一类新型时滞积分不等式及其应用

主要研究了一种新型时滞积分不等式u(t)≤a(t)+∫0α(t)f(t,s)w(u(s))ds+∫0α(t)g(t,s∫)0sh(s,τ)φ(u(τ))dτds up(t)≤a(t)+p/p-q∫0α(t)(f(t,s)uq(s)w(u(s))+g(t,s)uq(s))dsup(t)≤a(t)+p/p-q∫0α(t)f(t,s)uq(s)w(u(s))ds+p/p-q∫0tg(t,s)uq(s)w(u(s))ds这里p>q≥0是常数且t∈[0,∞).并且用此结果研究了时滞微分积分方程解的全局存在性和有界性.     

Ramsey Number of K_(2,s 1) vs.K_(1,n)

It is shown that the Ramsey number r(K_(2,s 1),K_(1,n))(?)n sn~(1/2) (s 3)/2 o(1) for large n,and r(K_(2,s 1),K_(1,n))∈{((q-1)~2/s) 1,((q-1)~2/s) 2},where n=((q-1)~2/s)-q 2 and q is a prime power such that s|(q-1).     

多元函数的微分法则

我们知道 ,若函数 x =φ( s,t) ,y =ψ( s,t)在点 ( s,t)有连续导数 ,函数 z =f ( x,y)在相应点 ( x,y) =(φ( s,t) ,ψ( s,t) )有连续偏导数 ,则复合函数 z=f (φ( s,t) ,ψ( s,t) )在点 ( x,t)可微 ,且dz =( z x x s+ z y y s) ds+( z x x t+ z y y t) dt同样有 ,若函数 x =φ( t) ,y =ψ( t)在点 t可微 ,函数 z =f ( x,y)在相应点 ( x,y) =(φ( t) ,ψ( t) )有连续偏导数 ,则复合函数 z =f (φ( t) ,ψ( t) )在点 t可微 ,且 dz =( z x+ z ydydt) dt;若函数 x =φ( s,t)在点 ( s,t)有连续偏导数 ,函数 z =f ( x)在相应点 x =φ( s,t)有…     

半拟线性p-Laplacian问题结点解的存在性

In this paper, we study the existence of nodal solutions for the following problem:-(φ_p(x′))′= α(t)φ_p(x~+) + β(t)φ_p(x~-) + ra(t)f(x), 0 t 1,x(0) = x(1) = 0,where φ_p(s) = |s|~(p-2)s, a ∈ C([0, 1],(0, ∞)), x~+= max{x, 0}, x~-=- min{x, 0}, α(t), β(t) ∈C[0, 1]; f ∈ C(R, R), sf(s) 0 for s ≠ 0, and f_0, f_∞∈(0, ∞), where f_0 = lim_|s|→0f(s)/φ_p(s), f_∞ = lim|s|→+∞f(s)/φ_p(s).We use bifurcation techniques and the approximation of connected components to prove our main results.     

ASYMPTOTIC BEHAVIOR OF VOLTERRA INTEGRODIFFERENTIAL EQUATIONS

ThisworkissupportedinpartbytheFoundationoftheSichuanEducationCommissionandtheNationalNaturalScienceFoundationofChina.ThepurposeofthispaperistostudytheasymptoticbehaviorandboundednessoftheVolterraintegrodifferentialequationwherex∈Rn,A(t)andC(t,s)arecontinuousn×nmatrices,andf(t)iscontinuousn-vectors.ThefunctionG(t,s,x(s))isunknownandrepresentsthenonlinearparameterperturbationwithrespecttothestatex(s)inthelinearintegralterm.Ingeneral,itisassumedthatGisboundedintheformwhereisanyvectorormat…     

RAMSEY NUMBER OF HYPERGRAPH PATHS

Let H =(V, E) be a k-uniform hypergraph. For 1 ≤ s ≤ k-1, an s-path P~(k,s)_n of length n in H is a sequence of distinct vertices v_1, v_2, ···, v_(s+n(k-s)) such that {v_(1+i(k-s)), ···, v_(s+(i+1)(k-s))} is an edge of H for each 0 ≤ i ≤ n-1.In this paper, we prove that R(P~(3 s,s)_n, P~(3 s,s)_3) =(2 n + 1)s + 1 for n ≥ 3.     

具有有理谱密度的平稳随机过程的外推、内插及过滤

引言平稳随机过程剑(s)的线性外推问题,在于从(s)在s≤t上的值(依过程的所有的过去的外推),或从(s)在t-T≤s≤t上的值(在有穷间隔上已知过程时的外推),求得一个线性泛函(t+τ),以使此线性泛函是(t+τ),τ>0,的值的最佳逼近(在最小二乘方的意义下)。线性过滤问题,在于从(s)的同样的值,求得一个泛函(t+τ),以使它是(t+τ)的最佳逼近,此处(s)是一个与(s)平稳     

循环图的支撑树数与Euler环游数的渐近计数定理

研究有向循环图C( p ,s1,s2 ,… ,sk)支撑树数与Euler环游数的渐近性质 ,得到其支撑树数T(C( p ,s1,s2 ,… ,sk) )与Euler环游数E(C( p ,s1,s2 ,… ,sk) )的渐近公式lim 1kp T(C( p ,s1,s2 ,… ,sk) ) =1 ,lim 1k !p E(C( p ,s1,s2 ,… ,sk) ) =1 ,　　　　p→∞ .在此基础上得到了其叠线图Euler环游与支撑树数的渐近公式 .对无向图也得到了平行的结果 .     

关于方程sum from j=1 to s(1/x_j 1/X_j…X_s)=1

关于方程 sum from j-1 to x (1/x_j 1/x_1…x_5=1),1相似文献   

一类新的包含Riemann Zeta函数的求和计算公式

1引 言 本文ζ(s)表示Riemann Zeta函数,当Re(s)>1时,ζ(s)=sum from n=1to∞(1/n~s).包含ζ(s)的形如