It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at least 2 √ d − 1 cos( π 2k ). A similar result has been proved by Friedman using more sophisticated tools.

We deal here with colorings of the pair (µ + , µ), when µ is a strong limit and singular cardinal. We show that there exists a coloring c, with no refinement. It follows, that the properties of identities of (µ + , µ) when µ is singular, differ in an essential way from the case of regular µ.

A multicircuit is a multigraph whose underlying simple graph is a circuit (a connected 2-regular graph). In this pair of papers, it is proved that every multicircuit C has total choosability (i.e., list total chromatic number) ch00(C ) equal to its ordinary total chromatic number 00(C ). In the present paper, the kernel method is used to prove this for every multicircuit that

Any multivariate density can be decomposed through successive conditionings into basic building blocks involving only pairs of variables. The various ways in which this can be done are called regular vines; C-vines and D-vines are prime examples of such structures. A pair-copula construction (PCC) is a modelling strategy in which conditional and unconditional bivariate copula densities are assi...

Given a sequence A of length M and a regular expression R of length P, an approximate regular expression pattern matching algorithm computes the score of the optimal alignment between A and one of the sequences B exactly matched by R. An alignment between sequences A = a 1 a 2 : : :a M and B = b 1 b 2 : : :b N is a list of ordered pairs, <(i 1 ; j 1); (i 2 ; j 2); : : :(i t ; j t)> such that i ...

A criterion for the approximability of all solutions heat equation in a bounded cylindrical domain that belong to Lebesgue class by more regular (e.g., Sobolev) same with larger base is obtained. Namely, complement smaller one must have no (nonempty connected) compact components. As an important corollary, we prove theorem on existence doubly orthogonal basis corresponding pair Hilbert spaces.

In this paper we provide a purely combinatorial proof of the Friendship Theorem, which has been first proven by P. Erdös et al. by using also algebraic methods. Moreover, we generalize this theorem in a natural way, assuming that every pair of nodes occupies ≥ 2 common neighbors. We prove that every graph, which satisfies this generalized -friendship condition, is a regular graph.

The amplitude of motor-evoked potentials (MEPs) elicited with transcranial magnetic stimulation (TMS) varies from trial-to-trial. Synchronous oscillations in cortical neuronal excitability contribute to this variability, however it is not known how different frequencies of stimulation influence MEP variability, and whether these oscillations are rhythmic or aperiodic. We stimulated the motor co...

We consider a special case of the generalized Pólya’s urn model introduced in [3]. Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability proportional to its current number of balls. A question of essential inter...

In a graph $$\Gamma $$ with vertex set V, subset C of V is called an (a, b)-regular if every in has exactly neighbors and $$V\setminus C$$ b C, where are nonnegative integers. the literature, (0, 1)-regular sets known as perfect codes (1, total codes. this paper, we prove that, for any finite group G, non-trivial normal subgroup H G code some Cayley then pair integers $$0\leqslant a\leqslant |H...