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2.
William D. BANKS Florian LUCA 《数学学报(英文版)》2007,23(10):1915-1918
In this note, we show that the number of composite integers n ≤ x such that φ(n)|n - 1 is at most O(x^1/2(loglog x)^1/2), thus improving earlier results by Pomerance and by Shan. 相似文献
3.
V. A. Belonogov 《Algebra and Logic》2005,44(6):357-369
Let P(n) be the set of all partitions of a natural number n. In the representation theory of symmetric groups, for every partition
α ∈ P(n), the partition h(α) ∈ P(n) is defined so as to produce a certain set of zeros in the character table for Sn. Previously, the analog f(α) of h(α) was obtained pointing out an extra set of zeros in the table mentioned. Namely, h(α)
is greatest (under the lexicographic ordering ≤) of the partitions β of n such that χα(gβ) ≠ 0, and f(α) is greatest of the partitions γ of n that are opposite in sign to h(α) and are such that χα(gγ) ≠ 0, where χα is an irreducible character of Sn, indexed by α, and gβ is an element in the conjugacy class of Sn, indexed by β. For α ∈ P(n), under some natural restrictions, here, we construct new partitions h′(α) and f′(α) of n possessing
the following properties. (A) Let α ∈ P(n) and n ⩾ 3. Then h′(α) is identical is sign to h(α), χα(gh′(α)) ≠ 0, but χα(gγ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of h(α), and h′(α) < γ < h(α). (B) Let α ∈ P(n), α ≠ α′,
and n ⩾ 4. Then f′(α) is identical in sign to f(α), χα(gf′(α)) ≠ 0, but χα(gγ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of f(α), and f′(α) < γ < f(α). The results obtained are
then applied to study pairs of semiproportional irreducible characters in An.
Supported by RFBR grant No. 04-01-00463.
__________
Translated from Algebra i Logika, Vol. 44, No. 6, pp. 643–663, November–December, 2005. 相似文献
4.
Florentina Chirte§ 《Central European Journal of Mathematics》2005,3(1):105-124
The aim of this paper is to define the localization LM
n
-algebra of an LM
n
—algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM
n
-algebra of fractions (defined in [3]) and the LM
n
-algebra of fractions relative to an Λ—closed system (defined in Section 2) are LM
n
-algebras of localization. 相似文献
5.
R. M. Mnatsakanov N. Misra Sh. Li E. J. Harner 《Mathematical Methods of Statistics》2008,17(3):261-277
For estimating the entropy of an absolutely continuous multivariate distribution, we propose nonparametric estimators based
on the Euclidean distances between the n sample points and their k
n
-nearest neighbors, where {k
n
: n = 1, 2, …} is a sequence of positive integers varying with n. The proposed estimators are shown to be asymptotically unbiased and consistent.
相似文献
6.
V. A. Belonogov 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):24-35
All finite Young diagrams not containing hooks of length 4 are found. Self-associated diagrams possessing this property are subdivided into three series. Sets of all hook lengths are determined for diagrams contained in each series. The research conducted has proven necessary for the study of certain pairs of irreducible characters of symmetric and alternating groups. 相似文献
7.
Tsachik Gelander 《Israel Journal of Mathematics》2008,167(1):15-26
We study some properties of the varieties of deformations of free groups in compact Lie groups. In particular, we prove a
conjecture of Margulis and Soifer about the density of non-virtually free points in such variety, and a conjecture of Goldman
on the ergodicity of the action of Aut(F
n
) on such variety when n ≥ 3.
The author was partially supported by NSF grant DMS-0404557, BSF grant 2004010, and the ‘Finite Structures’ Marie Curie Host
Fellowship, carried out at the Alfréd Rényi Institute of Mathematics in Budapest. 相似文献
8.
Let S be a pomonoid and I a proper right ideal of S. In a previous paper, using the amalgamated coproduct A(I) of two copies of
S
S over I, we were able to solve one of the problems posed in S. Bulman-Fleming et al. (Commun. Algebra 34:1291–1317, 2006). In the present paper, we investigate further flatness properties of A(I). We also solve another problem stated in the paper cited above. Namely, we determine the condition under which Rees factor
S-posets have property (P
w
).
Research supported by nwnu-kjcxgc-03-18. 相似文献
9.
Lower estimates for the mazimal weight multiplicities in irreducible representations of algebraic groups of type D
n
in characteristic 2 are found. lf n ≥ 8, then either such a multiplicity is at least n—4— [n]4, where [n]4 is the residue of n modulo 4, or all of its weight multiplicities arc equal to 1. For groups of types B
n
and D
n
in odd characteristic and of type C
n
, in characteristics greater than 7, similar results were obtained earlier. Bibliography: 11 titles. 相似文献
10.
11.
Guohua Wu 《Archive for Mathematical Logic》2003,42(2):201-204
We give a characterization of strongly compact cardinals in terms of Q
κ
λ. We also prove that weakly normal Q-measures on Q
κ
λ are ⊂κ-normal.
Received: 29 September 2000 / Revised version: March 2002 Published online: 5 November 2002
This project is supported by the New Zealand Marsden Fund. The author wishes to thank the referee for numerous comments and
suggestions which have been incorporated into this version of the paper. 相似文献
12.
R. A. Lasuriya 《Ukrainian Mathematical Journal》2005,57(4):600-609
We establish estimates for the rate of convergence of a group of deviations on a sphere in the space L(S
m
), m ≥ 3.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 496–504, April, 2005. 相似文献
13.
Summary In [6] we introduced and investigated the notions of fI -sets and fI -continuous functions in ideal topological spaces. In this paper, we investigate their further important properties. 相似文献
14.
Thomas Pietraho 《Journal of Algebraic Combinatorics》2008,27(2):247-262
We consider two families of equivalence classes in the Weyl groups of type B
n
which are suggested by the study of left cells in unequal parameter Iwahori-Hecke algebras. Both families are indexed by
a non-negative integer r. It has been shown that the first family coincides with left cells corresponding to the equal parameter Iwahori-Hecke algebra
when r=0; the equivalence classes in the second family agree with left cells corresponding to a special class of choices of unequal
parameters when r is sufficiently large. Our main result shows that the two families of equivalence classes coincide, suggesting the structure
of left cells for remaining choices of the Iwahori-Hecke algebra parameters.
相似文献
15.
Jinjin Li 《Czechoslovak Mathematical Journal》2005,55(4):941-945
In this note we study the relation between k
R
-spaces and k-spaces and prove that a k
R
-space with a σ-hereditarily closure-preserving k-network consisting of compact subsets is a k-space, and that a k
R
-space with a point-countable k-network consisting of compact subsets need not be a k-space.
This work was supported by the NSF of China (10271056). 相似文献
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17.
Thomas Vougiouklis 《数学学报(英文版)》2008,24(7):1067-1078
The hyperoperations, called theta-operations (δ), are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures. 相似文献
18.
Tunay Bilgin 《Czechoslovak Mathematical Journal》2005,55(3):691-697
The definition of lacunary strongly convergence is extended to the definition of lacunary strong (A
σ
, p)-convergence with respect to invariant mean when A is an infinite matrix and p = (p
i
) is a strictly positive sequence. We study some properties and inclusion relations. 相似文献
19.
Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties)
polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with
the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes
for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken
into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional
case provides interesting classes of groups.
Received: 13 December 2001 / Revised version: 24 June 2002
The second author was supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107
Mathematics Subject Classification (2000): 14L27, 14M25, 19C09, 52B20 相似文献
20.
Let ƒ be a transcendental meromorphic function, a a nonzero finite complex number, and n ⩾ 2 a positive integer. Then ƒ + a(ƒ′)
n
assumes every complex value infinitely often. This answers a question of Ye for n = 2. A related normality criterion is also given.
This work was supported by the National Natural Science Foundation of China (Grant No. 10771076), the Natural Science Foundation
of Guangdong Province, China (Grant No. 07006700) and by the German-Israeli Foundation for Scientific Research and Development
(Grant No. G-809-234.6/2003) 相似文献