Rainbow hamilton cycles in random graphs

One of the most famous results in the theory of random graphs establishes that the threshold for Hamiltonicity in the Erd?s‐Rényi random graph G_n,p is around . Much research has been done to extend this to increasingly challenging random structures. In particular, a recent result by Frieze determined the asymptotic threshold for a loose Hamilton cycle in the random 3‐uniform hypergraph by connecting 3‐uniform hypergraphs to edge‐colored graphs. In this work, we consider that setting of edge‐colored graphs, and prove a result which achieves the best possible first order constant. Specifically, when the edges of G_n,p are randomly colored from a set of (1 + o(1))n colors, with , we show that one can almost always find a Hamilton cycle which has the additional property that all edges are distinctly colored (rainbow).Copyright © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 44, 328‐354, 2014     

Separated sequences in nonreflexive Banach spaces

We prove that there is 1$"> such that the unit ball of any nonreflexive Banach space contains a -separated sequence. The supremum of these constants is estimated from below by and from above approximately by . Given any 1$">, we also construct a nonreflexive space so that if the convex hull of a sequence is sufficiently close to the unit sphere, then its separation constant does not exceed .

     

Measure of Noncompactness of Linear Operators between Spaces of Sequences That Are (N,q) Summable or Bounded

In this paper we investigate linear operators between arbitrary BK spaces X and spaces Y of sequences that are summable or bounded. We give necessary and sufficient conditions for infinite matrices A to map X into Y. Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for A to be a compact operator.     

-Sidon sets

The aim of this paper is to prove that for every , every -Rider set is a -Sidon set for all {\frac p{2-p}}\cdot$"> This gives some positive answers for the union problem of -Sidon sets. We also obtain some results on the behavior of the Fourier coefficient of a measure with spectrum in a -Rider set.

     

Exactly solvable models through the generalized empty interval method,for multi-species interactions

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for E _n(t)'s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time t. The constraints are solved for the single-species left-right-symmetric systems. Also, examples of multi-species system for which the evolution equations of E _n(t)'s are closed, are given. Received 25 September 2002 / Received in final form 3 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: mamwad@iasbs.ac.ir     

Magnetic properties of Yb Mo O and Gd Mo O from rare earth Mössbauer measurements

Using ¹⁷⁰Yb and ¹⁵⁵Gd M?ssbauer measurements down to ∼ 0.03 K, we have examined the semiconducting pyrochlore Yb₂Mo₂O₇ where the Mo intra-sublattice interaction is anti-ferromagnetic and the metallic pyrochlore Gd₂Mo₂O₇ where this interaction is ferromagnetic. Additional information was obtained from susceptibility, magnetisation and ¹⁷²Yb perturbed angular correlation measurements. The microscopic measurements evidence lattice disorder which is important in Yb₂Mo₂O₇ and modest in Gd₂Mo₂O₇. Magnetic irreversibilities occur at 17 K in Yb₂Mo₂O₇ and at 75 K in Gd₂Mo₂O₇ and below these temperatures the rare earths carry magnetic moments which are induced through couplings with the Mo sublattice. In Gd₂Mo₂O₇, we observe the steady state Gd hyperfine populations at 0.027 K are out of thermal equilibrium, indicating that Gd and Mo spin fluctuations persist at very low temperatures. Frustration is thus operative in this essentially isotropic pyrochlore where the dominant Mo intra-sublattice interaction is ferromagnetic. Received 13 January 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: hodges@drecam.saclay.cea.fr     

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N² bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N². The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q ³. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time. Received 12 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: stauffer@thp.uni-koeln.de     

Statistical equilibrium in simple exchange games I

This erratum corrects a mistake in reference [E. Scalas, U. Garibaldi, S. Donadio, Eur. Phys. J. B 53, 267 (2006)]. In that paper, we needed an aperiodic version of the BDY game, but, in formula (1), we incorrectly presented a periodic transition matrix of period 2 in the special case of g = 2 agents. Here, we present the right aperiodic version.     

Every Continuous Operator Has an Invariant Measure

We prove the existence of an invariant measure for a large class of random processes with discrete time without assuming their linearity. Our main examples are “processes with variable length”, in which components may appear and disappear in the course of functioning. One of these examples displays non-uniqueness of invariant measure in a 1-D process.     

随机排序模型及求解方法

本文介绍了随机排序模型,并对求解随机排序的基本方法作一简要综述。