Publication Date: 1998
Statistical Papers (09325026)39(4)pp. 347-360
Let X be a random variable and X(w) be a weighted random variable corresponding to X. In this paper, we intend to characterize the Pearson system of distributions by a relationship between reliability measures of X and X(w), for some weight function w>0.
Publication Date: 1998
Nagoya Mathematical Journal (21526842)151pp. 37-50
The first part of the paper is concerned, among other things, with a characterization of filter regular sequences in terms of modules of generalized fractions. This characterization leads to a description, in terms of generalized fractions, of the structure of an arbitrary local cohomology module of a finitely generated module over a notherian ring. In the second part of the paper, we establish homomorphisms between the homology modules of a Koszul complex and the homology modules of a certain complex of modules of generalized fractions. Using these homomorphisms, we obtain a characterization of unconditioned strong d-sequences.
Publication Date: 1998
Taiwanese Journal of Mathematics (10275487)(1)pp. 87-95
In the present paper, we shall establish one of our earlier conjectures by proving that on compact subsets of a *-foundation semigroup S with identity and with a locally bounded Borel measurable weight function w, the pointwise convergence and the uniform convergence of a sequence of w-bounded positive definite functions on S which are also continuous at the identity are equivalent.
Publication Date: 1998
Acta Mathematica Hungarica (15882632)81(1-2)pp. 109-119
Let A be a non-zero Artinian R-module. For an arbitrary ideal I of R, we show that the local homology module Hpx(A) is independent of the choice of x whenever 0:A I = 0:A(x1,..., xr). Thus, identifying these modules, we write HpI(A). In this paper we prove that there is a certain duality between HiI(A) and the local cohomology modules and provide some information about the vanishing local homology module HiI(A) which gives an improved form of the main results of [22].
Publication Date: 1998
Journal of Multivariate Analysis (0047259X)67(2)pp. 190-202
Recently attempts have been made to characterize probability distributions via truncated expectations in both univariate and multivariate cases. In this paper we will use a well known theorem of Lau and Rao (1982) to obtain some characterization results, based on the truncated expectations of a functionh, for the bivariate Gumbel distribution, a bivariate Lomax distribution, and a bivariate power distribution. The results of the paper subsume some earlier results appearing in the literature. © 1998 Academic Press.
Publication Date: 1999
Archiv der Mathematik (0003889X)73(2)pp. 104-108
In this note we prove that every infinite group G is 3-abelian (i.e. (ab)3 = a3b3 for all a, b in G) if and only if in every two infinite subsets X and Y of G there exist x ∈ X and y ∈ Y such that (xy)3 = x3y3.
Publication Date: 1999
Communications in Algebra (00927872)27(11)pp. 5633-5638
In this note we show that if G is a finitely generated soluble group, then every infinite subset of G contains two elements generating a nilpotent group of class at most k if and only if G is finite by a group in which every two generator subgroup is nilpotent of class at most k.
Publication Date: 1999
Journal of Statistical Planning and Inference (03783758)81(2)pp. 201-207
Many characterization results of the bivariate exponential distribution and the bivariate geometric distribution have been proved in the literature. Recently Nair and Nair (1988b, Ann. Inst. Statist. Math. 40 (2), 267-271) obtained a characterization result of the Gumbel bivariate exponential distribution and a bivariate geometric distribution based on truncated moments. In this note, we extend the results of to obtain a general result, characterizing these two bivariate distributions based on the truncated expectation of a function h, satisfying some mild conditions.
Publication Date: 1999
Journal of Algebra (00218693)221(2)pp. 570-578
Let n be an integer greater than 1. A group G is said to be n-permutable whenever for every n-tuple (x1,...,xn) of elements of G there exists a non-identity permutation σ of {1,...,n} such that x1···xn=xσ(1)···xσ(n). In this paper we prove that an infinite group G is n-permutable if and only if for every n infinite subsets X1,...,Xn of G there exists a non-identity permutation σ on {1,...,n} such that X1···Xn∪Xσ(1)···Xσ(n)≠∅. © 1999 Academic Press.
Publication Date: 1999
Journal of Algebra (00218693)214(2)pp. 571-624
In this paper we study the Weyl groups of reduced extended affine root systems, the root systems of extended affine Lie algebras. We start by describing the extended affine Weyl group as a semidirect product of a finite Weyl group and a Heisenberg-like normal subgroup. This provides a unique expression for the Weyl group elements (in terms of some naturally arisen transformations) which is crucial in the further study of extended affine Weyl groups. We use this to give a presentation, called a presentation by conjugation, for an important subclass of extended affine Weyl groups. Using a new notion, called the index which is an invariant of the extended affine root systems, we show that one of the important features of finite and affine root systems (related to Weyl group) holds for the class of extended affine root systems. © 1999 Academic Press.
Publication Date: 1999
Metrika (1435926X)49(2)pp. 121-126
In this paper, we characterize some multivariate distributions based on a relationship between the multivariate hazard rate, as defined by Johnson and Kotz (1975) and Marshall (1975), and the multivariate mean residual life as defined by Arnold and Zahedi (1988). The results are extensions of the results obtained earlier by Roy (1989, 1990) and Ma (1996, 1997).
Publication Date: 1999
Kyoto Journal of Mathematics (0023608X)39(4)pp. 607-618
Publication Date: 1999
Communications in Algebra (00927872)27(12)pp. 6191-6198
Publication Date: 1999
Journal of Algebra (00218693)222(1)pp. 174-189
Extended affine Weyl groups are the Weyl groups of root systems of a new class of Lie algebras called extended affine Lie algebras. In this paper we show that a (reduced) extended affine Weyl group is the homomorphic image of some indefinite Kac-Moody Weyl group where the homomorphism and its kernel are given explicitly. © 1999 Academic Press.
Publication Date: 2000
Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova (22402926)104pp. 129-134
Let α1,…, αn be nonzero integers whose greatest common divisor is d. We prove that an infinite group G is of finite exponent dividing d if and only if for every n infinite subsets X1, …, Xn of G there exist x1 ∈ X1, …, xn ∈ Xn such that x1α1…xαnn = 1. © Rendiconti del Seminario Matematico della Università di Padova, 2000, tous droits réservés.
Publication Date: 2000
Communications in Algebra (00927872)28(1)pp. 465-488
In 1985 K. Saito [Sa1] introduced the concept of an extended affine Weyl group (EAWG), the Weyl group of an extended affine root system (EARS). In [A2, Section 5], we gave a presentation called "a presentation by conjugation" for the class of EAWGs of index zero, a subclass of EAWGs. In this paper we will givo a presentation which we call a "generalized presentation by conjugation" for the class of reduced EAWGs. If the extended affine Weyl group is of index zero this presentation reduces to "a presentation by conjugation". Our main result states that when the nullity of the EARS is 2, these two presentations coincide that is, EAWGs of nullity 2 have "a presentation by conjugation". In [ST] another presentation for EAWGs of nullity 2 is given. Copyright © 2000 by Marcel Dekker, Inc.
Publication Date: 2000
Communications in Algebra (00927872)28(6)pp. 2753-2781
We first give a characterization of the core (modulo its center) of an extended affine Lie algebra and then use this characterization to show that as in the case of affine Kac-Moody Lie algebras, many of the known examples of EALAs can be constructed from standard examples by a process known as "twisting".
Publication Date: 2000
Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova (22402926)103pp. 47-49
In this note, we prove that, in every finitely generated soluble group G, G/Z2 (G) is finite if and only if in every infinite subset X of G there exist different x, y such that [x, y, y] = 1. © Rendiconti del Seminario Matematico della Università di Padova, 2000, tous droits réservés.
Publication Date: 2000
Statistics and Probability Letters (01677152)49(3)pp. 263-269
A direct approach to measure uncertainty in the residual life time distribution has been initiated by Ebrahimi (1996, Sankhya Ser. A 58, 48-57) and explored further by Ebrahimi and Pellerey (1995) and Ebrahimi and Kirmani (1996). In this paper, some new properties of the proposed measure in connection to order statistics and record values are derived. The generalized Pareto distribution has been widely used in the literature. We have also given several characterizations of this distribution in terms of the proposed measure.
Publication Date: 2000
Bulletin of the Australian Mathematical Society (00049727)62(1)pp. 141-148
Let k be a positive integer. We denote by εk(∞) the class of all groups in which every infinite subset contains two distinct elements cursive Greek chi, y such that [cursive Greek chi,k y] = 1. We say that a group G is an ε*k-group provided that whenever X,Y are infinite subsets of G, there exists cursive Greek chi ∈ X, y ∈ Y such that [cursive Greek chi,k y] = 1. Here we prove that: (1) If G is a finitely generated soluble group, then G ∈ ε3(∞) if and only if G is finite by a nilpotent group in which every two generator subgroup is nilpotent of class at most 3. (2) If G is a finitely generated metabelian group, then G ∈ εk(∞) if and only if G/Zk(G) is finite, where Zk(G) is the (k + 1)-th term of the upper central series of G. (3) If G is a finitely generated soluble εk(∞)-group, then there exists a positive integer t depending only on k such that G/Zt(G) is finite. (4) If G is an infinite ε*k-group in which every non-trivial finitely generated subgroup has a non-trivial finite quotient, then G is k-Engel. In particular, G is locally nilpotent.
Publication Date: 2000
Journal of Optimization Theory and Applications (00223239)107(1)pp. 89-122
For a general fixed-duration optimal control problem, the proximal aiming technique of nonsmooth analysis is employed in order to construct a discontinuous feedback law, whose Euler solutions are all optimal to within a prescribed tolerance, universally for all initial data in a prescribed bounded set. The technique is adapted in order to construct universal near-saddle points for two-player fixed-duration differential games of the Krasovskii-Subbotin type.
Publication Date: 2001
Bulletin of the Australian Mathematical Society (00049727)64(1)pp. 27-31
We use Ramsey's theorem to generalise a result of L. Babai and T.S. Sós on Sidon subsets and then use this to prove that for an integer n > 1 the class of groups in which every infinite subset contains a rewritable n-subset coincides with the class of groups in which every infinite subset contains n mutually disjoint non-empty subsets X1, ..., Xn such that X1 ⋯ Xn ∩ Xσ(1) ⋯ Xσ(n) ≠ 0 for some non-identity permutation σ on the set {1, ..., n}.
Publication Date: 2001
Communications in Algebra (00927872)29(4)pp. 1571-1581
Let n > 1 be an integer. A group G is said to be n-rewritable, whenever for any subset {x1, . . ., xn} of elements of G, there exist distinct permutations τ, σ of the set {1, 2, . . ., n} such that xτ(1) · · · xτ(n) = xσ(1) · · · xσ(n). In this paper we show that an infinite group G is n-rewritable if and only if for every n infinite subsets X1, . . ., Xn of G there exist distinct permutations τ, σ of the set {1, 2, . . ., n} such that Xτ(1) · · · Xτ(n) ∩ Xσ(n) · · · Xσ(n) ≠ 0.
Publication Date: 2001
Handbook of Statistics (01697161)20pp. 199-214
Publication Date: 2001
Colloquium Mathematicum (00101354)87(1)pp. 129-136
Let A be a Noetherian ring, let M be a finitely generated A-module and let φ be a system of ideals of A. We prove that, for any ideal a in φ, if, for every prime ideal p of A, there exists an integer k(p), depending on p, such that ak(p) kills the general local cohomology module Hjφ (Mp) for every integer j less than a fixed integer n, where φp := {ap : a ε φ}, then there exists an integer k such that akHjφ(M) = 0 for every j < n. © 2001, Instytut Matematyczny. All rights reserved.
Publication Date: 2001
Algebra Colloquium (02191733)8(2)pp. 153-157
Let α1,... ,αn ∈ ℕ. We prove that, in every infinite ring R, x1α1 ⋯xnαn = 0 for all x1,..., xn ∈ R if and only if, for any n infinite subsets X1,..., Xn of R, there exist x1 ∈ X1, ..., xn ∈ Xn such that x1α1 ⋯ xnαn = 0. © Inst. Math. CAS 2001.
