Let B (r) q = Kr−1 + qK1 be the graph consisting of q distinct r-cliques sharing a common (r − 1)-clique. We prove for p ≥ 2, r ≥ 3 fixed and q large r ( Kp+1, B (r) q ) = p (q + r − 2) + 1.

By fuzzifying the number of occurrences of an element of a multiset, we obtain a new fuzzy structure; similarly, by fuzzifying the number of occurrences of an element of a hybrid set, we obtain another new fuzzy structure. The aim of the present work is twofold: to provide a concise definition of these new fuzzy structures and their properties and to apply them in natural computing. More specif...

We study some generalized notions of cohesiveness which arise naturally in connection with effective versions of Ram-sey's Theorem. An infinite set A of natural numbers is n–cohesive (respectively, n–r–cohesive) if A is almost homogeneous for every computably enumerable (respectively, computable) 2–coloring of the n–element sets of natural numbers. (Thus the 1–cohesive and 1–r–cohesive sets coi...

Suppose that d ∈ N and p > 0. In this paper, we study the generalized Bessel functions for the surface {v ∈ Rd : |v|p = 1}, introduced by D.St.P. Richards. We derive a recurrence relation for these functions and utilize a series representation to relate them to the classical symmetric functions. These generalized Bessel functions are symmetric with respect to the action of the hyperoctahedral g...

We consider the reduced, quenched version of a generalized Yang–Mills action in 4k-dimensional spacetime. This is a new kind of matrix theory which is mapped through the Weyl–Wigner–Moyal correspondence into a field theory over a non-commutative phase space. We show that the “classical” limit of this field theory is encoded into the effective action of an open, (4k−1)-dimensional, bulk brane en...

A generalized p-cycle is a digraph whose set of vertices can be partitioned into p parts that are cyclically ordered in such a way that the vertices in one part are adjacent only to vertices in the next part. Any digraph can be shown as a p-cycle with p = 1, and bipartite digraphs are generalized p-cycles with p = 2. A maximally connected digraph is said to be superconnected if every disconnect...

is the ordinary formal power series generating function for the sequence {yn+i}„>0 (cf. [12]. Furthermore, it is easy to see [1] that when the discriminant A = X +4ju ofP(t) is nonnegative and X & 0, the ratios yn+l I yn converge (in the usual archimedean metric on U) to a reciprocal root a of P(t). In this article we show that ratios of these y n also exhibit rapid convergence properties relat...

In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson summation formulas for these sequences. Moreover, give some identities matrices related with Furthermore, show that there are close relations between p-Leonardo-Lucas, numbers Fibonacc...

We study two variants of P colonies with initial content of P colony and so called passive environment: P colonies with two objects inside each agent that can only consume or generate objects, and P colonies with one object inside each agent using rewriting and communication rules. We show that the first kind of P colonies with one consumer agent and one sender agent can generate all sets of na...