共查询到20条相似文献,搜索用时 31 毫秒
1.
Liudmila Ostroumova Prokhorenkova 《Optimization Letters》2017,11(2):279-298
This is a review paper that covers some recent results on the behavior of the clustering coefficient in preferential attachment networks and scale-free networks in general. The paper focuses on general approaches to network science. In other words, instead of discussing different fully specified random graph models, we describe some generic results which hold for classes of models. Namely, we first discuss a generalized class of preferential attachment models which includes many classical models. It turns out that some properties can be analyzed for the whole class without specifying the model. Such properties are the degree distribution and the global and average local clustering coefficients. Finally, we discuss some surprising results on the behavior of the global clustering coefficient in scale-free networks. Here we do not assume any underlying model. 相似文献
2.
In this paper, we show the existence of universal inequalities for the h*-vector of a lattice polytope P, that is, we show that there are relations among the coefficients of the h*-polynomial that are independent of both the dimension and the degree of P. More precisely, we prove that the coefficients h* 1 and h* 2 of the h*-vector (h* 0, h* 1,..., h* d) of a lattice polytope of any degree satisfy Scott’s inequality if h* 3 = 0. 相似文献
3.
Let K be a field of characteristic p>0 and let f(t 1,…,t d ) be a power series in d variables with coefficients in K that is algebraic over the field of multivariate rational functions K(t 1,…,t d ). We prove a generalization of both Derksen’s recent analogue of the Skolem–Mahler–Lech theorem in positive characteristic and a classical theorem of Christol, by showing that the set of indices (n 1,…,n d )∈? d for which the coefficient of \(t_{1}^{n_{1}}\cdots t_{d}^{n_{d}}\) in f(t 1,…,t d ) is zero is a p-automatic set. Applying this result to multivariate rational functions leads to interesting effective results concerning some Diophantine equations related to S-unit equations and more generally to the Mordell–Lang Theorem over fields of positive characteristic. 相似文献
4.
For integers m > r ≥ 0, Brietzke (2008) defined the (m, r)-central coefficients of an infinite lower triangular matrix G = (d, h) = (dn,k)n,k∈N as dmn+r,(m?1)n+r, with n = 0, 1, 2,..., and the (m, r)-central coefficient triangle of G as It is known that the (m, r)-central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array G = (d, h) with h(0) = 0 and d(0), h′(0) ≠ 0, we obtain the generating function of its (m, r)-central coefficients and give an explicit representation for the (m, r)-central Riordan array G(m,r) in terms of the Riordan array G. Meanwhile, the algebraic structures of the (m, r)-central Riordan arrays are also investigated, such as their decompositions, their inverses, and their recessive expressions in terms of m and r. As applications, we determine the (m, r)-central Riordan arrays of the Pascal matrix and other Riordan arrays, from which numerous identities are constructed by a uniform approach.
相似文献
$${G^{\left( {m,r} \right)}} = {\left( {{d_{mn + r,\left( {m - 1} \right)n + k + r}}} \right)_{n,k \in \mathbb{N}}}.$$
5.
Index sets of decidable models 总被引:1,自引:1,他引:0
E. B. Fokina 《Siberian Mathematical Journal》2007,48(5):939-948
We study the index sets of the class of d-decidable structures and of the class of d-decidable countably categorical structures, where d is an arbitrary arithmetical Turing degree. It is proved that the first of them is m-complete ∑ 3 0, d , and the second is m-complete ∑ 3 0, d \∑ 3 0, d in the universal computable numbering of computable structures for the language with one binary predicate. 相似文献
6.
Let Δ n,d (resp. Δ′ n,d ) be the simplicial complex and the facet ideal I n,d = (x 1... x d, x d?k+1... x 2d?k ,..., x n?d+1... x n ) (resp. J n,d = (x 1... x d , x d?k+1... x 2d?k ,..., x n?2d+2k+1... x n?d+2k , x n?d+k+1... x n x 1... x k)). When d ≥ 2k + 1, we give the exact formulas to compute the depth and Stanley depth of quotient rings S/J n,d and S/I n,d t for all t ≥ 1. When d = 2k, we compute the depth and Stanley depth of quotient rings S/Jn,d and S/I n,d , and give lower bounds for the depth and Stanley depth of quotient rings S/I n,d t for all t ≥ 1. 相似文献
7.
Quanwu Mu 《Frontiers of Mathematics in China》2017,12(6):1457-1468
Let d ? 3 be an integer, and set r = 2d?1 + 1 for 3 ? d ? 4, \(\tfrac{{17}}{{32}} \cdot 2^d + 1\) for 5 ? d ? 6, r = d2+d+1 for 7 ? d ? 8, and r = d2+d+2 for d ? 9, respectively. Suppose that Φ i (x, y) ∈ ?[x, y] (1 ? i ? r) are homogeneous and nondegenerate binary forms of degree d. Suppose further that λ1, λ2,..., λ r are nonzero real numbers with λ1/λ2 irrational, and λ1Φ1(x1, y1) + λ2Φ2(x2, y2) + · · · + λ r Φ r (x r , y r ) is indefinite. Then for any given real η and σ with 0 < σ < 22?d, it is proved that the inequality has infinitely many solutions in integers x1, x2,..., x r , y1, y2,..., y r . This result constitutes an improvement upon that of B. Q. Xue.
相似文献
$$\left| {\sum\limits_{i = 1}^r {{\lambda _i}\Phi {}_i\left( {{x_i},{y_i}} \right) + \eta } } \right| < {\left( {\mathop {\max \left\{ {\left| {{x_i}} \right|,\left| {{y_i}} \right|} \right\}}\limits_{1 \leqslant i \leqslant r} } \right)^{ - \sigma }}$$
8.
B. Grigelionis 《Lithuanian Mathematical Journal》2009,49(4):372-380
We consider centered conditionally Gaussian d-dimensional vectors X with random covariance matrix Ξ having an arbitrary probability distribution law on the set of nonnegative definite symmetric d × d matrices M d +. The paper deals with the evaluation problem of mean values \( E\left[ {\prod\nolimits_{i = 1}^{2n} {\left( {{c_i},X} \right)} } \right] \) for c i ∈ ? d , i = 1, …, 2n, extending the Wick theorem for a wide class of non-Gaussian distributions. We discuss in more detail the cases where the probability law ?(Ξ) is infinitely divisible, the Wishart distribution, or the inverse Wishart distribution. An example with Ξ \( = \sum\nolimits_{j = 1}^m {{Z_j}{\sum_j}} \), where random variables Z j , j = 1, …, m, are nonnegative, and Σ j ∈ M d +, j = 1, …, m, are fixed, includes recent results from Vignat and Bhatnagar, 2008. 相似文献
9.
The main result of this paper asserts that the distribution density of any non-constant polynomial f(ξ1,ξ2,...) of degree d in independent standard Gaussian random variables ξ1 (possibly, in infinitely many variables) always belongs to the Nikol’skii–Besov space B1/d (R1) of fractional order 1/d (see the definition below) depending only on the degree of the polynomial. A natural analog of this assertion is obtained for the density of the joint distribution of k polynomials of degree d, also with a fractional order that is independent of the number of variables, but depends only on the degree d and the number of polynomials. We also give a new simple sufficient condition for a measure on Rk to possess a density in the Nikol’skii–Besov class Bα(R)k. This result is applied for obtaining an upper bound on the total variation distance between two probability measures on Rk via the Kantorovich distance between them and a certain Nikol’skii–Besov norm of their difference. Applications are given to estimates of distributions of polynomials in Gaussian random variables. 相似文献
10.
Let G = (V,A) be a digraph and k ≥ 1 an integer. For u, v ∈ V, we say that the vertex u distance k-dominate v if the distance from u to v at most k. A set D of vertices in G is a distance k-dominating set if each vertex of V D is distance k-dominated by some vertex of D. The distance k-domination number of G, denoted by γ k (G), is the minimum cardinality of a distance k-dominating set of G. Generalized de Bruijn digraphs G B (n, d) and generalized Kautz digraphs G K (n, d) are good candidates for interconnection networks. Denote Δ k := (∑ j=0 k d j )?1. F. Tian and J. Xu showed that ?nΔ k ? γ k (G B (n, d)) ≤?n/d k? and ?nΔ k ? ≤ γ k (G K (n, d)) ≤ ?n/d k ?. In this paper, we prove that every generalized de Bruijn digraph G B (n, d) has the distance k-domination number ?nΔ k ? or ?nΔ k ?+1, and the distance k-domination number of every generalized Kautz digraph G K (n, d) bounded above by ?n/(d k?1+d k )?. Additionally, we present various sufficient conditions for γ k (G B (n, d)) = ?nΔ k ? and γ k (G K (n, d)) = ?nΔ k ?. 相似文献
11.
Yuval Filmus Hamed Hatami Nathan Keller Noam Lifshitz 《Israel Journal of Mathematics》2016,214(1):167-192
Let f: {-1, 1}n → [-1, 1] have degree d as a multilinear polynomial. It is well-known that the total influence of f is at most d. Aaronson and Ambainis asked whether the total L1 influence of f can also be bounded as a function of d. Ba?kurs and Bavarian answered this question in the affirmative, providing a bound of O(d3) for general functions and O(d2) for homogeneous functions. We improve on their results by providing a bound of d2 for general functions and O(d log d) for homogeneous functions. In addition, we prove a bound of d/(2p) + o(d) for monotone functions, and provide a matching example. 相似文献
12.
V. V. Shenmaier 《Journal of Applied and Industrial Mathematics》2012,6(3):381-386
We consider the following clustering problem: Given a vector set, find a subset of cardinality k and minimum square deviation from its mean. The distance between the vectors is defined by the Euclideanmetric. We present an approximation scheme (PTAS) that allows us to solve this problem with an arbitrary relative error ? in time O(n 2/?+1(9/?)3/? d), where n is the number of vectors of the input set and d denotes the dimension of the space. 相似文献
13.
Let CC d,k be the largest possible number of vertices in a cyclic Cayley graph of degree d and diameter k, and let AC d,k be the largest order in an Abelian Cayley graph for given d and k. We show that \({CC_{d,2} \geq \frac{13}{36} (d + 2)(d -4)}\) for any d= 6p?2 where p is a prime such that \({p \neq 13}\) , \({p \not\equiv 1}\) (mod 13), and \({AC_{d,3} \geq \frac{9}{128} (d + 3)^2(d - 5)}\) for d = 8q?3 where q is a prime power. 相似文献
14.
Let M be a finitely generated module of dimension d and depth t over a Noetherian local ring (A, \({\mathfrak{m}}\)) and I an \({\mathfrak{m}}\)-primary ideal. In the main result it is shown that the last t Hilbert coefficients \({e_{d-t+1}(I,M),\ldots, e_{d}(I,M)}\) are bounded below and above in terms of the first d ? t + 1 Hilbert coefficients \({e_{0}(I,M),\ldots,e_{d-t}(I,M)}\) and d. 相似文献
15.
Let L=?Δ+V be a Schrödinger operator on ? d , d≥3. We assume that V is a nonnegative, compactly supported potential that belongs to L p (? d ), for some p>d /2. Let K t be the semigroup generated by ?L. We say that an L 1(? d )-function f belongs to the Hardy space \(H^{1}_{L}\) associated with L if sup?t>0|K t f| belongs to L 1(? d ). We prove that \(f\in H^{1}_{L}\) if and only if R j f∈L 1(? d ) for j=1,…,d, where R j =(?/? x j )L ?1/2 are the Riesz transforms associated with L. 相似文献
16.
Under study are some commuting rank 2 differential operators with polynomial coefficients. We prove that, for every spectral curve of the form w2 = z3+c2z2+c1z+c0 with arbitrary coefficients ci, there exist commuting nonselfadjoint operators of orders 4 and 6 with polynomial coefficients of arbitrary degree. 相似文献
17.
In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3(n). The aim of this paper is to generalize Tong's method to a class of Dirichlet series L(s) which satisfies a functional equation. Let a(n) be an arithmetical function related to a Dirichlet series L(s), and let E(x) be the error term of ′n xa(n). In this paper, after introducing a class of Diriclet series with a general functional equation(which contains the well-known Selberg class), we establish a Tong-type identity and a Tong-type truncated formula for the error term of the Riesz mean of the coefficients of this Dirichlet series L(s). This kind of Tong-type truncated formula could be used to study the mean square of E(x) under a certain assumption. In other words, we reduce the mean square of E(x) to the problem of finding a suitable constant σ*which is related to the mean square estimate of L(s). We shall represent some results of functions in the Selberg class of degrees 2–4. 相似文献
18.
We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs (constructed in [LPS]). They are obtained as quotients of the buildings of typeà d?1 associated with PGL d (F) whereF is a local field of positive characteristic. 相似文献
19.
It is well-known that the rings Od of algebraic integers in \(\mathbb{Q}(\sqrt { - d} )\) for d = 19, 43, 67, and 163 are principal ideal domains but not Euclidean. In this article we shall provide a method, based on a result of P. M. Cohn, to construct explicitly pairs (b, a) of integers in Od for d = 19, 43, 67, and 163 such that, in Od, there exists no terminating division chain of finite length starting from the pairs (b, a). That is, a greatest common divisor of the pairs (b, a) exists in Od but it can not be obtained by applying a terminating division chain of finite length starting from (b, a). Furthermore, for squarefree positive integer d ? {1, 2, 3, 7, 11, 19, 43, 67, 163}, we shall also construct pairs (b, a) of integers in Od which generate Od but have no terminating division chain of finite length. It is of interest to note that our construction provides a short alternative proof of a theorem of Cohn which is related to the concept of GE2-rings. 相似文献
20.
Aaloka Kanhere 《印度理论与应用数学杂志》2012,43(2):155-178
Let C be a smooth (irreducible) curve of degree d in ?2. Let ?2 ? ?5 be the Veronese embedding and let I C denote the homogeneous ideal of C on ?5. In this note we explicitly write down the minimal free resolution of I C for d ≥ 2. 相似文献