共查询到20条相似文献,搜索用时 46 毫秒
1.
Let D = (V, E) be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD(v), is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu, we order the vertices of D so that exPD(V1) ≤ exPD(V2) …≤ exPD(Vn). Then exPD(Vk) is called the k- point exponent of D and is denoted by exPD (k), 1≤ k ≤ n. In this paper we define e(n, k) := max{expD (k) | D ∈ PD(n, 2)} and E(n, k) := {exPD(k)| D ∈ PD(n, 2)}, where PD(n, 2) is the set of all primitive digraphs of order n with girth 2. We completely determine e(n, k) and E(n, k) for all n, k with n ≥ 3 and 1 ≤ k ≤ n. 相似文献
2.
A. V. Kochergin 《Moscow University Mathematics Bulletin》2013,68(1):77-79
Realization of functions of the k-valued logic by circuits is considered over an arbitrary finite complete basis B. Asymptotic behavior of the Shannon function D B (n) of the circuit depth over B is examined. The value D B (n) is the minimal depth sufficient to realize every function of the k-valued logic of n variables by a circuit over B. It is shown that for each natural k ≥ 2 and for any finite complete basis B there exists a positive constant α B such that D B (n) ~ α B n for n → ∞. 相似文献
3.
Michel Talagrand 《Israel Journal of Mathematics》1992,79(2-3):207-224
Consider a setA of symmetricn×n matricesa=(a
i,j)
i,j≤n
. Consider an independent sequence (g
i)
i≤n
of standard normal random variables, and letM=Esupa∈A|Σi,j⪯nai,jgigj|. Denote byN
2(A, α) (resp.N
t(A, α)) the smallest number of balls of radiusα for thel
2 norm ofR
n
2 (resp. the operator norm) needed to coverA. Then for a universal constantK we haveα(logN
2(A, α))1/4≤KM. This inequality is best possible. We also show that forδ≥0, there exists a constantK(δ) such thatα(logN
t≤K(δ)M.
Work partially supported by an N.S.F. grant. 相似文献
4.
1.IntroductionLetG=(V,E,W)beaconnected,weightedandundirectedgraph,VeEE,w(e)(相似文献
5.
V. A. Belonogov 《Algebra and Logic》2005,44(6):357-369
Let P(n) be the set of all partitions of a natural number n. In the representation theory of symmetric groups, for every partition
α ∈ P(n), the partition h(α) ∈ P(n) is defined so as to produce a certain set of zeros in the character table for Sn. Previously, the analog f(α) of h(α) was obtained pointing out an extra set of zeros in the table mentioned. Namely, h(α)
is greatest (under the lexicographic ordering ≤) of the partitions β of n such that χα(gβ) ≠ 0, and f(α) is greatest of the partitions γ of n that are opposite in sign to h(α) and are such that χα(gγ) ≠ 0, where χα is an irreducible character of Sn, indexed by α, and gβ is an element in the conjugacy class of Sn, indexed by β. For α ∈ P(n), under some natural restrictions, here, we construct new partitions h′(α) and f′(α) of n possessing
the following properties. (A) Let α ∈ P(n) and n ⩾ 3. Then h′(α) is identical is sign to h(α), χα(gh′(α)) ≠ 0, but χα(gγ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of h(α), and h′(α) < γ < h(α). (B) Let α ∈ P(n), α ≠ α′,
and n ⩾ 4. Then f′(α) is identical in sign to f(α), χα(gf′(α)) ≠ 0, but χα(gγ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of f(α), and f′(α) < γ < f(α). The results obtained are
then applied to study pairs of semiproportional irreducible characters in An.
Supported by RFBR grant No. 04-01-00463.
__________
Translated from Algebra i Logika, Vol. 44, No. 6, pp. 643–663, November–December, 2005. 相似文献
6.
Seyed Mahmoud Sheikholeslami 《Central European Journal of Mathematics》2010,8(3):468-473
A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ
t
(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt
(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Karami, Khoeilar, Sheikholeslami and Khodkar,
(Graphs and Combinatorics, 2009, 25, 727–733) proved that for any connected graph G of order n ≥ 3, sdγ
t
(G) ≤ 2γ
t
(G) − 1 and posed the following problem: Characterize the graphs that achieve the aforementioned upper bound. In this paper
we first prove that sdγ
t
(G) ≤ 2α′(G) for every connected graph G of order n ≥ 3 and δ(G) ≥ 2 where α′(G) is the maximum number of edges in a matching in G and then we characterize all connected graphs G with sdγ
t
(G)=2γ
t
(G)−1. 相似文献
7.
THE SECOND EXPONENT SET OF PRIMITIVE DIGRAPHS 总被引:2,自引:0,他引:2
51.IntroductionandNotationsLetD=(V,E)beadigraphandL(D)denotethesetofcyclelengthsofD.ForuEVandintegeri21,letfo(u):={vEVIthereedestsadirectedwalkoflengthifromutov}.WedelveRo(u):={u}.Letu,vEV.IfN (v)=N (v)andN--(v)=N--(v),thenwecanvacopyofu.LotDbeaprimitivedigraphand7(D)denotetheexponentofD.In1950,H.WielandtI61foundthat7(D)5(n--1)' 1andshowedthatthereisapiquedigraphthatattainsthisbound.In1964,A.L.DulmageandN.S.Mendelsohn[2]ObservedthattherearegapsintheexponentsetEd={ry(D)IDEPD.}… 相似文献
8.
Let (B
δ (t))
t ≥ 0 be a Brownian motion starting at 0 with drift δ > 0. Define by induction S
1=− inf
t ≥ 0
B
δ (t), ρ1 the last time such that B
δ (ρ1)=−S
1, S
2=sup0≤ t ≤ρ 1
B
δ (t), ρ2 the last time such that B
δ (ρ2)=S
2 and so on. Setting A
k
=S
k
+S
k+1; k ≥ 1, we compute the law of (A
1,...,A
k
) and the distribution of (B
δ (t+ρ l) − B
δ (ρ
l
); 0 ≤ t ≤ ρ
l-1 − ρ
l
)2 ≤ l ≤ k
for any k ≥ 2, conditionally on (A
1,...,A
k
). We determine the law of the range R
δ (t) of (B
δ (s))
s≥ 0 at time t, and the first range time θδ (a) (i.e. θδ (a)=inf{t > 0; R
δ (t) > a}). We also investigate the asymptotic behaviour of θ δ (a) (resp. R
δ (t)) as a → ∞ (resp. t → ∞). 相似文献
9.
Hanno Lefmann 《Discrete and Computational Geometry》2008,40(3):401-413
We consider a variant of Heilbronn’s triangle problem by investigating for a fixed dimension d≥2 and for integers k≥2 with k≤d distributions of n points in the d-dimensional unit cube [0,1]
d
, such that the minimum volume of the simplices, which are determined by (k+1) of these n points is as large as possible. Denoting by Δ
k,d
(n), the supremum of this minimum volume over all distributions of n points in [0,1]
d
, we show that c
k,d
⋅(log n)1/(d−k+1)/n
k/(d−k+1)≤Δ
k,d
(n)≤c
k,d
′/n
k/d
for fixed 2≤k≤d, and, moreover, for odd integers k≥1, we show the upper bound Δ
k,d
(n)≤c
k,d
″/n
k/d+(k−1)/(2d(d−1)), where c
k,d
,c
k,d
′,c
k,d
″>0 are constants.
A preliminary version of this paper appeared in COCOON ’05. 相似文献
10.
11.
El Maati Ouhabaz 《Semigroup Forum》1998,57(3):305-314
m
σ/|α|=|β|=m Dα(a
αβDβ) is a higher order degenerate-elliptic operator on L2(RN) and V ∈ L1(RN) we show in particular that s(λ) > 0 for all λ > 0 provided that ∫RN V(x)dx≥ 0, V not equivalent to 0 and N ≤ 2m. 相似文献
12.
Wu Liangsen 《数学学报(英文版)》1992,8(4):406-412
LetA, B be unitalC
*-algebras,D
A
1
the set of all completely positive maps ϕ fromA toM
n
(C), with Tr ϕ(I)≤1(n≥3). If Ψ is an α-invariant affine homeomorphism betweenD
A
1
andD
B
1
with Ψ (0)=0, thenA is*-isomorphic toB.
Obtained results can be viewed as non-commutative Kadison-Shultz theorems.
This work is supported by the National Natural Science Foundation of China. 相似文献
13.
Maryam Atapour Seyyed Mahmoud Sheikholeslami Rana Hajypory Lutz Volkmann 《Central European Journal of Mathematics》2010,8(6):1048-1057
Let k ≥ 1 be an integer, and let D = (V; A) be a finite simple digraph, for which d
D
− ≥ k − 1 for all v ɛ V. A function f: V → {−1; 1} is called a signed k-dominating function (SkDF) if f(N
−[v]) ≥ k for each vertex v ɛ V. The weight w(f) of f is defined by $
\sum\nolimits_{v \in V} {f(v)}
$
\sum\nolimits_{v \in V} {f(v)}
. The signed k-domination number for a digraph D is γ
kS
(D) = min {w(f|f) is an SkDF of D. In this paper, we initiate the study of signed k-domination in digraphs. In particular, we present some sharp lower bounds for γ
kS
(D) in terms of the order, the maximum and minimum outdegree and indegree, and the chromatic number. Some of our results are
extensions of well-known lower bounds of the classical signed domination numbers of graphs and digraphs. 相似文献
14.
We obtain a new upper bound for the sum Σ
h≤H
Δ
k
(N, h) when 1 ≤ H ≤ N, k ∈ ℕ, k ≥ 3, where Δ
k
(N, h) is the (expected) error term in the asymptotic formula for Σ
N<n≤2N
d
k
(n)d
k
(n + h), and d
k
(n) is the divisor function generated by ζ(s)
k
. When k = 3, the result improves, for H ≥ N
1/2, the bound given in a recent work of Baier, Browning, Marasingha and Zhao, who dealt with the case k = 3. 相似文献
15.
For a finite p-group G and a positive integer k let I
k
(G) denote the intersection of all subgroups of G of order p
k
. This paper classifies the finite p-groups G with Ik(G) @ Cpk-1{{I}_k(G)\cong C_{p^{k-1}}} for primes p > 2. We also show that for any k, α ≥ 0 with 2(α + 1) ≤ k ≤ n−α the groups G of order p
n
with Ik(G) @ Cpk-a{{I}_k(G)\cong C_{p^{k-\alpha}}} are exactly the groups of exponent p
n-α
. 相似文献
16.
J. Naumann 《Rendiconti del Circolo Matematico di Palermo》1998,47(3):409-430
We consider weak solutions to the parabolic system ∂u
i∂t−D
α
A
i
α
(∇u)=B
i(∇u) in (i=1,...,) (Q=Ω×(0,T), R
n
a domain), where the functionsB
i may have a quadratic growth. Under the assumptionsn≤2 and ∇u ɛL
loc
4+δ
(Q; R
nN
) (δ>0) we prove that ∇u is locally H?lder continuous inQ. 相似文献
17.
Let n ≥ 2 be a fixed positive integer, q ≥ 3 and c be two integers with (n, q) = (c, q) = 1. We denote by rn(51, 52, C; q) (δ 〈 δ1,δ2≤ 1) the number of all pairs of integers a, b satisfying ab ≡ c(mod q), 1 〈 a ≤δ1q, 1 ≤ b≤δ2q, (a,q) = (b,q) = 1 and nt(a+b). The main purpose of this paper is to study the asymptotic properties of rn (δ1, δ2, c; q), and give a sharp asymptotic formula for it. 相似文献
18.
Robert S. Strichartz 《Journal of Geometric Analysis》1991,1(3):269-289
Let μ be a measure on ℝn that satisfies the estimate μ(B
r(x))≤cr
α for allx ∈ ℝn and allr ≤ 1 (B
r(x) denotes the ball of radius r centered atx. Let ϕ
j,k
(ɛ)
(x)=2
nj2ϕ(ɛ)(2
j
x-k) be a wavelet basis forj ∈ ℤ, κ ∈ ℤn, and ∈ ∈E, a finite set, and letP
j
(T)=Σɛ,k
<T,ϕ
j,k
(ɛ)
>ϕ
j,k
(ɛ)
denote the associated projection operators at levelj (T is a suitable measure or distribution). Iff ∈Ls
p(dμ) for 1 ≤p ≤ ∞, we show thatP
j(f dμ) ∈ Lp(dx) and ||P
j
(fdμ)||L
p(dx)≤c2
j((n-α)/p′))||f||L
p(dμ) for allj ≥ 0. We also obtain estimates for the limsup and liminf of ||P
j
(fdμ)||L
p(dx) under more restrictive hypotheses.
Communicated by Guido Weiss 相似文献
19.
We present results on total domination in a partitioned graph G = (V, E). Let γ
t
(G) denote the total dominating number of G. For a partition , k ≥ 2, of V, let γ
t
(G; V
i
) be the cardinality of a smallest subset of V such that every vertex of V
i
has a neighbour in it and define the following
We summarize known bounds on γ
t
(G) and for graphs with all degrees at least δ we derive the following bounds for f
t
(G; k) and g
t
(G; k).
相似文献
(i) | For δ ≥ 2 and k ≥ 3 we prove f t (G; k) ≤ 11|V|/7 and this inequality is best possible. |
(ii) | for δ ≥ 3 we prove that f t (G; 2) ≤ (5/4 − 1/372)|V|. That inequality may not be best possible, but we conjecture that f t (G; 2) ≤ 7|V|/6 is. |
(iii) | for δ ≥ 3 we prove f t (G; k) ≤ 3|V|/2 and this inequality is best possible. |
(iv) | for δ ≥ 3 the inequality g t (G; k) ≤ 3|V|/4 holds and is best possible. |
20.
Aihua Fan 《Israel Journal of Mathematics》2002,131(1):157-184
Consider the Dvoretzky random covering with length sequence {α/n}
n≥1 (α>0). We are interested in the setF
β
of points on the circle which are covered by a numberβ logn of the firstn randomly placed intervals. It is proved among others that for a certain interval ofβ>0, the Hausdorff dimension ofF
β
is equal to 1−[βlog(β/α)−(β−α)]. This implies that points on the circle are differently covered.
The research was partially supported by the Zheng Ge Ru Foundation and the RGC grant of Hong Kong. 相似文献