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1.
Edge colorings of r-uniform hypergraphs naturally define a multicoloring on the 2-shadow, i.e., on the pairs that are covered by hyperedges.
We show that in any (r – 1)-coloring of the edges of an r-uniform hypergraph with n vertices and at least
(1-e)( *20c nr)(1-\varepsilon)\left( {\begin{array}{*{20}c} n\\ r\\ \end{array}}\right) edges, the 2-shadow has a monochromatic matching covering all but at most o(n) vertices. This result confirms an earlier conjecture and implies that for any fixed r and sufficiently large n, there is a monochromatic Berge-cycle of length (1 – o(1))n in every (r – 1)-coloring of the edges of K(r)n{K^{(r)}_{n}}, the complete r-uniform hypergraph on n vertices. 相似文献
2.
LetK be a field, charK=0 andM
n
(K) the algebra ofn×n matrices overK. If λ=(λ1,…,λ
m
) andμ=(μ
1,…,μ
m
) are partitions ofn
2 let
wherex
1,…,x
n
2,y
1,…,y
n
2 are noncommuting indeterminates andS
n
2 is the symmetric group of degreen
2.
The polynomialsF
λ, μ
, when evaluated inM
n
(K), take central values and we study the problem of classifying those partitions λ,μ for whichF
λ, μ
is a central polynomial (not a polynomial identity) forM
n
(K).
We give a formula that allows us to evaluateF
λ, μ
inM(K) in general and we prove that if λ andμ are not both derived in a suitable way from the partition δ=(1, 3,…, 2n−3, 2n−1), thenF
λ, μ
is a polynomial identity forM
n
(K). As an application, we exhibit a new class of central polynomials forM
n
(K).
In memory of Shimshon Amitsur
Research supported by a grant from MURST of Italy. 相似文献
3.
LetH be a fixed graph of chromatic numberr. It is shown that the number of graphs onn vertices and not containingH as a subgraph is
. Leth
r
(n) denote the maximum number of edges in anr-uniform hypergraph onn vertices and in which the union of any three edges has size greater than 3r – 3. It is shown thath
r
(n) =o(n
2) although for every fixedc < 2 one has lim
n
h
r
(n)/n
c
= . 相似文献
4.
Wei Cao 《Discrete and Computational Geometry》2011,45(3):522-528
Let f(X) be a polynomial in n variables over the finite field
\mathbbFq\mathbb{F}_{q}. Its Newton polytope Δ(f) is the convex closure in ℝ
n
of the origin and the exponent vectors (viewed as points in ℝ
n
) of monomials in f(X). The minimal dilation of Δ(f) such that it contains at least one lattice point of $\mathbb{Z}_{>0}^{n}$\mathbb{Z}_{>0}^{n} plays a vital pole in the p-adic estimate of the number of zeros of f(X) in
\mathbbFq\mathbb{F}_{q}. Using this fact, we obtain several tight and computational bounds for the dilation which unify and improve a number of previous
results in this direction. 相似文献
5.
Isabella Novik 《Israel Journal of Mathematics》1998,108(1):45-82
In this paper we prove the Upper Bound Conjecture (UBC) for some classes of (simplicial) homology manifolds: we show that
the UBC holds for all odd-dimensional homology manifolds and for all 2k-dimensional homology manifolds Δ such that β
k
(Δ)⩽Σ{β
i
(Δ):i ≠k-2,k,k+2 and 1 ⩽i⩽2k-1}, where β
i
(Δ) are reduced Betti numbers of Δ. (This condition is satisfied by 2k-dimensional homology manifolds with Euler characteristic χ≤2 whenk is even or χ≥2 whenk is odd, and for those having vanishing middle homology.)
We prove an analog of the UBC for all other even-dimensional homology manifolds.
Kuhnel conjectured that for every 2k-dimensional combinatorial manifold withn vertices,
. We prove this conjecture for all 2k-dimensional homology manifolds withn vertices, wheren≥4k+3 orn≤3k+3. We also obtain upper bounds on the (weighted) sum of the Betti numbers of odd-dimensional homology manifolds. 相似文献
6.
Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^*, and C be a nonempty closed convex subset of E. Let {T(t) : t ≥ 0} be a nonexpansive semigroup on C such that F :=∩t≥0 Fix(T(t)) ≠ 0, and f : C → C be a fixed contractive mapping. If {αn}, {βn}, {an}, {bn}, {tn} satisfy certain appropriate conditions, then we suggest and analyze the two modified iterative processes as:{yn=αnxn+(1-αn)T(tn)xn,xn=βnf(xn)+(1-βn)yn
{u0∈C,vn=anun+(1-an)T(tn)un,un+1=bnf(un)+(1-bn)vn
We prove that the approximate solutions obtained from these methods converge strongly to q ∈∩t≥0 Fix(T(t)), which is a unique solution in F to the following variational inequality:
〈(I-f)q,j(q-u)〉≤0 u∈F Our results extend and improve the corresponding ones of Suzuki [Proc. Amer. Math. Soc., 131, 2133-2136 (2002)], and Kim and XU [Nonlear Analysis, 61, 51-60 (2005)] and Chen and He [Appl. Math. Lett., 20, 751-757 (2007)]. 相似文献
{u0∈C,vn=anun+(1-an)T(tn)un,un+1=bnf(un)+(1-bn)vn
We prove that the approximate solutions obtained from these methods converge strongly to q ∈∩t≥0 Fix(T(t)), which is a unique solution in F to the following variational inequality:
〈(I-f)q,j(q-u)〉≤0 u∈F Our results extend and improve the corresponding ones of Suzuki [Proc. Amer. Math. Soc., 131, 2133-2136 (2002)], and Kim and XU [Nonlear Analysis, 61, 51-60 (2005)] and Chen and He [Appl. Math. Lett., 20, 751-757 (2007)]. 相似文献
7.
We prove inequalities about the quermassintegralsV
k
(K) of a convex bodyK in ℝ
n
(here,V
k
(K) is the mixed volumeV((K, k), (B
n
,n − k)) whereB
n
is the Euclidean unit ball). (i) The inequality
holds for every pair of convex bodiesK andL in ℝ
n
if and only ifk=2 ork=1. (ii) Let 0≤k≤p≤n. Then, for everyp-dimensional subspaceE of ℝ
n
,
whereP
E
K denotes the orthogonal projection ofK ontoE. The proof is based on a sharp upper estimate for the volume ratio |K|/|L| in terms ofV
n−k
(K)/V
n−k
(L), wheneverL andK are two convex bodies in ℝ
n
such thatK ⊆L. 相似文献
8.
G. Bouchitte 《Annali dell'Universita di Ferrara》1987,33(1):113-156
Résumé Partant d’un résultat abstrait de représentation intègrale pour une fonctionnelle convexe faiblement s.c.i. sur [M
b
(Ω)]
d
(obtenu grace à [1]); on établit un résultat de convergence pour une suite de fonctionnelles du type
μ
n
εM
b
+
(Ω),f
n
: Ω×R
d
→−∞, +∞] inté
Quelques exemples motivés par des applications à la mécanique sont ensuite traités.
Riassunto Partendo da un risultato astratto di rappresentazione integrale per un funzionale convesso debolmente s.c.i. su [M b (Ω)] d (ottenuto grazie a [1]), si dimostra un risultato di convergenza per una successione di funzionali del tipo con μ n εM b + (Ω),f n : Ω×R d →−∞, +∞] integrando normale convesso. Vengono inoltre trattati alcuni esempi motivati da applicazioni alla Meccanica.相似文献
9.
Let Δn−1 denote the (n − 1)-dimensional simplex. Let Y be a random 2-dimensional subcomplex of Δn−1 obtained by starting with the full 1-dimensional skeleton of Δn−1 and then adding each 2−simplex independently with probability p. Let
denote the first homology group of Y with mod 2 coefficients. It is shown that for any function ω(n) that tends to infinity
* Supported by an Israel Science Foundation grant. 相似文献
10.
E. S. Dubtsov 《Journal of Mathematical Sciences》2010,166(1):23-30
Let B
n
denote the unit ball in
\mathbbC \mathbb{C}
n
, n ≥ 1. Let K \mathcal{K}
0(n) denote the class of functions defined for z ∈ B
n
as a constant plus the integral of the kernel log(1/(1 −〈z, ζ〉)) against a complex Borel measure on the sphere {ζ ∈
\mathbbC \mathbb{C}
n
,: |ζ| = 1}. Properties of holomorphic functions g such that fg ∈ K \mathcal{K}
0(n) for all f ∈ K \mathcal{K}
0(n) are studied. The extended Cesàro operators are investigated on the spaces K \mathcal{K}
0(n), n ≥ 1. Bibliography: 15 titles. 相似文献
11.
In this paper, the sharp estimates of all homogeneous expansions for f are established, where f(z) = (f
1(z), f
2(z), …, f
n
(z))′ is a k-fold symmetric quasi-convex mapping defined on the unit polydisk in ℂ
n
and
$
\begin{gathered}
\frac{{D^{tk + 1} + f_p \left( 0 \right)\left( {z^{tk + 1} } \right)}}
{{\left( {tk + 1} \right)!}} = \sum\limits_{l_1 ,l_2 ,...,l_{tk + 1} = 1}^n {\left| {apl_1 l_2 ...l_{tk + 1} } \right|e^{i\tfrac{{\theta pl_1 + \theta pl_2 + ... + \theta pl_{tk + 1} }}
{{tk + 1}}} zl_1 zl_2 ...zl_{tk + 1} ,} \hfill \\
p = 1,2,...,n. \hfill \\
\end{gathered}
$
\begin{gathered}
\frac{{D^{tk + 1} + f_p \left( 0 \right)\left( {z^{tk + 1} } \right)}}
{{\left( {tk + 1} \right)!}} = \sum\limits_{l_1 ,l_2 ,...,l_{tk + 1} = 1}^n {\left| {apl_1 l_2 ...l_{tk + 1} } \right|e^{i\tfrac{{\theta pl_1 + \theta pl_2 + ... + \theta pl_{tk + 1} }}
{{tk + 1}}} zl_1 zl_2 ...zl_{tk + 1} ,} \hfill \\
p = 1,2,...,n. \hfill \\
\end{gathered}
相似文献
12.
LetH r be anr-uniform hypergraph. Letg=g(n;H r ) be the minimal integer so that anyr-uniform hypergraph onn vertices and more thang edges contains a subgraph isomorphic toH r . Lete =f(n;H r ,εn) denote the minimal integer such that everyr-uniform hypergraph onn vertices with more thane edges and with no independent set ofεn vertices contains a subgraph isomorphic toH r . We show that ifr>2 andH r is e.g. a complete graph then $$\mathop {\lim }\limits_{\varepsilon \to 0} \mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} f(n;H^r ,\varepsilon n) = \mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} g(n;H^r )$$ while for someH r with \(\mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} g(n;H^r ) \ne 0\) $$\mathop {\lim }\limits_{\varepsilon \to 0} \mathop {\lim }\limits_{n \to \infty } \left( {\begin{array}{*{20}c} n \\ r \\ \end{array} } \right)^{ - 1} f(n;H^r ,\varepsilon n) = 0$$ . This is in strong contrast with the situation in caser=2. Some other theorems and many unsolved problems are stated. 相似文献
13.
Let A and B denote two families of subsets of an n-element set. The pair (A,B) is said to be ℓ-cross-intersecting iff |A∩B|=ℓ for all A∈ A and B∈B. Denote by P
e
(n) the maximum value of |A||B| over all such pairs. The best known upper bound on P
e
(n) is Θ(2
n
), by Frankl and R?dl. For a lower bound, Ahlswede, Cai and Zhang showed, for all n ≥ 2ℓ, a simple construction of an ℓ-cross-intersecting pair (A,B) with |A||B| = $
\left( {{*{20}c}
{2\ell } \\
\ell \\
} \right)
$
\left( {\begin{array}{*{20}c}
{2\ell } \\
\ell \\
\end{array} } \right)
2
n−2ℓ
= Θ(2
n
/$
\sqrt \ell
$
\sqrt \ell
), and conjectured that this is best possible. Consequently, Sgall asked whether or not P
e
(n) decreases with ℓ. 相似文献
14.
We show that for every ? > 0 there exist δ > 0 and n0 ∈ ? such that every 3-uniform hypergraph on n ≥ n0 vertices with the property that every k-vertex subset, where k ≥ δn, induces at least \(\left( {\frac{1}{2} + \varepsilon } \right)\left( {\begin{array}{*{20}c} k \\ 3 \\ \end{array} } \right)\) edges, contains K4? as a subgraph, where K4? is the 3-uniform hypergraph on 4 vertices with 3 edges. This question was originally raised by Erd?s and Sós. The constant 1/4 is the best possible. 相似文献
15.
Let PG2(2) be the Fano plane, i. e., the unique hypergraph with 7 triples on 7 vertices in which every pair of vertices is contained
in a unique triple. In this paper we prove that for sufficiently large n, the maximum number of edges in a 3-uniform hypergraph on n vertices not containing a Fano plane is
16.
Mikihiro Hayashi Yasuyuki Kobayashi Mitsuru Nakai 《Journal d'Analyse Mathématique》2000,82(1):267-283
LetR=Δ0\∪nΔn be a Zalcman domain (or L-domain), where Δ0 : 0<|z| <1, Δn : |z-c
n|≤r
n,cn ↘0, Δn ⊂ Δ0 and Δn ∩ Δm= φ(n≠m). 0217 0115 V 3 For
an unlimited two-sheeted covering
with the branch points {φ-1(c
n)}, set
. In the casec
n=2−n
, it was proved that if a uniqueness theorem is valid forH
∞ (R) atz=0, then the Myrberg phenomenon
occurs. One might suspect that the converse also holds. In this paper, contrary to this intuition, we show that the converse
of this previous result is not true. In addition, we generalize the previous result for more general sequences {c
n}. By this generalization we can even partly simplify the previous proof.
To complete the present work the first and second (third, resp.) named authors were supported in part by Grant-in-Aid for
Scientific Research, No. 10304010 (10640190, 11640187, resp.), Japanese Ministry of Education, Science and Culture. 相似文献
17.
Melvin Hausner 《Combinatorica》1985,5(3):215-225
Ifμ is a positive measure, andA
2, ...,A
n
are measurable sets, the sequencesS
0, ...,S
n
andP
[0], ...,P
[n] are related by the inclusion-exclusion equalities. Inequalities among theS
i
are based on the obviousP
[k]≧0. Letting
=the average average measure of the intersection ofk of the setsA
i
, it is shown that (−1)
k
Δ
k
M
i
≧0 fori+k≦n. The casek=1 yields Fréchet’s inequalities, andk=2 yields Gumbel’s and K. L. Chung’s inequalities. Generalizations are given involvingk-th order divided differences. Using convexity arguments, it is shown that forS
0=1,
whenS
1≧N−1, and
for 1≦k<N≦n andv=0, 1, .... Asymptotic results asn → ∞ are obtained. In particular it is shown that for fixedN,
for all sequencesM
0, ...,M
n
of sufficiently large length if and only if
for 0<t<1. 相似文献
18.
Giovanni Sansone 《Annali di Matematica Pura ed Applicata》1926,3(1):73-107
Sommario Introduzione — § 1 – 1. L'indice μ(n) dei sottogruppi Гμ(n) del gruppo Γ di sostituzioni lineari unimodulari con coefficienti del campo diJacobi-Eisenstein
— 2. Il poliedro fondamentale del sottogruppo Гμ(1−ε) — § 2 – 3. I campi fondamentali dei gruppi Гμ(n) — 4. Impossibilità di limitare con un numero finito di piani e sfere di riflessione i poliedri fondamentali dei gruppi Гμ(n), conn intero razionale pari, diverso da 2 — § 3 – 5. Relazioni fondamentali fra le sostituzioni generatrici del gruppo
di sostituzioni lineari con coefficienti del corpo Kε con determinante ±1 — § 4 – 6. Sulla indipendenza delle sostituzioniS,T,U, generatrici del gruppo finito G2μ(n) e sulle loro relazioni caratteristiche nel gruppo G2μ(n) — § 5 – 7. Dimostrazione del teorema fondamentale sui gruppi G2μ(n). Lemmi preliminari — 8, Dimostrazione del teorema fondamentale nel caso di moduli primi con 2(1−ε) — § 6 – 9. Il teorema
fondamentale per i modulim(1−ε), 3m, 2m, 2m(1−ε), 6m conm primo con 6 – 10. Immagine geometrica dei gruppi G2μ(1−ε) — § 7 – 11. Il gruppo delle sostituzioni unimodulari
, [c/1+4ma]=+1, e il caso eccezionale dei moduli 4m – 12. Il gruppo delle sostituzioni unimodulari
[c/1+3m(1−ε)a]3=+1 e il caso eccezionale dei moduli 3(1−ε)m. 相似文献
19.
Li Xin Zhang 《数学学报(英文版)》2008,24(4):631-646
Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 +... + Xn, n≥1. The author proves that, if EX^2I{|X|≥t} = 0((log log t)^-1) as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1+a(1/√1+a-ε)b+1 ∑n=1^∞(logn)^a(loglogn)^b/nP{max κ≤n|Sκ|≤√σ^2π^2n/8loglogn(ε+an)}=4/π(1/2(1+a)^3/2)^b+1 Г(b+1),whenever an = o(1/log log n). The author obtains the sufficient and necessary conditions for this kind of results to hold. 相似文献
20.
Lou Yuanren 《分析论及其应用》1990,6(1):46-64
Let f∈Ap. For any positive integer l, the quantity Δ1,n−1(f:z) has been studied extensively. Here we give some quantitative estimates for
and investigate some pointwise estimates of Δ
l,n−1
(r)
(f;z).
Supported by National Science Foundation of China 相似文献
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