共查询到20条相似文献,搜索用时 31 毫秒
1.
Noga Alon 《Israel Journal of Mathematics》1986,53(1):97-120
All graphs considered are finite, undirected, with no loops, no multiple edges and no isolated vertices. For two graphsG, H, letN(G, H) denote the number of subgraphs ofG isomorphic toH. Define also, forl≧0,N(l, H)=maxN(G, H), where the maximum is taken over all graphsG withl edges. We determineN(l, H) precisely for alll≧0 whenH is a disjoint union of two stars, and also whenH is a disjoint union ofr≧3 stars, each of sizes ors+1, wheres≧r. We also determineN(l, H) for sufficiently largel whenH is a disjoint union ofr stars, of sizess
1≧s
2≧…≧s
r>r, provided (s
1−s
r)2<s
1+s
r−2r. We further show that ifH is a graph withk edges, then the ratioN(l, H)/l
k tends to a finite limit asl→∞. This limit is non-zero iffH is a disjoint union of stars. 相似文献
2.
Bodh Raj Gulati 《Annals of the Institute of Statistical Mathematics》1971,23(1):279-292
Summary This investigation was originally motivated by the problem of determining the maximum number of points in finiten-dimensional projective spacePG(n, s) based on the Galois fieldGF(s) of orders=p
h
(wherep andh are positive integers andp is the prime characteristic of the field), such that not of these chosen points are linearly dependent. A set ofk distinct points inPG(n, s), not linearly dependent, is called a (k, t)-set fork
1
>k. The maximum value ofk is denoted bym
t
(n+1, s). The purpose of this paper is to find new upper bounds for some values ofn, s andt. These bounds are of importance in the experimental design and information theory problems. 相似文献
3.
We study the velocity field induced by a vorticity distribution decaying rapidly in the distancer from the origin. In the far field, the vector potential for the velocity field can be represented by a series A
(n), withA
(n) proportional tor
–n–1, forn=1, 2, .... We show thatA
(n) can be expressed as a linear combination ofM
n linearly independent vector functions. The numberM
n is equal to 3 forn=1 and 4n forn2 and the coefficient of a vector function is defined by a linear combination of
nth moments of vorticity. We then show that only 2n+1 linear combinations of thoseM
n vector functions contribute to the far field velocity which is irrotational. The corresponding scalar potential
(n)
is then represented by a linear combination of 2n+1 spherical harmonics ofnth order whose coefficients are again linear combinations ofnth moments of vorticity.
Zusammenfassung Die vorliegende Arbeit beschreibt das Geschwindigkeitsfeld fernab einer Wirbelverteilung, welche mit dem Abstandr vom Ursprung eines geeigneten Bezugssystems hinreichend schnell abklingt. Die Geschwindigkeit besitzt ein Vektorpotential, dessen Fernfeldverhalten einer Reihenentwicklung A (n), genügt. Dabei istA (n) proportional zur –n–1 fürn=1, 2, .... Wir entwickeln eine explizite Darstellung vonA (n) als Linearkombination vonM n linear unabhängigen Vektorfunktionen. Die auftretenden Koeffizienten sind ihrerseits Kombinationenn-ter Momente der Wirbelverteilung. Die ZahlM 1 ist gleich 3 und es istM n=4n fürn2, während die Gesamtzahl dernten Momente beträgt. Weiterhin zeigen wir, da\ nur 2n+1 dieser Vektorfunktionen auch zum drehungsfreien Fernfeld der Geschwindigkeitn-ter Ordnung beitragen können und identifizieren die zugehörigen Kombinationen von Wirbelmomenten. Dieselben Kombinationen liefern dann auch die Koeffizienten in einer Entwicklung desskalaren Fernfeldpotentials nach Kugelfunktionen.相似文献
4.
Jie Du 《manuscripta mathematica》1992,75(1):411-427
The structure of Schur algebrasS(2,r) over the integral domainZ is intensively studied from the quasi-hereditary algebra point of view. We introduce certain new bases forS(2,r) and show that the Schur algebraS(2,r) modulo any ideal in the defining sequence is still such a Schur algebra of lower degree inr. A Wedderburn-Artin decomposition ofS
K
(2,r) over a fieldK of characteristic 0 is described. Finally, we investigate the extension groups between two Weyl modules and classify the
indecomposable Weyl-filtered modules for the Schur algebrasS
Zp(2,r) withr<p
2
.
Research supported by ARC Large Grant L20.24210 相似文献
5.
Shun-Hwa Li Wen-Jang Huang Mong-Na Lo Huang 《Annals of the Institute of Statistical Mathematics》1994,46(2):351-360
Given two independent positive random variables, under some minor conditions, it is known that fromE(XrX+Y)=a(X+Y)r andE(XsX+Y)=b(X+Y)s, for certain pairs ofr ands, wherea andb are two constants, we can characterizeX andY to have gamma distributions. Inspired by this, in this article we will characterize the Poisson process among the class of renewal processes via two conditional moments. More precisely, let {A(t), t0} be a renewal process, with {S
k, k1} the sequence of arrival times, andF the common distribution function of the inter-arrival times. We prove that for some fixedn andk, kn, ifE(S
k
r
A(t)=n)=atr andE(S
k
s
A(t)=n)=bts, for certain pairs ofr ands, wherea andb are independent oft, then {A(t), t0} has to be a Poisson process. We also give some corresponding results about characterizingFto be geometric whenF is discrete.Support for this research was provided in part by the National Science Council of the Republic of China, Grant No. NSC 81-0208-M110-06. 相似文献
6.
Rolf Kultze 《manuscripta mathematica》1990,69(1):31-42
LetX be a connected, locally finite spectrum and letk(n) (n>-1) denote the (−1)-connected cover of then-th MoravaK-Theory associated to the primep.k(n) is aBP-module spectrum with π*(k(n)) ≅ ℤ
p
[υ
n
] where |v
n
| = 2(p
n
-1). We prove the following splitting theorem: Thek(n)
*-torsion ofk(n)
* (X) is already annihilated byv
n
e
(e≥1) if and only ifk(n)ΛX is homotopy equivalent to a wedge of spectrak(n) and
r
k(n) (0≤r≤e-1) where
r
k(n) denotes ther-th Postnikov factor ofk(n). Moreover we investigate splitting conditions for
r
k(n)ΛX. 相似文献
7.
LetF be a distribution and letf be a locally summable function. The distributionF(f) is defined as the neutrix limit of the sequenceF
n
(f), whereF
n
(x) = F(x) * δ
n
(x) andδ
n
(x) is a certain sequence of infinitely differentiable functions converging to the Dirac delta-functionδ(x). The distribution (xr)−s is valuated forr, s = 1,2, …. 相似文献
8.
Herbert E. Salzer 《Numerische Mathematik》1962,4(1):381-392
Equally-weighted formulas for numerical differentiation at a fixed pointx=a, which may be chosen to be 0 without loss in generality, are derived for (1)
whereR
2n
=0 whenf(x) is any (2n)th degree polynomial. Equation (1) is equivalent to (2)
,r=1,2,..., 2n. By choosingf(x)=1/(z–x),x
i
fori=1,..., n andx
i
fori=n+1,..., 2n are shown to be roots ofg
n
(z) andh
n
(z) respectively, satisfying (3)
. It is convenient to normalize withk=(m–1)!. LetP
s
(z) denotez
s
· numerator of the (s+1)th diagonal member of the Padé table fore
x
, frx=1/z, that numerator being a constant factor times the general Laguerre polynomialL
s
–2s–1
(x), and letP
s
(X
i
)=0, i=1, ...,s. Then for anym, solutions to (1) are had, for2n=2ms, forx
i
, i=1, ...,ms, andx
i
, i=ms+1,..., 2ms, equal to all them
th rootsX
i
1/m
and (–X
i
)1/m
respectively, and they give {(2s+1)m–1}th degree accuracy. For2sm2n(2s+1)m–1, these (2sm)-point solutions are proven to be the only ones giving (2n)th degree accuracy. Thex
i
's in (1) always include complex values, except whenm=1, 2n=2. For2sm<2n(2s+1)m–1,g
n
(z) andh
n
(z) are (n–sm)-parameter families of polynomials whose roots include those ofg
ms
(z) andh
ms
(z) respectively, and whose remainingn–ms roots are the same forg
n
(z) andh
n
(z). Form>1, and either 2n<2m or(2s+1)m–1<2n<(2s+2)m, it is proven that there are no non-trivial solutions to (1), real or complex. Form=1(1)6, tables ofx
i
are given to 15D, fori=1(1)2n, where 2n=2ms ands=1(1) [12/m], so that they are sufficient for attaining at least 24th degree accuracy in (1).Presented at the Twelfth International Congress of Mathematicians, Stockholm, Sweden, August 15–22, 1962.General Dynamics/Astronautics. A Division of General Dynamics Corporation. 相似文献
9.
F. Yu. Vorob’ev 《Computational Mathematics and Modeling》2008,19(3):304-331
Let F
k
(n, m) be a random k-CNF obtained by a random, equiprobable, and independent choice of m brackets from among all k-literal brackets on n variables. We investigate the structure of the set of satisfying assignments of F
k
(n, m). A method is proposed for finding r(k, s)such that the probability of presence of ns-dimensional faces (0 < s < 1) in the set of satisfying assignments of the formula F
k
s(n, r(k, s)n) goes to 1 as n goes to infinity. We prove the existence of a sequential threshold for the property of having ns-dimensional faces (0 < s < 1). In other words, there exists a sequence r
n
(k, s) such that the probability of having an ns-dimensional face in the set of satisfying assignments of the formula F
k
(n, r
n
(k, s)(1 + d)n) goes to 0 for all d > 0 and to 1 for all d < 0.
__________
Translated from Prikladnaya Matematika i Informatika, No. 26, pp. 61–95, 2007. 相似文献
10.
Vladimir Nikiforov 《Journal of Graph Theory》2009,62(4):362-368
In this note we strengthen the stability theorem of Erd?s and Simonovits. Write Kr(s1, …, sr) for the complete r‐partite graph with classes of sizes s1, …, sr and Tr(n) for the r‐partite Turán graph of order n. Our main result is: For all r≥2 and all sufficiently small c>0, ε>0, every graph G of sufficiently large order n with e(G)>(1?1/r?ε)n2/2 satisfies one of the conditions:
- (a) G contains a $K_{r+1} (\lfloor c\,\mbox{ln}\,n \rfloor,\ldots,\lfloor c\,\mbox{ln}\,n \rfloor,\lceil n^{{1}-\sqrt{c}}\rceil)
In this note we strengthen the stability theorem of Erd?s and Simonovits. Write Kr(s1, …, sr) for the complete r‐partite graph with classes of sizes s1, …, sr and Tr(n) for the r‐partite Turán graph of order n. Our main result is: For all r≥2 and all sufficiently small c>0, ε>0, every graph G of sufficiently large order n with e(G)>(1?1/r?ε)n2/2 satisfies one of the conditions: - (a) G contains a $K_{r+1} (\lfloor c\,\mbox{ln}\,n \rfloor,\ldots,\lfloor c\,\mbox{ln}\,n \rfloor,\lceil n^{{1}-\sqrt{c}}\rceil)$;
- (b) G differs from Tr(n) in fewer than (ε1/3+c1/(3r+3))n2 edges.
- (a) G contains a $K_{r+1}(\lfloor c\,\mbox{ln}\,n\rfloor,\ldots,\lfloor c\,\mbox{ln}\,n\rfloor,\lceil n^{1-\sqrt{c}}\rceil)$;
- (b) G differs from Tr(n) in fewer than (ε1/4+c1/(8r+8))n2 edges.
11.
Michele Capon 《Israel Journal of Mathematics》1982,42(1-2):87-98
In this article we show thatL
p(L
r) is primary forp andr in ]1,+∞[. If (h
k)
k≧1 denote the Haar basis, we begin with a study of the sequence (h
k ⊗h
i) and, in particular, the space generated by a subsequence of this sequence. In the first part we study the base ofL
p(L
r) and in the second part we show that this space is primary. 相似文献
12.
Vicent Caselles 《Israel Journal of Mathematics》1987,58(2):144-160
We prove that ifE is a Banach lattice andS, T ∈ ℒ (E) are such that 0≦s≦T,r(s)=r(T) andr(T) is a Riesz point ofσ(T) thenr(S) is a Riesz point ofσ(S). We prove also some results on compact positive perturbations of positive irreducible operators and lattice homomorphisms. 相似文献
13.
Isha Bagai B. L. S. Prakasa Rao 《Annals of the Institute of Statistical Mathematics》1995,47(2):253-266
Let {X
n
,n1} be a strictly stationary sequence of associated random variables defined on a probability space (,B, P) with probability density functionf(x) and failure rate functionr(x) forX
1. Letf
n
(x) be a kerneltype estimator off(x) based onX
1,...,X
n
. Properties off
n
(x) are studied. Pointwise strong consistency and strong uniform consistency are established under a certain set of conditions. An estimatorr
n
(x) ofr(x) based onf
n
(x) andF
n
(x), the empirical survival function, is proposed. The estimatorr
n
(x) is shown to be pointwise strongly consistent as well as uniformly strongly consistent over some sets. 相似文献
14.
For an integers letl
s
(n), thes-iterated logarithm function, be defined inductively:l
0
(n)=n,l
s+1
(n)=log2 (l
2
(n)) fors0. We show that for every fixeds and alln large enough, there is ann-vertex 3-pushdown graph whose smallest separator contains at least(n/l
s
(n)) vertices.The work of the first author was supported in part by NSF Grants MCS-83-03139, DCR-85-11713 and CCR-86-05353.The work of the second author was supported in part by NSF Grants MCS-84-16190. 相似文献
15.
Stephen Mellendorf 《Journal of Graph Theory》1997,24(1):85-115
We define the multicycle C(r)m as a cycle on m vertices where each edge has multiplicity r. So C(r)m can be decomposed into r Hamilton cycles. We provide a complete answer to the following question: for which positive integers m, n, r, s with m, n ≥ 3 can the Cartesian product of two multicycles C(r)m x C(s)n be decomposed into r + s Hamilton cycles? We find some interesting characterizations of Hamilton cycles of Cm x Cn while answering the above question. © 1997 John Wiley & Sons, Inc. 相似文献
16.
Michael Kallay 《Israel Journal of Mathematics》1984,49(4):360-364
The minimal number of circuits (i.e., minimal affinely dependent subsets) in a set ofs points inR
2k−1 isr(
3
4
)+(k−r)(
3
4⋅1
) as conjectured by J.-P. Doignon, wheres=qk+r, 0≦r<q. 相似文献
17.
An upper bound on the Ramsey number r(K2,n‐s,K2,n) where s ≥ 2 is presented. Considering certain r(K2,n‐s,K2,n)‐colorings obtained from strongly regular graphs, we additionally prove that this bound matches the exact value of r(K2,n‐s,K2,n) in infinitely many cases if holds. Moreover, the asymptotic behavior of r(K2,m,K2,n) is studied for n being sufficiently large depending on m. We conclude with a table of all known Ramsey numbers r(K2,m,K2,n) where m,n ≤ 10. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 252–268, 2003 相似文献
18.
Phil Hanlon 《Inventiones Mathematicae》1986,86(1):131-159
Summary LetA+(k) denote the ring [t]/t
k+1
and letG be a reductive complex Lie algebra with exponentsm
1, ...,m n. This paper concerns the Lie algebra cohomology ofGA
+(k) considered as a bigraded algebra (here one of the gradings is homological degree and the other, which we callweight, is inherited from the obvious grading ofGA
+(k)). We conjecture that this Lie algebra cohomology is an exterior algebra withk+1 generators of homological degree 2m
s
+1 fors=1,2, ...,n. Of thesek+1 generators of degree 2m
s
+1, one has weight 0 and the others have weights (k+1)m
s
+t fort=1,2, ...,k.It is shown that this conjecture about the Lie algebra cohomology of A
+(k) implies the Macdonald root system conjectures. Next we consider the case thatG is a classical Lie algebra with root systemA
n
,B
n
,C
n
, orD
n. It is shown that our conjecture holds in the limit onn asn approaches infinity which amounts to the computation of the cyclic and dihedral cohomologies ofA+(k). Lastly we discuss the relevance of this limiting case to the case of finiten in this situation.Partially supported by NSF grant number MCS-8401718 and a Bantrell Fellowship 相似文献
19.
Hubert Delange 《Monatshefte für Mathematik》1988,106(2):115-138
We show how are located the positive roots of the Euler polynomiale
n
of degreen. We give an upper bound and a lower bound for the greatest root. This permits to determine an integerv
(n) such that the number of positive roots ofE
n
is eitherv
(n)
orv
(n)
+2. We also study the behaviour of ther-th positive root ofE
n
asn tends to infinity. 相似文献
20.
Philip W. Steitz 《Israel Journal of Mathematics》1992,77(3):335-343
We establish a sharp upper bound for growth in the sequences
k
(T):=the number ofk-types consistent withT, forT ω-categorical andω-stable.
This paper forms part of the author’s doctoral dissertation written at the University of Maryland under the direction of David
W. Kueker. 相似文献