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1.
Let π = (d
1, d
2, ..., d
n
) and π′ = (d′
1, d′
2, ..., d′
n
) be two non-increasing degree sequences. We say π is majorizated by π′, denoted by π ⊲ π′, if and only if π ≠ π′, Σ
i=1
n
d
i
= Σ
i=1
n
d′
i
, and Σ
i=1
j
d
i
≤ Σ
i=1
j
d′
i
for all j = 1, 2, ..., n. Weuse C
π
to denote the class of connected graphs with degree sequence π. Let ρ(G) be the spectral radius, i.e., the largest eigenvalue of the adjacent matrix of G. In this paper, we extend the main results of [Liu, M. H., Liu, B. L., You, Z. F.: The majorization theorem of connected
graphs. Linear Algebra Appl., 431(1), 553–557 (2009)] and [Bıyıkoğlu, T., Leydold, J.: Graphs with given degree sequence and maximal spectral radius. Electron. J. Combin., 15(1), R119 (2008)]. Moreover, we prove that if π and π′ are two different non-increasing degree sequences of unicyclic graphs with π ⊲ π′, G and G′ are the unicyclic graphs with the greatest spectral radii in C
π
and C′
π
, respectively, then ρ(G) < ρ(G′). 相似文献
2.
For given a graph H, a graphic sequence π = (d
1, d
2,..., d
n) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K
5 − e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to
be potentially K
5-graphic, where K
r is a complete graph on r vertices and K
r-e is a graph obtained from K
r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence
π to be potentially K
6-graphic.
Project supported by National Natural Science Foundation of China (No. 10401010). 相似文献
3.
A composition of a positive integer n is a finite sequence π1π2...π
m
of positive integers such that π1+...+π
m
= n. Let d be a fixed number. We say that we have an ascent of size d or more (respectively, less than d) if π
i+1 ≥ π
i
+d (respectively, π
i
< π
i+1 < π
i
+ d). Recently, Brennan and Knopfmacher determined the mean, variance and limiting distribution of the number of ascents of size
d or more in the set of compositions of n. In this paper, we find an explicit formula for the multi-variable generating function for the number of compositions of
n according to the number of parts, ascents of size d or more, ascents of size less than d, descents and levels. Also, we extend the results of Brennan and Knopfmacher to the case of ascents of size less than d. More precisely, we determine the mean, variance and limiting distribution of the number of ascents of size less than d in the set of compositions of n. 相似文献
4.
Let the finite groupG =AB be the product of two soluble subgroupsA andB, and letπ be a set of primes. We investigate under which conditions for the maximal normalπ-subgroups ofA, B andG the following holds:O
π
(G) ∩O
π
(G) ⊆O
π
(G).
The second author would like to thank the Department of Mathematics of the University of Mainz and the Mathematische Forschungsinstitut
Oberwolfach for their excellent hospitality during the preparation of this paper. 相似文献
5.
Wen Bin Guo 《数学学报(英文版)》2008,24(10):1751-1757
In this paper, we prove the following theorem: Let p be a prime number, P a Sylow psubgroup of a group G and π = π(G) / {p}. If P is seminormal in G, then the following statements hold: 1) G is a p-soluble group and P' ≤ Op(G); 2) lp(G) ≤ 2 and lπ(G) ≤ 2; 3) if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble. 相似文献
6.
Fabio Conforto 《Annali di Matematica Pura ed Applicata》1948,27(1):273-291
Sunto. Si precisa la natura del problema di determinare le trasformazioni in sè della varietà quasi abeliana diJacobi, relativa ad una curva di genere virtualeπ, ottenuta da una curva di genere effettivop considerando su questaδ
1 coppie neutre a punti distinti eδ
2 coppie neutre a punti coincidenti, in modo che siaπ=p+δ
1+δ2. Come nel coso abeliano (δ
1=δ2=0), tale problema ha un aspetto aritmetico, che si collega alla considerazione di relazioni, che generalizzano quelle note
diHurwitz. Nel casop=0 si trovano tutte le trasformazioni in sè dellaV
π diJacobi, mostrando che queste costituiscono un gruppo formato sempre da infinite schiere ∞π (tranne nel casoπ=δ
1=1, δ2=0), dipendenti da parametri in parte variabili in modo continuo ed in parte in modo discreto. Le trasformazioni sono tutte
birazionali seδ
1=0 oδ
2=0, mentre seδ
1 ≠ 0 eδ
2 ≠ 0 si presentano anche trasformazioni trascendenti. 相似文献
7.
William A. Veech 《Journal d'Analyse Mathématique》1990,55(1):117-171
The cotangent bundle ofJ (g, n) is a union of complex analytic subvarieties, V(π), the level sets of the function “singularity pattern” of quadratic differentials.
Each V(π) is endowed with a natural affine complex structure and volume element. The latter contracts to a real analytic volume
element, Μπ, on the unit hypersurface, V1(π), for the Teichmüller metric. Μπ is invariant under the pure mapping class group, γ(g, n), and a certain class of functions is proved to be Lp(Μπ), 0 <p < 1, over the moduli space V1(π)/γ (g, n). In particular, Μπ(V1(π)/γ(g, n)) < ∞, a statement which generalizes a theorem by H. Masur.
Research supported by NSF-MCS-8219148 and NSF-DMS-8521620. 相似文献
8.
M. M. Gekhtman 《Mathematical Notes》1977,21(2):117-118
Let A>0 be an unbounded self-adjoint operator in a Hilbert space H. In the Hilbert space H1=L2 (0, π; H) we study the spectrum of the differential equations−y″(x)+Ay=λy, y (0)=y(π)=0,−y″(x)+Ay=λy, y′(0) =y′(π)=0. We find the principal terms of the asymptotics of the functions N(λ) for these problems and we ascertain the conditions
under which they are asymptotically not equivalent.
Translated from Matematicheskie Zametki, Vol. 21, No. 2, pp. 209–212, February, 1977. 相似文献
9.
Cecilia Salgado 《Bulletin of the Brazilian Mathematical Society》2012,43(1):7-16
Let X be an elliptic K3 surface endowed with two distinct Jacobian elliptic fibrations π
i
, i = 1, 2, defined over a number field k. We prove that there is an elliptic curve C ⊂ X such that the generic rank over k of X after a base extension by C is strictly larger than the generic rank of X. Moreover, if the generic rank of π
j
is positive then there are infinitely many fibers of π
i
(j ≠ i) with rank at least the generic rank of π
i
plus one. 相似文献
10.
Qing Feng Sun 《数学学报(英文版)》2011,27(7):1449-1454
Let π
Δ be the automorphic representation of GL(2,ℚA) associated with Ramanujan modular form Δ and L(s, π
Δ) the global L-function attached to π
Δ. We study Selberg’s integral for the automorphic L-function L(s, π
Δ) under GRH. Our results give the information for the number of primes in short intervals attached to Ramanujan automorphic
representation. 相似文献
11.
Yan QU 《数学学报(英文版)》2007,23(10):1903-1908
Let π be an irreducible unitary cuspidal representation of GLm(AQ) with m ≥ 2, and L(s, Tr) the L-function attached to π. Under the Generalized Riemann Hypothesis for L(s,π), we estimate the normal density of primes in short intervals for the automorphic L-function L(s, π). Our result generalizes the corresponding theorem of Selberg for the Riemann zeta-function. 相似文献
12.
M. Yu. Yurkin 《Mathematical Notes》1995,58(5):1223-1226
A proof is given of the stability theorem for minimal systems of exponentialse(Λ) = {e
iλx
}λ∈Λ inL
p
[−π, π], where Λ ⊂ ℂ is a discrete subset. Geometric minimality conditions for such systems are obtained.
Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 773–777, November, 1995.
I wish to express gratitude to A. A. Shkalikov, who posed the problem and paid constant attention to this work. 相似文献
13.
For a finite group G, let πe(G) be the set of order of elements in G and denote S
n the symmetric group on n letters. We will show that if πe(G ) = πe(H), where H is S
p or S
p+1 and p is a prime with 50 < p < 100, then G
≅ H.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
14.
Fang Gensun 《中国科学A辑(英文版)》2001,44(9):1126-1131
The main result of this paper asserts that if a function f is in the class Bπ,p, 1 <p < ∞; that is, those p-integrable functions whose Fourier transforms are supported in the interval [ - π, π], then f and its
derivatives f(j) j = 1, 2, …, can be recovered from its sampling sequence{f(k)} via the cardinal interpolating spline of degree m in the metric
ofL
q(ℝ)), 1 <p=q < ∞, or 11 <p=q < ⩽ ∞. 相似文献
15.
Michael Ferrara 《Graphs and Combinatorics》2007,23(3):263-269
An integer sequence π is said to be graphic if it is the degree sequence of some simple graph G. In this case we say that G is a realization of π. Given a graph H, and a graphic sequence π we say that π is potentially H-graphic if there is some realization of π that contains H as a subgraph. We define σ(H,n) to be the minimum even integer such that every graphic sequence with sum at least σ(H,n) is potentially H-graphic. In this paper, we determine σ(H,n) for the graph H = Km1∪ Km2∪...∪ Kmk when n is a sufficiently large integer. This is accomplished by determining σ(Kj + kK2,n) where j and k are arbitrary positive integers, and considering the case where j = m − 2k and m = ∑ mi. 相似文献
16.
D. O. Revin 《Siberian Mathematical Journal》2011,52(2):340-347
Given a set π of primes, say that the Baer-Suzuki π-theorem holds for a finite group G if only an element of O
π(G) can, together with each conjugate element, generate a π-subgroup. We find a sufficient condition for the Baer-Suzuki π-theorem to hold for a finite group in terms of nonabelian composition factors. We show also that in case 2 ∉ π the Baer-Suzuki π-theorem holds for every finite group. 相似文献
17.
I. V. Dombrovskii 《Ukrainian Mathematical Journal》1999,51(11):1779-1781
We establish conditions for the existence of a smooth solution of a quasilinear hyperbolic equationu
tt
- uxx = ƒ(x, t, u, u, u
x),u (0,t) = u (π,t) = 0,u (x, t+ T) = u (x, t), (x, t) ∈ [0, π] ×R, and prove a theorem on the existence and uniqueness of a solution.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1574–1576, November, 1999. 相似文献
18.
We consider a variation of a classical Turán-type extremal problem as follows: Determine the smallest even integer σ(Kr,r,n) such that every n-term graphic sequence π = (d1,d2,...,dn) with term sum σ(π) = d1 + d2 + ... + dn ≥ σ(Kr,r,n) is potentially Kr,r-graphic, where Kr,r is an r × r complete bipartite graph, i.e. π has a realization G containing Kr,r as its subgraph. In this paper, the values σ(Kr,r,n) for even r and n ≥ 4r2 - r - 6 and for odd r and n ≥ 4r2 + 3r - 8 are determined. 相似文献
19.
Rao’s flag-transitive plane π of order 49 and π
t
, the plane obtained by transposing matrices of a representative set of π, has been studied. It is shown that π
t
is flag-transitive, π
t
is not isomorphic to π, and π
t
is obtained from π by replacement of a net of degree 25. Further, (1) the flag-transitive planes associated with 1-spread sets S
2b
and S
2a
in the classified list of translation planes of order 49 enumerated by Mathon et al, are respectively isomorphic to π and π
t
(2) The flag-transitive planes associated with the 1-spread sets of 0an* in the classified list of translation planes of
order 49 enumerated by Charnes et al are isomorphic to π and π
t
in some order. 相似文献
20.
Hai Jinke 《中国科学A辑(英文版)》2006,49(5):620-625
Let π be a set of primes and G a π-separable group. Isaacs defines the B
π
characters, which can be viewed as the “π-modular” characters in G, such that the B
p′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs’ work, Slattery has developed some Brauer’s ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer’s three main theorems to the π-blocks. In this paper, depending on Isaacs’ and Slattery’s work, we will extend the first main theorem for π-blocks. 相似文献