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21.
A 1‐factorization of a graph G is a collection of edge‐disjoint perfect matchings whose union is E(G). In this paper, we prove that for any ?>0, an (n,d,λ)‐graph G admits a 1‐factorization provided that n is even, C0 ≤ d ≤ n?1 (where C0=C0(?) is a constant depending only on ?), and λ ≤ d1??. In particular, since (as is well known) a typical random d‐regular graph Gn,d is such a graph, we obtain the existence of a 1‐factorization in a typical Gn,d for all C0 ≤ d ≤ n?1, thereby extending to all possible values of d results obtained by Janson, and independently by Molloy, Robalewska, Robinson, and Wormald for fixed d. Moreover, we also obtain a lower bound for the number of distinct 1‐factorizations of such graphs G, which is better by a factor of 2nd/2 than the previously best known lower bounds, even in the simplest case where G is the complete graph. 相似文献
22.
R. Farhi A. Andreau E. Andreoli De Oliveira J-P. Marcerou H. T. Nguyen J-M. Tarascon 《Molecular Crystals and Liquid Crystals》2013,570(1):875-882
Abstract The use of Raman scattering technique as a tool for studying local order in complex liquid crystal systems is illustrated by three examples, namely the locally anisotropic liquid L-phase, lipid membranes, and PDLC's. 相似文献
23.
Bakir Farhi 《Journal of Number Theory》2008,128(8):2214-2230
Let A be an additive basis of order h and X be a finite nonempty subset of A such that the set A?X is still a basis. In this article, we give several upper bounds for the order of A?X in function of the order h of A and some parameters related to X and A. If the parameter in question is the cardinality of X, Nathanson and Nash already obtained some of such upper bounds, which can be seen as polynomials in h with degree (|X|+1). Here, by taking instead of the cardinality of X the parameter defined by , we show that the order of A?X is bounded above by . As a consequence, we deduce that if X is an arithmetic progression of length ?3, then the upper bounds of Nathanson and Nash are considerably improved. Further, by considering more complex parameters related to both X and A, we get upper bounds which are polynomials in h with degree only 2. 相似文献
24.
In this paper we investigate some properties of forcing which can be considered “nice” in the context of singularizing regular cardinals to have an uncountable cofinality. We show that such forcing which changes cofinality of a regular cardinal, cannot be too nice and must cause some “damage” to the structure of cardinals and stationary sets. As a consequence there is no analogue to the Prikry forcing, in terms of “nice” properties, when changing cofinalities to be uncountable. 相似文献
25.
We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in (Angel and Ray, Ann Probab, in press). We show that almost surely the walker escapes the boundary of the map in positive speed and that the return probability to the starting point after n steps scales like © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 213–234, 2016 相似文献
26.
A celebrated result of Gowers states that for every ?>0 there is a graph G such that every ?-regular partition of G (in the sense of Szemerédi’s regularity lemma) has order given by a tower of exponents of height polynomial in 1/?. In this note we give a new proof of this result that uses a construction and proof of correctness that are significantly simpler and shorter. 相似文献
27.
Muhammad Ibrahim Asaf Khan F. M. Allehiany Gul Zaman Vakkar Ali Tareq Saeed 《Mathematical Methods in the Applied Sciences》2024,47(2):660-679
This paper addresses the dynamics of COVID-19 using the approach of age-structured modeling. A particular case of the model is presented by taking into account age-free parameters. The sub-model consisting of ordinary differential equations (ODEs) is investigated for possible equilibria, and qualitative aspects of the model are rigorously presented. In order to control the spread of the disease, we considered two age- and time-dependent non-pharmaceutical control measures in the age-structured model, and an optimal control problem using a general maximum principle of Pontryagin type is achieved. Finally, sample simulations are plotted which support our theoretical work. 相似文献
28.
A new sample component is presented for the Monte Carlo, ray-tracing program, McStas, which is widely used to simulate neutron scattering instruments. The new component allows the sample to be described by its material dynamic structure factor, which is separated into coherent and incoherent contributions. The effects of absorption and multiple scattering are treated and results from simulations and previous experiments are compared. 相似文献
29.
Asaf Kleopas Sugih 《European Polymer Journal》2009,45(1):155-164
The ring opening polymerization (ROP) of p-dioxanone using a protected monosaccharide (1,2;3,4-di-O-isopropylidene-α-d-galactopyranose)/Al(OiPr)3 initiator system to yield polydioxanone with a protected monosaccharide end-group is described. The products were synthesized at 60-100 °C and characterized by 1H and 13C NMR, and MALDI-TOF mass spectrometry. Besides the desired polydioxanone functionalised with a monosaccharide end-group, also polydioxanone with an OiPr end-group was formed (20-30%). Systematic studies showed that the polymer yield is a function of the reaction temperature and the reaction time, with higher temperatures (100 °C) leading to lower yields. The average chain length of the polymers is between 7 and 58 repeating units and may be tuned by the monomer to monosaccharide ratio (at constant Al(OiPr)3 intake). A statistical model has been developed that successfully describes the experimentally observed relation between the average chain length of the functionalized polymer and reaction parameters. 相似文献
30.
Asaf Nachmias 《Geometric And Functional Analysis》2009,19(4):1171-1194
Let {G n } be a sequence of finite transitive graphs with vertex degree d = d(n) and |G n | = n. Denote by p t (v, v) the return probability after t steps of the non-backtracking random walk on G n . We show that if p t (v, v) has quasi-random properties, then critical bond-percolation on G n behaves as it would on a random graph. More precisely, if $\mathop {\rm {lim\, sup\,}} \limits_{n} n^{1/3} \sum\limits_{t = 1}^{n^{1/3}} {t{\bf p}^t(v,v) < \infty ,}$ then the size of the largest component in p-bond-percolation with ${p =\frac{1+O(n^{-1/3})}{d-1}}Let {G
n
} be a sequence of finite transitive graphs with vertex degree d = d(n) and |G
n
| = n. Denote by p
t
(v, v) the return probability after t steps of the non-backtracking random walk on G
n
. We show that if p
t
(v, v) has quasi-random properties, then critical bond-percolation on G
n
behaves as it would on a random graph. More precisely, if
lim sup n n1/3 ?t = 1n1/3 tpt(v,v) < ¥,\mathop {\rm {lim\, sup\,}} \limits_{n} n^{1/3} \sum\limits_{t = 1}^{n^{1/3}} {t{\bf p}^t(v,v) < \infty ,} 相似文献 |