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1.
We introduce a new class of graphs which we call P
3-dominated graphs. This class properly contains all quasi-claw-free graphs, and hence all claw-free graphs. Let G be a 2-connected P
3-dominated graph. We prove that G is hamiltonian if α(G
2) ≤ κ(G), with two exceptions: K
2,3 and K
1,1,3. We also prove that G is hamiltonian, if G is 3-connected and |V(G)| ≤ 5δ(G) − 5. These results extend known results on (quasi-)claw-free graphs.
This paper was completed when both authors visited the Center for Combinatorics, Nankai University, Tianjin. They gratefully
acknowledge the hospitality and support of the Center for Combinatorics and Nankai University. The work of E.Vumar is sponsored
by SRF for ROCS, REM. 相似文献
2.
3.
Let G = ℤ
p
, p an odd prime, act freely on a finite-dimensional CW-complex X with mod p cohomology isomorphic to that of a lens space L
2m−1(p; q
1, …, q
m
). In this paper, we determine the mod p cohomology ring of the orbit space X/G, when p
2 ∤ m. 相似文献
4.
In modern number theory there are famous theorems on the modularity of Dirichlet series attached to geometric or arithmetic
objects. There is Hecke’s converse theorem, Wiles proof of the Taniyama-Shimura conjecture, and Fermat’s Last Theorem to name
a few. In this article in the spirit of the Langlands philosophy we raise the question on the modularity of the GL2-twisted spinor L-function Z
G
⊗
h
(s) related to automorphic forms G,h on the symplectic group GSp2 and GL2. This leads to several promising results and finally culminates into a precise very general conjecture. This gives new insights
into the Miyawaki conjecture on spinor L-functions of modular forms. We indicate how this topic is related to Ramakrishnan’s
work on the modularity of the Rankin-Selberg L-series. 相似文献
5.
Olivier Brunat 《manuscripta mathematica》2009,129(4):483-497
This note is concerned with the unipotent characters of the Ree groups of type G
2. We determine the roots of unity associated by Lusztig and Digne-Michel to each unipotent character for and prove that the Fourier matrix of defined by Geck and Malle satisfies a conjecture of Digne-Michel. Our main tool is the Shintani descent of Ree groups of
type G
2. 相似文献
6.
We construct examples of exponentially asymptotically cylindrical (EAC) Riemannian 7-manifolds with holonomy group equal to
G
2. To our knowledge, these are the first such examples. We also obtain EAC coassociative calibrated submanifolds. Finally,
we apply our results to show that one of the compact G
2-manifolds constructed by Joyce by desingularisation of a flat orbifold T
7/Γ can be deformed to give one of the compact G
2-manifolds obtainable as a generalized connected sum of two EAC SU(3)-manifolds via the method of Kovalev (J Reine Angew Math 565:125–160, 2003). 相似文献
7.
Iwasawa theory of quadratic twists of <Emphasis Type="Italic">X</Emphasis><Subscript>0</Subscript>(49)
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The field \(K = \mathbb{Q}\left( {\sqrt { - 7} } \right)\) is the only imaginary quadratic field with class number 1, in which the prime 2 splits, and we fix one of the primes p of K lying above 2. The modular elliptic curve X 0(49) has complex multiplication by the maximal order O of K, and we let E be the twist of X 0(49) by the quadratic extension \(KK(\sqrt M )/K\), where M is any square free element of O with M ≡ 1 mod 4 and (M,7) = 1. In the present note, we use surprisingly simple algebraic arguments to prove a sharp estimate for the rank of the Mordell-Weil group modulo torsion of E over the field F ∞ = K(E p∞), where E p∞ denotes the group of p∞-division points on E. Moreover, writing B for the twist of X 0(49) by \(K(\sqrt[4]{{ - 7}})/K\), our Iwasawa-theoretic arguments also show that the weak form of the conjecture of Birch and Swinnerton-Dyer implies the non-vanishing at s = 1 of the complex L-series of B over every finite layer of the unique Z2-extension of K unramified outside p. We hope to give a proof of this last non-vanishing assertion in a subsequent paper. 相似文献
8.
We show that a one-to-one bounded linear operator T from a separable Banach space E to a Banach space X is a G
δ-embedding if and only if every T-null tree in S
E
has a branch which is a boundedly complete basic sequence. We then consider the notions of regulators and skipped blocking
decompositions of Banach spaces and show, in a fairly general set up, that the existence of a regulator is equivalent to that
of special skipped blocking decomposition. As applications, the following results are obtained.
(a) A separable Banach space E has separable dual if and only if every w*-null tree in S
E
* has a branch which is a boundedly complete basic sequence.
(b) A Banach space E with separable dual has the point of continuity property if and only if every w-null tree in S
E
has a branch which is a boundedly complete basic sequence.
We also give examples to show that the tree hypothesis in both the cases above cannot be replaced in general with the assumption
that every normalized w*-null (w-null in (b)) sequence has a subsequence which is a boundedly complete basic sequence.
The research of S. Dutta was supported in part by the Institute for Advanced Studies in Mathematics at Ben-Gurion University
of the Negev.
The research of V. P. Fonf was supported in part by Israel Science Foundation, Grant No. 139/03. 相似文献
9.
Flavia Bonomo Guillermo Durán Frederic Maffray Javier Marenco Mario Valencia-Pabon 《Graphs and Combinatorics》2009,25(2):153-167
A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the
colors not assigned to it. The b-chromatic number of a graph G, denoted by χ
b
(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every . We define a graph G to be b-monotonic if χ
b
(H
1) ≥ χ
b
(H
2) for every induced subgraph H
1 of G, and every induced subgraph H
2 of H
1. In this work, we prove that P
4-sparse graphs (and, in particular, cographs) are b-continuous and b-monotonic. Besides, we describe a dynamic programming
algorithm to compute the b-chromatic number in polynomial time within these graph classes.
Flavia Bonomo: Partially supported by ANPCyT PICT-2007-00533 and PICT-2007-00518, and UBACyT Grants X069 and X606 (Argentina).
Guillermo Durán: Partially supported by FONDECyT Grant 1080286 and Millennium Science Institute “Complex Engineering Systems”
(Chile), and ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina).
Javier Marenco: Partially supported by ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina). 相似文献
10.
11.
LetG be an algebraic group over a fieldk. We callg εG(k)
real ifg is conjugate tog
−1 inG(k). In this paper we study reality for groups of typeG
2 over fields of characteristic different from 2. LetG be such a group overk. We discuss reality for both semisimple and unipotent elements. We show that a semisimple element inG(k) is real if and only if it is a product of two involutions inG(k). Every unipotent element inG(k) is a product of two involutions inG(k). We discuss reality forG
2 over special fields and construct examples to show that reality fails for semisimple elements inG
2 over ℚ and ℚp. We show that semisimple elements are real forG
2 overk withcd(k) ≤ 1. We conclude with examples of nonreal elements inG
2 overk finite, with characteristick not 2 or 3, which are not semisimple or unipotent. 相似文献
12.
N. S. Semenov 《Journal of Mathematical Sciences》2005,130(3):4768-4773
The paper is devoted to the problem concerning the Hurwitz generation of the group Gsc(E6, q). All possibilities for Hurwitz generators, except for just one, are excluded. Bibliography: 25 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 228–237. 相似文献
13.
E. I. Bunina 《Journal of Mathematical Sciences》2008,155(6):795-814
In the paper, we prove that every automorphism of any adjoint Chevalley group of type B
2 or G
2 is standard, i.e., it is a composition of an “inner” automorphism, a ring automorphism, and a central automorphism.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 4, pp. 3–29, 2007. 相似文献
14.
László Verhóczki 《Monatshefte für Mathematik》2004,141(4):323-335
In the present paper we discuss in detail the cohomogeneity one isometric actions of the Lie groups SU(3) × SU(3) and SU(3) on the exceptional compact symmetric spaces G2 and G2/SO(4), respectively. We show that the principal orbits coincide with the tubular hypersurfaces around the totally geodesic singular orbits, and the symmetric spaces G2 and G2/SO(4) can be thought of as compact tubes around SU(3) and P2, respectively. Moreover, we determine the radii of these tubes and describe the shape operators of the principal orbits. Finally, we apply these results to compute the volumes of the two symmetric spaces.The author was partially supported by the Hungarian National Science and Research Foundation OTKA T032478. 相似文献
15.
The main purpose of this paper is to use the strong stability method to approximate the characteristics of the M
2/G
2/1 queue with preemptive priority by those of the classical M/G/1 queue. The latter is simpler and more exploitable in practice. After perturbing the arrival intensity of the priority requests,
we derive the stability conditions and next obtain the stability inequalities with an exact computation of constants. From
those theoretical results, we elaborate an algorithm allowing us to verify the approximation conditions and to provide the
made numerical error. In order to have an idea about the efficiency of this approach, we consider a concrete example whose
results are compared with those obtained by simulation. 相似文献
16.
Lascar described E
KP
as a composition of E
L
and the topological closure of E
L
(Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated
by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an affine copy of G and in M′ we have the structure of M and the action of G on X. We prove that the Lascar group of M′ is a semi-direct product of the Lascar group of M and G/G
L
. We discuss the relationship between G-compactness of M and M′. This example may yield new examples of non-G-compact theories.
The first author is supported by the Polish Goverment grant N N201 384134. The second author is supported by the Polish Goverment
grant N201 032 32/2231. 相似文献
17.
Lingli Wang 《Frontiers of Mathematics in China》2010,5(1):179-190
Let G be a finite group, and let π
e
(G) be the spectrum of G, that is, the set of all element orders of G. In 1987, Shi Wujie put forward the following conjecture. If G is a finite group and M is a non-abelian simple group, then G ≅ M if and only if |G| = |M| and π
e
(G) = π
e
(M). In this short paper, we prove that if G is a finite group, then G ≅ M if and only if |G| = |M| and π
e
(G) = π
e
(M), where M = D
n
(2) and n is even. 相似文献
18.
A k-total coloring of a graph G is a mapping ?: V (G) ? E(G) → {1; 2,..., k} such that no two adjacent or incident elements in V (G) ? E(G) receive the same color. Let f(v) denote the sum of the color on the vertex v and the colors on all edges incident with v: We say that ? is a k-neighbor sum distinguishing total coloring of G if f(u) 6 ≠ f(v) for each edge uv ∈ E(G): Denote χ Σ ″ (G) the smallest value k in such a coloring of G: Pil?niak and Wo?niak conjectured that for any simple graph with maximum degree Δ(G), χ Σ ″ ≤ Δ(G)+3. In this paper, by using the famous Combinatorial Nullstellensatz, we prove that for K 4-minor free graph G with Δ(G) > 5; χ Σ ″ = Δ(G) + 1 if G contains no two adjacent Δ-vertices, otherwise, χ Σ ″ (G) = Δ(G) + 2. 相似文献
19.
We continue a study of automorphisms of order 2 of algebraic groups. In particular we look at groups of type G2 over fields k of characteristic two. Let C be an octonion algebra over k; then Aut(C) is a group of type G2 over k. We characterize automorphisms of order 2 and their corresponding fixed point groups for Aut(C) by establishing a connection between the structure of certain four dimensional subalgebras of C and the elements in Aut(C) that induce inner automorphisms of order 2. These automorphisms relate to certain quadratic forms which, in turn, determine the Galois cohomology of the fixed point groups of the involutions. The characteristic two case is unique because of the existence of four dimensional totally singular subalgebras. Over finite fields we show how our results coincide with known results, and we establish a classification of automorphisms of order 2 over infinite fields of characteristic two. 相似文献
20.
As the main result, we show that if G is a finite group such that Γ(G) = Γ(2
F
4(q)), where q = 22m+1 for some m ≧ 1, then G has a unique nonabelian composition factor isomorphic to 2
F
4(q). We also show that if G is a finite group satisfying |G| =|2
F
4(q)| and Γ(G) = Γ(2
F
4(q)), then G ≅ 2
F
4(q). As a consequence of our result we give a new proof for a conjecture of W. Shi and J. Bi for 2
F
4(q).
The third author was supported in part by a grant from IPM (No. 87200022). 相似文献