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1.
Let T X denote the full transformation semigroup on a set X. For an equivalence E on X, let Then T ?(X) is exactly the semigroup of mappings on the topological space X for which the collection of all E-classes is a basis. In this paper, we discuss regularity of elements and Green’s relations for T ?(X).
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$T_{\exists}(X)=\{\alpha\in T_X:\forall x,y\in X,(x\alpha,y\alpha)\in E\Rightarrow(x,y)\in E\}.$
2.
Cameron, Goethals, Seidel, and Shult classified the graphs with eigenvalues at least – 2 by viewing their vertices as elements of a root system of type An, Dn, E6, E7, or E8. In this paper we characterize graphs satisfying more general algebraic conditions by viewing edges as elements in a root system. Specifically, vertices are viewed as equal length vectors spanning some Euclidean space that is also spanned by a root system Φ, such that vertices are adjacent if and only if their differences is in Φ. We conclude with some open problems. 相似文献
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4.
P. A. Borodin 《Mathematical Notes》2010,87(3-4):485-488
For each n = 3, 4, …, we construct an example of a Banach space X and elements x 1, …, x n in this space such that X does not have any element with the minimal sum of distances to the elements x k . 相似文献
5.
When is c(x) a Clean Ring? 总被引:1,自引:0,他引:1
F. Azarpanah 《Acta Mathematica Hungarica》2002,94(1-2):53-58
An element of a ring R is called clean if it is the sum of a unit and an idempotent and a subset A of R is called clean if every element of A is clean. A topological characterization of clean elements of C(X) is given and it is shown that C(X) is clean if and only if X is strongly zero-dimensional, if and only if there exists a clean prime ideal in C(X). We will also characterize topological spaces X for which the ideal CK(X) is clean. Whenever X is locally compact, it is shown that CK(X) is clean if and only if X is zero-dimensional. 相似文献
6.
It is known that if we know all XI-subsemilattices of a given X-semilattice of unions, then we can determine all idempotent elements of the semigroup, and the structure of idempotent elements is characterized. In this work, we find idempotent elements of the semigroup corresponding to X-semilattices of unions of the class ??16(X, 6). Moreover, we give formulas for the number of idempotent elements, where X is finite. 相似文献
7.
We give a criterion to decide if a given w-homogeneous derivation on A?k[X1,X2,X3] is locally nilpotent. We deduce an algorithm which decides if a k-subalgebra of A, which is finitely generated by w-homogeneous elements, is the kernel of some locally nilpotent derivation. 相似文献
8.
Let E=[eij] be a matrix with integral elements, and let x be an indeterminate defined over the rational field Q. We investigate matrices of the form X=[xeij] (i = 1,…, m; j = 1,…, n; m ⩽ n). We may multiply the lines (rows or columns) of the matrix X by suitable integral powers of x in various ways and thereby transform X into a matrix Y=[xfij] such that the fij are nonnegative integers and each line of Y contains at least one element x0 = 1. We call Y a normalized form of X, and we denote by S(X) the class of all normalized forms associated with a given matrix X. The classes S(X) have a fascinating combinatorial structure, and the present paper is a natural outgrowth and extension of an earlier study. We introduce new concepts such as an elementary transformation called an interchange. We prove, for example, that two matrices in the same class are transformable into one another by interchanges. Our analysis of the class S(X) also yields new insights into the structure of the optimal assignments of the matrix E by way of the diagonal products of the matrix X. 相似文献
9.
J.R. Tort 《Discrete Mathematics》1983,44(2):181-185
Let X be a set of n elements. Let 3(X) be the set of all triples of X. We define a clique as a set of triples which intersect pairwise in two elements. In this paper we prove that if n?6, the minimum cardinality of a partition of 3(X) into cliques is . 相似文献
10.
Convergence in probability of the linear forms Σk=1∞ankXk is obtained in the space D[0, 1], where (Xk) are random elements in D[0, 1] and (ank) is an array of real numbers. These results are obtained under varying hypotheses of boundedness conditions on the moments and conditions on the mean oscillation of the random elements (Xn) on subintervals of a partition of [0, 1]. Since the hypotheses are in general much less restrictive than tightness (or convex tightness), these results represent significant improvements over existing weak laws of large numbers and convergence results for weighted sums of random elements in D[0, 1]. Finally, comparisons to classical hypotheses for Banach space and real-valued results are included. 相似文献
11.
We consider Bühlmann's classical model in credibility theory and we assume that the set of possible values of the observable random variables X1, X2,… is finite, say with n elements. Then the distribution of a couple (Xr, Xs) (r ≠ s) amounts to a square real matrix of order n, that we call a credibility matrix. In order to estimate credibility matrices or to adjust roughly estimated credibility matrices, we study the set of all credibility matrices and some particular subsets of it. 相似文献
12.
Althoen Steven C. 《Journal of Pure and Applied Algebra》1978,10(3):257-269
If the path connected topological space X has a countable open cover with path connected elements, then π2(X,1) is computed as a colimit determined by the second homotopy groups of the intersection of elements of and the indices of the fundamental group injections of these intersections into the fundamental group of X. Aside from assuming that the inclusions induce such monomorphisms, certain other inclusions are also required to induce monomorphisms of fundamental groups and restrictions are placed on the arrangement of the elements of . 相似文献
13.
Robert Archbold 《Journal of Functional Analysis》2006,235(1):90-121
Let (G,X) be a second-countable transformation group with G acting freely on X. It is shown that measure-theoretic accumulation of the action and topological strength of convergence in the orbit space X/G provide equivalent ways of quantifying the extent of nonproperness of the action. These notions are linked via the representation theory of the transformation-group C∗-algebra C0(X)?G. 相似文献
14.
REIDER Igor 《中国科学 数学(英文版)》2013,56(1):1-42
The nonabelian Jacobian J(X;L,d) of a smooth projective surface X is inspired by the classical theory of Jacobian of curves.It is built as a natural scheme interpolating between the Hilbert scheme X [d] of subschemes of length d of X and the stack M X(2,L,d) of torsion free sheaves of rank 2 on X having the determinant OX(L) and the second Chern class(= number) d.It relates to such influential ideas as variations of Hodge structures,period maps,nonabelian Hodge theory,Homological mirror symmetry,perverse sheaves,geometric Langlands program.These relations manifest themselves by the appearance of the following structures on J(X;L,d):1) a sheaf of reductive Lie algebras;2)(singular) Fano toric varieties whose hyperplane sections are(singular) Calabi-Yau varieties;3) trivalent graphs.This is an expository paper giving an account of most of the main properties of J(X;L,d) uncovered in Reider 2006 and ArXiv:1103.4794v1. 相似文献
15.
Kwang-Wu Chen 《Journal of Number Theory》2005,111(2):372-391
In this paper, our aim is to investigate the summation form of Bernoulli numbers Bn, such as . We derive some basic identities among them. These numbers can form a Seidel matrix. The upper diagonal elements of this Seidel matrix are called “the median Bernoulli numbers”. We determine the prime divisors of their numerators and denominators. And we characterize their ordinary generating function as the unique solution of some functional equation. At last, we also obtain the continued fraction representation of their ordinary generating function and their value of Hankel determinant. 相似文献
16.
Peter C Fishburn 《Journal of Combinatorial Theory, Series B》1974,17(3):240-243
Given a partial order P defined on a finite set X, a binary relation ?P may be defined on X by setting x ?Py for elements x and y in X just when more linear extensions L of P on X have xLy than yLx. A linear extension L of P on X is a linear order on X with P ? L. There exist partial orders P such that ?P includes cycles. Thus, in a voting situation in which voters are unanimous in their preferences on the pairs in P and express all possible linearly ordered preferences on X which are consistent with P, with no two voters having the same preference order, strict simple majorities as given by ?P can cycle. 相似文献
17.
Let T n be the full transformation semigroup on a finite set X n ={1,2,??,n}. Let ?? be an equivalence relation on X n and ? be a total order on the partition set X n /??. We describe all automorphisms of the partition order-decreasing transformation monoid: $$T(\rho,\preceq)=\bigl\{\alpha\in T_{n}: (x\alpha)\rho\preceq x\rho, \forall x\in X_{n}\bigr\} $$ that generalizes the results of Schreier (Fundam. Math., 28:261?C264, 1936) and ?utov (Izv. Vys?. U?ebn. Zaved., Mat., 3:177?C184, 1961). 相似文献
18.
Stephen D Fisher 《Journal of Functional Analysis》1979,31(2):218-223
Let A and B be closed subalgebras of Cr(X) whose direct sum is Cr(X). Some consequences of this relation are explored in this paper. For example if 1 ?A (as may be assumed) it is shown that the norm of the projection onto A is an odd integer and there is a retraction of X onto the set of common zeros of elements of B. 相似文献
19.
M.R. Koushesh 《Topology and its Applications》2007,154(3):698-721
For a non-compact metrizable space X, let E(X) be the set of all one-point metrizable extensions of X, and when X is locally compact, let EK(X) denote the set of all locally compact elements of E(X) and be the order-anti-isomorphism (onto its image) defined in [M. Henriksen, L. Janos, R.G. Woods, Properties of one-point completions of a non-compact metrizable space, Comment. Math. Univ. Carolin. 46 (2005) 105-123; in short HJW]. By definition λ(Y)=?n<ωclβX(Un∩X)\X, where Y=X∪{p}∈E(X) and {Un}n<ω is an open base at p in Y. We characterize the elements of the image of λ as exactly those non-empty zero-sets of βX which miss X, and the elements of the image of EK(X) under λ, as those which are moreover clopen in βX\X. This answers a question of [HJW]. We then study the relation between E(X) and EK(X) and their order structures, and introduce a subset ES(X) of E(X). We conclude with some theorems on the cardinality of the sets E(X) and EK(X), and some open questions. 相似文献
20.
LetT be a continuous transformation of a compact metric spaceX. T induces in a natural way a transformationT M on the spaceM (X) of probability measures onX, and a transformationT K on the spaceK (X) of closed subsets ofX. This note investigates which of the topological properties ofT∶X→X (like distality, transitivity, mixing property etc. ...) are “inherited” byT M∶M (X)→M (X) andT K∶K (X)→K (X). 相似文献