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Maximal sumfree sets chosen from the non-zero elements of galois group of order 26 (i.e. GF(26)?{0}) are found to be of size 13, 17, 18, 20 and 32 only. This gives a negative result to an investigation which would otherwise have delivered an exact value of the Ramsey number R(3,3,3,3;2). 相似文献
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Spatially homogeneous random evolutions arise in the study of the growth of a population in a spatially homogeneous random environment. The random evolution is obtained as the solution of a bilinear stochastic evolution equation. The main results are concerned with the asymptotic behavior of the solution for large times. In particular, conditions for the existence of a stationary random field are established. Furthermore space-time renormalization limit theorems are obtained which lead to either Gaussian or non-Gaussian generalized processes depending on the case under consideration. 相似文献
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Networks of dynamical nodes serve as generic models for real-world systems in many branches of science ranging from mathematics to physics, technology, sociology and biology. Collective behavior of agents interacting over complex networks is important in many applications. The cooperation between selfish individuals is one of the most interesting collective phenomena. In this paper we address the interplay between the motifs’ cooperation properties and their abundance in a number of real-world networks including yeast protein-protein interaction, human brain, protein structure, email communication, dolphins’ social interaction, Zachary karate club and Net-science coauthorship networks. First, the amount of cooperativity for all possible undirected subgraphs with three to six nodes is calculated. To this end, the evolutionary dynamics of the Prisoner’s Dilemma game is considered and the cooperativity of each subgraph is calculated as the percentage of cooperating agents at the end of the simulation time. Then, the three- to six-node motifs are extracted for each network. The significance of the abundance of a motif, represented by a Z-value, is obtained by comparing them with some properly randomized versions of the original network. We found that there is always a group of motifs showing a significant inverse correlation between their cooperativity amount and Z-value, i.e. the more the Z-value the less the amount of cooperativity. This suggests that networks composed of well-structured units do not have good cooperativity properties. 相似文献
79.
In this survey paper, we shall establish sufficient conditions for the existence and uniqueness of solutions for various classes
of initial and boundary value problem for fractional differential equations and inclusions involving the Caputo fractional
derivative. The both cases of convex and nonconvex valued right hand side are considered. The topological structure of the
set of solutions is also considered. 相似文献
80.
In this paper we investigate the monotonicity properties of an unreliable M/G/1 retrial queue using the general theory of
stochastic ordering. We show the monotonicity of the transition operator of the embedded Markov chain relative to the strong
stochastic ordering and increasing convex ordering. We obtain conditions of comparability of two transition operators and
we obtain comparability conditions of the number of customers in the system. Inequalities are derived for the mean characteristics
of the busy period, number of customers served during a busy period, number of orbit busy periods and waiting times. Inequalities
are also obtained for some probabilities of the steady-state distribution of the server state. An illustrative numerical example
is presented. 相似文献