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1.
A. D. Korshunov 《Mathematical Notes》1971,9(3):155-160
LetG(n) be the set of all nonoriented graphs with n enumerated points without loops or multiple lines, and let vk(G) be the number of mutually nonisomorphic k-point subgraphs of G G(n). It is proved that at least |G(n)| (1–1/n) graphs G G(n) possess the following properties: a) for any k [6log2n], where c=–c log2c–(1–c)×log2(1–c) and c>1/2, we havev
k(G) > C
n
k
(1–1/n2); b) for any k [cn + 5 log2n] we havev
k(G) = C
n
k
. Hence almost all graphs G G(n) containv(G) 2n pairwise nonisomorphic subgraphs.Translated from Matematicheskie Zametki, Vol. 9, No. 3, pp. 263–273, March, 1971. 相似文献
2.
N. Christopher Phillips 《K-Theory》1989,3(5):479-504
We generalize the Atiyah-Segal completion theorem to C
*-algebras as follows. Let A be a C
*-algebra with a continuous action of the compact Lie group G. If K
*
G
(A) is finitely generated as an R(G)-module, or under other suitable restrictions, then the I(G)-adic completion K
*
G
(A) is isomorphic to RK
*([A C(EG)]G), where RK
* is representable K-theory for - C
*-algebras and EG is a classifying space for G. As a corollary, we show that if and are homotopic actions of G, and if K
*(C
*
(G,A,)) and K
*(C
*
(G,A,)) are finitely generated, then K
*(C
*(G,A,))K*(C
*
(G,A,)). We give examples to show that this isomorphism fails without the completions. However, we prove that this isomorphism does hold without the completions if the homotopy is required to be norm continuous.This work was partially supported by an NSF Graduate Fellowship and by an NSF Postdoctoral Fellowship. 相似文献
3.
Let G be a locally compact abelian group. The concern of the present note is to extend (for exponents p>2) the saturation theorem on G stated as Theorem 4 in [5]. The extension will be established for approximation processes (It)t>0 acting on the submodule CP(G), p]1,+[, of the convolutionM
1(G)-module LP(G) which consists of all functions fLP(G) admitting as their Fourier transformsF
Gf (in the sense of the theory of quasimeasures) complex Radon measures not necessarily absolutely continuous with respect to any Haar measure on the dual group . Moreover, the relationship of the complex vector spaces CP(G) to some other function spaces, in particular to the vector spaces BP(G) introduced in [5], will be investigated. 相似文献
4.
Guiyun Chen 《Southeast Asian Bulletin of Mathematics》2002,25(3):389-401
The author defined the concept order components in [2] and gave a new characterization of sporadic simple groups by their order components in [7]. Afterwards the following groups were characterized by the author: G2(q), q = 0 (mod 3)[8]; E8(q)[9]; Suzuki-Ree groups[10]; PSL2(q)[11]. Here the author will continue such kind of characterization and prove that:Theorem 1. Let G be a finite group, M = 3D4(q). If G and M has the same order components, then G M.And the following theorems follows from Theorem 1.Theorem 2. (Thompsons Conjecture) Let G be a finite group, Z(G) = 1,M = 3D4(q). If N(G) = N(M), then G M. (ref. [6])Theorem 3. (Wujie Shi) Let G be a finite group, M = 3D4(q). If|G| = |M|, e(G) = e(M), then G M. (ref. [15])All notations are the same as in [2]. According to the classification theorem of finite simple groups, [12] and [13], we can list the order components of finite simple groups with nonconnected prime graphs in Tables 1-4 (ref. [5]).American Mathematics Society Classification 20D05 20D60The author is indebted to Fred and Barbara Kort Sino-Israel Postdoctoral Programme for supporting my post-doctoral position (1999.10-2000.10) at Bar-Ilan University, also to Emmy Noether Mathematics Institute and NSFC for partially financial support. 相似文献
5.
V. P. Burichenko 《Algebra and Logic》2008,47(6):384-394
Let G = SL(n, q), where q is odd, V be a natural module over G, and L = S2(V) be its symmetric square. We construct a 2-cohomology group H2(G, L). The group is one-dimensional over F
q if n = 2 and q ≠ 3, and also if (n, q) = (4, 3). In all other cases H2(G, L) = 0. Previously, such groups H2(G, L) were known for the cases where n = 2 or q = p is prime. We state that H2(G, L) are trivial for n ⩾ 3 and q = pm, m ⩾ 2. In proofs, use is made of rather elementary (noncohomological) methods.
__________
Translated from Algebra i Logika, Vol. 47, No. 6, pp. 687–704, November–December, 2008. 相似文献
6.
Theodor Bröcker 《manuscripta mathematica》1971,5(1):91-102
Let G be a discrete group,o(G) the orbit category of G and M:o(G)a a covariant (contravariant) functor to abelian groups. We define a singular equivariant homology theory H*(X;M) (resp. H*(X;M)) which satisfies a dimension axiom, in the sense of Bredon (Lecture notes 34). It turns out, that all fundamental properties of these theories directly follow by naturality from the analogous theorems in the classical non equivariant case. 相似文献
7.
Yong-hui Wu 《Mathematical Methods in the Applied Sciences》1997,20(11):933-943
In this paper, we consider the Cauchy problem: (ECP) ut−Δu+p(x)u=u(x,t)∫u2(y,t)/∣x−y∣dy; x∈ℝ3, t>0, u(x, 0)=u0(x)⩾0 x∈ℝ3, (0.2) The stationary problem for (ECP) is the famous Choquard–Pekar problem, and it has a unique positive solution ū(x) as long as p(x) is radial, continuous in ℝ3, p(x)⩾ā>0, and lim∣x∣→∞p(x)=p¯>0. In this paper, we prove that if the initial data 0⩽u0(x)⩽(≢)ū(x), then the corresponding solution u(x, t) exists globally and it tends to the zero steady-state solution as t→∞, if u0(x)⩾(≢)ū(x), then the solution u(x,t) blows up in finite time. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
8.
V. G. Bardakov 《Acta Appl Math》2005,85(1-3):41-48
In this paper we prove that the braid group Bn(S2) of 2-sphere, mapping class group M(0,n) of the n-punctured 2-sphere and the braid group B3(P2) of the projective plane are linear.
Partially supported by the Russian Foundation for Basic Research (grant number 02-01-01118).Mathematics Subject Classifications (2000) 20F28, 20F36, 20G35. 相似文献
9.
10.
We compute the equivariant K-theory K
G
*
(G)for a compact connected Lie group Gsuch that 1
(G)is torsion free (where Gacts on itself by conjugation). We prove that K
G
*
(G)is isomorphic to the algebra of Grothendieck differentials on the representation ring. We also study a special example of a compact connected Lie group Gwith 1
(G)torsion, namely PSU(3), and compute the corresponding equivariant K-theory. 相似文献
11.
Edward A. Bertram 《Israel Journal of Mathematics》1991,75(2-3):243-255
We prove first that if G is a finite solvable group of derived length d ≥ 2, then k(G) > |G|1/(2d−1), where k(G) is the number of conjugacy classes in G. Next, a growth assumption on the sequence [G(i): G(i+1)]
1
d−1
, where G(i) is theith derived group, leads to a |G|1/(2d−1) lower bound for k(G), from which we derive a |G|c/log
2log2|G| lower bound, independent of d(G). Finally, “almost logarithmic” lower bounds are found for solvable groups with a nilpotent
maximal subgroup, and for all Frobenius groups, solvable or not. 相似文献
12.
In the present paper, for any finite group G of Lie type (except for 2
F
4(q)), the order a(G) of its large Abelian subgroup is either found or estimated from above and from below (the latter is done for the groups F
4
(q), E
6
(q), E
7
(q), E
8
(q), and 2
E
6(q
2)). In the groups for which the number a(G) has been found exactly, any large Abelian subgroup coincides with a large unipotent or a large semisimple Abelian subgroup. For the groups F
4
(q), E
6
(q), E
7
(q), E
8
(q), and 2
E
6(q
2)), it is shown that if an Abelian subgroup contains a noncentral semisimple element, then its order is less than the order of an Abelian unipotent group. Hence in these groups the large Abelian subgroups are unipotent, and in order to find the value of a(G) for them, it is necessary to find the orders of the large unipotent Abelian subgroups. Thus it is proved that in a finite group of Lie type (except for 2
F
4(q))) any large Abelian subgroup is either a large unipotent or a large semisimple Abelian subgroup. 相似文献
13.
LetG=H
p
(H
k
n
) be the (2n+1)-dimensional Heisenberg group over local fieldK. In this paper we prove some theorems about convolution operators onH
p
(G) and vector-valued Hardy spaces. As an example, the distribution
for some φ∈S(G), ξ φ=0 is a ramified 0-type kernel. These results can be applied to characterizeH
p
(G) spaces by square functions. 相似文献
14.
Jiang 《Semigroup Forum》2008,67(1):50-62
Abstract.
We introduce a class of strongly E
*
-unitary inverse semigroups S
i
(G,P) (i=1,2) determined by a group G and a submonoid P of G and give an embedding theorem for S
i
(G,P) . Moreover we characterize 0 -bisimple strongly E
*
-unitary inverse monoids and 0 -bisimple strongly F
*
-inverse monoids by using S
i
(G,P) . 相似文献
15.
IfK is the underlying point-set of a simplicial complex of dimension at mostd whose vertices are lattice points, and ifG(K) is the number of lattice points inK, then the lattice point enumeratorG(K,t)=1+
n1
G(nK)t
n
takes the formC(K, t)/(1–t)
d+1, for some polynomialC(K, t). Here,C(K, t) is expressed as a sum of local terms, one for each face ofK. WhenK is a polytope or its boundary, there result inequalities between the numbersG
r
(K), whereG(n K)=
r=0
d
n
r
G
r
(K). 相似文献
16.
For a closed normal subgroupN of a locally compact groupG view a closed subset
of Prim*
L
1
(G/N) as a subsetE of Prim*
L
1
(G) in the canonical way and writeN
for Prim*
L
1
(G/N) as a subset of Prim*
L
1
(G); then the injection theorem says: IfE is spectral (i.e. of synthesis), then
is so; and if
andN
are spectral, thenE is too. In case of a group of polynomial growth with symmetricL
1-algebra, where smallest idealsj (E) with given hulls exist, it is known thatN
is always spectral. For a closed,G-invariant subsetF of Prim*
L
1
(N) define a closed subsetE of Prim*
L
1
(G) by
. Denote by e (I') the ideal generated byC
00
(G)*I', where theG-invariant idealI' ofL
1
(N) is viewed as a subset of measures onG, then the projection theorem states: IfE is spectral, thenF is so, and ifF is spectral withe (j (F))=j (E) thenE is spectral. All assumptions are fulfilled for instance, ifG andN are of polynomial growth with symmetricL
1-algebra and eitherSIN-groups or solvable. 相似文献
17.
Houshang Behravesh 《Southeast Asian Bulletin of Mathematics》2002,25(4):577-580
By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. For a given finite group G, let c(G) denote the minimal degree of a faithful representation of G by complex quasi-permutation matrices and let r(G) denote the minimal degree of a faithful rational valued character of G. Also let G denote one of the symbols Al, Bl, Cl, Dl, E6, E7, E8, G2, F4, 2B2, 2E4, 2G2, and 3D4. Let G(q) denote simple group of type G over GF(q). Let c(q) = c(G(q)) and r(q) = r(G(q)). Then we will show that lim Limq
= 1. 相似文献
18.
The oriented chromatic number χo(G →) of an oriented graph G → = (V, A) is the minimum number of vertices in an oriented graph H → for which there exists a homomorphism of G → to H →. The oriented chromatic number χo(G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the orientations of G. This paper discusses the relations between the oriented chromatic number and the acyclic chromatic number and some other parameters of a graph. We shall give a lower bound for χo(G) in terms of χa(G). An upper bound for χo(G) in terms of χa(G) was given by Raspaud and Sopena. We also give an upper bound for χo(G) in terms of the maximum degree of G. We shall show that this upper bound is not far from being optimal. © 1997 John Wiley & Sons, Inc. 相似文献
19.
Let G be a locally compact group with a fixed right Haar measure andX a separable Banach space. LetL
p
(G, X) be the space of X-valued measurable functions whose norm-functions are in the usualL
p
. A left multiplier ofL
p
(G, X) is a bounded linear operator onB
p
(G, X) which commutes with all left translations. We use the characterization of isometries ofL
p
(G, X) onto itself to characterize the isometric, invertible, left multipliers ofL
p
(G, X) for 1 ≤p ∞,p ≠ 2, under the assumption thatX is not thel
p
-direct sum of two non-zero subspaces. In fact we prove that ifT is an isometric left multiplier ofL
p
(G, X) onto itself then there existsa y ∃ G and an isometryU ofX onto itself such thatTf(x) = U
(R
y
f)(x). As an application, we determine the isometric left multipliers of L1 ∩L
p
(G, X) and L1 ∩C
0
(G, X) whereG is non-compact andX is not the lp-direct sum of two non-zero subspaces. If G is a locally compact abelian group andH is a separable Hubert space, we define
where г is the dual group of G. We characterize the isometric, invertible, left multipliers ofA
p
(G, H), provided G is non-compact. Finally, we use the characterization of isometries ofC(G, X) for G compact to determine the isometric left multipliers ofC(G, X) providedX
*
is strictly convex. 相似文献
20.
Andrija Raguž 《PAMM》2016,16(1):661-662
We solve a minimization problem associated to a generalization of the Müller functional studied in the paper G. Alberti, S. Müller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54 , 761–825 (2001), whereby the lower order term ∫10a(s)v2(s)ds (involving a primitive of the mass density function, v = v(s) , and the weight function a = a(s) ) is replaced by ∫10a(s, v(s), v′(s))v2(s)ds (where a belongs to a suitable Carathéodory class). We calculate the rescaled asymptotic energy of the functional as small parameter epsilon tends to zero. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献