1‐Factorizations of pseudorandom graphs

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 ≤ d^1??. In particular, since (as is well known) a typical random d‐regular graph G_n,d is such a graph, we obtain the existence of a 1‐factorization in a typical G_n,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 2^nd/2 than the previously best known lower bounds, even in the simplest case where G is the complete graph.     

Restrictions on forcings that change cofinalities

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.     

Random walks on stochastic hyperbolic half planar triangulations

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     

A short proof of Gowers’ lower bound for the regularity lemma

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.     

Optimal control theory of an age-structured coronavirus disease model and the dynamical analysis of the underlying ordinary differential equation model having constant parameters

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.     

Experimental studies on the ring opening polymerization of p-dioxanone using an Al(OPr)3-monosaccharide initiator system

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.     

Mean-Field Conditions for Percolation on Finite Graphs

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 ,}      18. Approximation algorithms for maximum latency and partial cycle cover      Refael Hassin  Asaf Levin  Shlomi Rubinstein 《Discrete Optimization》2009,6(2):197-205       19. Directed self-assembly of gold-tipped CdSe nanorods      Salant A  Amitay-Sadovsky E  Banin U 《Journal of the American Chemical Society》2006,128(31):10006-10007 Gold-tipped CdSe rods (nanodumbbells) were solubilized in an aqueous phase and self-assembled in a head-to-tail manner using biotin disulfide and avidin. The disulfide end of the biotin molecule attaches to the gold tip of the nanodumbbell, and the biotin end of the molecule is able to conjugate to an avidin protein. The avidin can strongly conjugate up to four biotin molecules. Changing the ratios of biotin to nanodumbbells leads to the formation of dimers, trimers, and flowerlike structures. To further improve the distribution of chain lengths, a separation method based upon weight was applied using a concentration gradient. The gold tips provide effective anchor points for constructing complex nanorod structures by self-assembly.      20. The Local Limit of the Uniform Spanning Tree on Dense Graphs      Jan?HladkyView author&#;s OrcID profile  Asaf?NachmiasEmail author  Tuan?Tran 《Journal of statistical physics》2018,173(3-4):502-545 Let G be a connected graph in which almost all vertices have linear degrees and let \(\mathcal {T}\) be a uniform spanning tree of G. For any fixed rooted tree F of height r we compute the asymptotic density of vertices v for which the r-ball around v in \(\mathcal {T}\) is isomorphic to F. We deduce from this that if \(\{G_n\}\) is a sequence of such graphs converging to a graphon W, then the uniform spanning tree of \(G_n\) locally converges to a multi-type branching process defined in terms of W. As an application, we prove that in a graph with linear minimum degree, with high probability, the density of leaves in a uniform spanning tree is at least \(e^{-1}-\mathsf {o}(1)\), the density of vertices of degree 2 is at most \(e^{-1}+\mathsf {o}(1)\) and the density of vertices of degree \(k\geqslant 3\) is at most \({(k-2)^{k-2} \over (k-1)! e^{k-2}} + \mathsf {o}(1)\). These bounds are sharp.      [首页] « 上一页 [1] 2 [3] [4] [5] [6] [7] [8] [9] [10] 下一页 » 末  页»

Directed self-assembly of gold-tipped CdSe nanorods

Gold-tipped CdSe rods (nanodumbbells) were solubilized in an aqueous phase and self-assembled in a head-to-tail manner using biotin disulfide and avidin. The disulfide end of the biotin molecule attaches to the gold tip of the nanodumbbell, and the biotin end of the molecule is able to conjugate to an avidin protein. The avidin can strongly conjugate up to four biotin molecules. Changing the ratios of biotin to nanodumbbells leads to the formation of dimers, trimers, and flowerlike structures. To further improve the distribution of chain lengths, a separation method based upon weight was applied using a concentration gradient. The gold tips provide effective anchor points for constructing complex nanorod structures by self-assembly.     

The Local Limit of the Uniform Spanning Tree on Dense Graphs

Let G be a connected graph in which almost all vertices have linear degrees and let \(\mathcal {T}\) be a uniform spanning tree of G. For any fixed rooted tree F of height r we compute the asymptotic density of vertices v for which the r-ball around v in \(\mathcal {T}\) is isomorphic to F. We deduce from this that if \(\{G_n\}\) is a sequence of such graphs converging to a graphon W, then the uniform spanning tree of \(G_n\) locally converges to a multi-type branching process defined in terms of W. As an application, we prove that in a graph with linear minimum degree, with high probability, the density of leaves in a uniform spanning tree is at least \(e^{-1}-\mathsf {o}(1)\), the density of vertices of degree 2 is at most \(e^{-1}+\mathsf {o}(1)\) and the density of vertices of degree \(k\geqslant 3\) is at most \({(k-2)^{k-2} \over (k-1)! e^{k-2}} + \mathsf {o}(1)\). These bounds are sharp.