Green's Equivalences on Semigroups of Transformations Preserving Order and an Equivalence Relation

Let ${\cal T}_X$ be the full transformation semigroup on the set $X$, \[ T_{E}(X)=\{f\in {\cal T}_X\colon \ \forall(a,b)\in E,(f(a),f(b))\in E\} \] be the subsemigroup of ${\cal T}_X$ determined by an equivalence $E$ on $X$. In this paper the set $X$ under consideration is a totally ordered set with $mn$ points where $m\geq 2$ and $n\geq 3$. The equivalence $E$ has $m$ classes each of which contains $n$ consecutive points. The set of all order preserving transformations in $T_{E}(X)$ forms a subsemigroup of $T_E(X)$ denoted by \[ {\cal O}_{E}(X)=\{f\in T_{E}(X)\colon \ \forall\, x, y\in X, \ x\leq y \mbox{ implies } f(x)\leq f(y)\}. \] The nature of regular elements in ${\cal O}_{E}(X)$ is described and the Green's equivalences on ${\cal O}_{E}(X)$ are characterized completely.     

On a field equation generating a new class of particular solutions to the Yang-Mills equations

In a pseudo-Euclidean space, a field equation (system of equations) is considered that is invariant under orthogonal (from the group O(p, q)) coordinate transformations and invariant under gauge transformations from the spinor group Pin(p, q). The solutions to the field equation are connected with a class of new particular solutions to the Yang-Mills equations.     

BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL INTEGRATION ON HERZ-TYPE SPACES

1 IntroductionLgt b E BMO(Rn) and 11 be a fractional integration with 0 < I < n. The commutator[b, II] generated by b and 11 is defined by[b, II]f(x) = b(x)llf(x) ~ II(sf)(x).S.Chanillolz] stated that the operator [b, II] is a bounded operator from LPI (R") on LPZ(R")for 1/Pz = 1/pl -- l/n and 1 < pl < n/l. Recently, Lu Shanzhen and Yang Dachun[9] studiedthe commutator [b,ll] on Herz spaces and a new class of Herz-type Hardy spaces introducedby them and established the correspondi…     

磁流体方程组弱解在负指标Besov空间中基于旋度和电流的正则性标准

本文研究了不可压磁流体方程组弱解的正则性准则,设(u(t,x),6(t,x))是不可压磁流体方程组在(O,T)上的光滑解,如果旋度和电流密度满足(▽× u,▽× b) ∈ L 2-a/2 (O, T;B-aa∞, ∞(R3)) ηL1-a/2(O,T;B-∞1,-a∞(R3)),0＜α＜1,则光滑解(u(t,x),b(t,x))可以连续延拓到(O,T'),T'＞T.而且这个条件可以保证满足能量不等式的弱解是(O,T)上的光滑解.     

Comparison between the best approximations by lacunary and ordinary polynomials

We denote E_n(f) and E _k ⁿ (f) the best uniform approximations to a continuous function f defined on [a,b] by the sets of algebraic polynomials of degree ≤n and algebraic polynomials of degree ≤n with the coefficients of x^k (k≤n) being zero. In this paper, in cases of r<k and r≥k while [a, b]=[−1,1] (or r<k,k≤r<2k and r>2k while [a,b]=[0, 1]), we separately discuss the condtions for r-times continuously differentiable function f which enables .     

The joint of the pseudovarieties of idempotent semigroups and locally trivial semigroups

Communicated by J.-E. Pin     

图有特殊[a,b]-因子的度条件

设G是一个n阶图 .设 1 a 相似文献   

哈密尔顿性和部分平方图的独立集

设G是一个图,G的部分平方图G*满足V(G*)=V(G),E(G*)=E(G)∪{uv:uv■E(G),且J(u,v)≠■},这里J(u,v)={w∈N(u)∩N(v):N(w)■N[u]∪N[v]}.利用插点方法,证明了如下结果:设G是k-连通图(k2),b是整数,0min {k,(2b-1+k)/2}(n(Y)-1),则G是哈密尔顿图.同时给出图是1-哈密尔顿的和哈密尔顿连通的相关结果.     

Banach空间中的平均非扩张映象:不动点的存在定理

<正> 设X是Banach空间,E是X中的集合,T是映集合E到自身的映象.若T满足条件(称为平均非扩张条件)其中x,y∈E,a,b,c≥0且a+2b+2c≤1,则称T是平均非扩张映象. 文[1]概括了近年来研究关于平均非扩张映象不动点的一些主要结果.本文进     

Banach空间中非线性奇异两点边值问题的多重正解

本文研究Banach空间E中非线性奇异边值问题-x'=f(t,x), t∈(0,1), a₁x(0)-a₂x'(0)=θ, b₁x(0)-b₂x'(1)=θ.其中θ是E中的零元素, f({t,x})在端点t=0和t=1处具有奇性. 利用不动点定理获得了该问题至少有两个正解的结果.     

关于图中存在不含给定k-因子的[a,b]-因子的度条件

设$1\leq a<b, 0\leq k$是整数. 设$G$是一个含有$k$-因子$Q$且阶为$|G|$的图. 设\delta(G)$表示$G$的最小度, 且$\delta(G)\geq a+k$. 如果$Q$连通, 设$\varepsilon=k$, 否则设$\varepsilon=k+1$.证明:当$b\geq a+\varepsilon-1$时, 如果对$G$的任意两个不相邻的点$x$和$y$都有max$\{d_G(x),d_G(y)\}\geq {\rm max}\{{{a|G|} \over {a+b}},{{(|G|+(a-1)(2a+b+\varepsilon-2))} \over {b+1}}\}+k$, 那么$G$有一个$[a, b]$-因子$F$ 使得 $E(F)\cap E(Q)=\emptyset$. 这个度条件是最佳的, 条件$b\geqa+\varepsilon-1$不能去掉. 进一步,得到图存在含给定$k$-因子的$[a, b]$-因子的度条件.     

An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient

We define a partial order on the set N_o,c of pairs (O,C), where O is a nilpotent orbit and C is a conjugacy class in A(O), Lusztig’s canonical quotient of A(O). We then show that there is a unique order-reversing duality map N_o,c → ^LN_o,c that has certain properties analogous to those of the original Lusztig–Spaltenstein duality map. This generalizes work of E. Sommers.     

The Hausdorff–Young Theorems of Fourier Analysis and Their Impact

This paper is devoted to a study of the Hausdorff-Young theorems from a historical perspective, beginning with the F. Riesz-Fischer theorem. Introduced by W. H. Young (1912), these theorems were considered and extended by F. Hausdorff (1923), F. Riesz (1923), E.C. Titchmarsh (1924), G. H. Hardy and J.E. Littlewood (1926), M. Riesz (1927), and O. Thorin (1939/48). Special emphasis is placed upon the development of the proofs of the two Hausdorff-Young inequalities and their impact upon Fourier analysis as a whole, in particular on the M. Riesz-Thorin convexity theoremand on the interpolation of operators. The golden thread connecting the various extensions and generalizations is the concept of logarithmic convexity, one that goes back to the work of J. Hadamard (1896), A. Liapounoff (1901), J.L.W.V. Jensen (1906), and O. Blumenthal (1907).     

Discussion on Fractional (a,b, k)-critical Covered Graphs

A graph G is called a fractional [a, b]-covered graph if for each e ∈ E(G), G contains a fractional[a, b]-factor covering e. A graph G is called a fractional(a, b, k)-critical covered graph if for any W ? V(G) with|W| = k, G-W is fractional [a, b]-covered, which was first defined and investigated by Zhou, Xu and Sun [S.Zhou, Y. Xu, Z. Sun, Degree conditions for fractional(a, b, k)-critical covered graphs, Information Processing Letters 152(2019)105838]. In this work, we proceed to study fraction...     

完全可控线性系统的谱分布

<正> 其中x(·)∈R_n,u(·)∈R_r,A,B分别为n×n,n×r阶复常数阵,R_n,R_r分别为n,r维酉空间,有如下熟知结果:任给n个复数λ_1,…,λ_n,恒存在r×n阶复数阵C,使阵的谱集σ(A+BC)={λ_1,…,λ_n}的充要条件为     

A-拓扑以及A-拓扑空间的相关性质

设E是一个A rch im edean R iesz空间,a∈E,Φ≠A E,则有如下的两个结论:1)由a生成的a-拓扑空间E是一个H ausdorff空间;2)若以下条件之一成立,则由A生成的A-拓扑空间E是一个H ausdorff空间:(a)子集{a:a∈A}有上界;(b)E具有强单位元;(c)若E=C(X),其中X是一个局部紧H ausdorff空间.     

K(o)the-Bochner空间的凸性

本文利用K(o)the函数空间的性质以及K(o)the函数空间与K(o)the-Bochner空间的关系,讨论了K(o)the-Bochner空间E(X)的凸性,主要结果如下:(a)给出E(X)的端点的充分条件,得到了E(X)严格凸的判据,相应地推广了Lp(μ,X)以及LΦ(X)的结果;(b)讨论了E(X)的弱局部一致凸和局部完全k-凸;(c)刻画了E(X)的强凸,给出了E(X)强凸的充要条件.     

Subclasses of meromorphic functions associated with the Cho-Kwon-Srivastava operator

We consider a multiplier transformation and some subclasses of the class of meromorphic functions which was defined by means of the Hadamard product by N.E. Cho, O.S. Kwon and H.M. Srivastava in [N.E. Cho, O.S. Kwon, H.M. Srivastava, Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations, J. Math. Anal. Appl. 300 (2004) 505-520].     

凸函数的双参数平均不等式的新证明

利用 Tchebycheff积分不等式和积分形式的 Cauchy中值定理证明了下列结论 :设 f(x)是 [a,b]上的正连续函数 ,且在 (a,b)内可微 ,若 f′(x)单调递增 ,则对任意的 p,q,有 Mp,q(f) 相似文献   

连续时间下非参数回归模型的误差密度估计的渐近均方误差

本文研究了连续时间下非参数回归的误差官度估计的收敛速度，给出了一定条件下误差密度的估计量^fT(x)的均方收敛速度，详细说明了以下重要结果：E[^fT(x)-f(x)]^2＝O(T^-1/4)其中f(x)表示误差过程｛et,t≥0｝的未知密度。