xe-2） which is a function of e variables over Z/（p）. Then the compressing mapφe-1 ： G＇（f（x）,p^e） → （Z/（p））^∞ ,a-→φe-1（a-0,a-1, … ,a-e-1） is injective. That is, for a-,b-∈ G＇（f（x）,p^e）, a- = b- if and only if φe-1 （a-0,a-1, … ,a-e-1） = φe-1（b-0, b-1,… ,b-e-1）. As for the case of e = 2, similar result is also given. Furthermore, if functions φe-1 and ψe-1 over Z/（p） are both of the above form and satisfy φe-1（a-0,a-1,…,a-e-1）=ψe-1（b-0, b-1,… ,b-e-1） for a-,b-∈G＇（f（x）,p^e）, the relations between a- and b-, φe-1 and ψe-1 are discussed
基金Sponsored by the National Natural Science Foundation of China(Grant.50139010).
文摘Bin-objective shape optimization of arch dam based on linear programming model is discussed to minimize both dam volume and maximal tensile stress.The importance of weight coefficient of the above two objectives is chosen according to the value of importance ratio.The influence of weight coefficient to the optimization result is discussed in detail and the numerical example shows that both the model and method proposed is doable.
文摘Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)=Ann(M/N).
基金National Natural Science Foundation of China(60673081)the National 863 Plan(2006AA01Z417).
文摘. The expression of cyclotomic polynomial Фpq （x） is concerned for a long time. A simple and explicit expression of Фpq （x） in Z[x] has been showed. The form of the factors of Фpq （x） over F2 and the upper, lower bounds of their Hamming weight are provided.
文摘Some new properties of polarizable Carnot group are given.By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed.Thus the multi-solution property of corresponding non-homogeneous Dirichlet problem is proved and the best possible of LQ norm in the famous Alexandrov-Bakelman-Pucci type estimate is discussed.
