共查询到20条相似文献,搜索用时 31 毫秒
1.
The study of the CO‐irredundant Ramsey numbers t(n1, ···, nk) is initiated. It is shown that several values and bounds for these numbers may be obtained from the well‐studied generalized graph Ramsey numbers and the values of t(4, 5), t(4, 6) and t(3, 3, m) are calculated. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 258–268, 2000 相似文献
2.
A. Bodin 《Commentarii Mathematici Helvetici》2003,78(1):134-152
We give a global version of Lê-Ramanujam μ-constant theorem for polynomials. Let , , be a family of polynomials of n complex variables with isolated singularities, whose coefficients are polynomials in t. We consider the case where some numerical invariants are constant (the affine Milnor number μ(t), the Milnor number at infinity λ(t), the number of critical values, the number of affine critical values, the number of critical values at infinity). Let n=2, we also suppose the degree of the is a constant, then the polynomials and are topologically equivalent. For we suppose that critical values at infinity depend continuously on t, then we prove that the geometric monodromy representations of the are all equivalent.
Received: January 14, 2002 相似文献
3.
By the extremal number
ex(n; t) = ex(n; {C
3, C
4, . . . , C
t
}) we denote the maximum size (that is, number of edges) in a graph of order n > t and girth at least g ≥ t + 1. The set of all the graphs of order n, containing no cycles of length ≥ t, and of size ex(n; t), is denoted by EX(n; t) = EX(n; {C
3, C
4, . . . , C
t
}), these graphs are called EX graphs. In 1975, Erdős proposed the problem of determining the extremal numbers ex(n; 4) of a graph of order n and girth at least 5. In this paper, we consider a generalized version of this problem, for t ≥ 5. In particular, we prove that ex(29; 6) = 45, also we improve some lower bounds and upper bounds of ex
u
(n; t), for some particular values of n and t. 相似文献
4.
Let {Xn} be a strictly stationary φ-mixing process with Σj=1∞ φ1/2(j) < ∞. It is shown in the paper that if X1 is uniformly distributed on the unit interval, then, for any t [0, 1], |Fn−1(t) − t + Fn(t) − t| = O(n−3/4(log log n)3/4) a.s. and sup0≤t≤1 |Fn−1(t) − t + Fn(t) − t| = (O(n−3/4(log n)1/2(log log n)1/4) a.s., where Fn and Fn−1(t) denote the sample distribution function and tth sample quantile, respectively. In case {Xn} is strong mixing with exponentially decaying mixing coefficients, it is shown that, for any t [0, 1], |Fn−1(t) − t + Fn(t) − t| = O(n−3/4(log n)1/2(log log n)3/4) a.s. and sup0≤t≤1 |Fn−1(t) − t + Fn(t) − t| = O(n−3/4(log n)(log log n)1/4) a.s. The results are further extended to general distributions, including some nonregular cases, when the underlying distribution function is not differentiable. The results for φ-mixing processes give the sharpest possible orders in view of the corresponding results of Kiefer for independent random variables. 相似文献
5.
Let t(n) denote the greatest number of arcs in a diagraph of orders n which does not contain any antidrected cycles. We show that [16/5(n ? 1)] ≤ t(n) ≤ 1/2 (n ? 1) for n ≥ 5. Let tr (n) denote the corresponding quantity for r-colorable digraphs. We show that [16/5(n ? 1)] ≤ t5(n) ≤ t6(n) ≤ 10/3(n ? 1) for n ≥ 5 and that t4(n) = 3(n ? 1) for n ≥ 3. 相似文献
6.
Thomas Shermer 《Computational Geometry》1991,1(2)
Shermer, T., Computing bushy and thin triangulations, Computational Geometry: Theory and Applications 1 (1991) 115–125. Given a triangulation of a simple polygon P, let t2 be the number of leaves in the dual tree of the triangulation. Also, define tmax(P) and tmin(P) as the maximum and minimum values of t2 over all triangulations of P. We present an O(n) time, O(n) space algorithm for finding a triangulation with t2 = tmax(P), assuming that we are given any triangulation of P. We also show a triangulation with t2 = tmin(P) can be found in O(n3) time, using O(n2) space. 相似文献
7.
We consider the M(t)/M(t)/m/m queue, where the arrival rate λ(t) and service rate μ(t) are arbitrary (smooth) functions of time. Letting pn(t) be the probability that n servers are occupied at time t (0≤ n≤ m, t > 0), we study this distribution asymptotically, for m→∞ with a comparably large arrival rate λ(t) = O(m) (with μ(t) = O(1)). We use singular perturbation techniques to solve the forward equation for pn(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability
pm(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n0 servers are occupied, 0≤ n0≤ m). Numerical studies back up the asymptotic analysis.
AMS subject classification: 60K25,34E10
Supported in part by NSF grants DMS-99-71656 and DMS-02-02815 相似文献
8.
Tibor Jordn 《Journal of Graph Theory》1999,31(3):179-193
Let A(n, k, t) denote the smallest integer e for which every k‐connected graph on n vertices can be made (k + t)‐connected by adding e new edges. We determine A(n, k, t) for all values of n, k, and t in the case of (directed and undirected) edge‐connectivity and also for directed vertex‐connectivity. For undirected vertex‐connectivity we determine A(n, k, 1) for all values of n and k. We also describe the graphs that attain the extremal values. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 179–193, 1999 相似文献
9.
We introduce a new class H
n of univalent polynomials and establish that for every polynomial in H
n the Hele–Shaw problem has a polynomial solution w(z;t) for all values t>0. We also demonstrate that the members of H
n are starlike. 相似文献
10.
Fu Qing GAO 《数学学报(英文版)》2007,23(8):1527-1536
Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E(X1) and let {N(t); t ≥0} be a random process taking non-negative integer values with finite mean λ(t) = E(N(t)) and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P((X1 +… +XN(t)) -λ(t)μ 〉 x) uniformly for x ∈[γb(t), ∞) are obtained, where γ〉 0 and b(t) can be taken to be a positive function with limt→∞ b(t)/λ(t) = 0. 相似文献
11.
Gerald Kuba 《Mathematica Slovaca》2009,59(3):349-356
Let ℛ
n
(t) denote the set of all reducible polynomials p(X) over ℤ with degree n ≥ 2 and height ≤ t. We determine the true order of magnitude of the cardinality |ℛ
n
(t)| of the set ℛ
n
(t) by showing that, as t → ∞, t
2 log t ≪ |ℛ2(t)| ≪ t
2 log t and t
n
≪ |ℛ
n
(t)| ≪ t
n
for every fixed n ≥ 3. Further, for 1 < n/2 < k < n fixed let ℛ
k,n
(t) ⊂ ℛ
n
(t) such that p(X) ∈ ℛ
k,n
(t) if and only if p(X) has an irreducible factor in ℤ[X] of degree k. Then, as t → ∞, we always have t
k+1 ≪ |ℛ
k,n
(t)| ≪ t
k+1 and hence |ℛ
n−1,n
(t)| ≫ |ℛ
n
(t)| so that ℛ
n−1,n
(t) is the dominating subclass of ℛ
n
(t) since we can show that |ℛ
n
(t)∖ℛ
n−1,n
(t)| ≪ t
n−1(log t)2.On the contrary, if R
n
s
(t) is the total number of all polynomials in ℛ
n
(t) which split completely into linear factors over ℤ, then t
2(log t)
n−1 ≪ R
n
s
(t) ≪ t
2 (log t)
n−1 (t → ∞) for every fixed n ≥ 2.
相似文献
12.
The nilpotent Lie algebras L of dimension n whose multipliers have dimension ½n(n-1)-t(L) have been found in [2] for t(L) = 0,1,2. Using a different method, we find similar results for t(L) = 3,4,5,6. The first author is extending the results to t(L) = 7 and 8. 相似文献
13.
Let k be a positive number and t
k(n) denote the number of representations of n as a sum of k triangular numbers. In this paper, we will calculate t
2k
(n) in the spirit of Ramanujan. We first use the complex theory of elliptic functions to prove a theta function identity. Then from this identity we derive two Lambert series identities, one of them is a well-known identity of Ramanujan. Using a variant form of Ramanujan's identity, we study two classes of Lambert series and derive some theta function identities related to these Lambert series . We calculate t
12(n), t
16(n), t
20(n), t
24(n), and t
28(n) using these Lambert series identities. We also re-derive a recent result of H. H. Chan and K. S. Chua [6] about t
32(n). In addition, we derive some identities involving the Ramanujan function (n), the divisor function 11(n), and t
24(n). Our methods do not depend upon the theory of modular forms and are somewhat more transparent. 相似文献
14.
Qiyi Fan Wentao Wang Xuejun Yi 《Journal of Computational and Applied Mathematics》2009,230(2):762-769
In this paper, we use the Leray–Schauder degree theory to establish new results on the existence and uniqueness of anti-periodic solutions for a class of nonlinear nth-order differential equations with delays of the form
x(n)(t)+f(t,x(n−1)(t))+g(t,x(t−τ(t)))=e(t).