亚椭圆卷积算子与Rockland条件 *

设G是连通且单连通的二步齐次群,K是G上齐次、左不变卷积算子.若K具亚椭圆性,则K必满足Rockland条件:对于G的所有非平凡不可约酉表示π,π(K)是C^∞(π)上的内射.     

实数加群上算子调和分析中F.和M.Riesz定理

设G是实数加群,B表示G上的无Order齐次Banach代数,表示B中的右平移可积算子全体.在一些合宜条件下,我们得到如下结果:(1)在中的算子关于F.Riesz和M.Riesz第一定理成立。(2)在中解析算子关于F.Riesz和M.Riesz第二定理成立。     

Best Simultaneous Approximation in L~Φ(I,X)

Let X be a Banach space and Φ be an Orlicz function.Denote by LΦ(I,X) the space of X-valued Φ-integrable functions on the unit interval I equipped with the Luxemburg norm.For f1,f2,...,fm ∈ LΦ(I,X),a distance formula distΦ(f1,f2,...,fm,LΦ(I,G)) is presented,where G is a close subspace of X.Moreover,some existence and characterization results concerning the best simultaneous approximation of LΦ(I,G) in LΦ(I,X) are given.     

环Z/(p~e)上本原序列压缩映射的新结果

令Z/(pe)表示整数剩余类环,其中p为素数且e 2为正整数.令f(x)表示Z/(pe)上的n次本原多项式,G′(f(x),pe)表示Z/(pe)上所有由f(x)生成的本原序列构成的集合.设序列a∈G′(f(x),pe),它有唯一的p进制展开a=a0+a1p+···+ae-1pe-1.令φ(x0,x1,...,xe-1)=g(xe-1)+μ(x0,x1,...,xe-2)表示由Fe p到Fp的一个e变元多项式.那么,φ可以诱导出一个从G′(f(x),pe)到F∞p的压缩映射.在p为奇素数且f(x)为强本原多项式的条件下,人们已经证明该压缩映射是保熵的.而本文证明该压缩映射在f(x)为本原多项式的条件下仍然是保熵的.当deg(g(x))2时,我们还要求deg(g(x))为奇数,或者g(x)=xk+∑k-2i=0cixi.     

Gargano,Lewinter and Malerba问题的解

§1　IntroductionLet G be a graph with vertex-set V(G) ={ v1 ,v2 ,...,vn} .A labeling of G is a bijectionL:V(G)→{ 1,2 ,...,n} ,where L (vi) is the label of a vertex vi.A labeled graph is anordered pair (G,L) consisting of a graph G and its labeling L.Definition1.An increasing nonconsecutive path in a labeled graph(G,L) is a path(u1 ,u2 ,...,uk) in G such thatL(ui) + 1相似文献   

关于广义二次算子

设B(H)表示定义在希尔伯特空间H,上的所有有界线性算子的全体.如果A∈B(H)满足二次算子方程A2=αA βP,其中α,β∈C,P是一个非零的幂等算子且AP=PA=A,则称A为广义二次算子.记L(P)为关于幂等算子P的广义二次算子之集.我们用算子谱论的方法研究了L(P)的谱和群逆等相关性质,并推广了R. W. Farebrother和G. Trenkler的结论.     

圈的$L(d_1,d_2,\ldots,d_t)$-数$\lambda(C_n;d_1,d_2,\ldots,d_t)$

An L（d0,d2,...,dt）-labeling of a graph G is a function f from its vertex set V（G） to the set {0,1,..., k} for some positive integer k such that If（x） - f（y）l ≥di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L（d1,d2,...,dt）-number λ（G;d1,d2,... ,dt） of G is the smallest integer number k such that G has an L（d1,d2,...,dr）- labeling with max{f （x）｜x ∈ V（G）} = k. In this paper, we obtain the exact values for λ（Cn; 2, 2, 1） and λ（Cn; 3, 2, 1）, and present lower and upper bounds for λ（Cn; 2,..., 2, 1,..., 1）     

弱Hardy空间上的参数型Marcinkiewicz积分(英文)

证明了参数型Marcinkiewicz积分μρΩ是(Hp,∞,Lp,∞)(0相似文献   

L(d1, d2,..., dt)-Number λ(Cn; d1, d2,...,dt) of Cycles

An L(d1,d2,...,dt)-labeling of a graph G is a function f from its vertex set V(G) to the set {0, 1,..., k} for some positive integer k such that {f(x) - f(y)| ≥ di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L(d1,d2,...,dt)-number λ(G;d1,d2,... ,dt) of G is the smallest integer number k such that G has an L(d1,d2,... ,dt)labeling with max{f(x)|x ∈ V(G)} = k. In this paper, we obtain the exact values for λ(Cn; 2, 2,1) and λ(Cn; 3, 2, 1), and present lower and upper bounds for λ(Cn; 2,..., 2,1,..., 1)     

包含紧算子理想的Toeplitz算子代数的刻画

设G为一个torsion-free的离散群,（G,G＋）为一个拟序群,记T^G (G)为相应的Toeplitz算子代数,K(l^2(G 1)为l^2(G )上的紧算子全体,本文证明了K(l^2(G ))增包含于T^G (G)当且仅当下列两个条件时满足。（1）（G,G＋）为一个序群,（2）G中存在一个最小的正元。     

可圈的一个充分条件

本文我们证明如下结果:设G=(V,E)是一个n(n≥3)阶k-连通(k≥2)图,记X1,X2,…,Xk为V的子集,X=X1∪X2∪…∪Xk.若对每个I,I=1,2,…,k,满足:对任意的u,v∈Xi,有d(u) d(v)≥n或|N(u)∪N(v)|≥n-δ或|N(u)∩N(v)|≥α,这里δ是G的最小度,α是G的独立数,则G是X-可圈的.     

不含4-圈与7-圈的平面图是(2,0,0)-可染的

设d1,d2,...,dk是k个非负整数.若图G=(V,E)的顶点集V可剖分成k个子集V1,V2,...,Vk使得对i=1,2,...,k,由Vi所导出的子图G[Vi]的最大度至多为di,则称G是(d1,d2,...,dk)-可染的.本文证明不含4-圈和7-圈的平面图是(2,0,0)-可染的.     

On intersections of independent anisotropic Gaussian random fields

Let XH = {XH(s),s ∈RN1} and X K = {XK(t),t ∈R N2} be two independent anisotropic Gaussian random fields with values in R d with indices H =(H1,...,HN1) ∈(0,1)N1,K =(K1,...,KN2) ∈(0,1) N2,respectively.Existence of intersections of the sample paths of X H and X K is studied.More generally,let E1■RN1,E2■RN2 and FRd be Borel sets.A necessary condition and a sufficient condition for P{(XH(E1)∩XK(E2))∩F≠Ф}>0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1×E2×F in the metric space(RN1+N2+d,) are proved,where  is a metric defined in terms of H and K.These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.     

Best Simultaneous Approximation in LΦ(I,X)

Let X be a Banach space and Φ be an Orlicz function.Denote by LΦ(I,X)the space of X-valued Φ-integrable functions on the unit interval I equipped with the Luxemburg norm.For f1,f2,...,fm ∈ LΦ(I,X),a distance formula disΦ(f1,f2,...,fm,LΦ(I,G))is presented,where G is a close subspace of X.Moreover,some existence and characterization results concerning the best simultaneous approximation of LΦ(I,G)in LΦ(I,X)are given.     

Some graphs which have ascending subgraph decomposition

1.IntroductionIn[1],Alavietal.gavethefollowingdecompositionconjecture.Conjecture.LetGbeagraphwith("1')edges.ThentheedgesetofGcanbedecomposedintonsetsgeneratinggraphsGI,G2,'IG.suchthatIE(Gi)I=i(fori=1,2,',n)andGiisisomorphictoasubgraphofGi 1fori=1,2,'.)n--1.AgraphGthatcanbedecomposedasdescribedinConjecturewillbesaidtohaveanAscendingSubgraphDecomposition(AlsoabbreviatedasASD).ThesubgraphsGIIG2,',G.aresaidtobemembersofsuchadecomposition.Furthermore,ifeachGiisastar(matching,pat…     

二分（0，mf—m＋1）-图的正交（0，f）-因子分解

设G=（X,Y,E（G））是一个二分图,分别用V（G）=X∪Y和E（G）表示G的顶点集和边集．设f是定义在V（G）上的整数值函数且对任意x∈V（G）有f（x）≥k．设H1,H2,…,Hk是G的k个顶点不相交的子图,且｜E（Hi）｜=m,1≤i≤k．本文证明了每个二分（0,mf—m＋1）．图G有一个（0,f）-因子分解正交于Hi（i=1,2,…,k）     

Poincaré and Sobolev Inequalities for Vector Fields Satisfying Hrmander's Condition in Variable Exponent Sobolev Spaces

In this paper,we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces.The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebesgue spaces on spaces of homogeneous type.We obtain the first order Poincare inequalities for vector fields satisfying Hrmander's condition in variable non-isotropic Sobolev spaces.We also set up the higher order Poincare inequalities with variable exponents on stratified Lie groups.Moreover,we get the Sobolev inequalities in variable exponent Sobolev spaces on whole stratified Lie groups.These inequalities are important and basic tools in studying nonlinear subelliptic PDEs with variable exponents such as the p(x)-subLaplacian.Our results are only stated and proved for vector fields satisfying Hrmander's condition,but they also hold for Grushin vector fields as well with obvious modifications.     

共振情形m-点边值问题解的存在性

研究一类共振情形二阶微分方程m-点边值问题其中m≥3为整数,ai≥0,ξi∈(0,1)(i=1,2,…,m-2)为常数满足∑i=1m=2 ai=1, 0<ξ1<ξ2<…<ξm-2．利用Mawhin重合度拓展定理,作者得到了边值问题解存在的新结果．有意义的是本文允许函数．f(t,x,y)关于变量x和y的次数大于1,特别是允许变量x的次数大于y的次数,这些结果与已有工作是不同的．     

Algebraic-polynomial approximation of functions satisfying a Lipschitz condition

For functionsf(x) ε KH^(α) [satisfying the Lipschitz condition of order α (0 < α < 1) with constant K on [?1, 1], the existence is proved of a sequence P_n (f; x) of algebraic polynomials of degree n = 1, 2,..., such that $$|f(x) - P_{n - 1} (f;x)| \leqslant \mathop {\sup }\limits_{f \in KH^{(\alpha )} } E_n (f)[(1 - x^2 )^{a/2} + o(1)],$$ when n → ∞, uniformly for x ε [?1, 1], where E_n(f) is the best approximation off(x) by polynomials of degree not higher than n.