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1.
We define 〈q, r〉-linear arithmetical functions attached to the 〈q, r〉-number systems and give a necessary and sufficient condition for their generating power series to be algebraically independent
over
\Bbb C(z){\Bbb C}(z)
. We also deduce algebraic independence of the functions values at a nonzero algebraic number in the circle of convergence. 相似文献
2.
V. D. Mazurov 《Algebra and Logic》2006,45(2):117-123
Let G be a group. A subset X of G is called an A-subset if X consists of elements of order 3, X is invariant in G, and every
two non-commuting members of X generate a subgroup isomorphic to A4 or to A5. Let X be the A-subset of G. Define a non-oriented graph Γ(X) with vertex set X in which two vertices are adjacent iff they
generate a subgroup isomorphic to A4. Theorem 1 states the following. Let X be a non-empty A-subset of G. (1) Suppose that C is a connected component of Γ(X)
and H = 〈C〉. If H ∩ X does not contain a pair of elements generating a subgroup isomorphic to A5 then H contains a normal elementary Abelian 2-subgroup of index 3 and a subgroup of order 3 which coincides with its centralizer
in H. In the opposite case, H is isomorphic to the alternating group A(I) for some (possibly infinite) set I, |I| ≥ 5. (2)
The subgroup 〈XG〉 is a direct product of subgroups 〈C
α〉-generated by some connected components C
α of Γ(X). Theorem 2 asserts the following. Let G be a group and X⊆G be a non-empty G-invariant set of elements of order 5 such that every two non-commuting members of X generate a subgroup
isomorphic to A5. Then 〈XG〉 is a direct product of groups each of which either is isomorphic to A5 or is cyclic of order 5.
Supported by RFBR grant No. 05-01-00797; FP “Universities of Russia,” grant No. UR.04.01.028; RF Ministry of Education Developmental
Program for Scientific Potential of the Higher School of Learning, project No. 511; Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-2069.2003.1.
__________
Translated from Algebra i Logika, Vol. 45, No. 2, pp. 203–214, March–April, 2006. 相似文献
3.
We obtain a nonsimplicity criterion of an infinite group containing an infinite class of Frobenius groups L
g
= 〈a, g
−1
ag〉 with complement SL
2(3).
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 6, pp. 765–777, June, 2006. 相似文献
4.
We define 〈q, r〉-linear arithmetical functions attached to the 〈q, r〉-number systems and give a necessary and sufficient condition for their generating power series to be algebraically independent
over
. We also deduce algebraic independence of the functions values at a nonzero algebraic number in the circle of convergence. 相似文献
5.
S. V. Lyudkovskii 《Theoretical and Mathematical Physics》1999,119(3):698-711
Nondegenerate σ-additive measures with ranges in ℝ and ℚq (q≠p are prime numbers) that are quasi-invariant and pseudodifferentiable with respect to dense subgroups G′ are constructed
on diffeomorphism and homeomorphism groups G for separable non-Archimedean Banach manifolds M over a local fieldK,K ⊃ ℚq, where ℚq is the field of p-adic numbers. These measures and the associated irreducible representations are used in the non-Archimedean
gravitation theory.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 3, pp. 381–396, June, 1999. 相似文献
6.
7.
Branko Dragovich Zoran Rakić 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(4):322-340
Feynman’s path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes K(x″, t″; x′, t′) for two-dimensional systems with quadratic Lagrangians are evaluated analytically and obtained expressions are generalized
to any finite-dimensional spaces. These general formulas are presented in the form which is invariant under interchange of
the number fields ℝ ↔ ℚ
p
and ℚ ↔ ℚ
p
, p ≠ p′. According to this invariance we have that adelic path integral is a fundamental object in mathematical physics of quantum
phenomena. 相似文献
8.
Barak Weiss 《Israel Journal of Mathematics》1998,106(1):189-207
LetH be an ℝ-subgroup of a ℚ-algebraic groupG. We study the connection between the dynamics of the subgroup action ofH onG/G
ℤ and the representation-theoretic properties ofH being observable and epimorphic inG. We show that ifH is a ℚ-subgroup thenH is observable inG if and only if a certainH orbit is closed inG/G
ℤ; that ifH is epimorphic inG then the action ofH onG/G
ℤ is minimal, and that the converse holds whenH is a ℚ-subgroup ofG; and that ifH is a ℚ-subgroup ofG then the closure of the orbit underH of the identity coset image inG/G
ℤ is the orbit of the same point under the observable envelope ofH inG. Thus in subgroup actions on homogeneous spaces, closures of ‘rational orbits’ (orbits in which everything which can be defined
over ℚ, is defined over ℚ) are always submanifolds. 相似文献
9.
S. B. Damelin 《Monatshefte für Mathematik》2003,4(1):111-131
For a real interval I of positive length, we prove a necessary and sufficient condition which ensures that the continuous L
p
(0 < p ⩽ ∞) norm of a weighted polynomial, P
n
w
n
, deg P
n
⩽ n, n ⩾ 1 is in an nth root sense, controlled by its corresponding discrete H?lder norm on a very general class of discrete subsets of I. As a by product of our main result, we establish inequalities and theorems dealing with zero distribution, zero location and sup and L
p
infinite–finite range inequalities. 相似文献
10.
Emad-Eldin A. A. Aly Nadjib Bouzar 《Annals of the Institute of Statistical Mathematics》2003,55(3):523-535
A continuous composition semigroup of probability generating functionsF≔(F
t
,t≥0) and the corresponding multiplication ⊙
F
of van Harnet al. (1982,Z. Wahrsch. Verw. Gebiete,61, 97–118) are used to introduce the concept of [F; α]-unimodality which generalizes the discrete α-unimodality due to Abouammoh (1987,Statist. Neerlandica,41, 239–244) and Alamatsaz (1993,Statist. Neerlandica,47, 245–252). We offer various characterizations and other properties of [F;α]-unimodality. Notably, several convolution results are presented. Moreover, we explore the relationship between [F;α]-unimodality and the concepts of discrete self-decomposability and stability. Finally, lower bounds for variances of [F;α]-monotone and [F;α]-unimodal random variables are derived and some examples are also mentioned.
Research supported by Grant SS024 of the Research Center of Kuwait University. 相似文献
11.
We show that two naturally occurring matroids representable over ℚ are equal: thecyclotomic matroid μn represented by then
th roots of unity 1, ζ, ζ2, …, ζn-1 inside the cyclotomic extension ℚ(ζ), and a direct sum of copies of a certain simplicial matroid, considered originally by
Bolker in the context of transportation polytopes. A result of Adin leads to an upper bound for the number of ℚ-bases for
ℚ(ζ) among then
th roots of unity, which is tight if and only ifn has at most two odd prime factors. In addition, we study the Tutte polynomial of μn in the case thatn has two prime factors.
First author supported by NSF Postdoctoral Fellowship. Second author supported by NSF grant DMS-0245379. 相似文献
12.
Let C(X, ℤ), C(X, ℂ) and C(X) denote the ℓ-groups of integer-valued, rational-valued and real-valued continuous functions on a topological space X, respectively. Characterizations are given for the extensions C(X, ℤ) ⩽ C(X, ℚ) ⩽ C(X) to be rigid, major, and dense. 相似文献
13.
Research on finite solvable groups with C-closed invariant subgroups has given rise to groups structured as follows. Let p,
q1, q2, ..., qm be distinct primes, ni be the exponent of p modulo qi, and n be the exponent of p modulo
. Then G = Pλ〈x〉, where P is a group and
; Zi; here, Zi and P/Z(P) are elementary Abelian groups of respective orders
and pn, |x| = r, the element x acts irreducibly on P/Z(P) and on each of the subgroups Zi, and
. We state necessary and sufficient conditions for such groups to exist.
__________
Translated from Algebra i Logika, Vol. 45, No. 4, pp. 379–389, July–August, 2006. 相似文献
14.
15.
We give a shorter proof of Kanter’s (J. Multivariate Anal. 6, 222–236, 1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide
sharp upper bounds for the sum of modified Bessel functions I0(x) + I1(x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent
random variables due to Čekanavičius & Roos (Lith. Math. J. 46, 54–91, 2006); Roos (Bernoulli, 11, 533–557, 2005), Barbour & Xia (ESAIM Probab. Stat. 3, 131–150, 1999), and Le Cam (Asymptotic Methods in Statistical Decision Theory. Springer, Berlin Heidelberg New York, 1986).
相似文献
16.
S. B. Damelin 《Monatshefte für Mathematik》2003,138(2):111-131
For a real interval I of positive length, we prove a necessary and sufficient condition which ensures that the continuous L
p
(0 < p ⩽ ∞) norm of a weighted polynomial, P
n
w
n
, deg P
n
⩽ n, n ⩾ 1 is in an nth root sense, controlled by its corresponding discrete H?lder norm on a very general class of discrete subsets of I. As a by product of our main result, we establish inequalities and theorems dealing with zero distribution, zero location and sup and L
p
infinite–finite range inequalities.
Received April 4, 2001; in final form June 21, 2002 相似文献
17.
Tullio G. Ceccherini-Silberstein 《manuscripta mathematica》2002,107(4):451-461
Let denote the free group of rank 2g. An automorphism φ? Aut(F
2
g
) is generating if N
a
φ (N
b
) = F
2
g
, where N
a
is the normal closure of and N
b
is defined analogously. We present a characterization of generating automorphisms in Aut(F
2) and observe that there exists a unique (up to equivalence) epimorphism F
2→Z×Z: this is a particular case of the Grigorchuk–Kurchanov conjecture.
This leads to further investigations for splitting homomorphisms for the pairs (F
2
g
, F
g) and (G
g, F
g) where G
g denotes the fundamental group of a closed orientable surface of genus g and a reformulation of the Poincaré and Grigorchuk–Kurchanov conjectures is derived.
Received: 1 October 2001 相似文献
18.
Jack Sonn 《Israel Journal of Mathematics》2000,119(1):1-8
Letp be a prime and let ℚ(p) denote the maximalp-extension of ℚ. We prove that for every primep, the free pro-p group on countably many generators is realizable as a regular extension of ℚ(p)(t). As a consequence, if ℚ
nil
denotes the maximal nilpotent extension of ℚ, then every finite nilpotent group is realizable as a regular extension of ℚ
nil
(t). 相似文献
19.
Campanino Massimo Ioffe Dmitry Velenik Y van 《Probability Theory and Related Fields》2003,125(3):305-349
We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈Σ0Σ
x
〉β in the general context of finite range Ising type models on ℤ
d
. The proof relies in an essential way on the a-priori knowledge of the strict exponential decay of the two-point function
and, by the sharp characterization of phase transition due to Aizenman, Barsky and Fernández, goes through in the whole of
the high temperature region β<β
c
. As a byproduct we obtain that for every β<β
c
, the inverse correlation length ξβ is an analytic and strictly convex function of direction.
Received: 10 January 2002 / Revised version: 19 June 2002 / Published online: 14 November 2002
Partly supported by Italian G. N. A. F. A, EC grant SC1-CT91-0695 and the University of Bologna. Funds for selected research
topics.
Partly supported by the ISRAEL SCIENCE FOUNDATION founded by The Israel Academy of Science and Humanities.
Partly supported by the Swiss National Science Foundation grant #8220-056599.
Mathematics Subject Classification (2000): 60F15, 60K15, 60K35, 82B20, 37C30
Key words or phrases: Ising model – Ornstein-Zernike decay of correlations – Ruelle operator – Renormalization – Local limit theorems 相似文献
20.
Abdelmalek Azizi 《Rendiconti del Circolo Matematico di Palermo》1999,48(1):71-92
Let ℕ,i=√−1,k=ℚ(√d,i) andC
2 the 2-part of the class group ofk. Our goal is to determine alld such thatC
2⋍ℤ/2ℤ×ℤ/2ℤ.
Soientd∈ℕ,i=√−1,k=ℚ(√d,i), etC
2 la 2-partie du groupe de classes dek. On s'intéresse à déterminer tous lesd tel queC
2⋍ℤ/2ℤ×ℤ/2ℤ.
相似文献