Let Z and IR (C) denote the ring of the integers and the field of real (complex) numbers, respectively. For a field F, we put i* = F\{0}. Fix A GC and B G C*, and let X(A, B) consist of all those second-order recurrent sequences {wn}neZ of complex numbers satisfying the recursion: n+i = „ ~ n-i (i.e., Bwn_Y = Awn wn+l) for n = 0, ± 1, ± 2,.... (1) For sequences in SE(A,B), the corresponding cha...

let $g$ be a simple graph‎, ‎and $g^{sigma}$‎ ‎be an oriented graph of $g$ with the orientation ‎$sigma$ and skew-adjacency matrix $s(g^{sigma})$‎. ‎the $k-$th skew spectral‎ ‎moment of $g^{sigma}$‎, ‎denoted by‎ ‎$t_k(g^{sigma})$‎, ‎is defined as $sum_{i=1}^{n}( ‎‎‎lambda_{i})^{k}$‎, ‎where $lambda_{1}‎, ‎lambda_{2},cdots‎, ‎lambda_{n}$ are the eigenvalues of $g^{sigma}$‎. ‎suppose‎ ‎$g^{sigma...

where two particular combinations of the rate constants for primary nucleation (kn), elongation (k+), and fibril-catalysed secondary nucleation (k2) define much of the macroscopic behaviour; these parameters are related to the rate of formation of new aggregates through primary pathways λ = �2k+knm(0)c and through secondary pathways κ = �2k+k2m(0)2. Indeed, Eq. 1 depends on the rate constants t...

By w, we denote the space of all real or complex valued sequences. If x ∈ w, then we simply write x xk instead of x xk ∞ k 1. Also, we will use the conventions that e 1, 1, . . . . Any vector subspace of w is called a sequence space. We will write l∞, c, and c0 for the sequence spaces of all bounded, convergent, and null sequences, respectively. Further, by lp 1 ≤ p < ∞ , we denote the sequence...

These short notes provide descriptions and references relative to the construction of parsing tables for SLR(1), for LR(1), and for LALR(1) grammars. 1 Notation and basic definitions Basic definitions and notational conventions are summerized below. A context-free grammar is a tuple G = (V, T, S,P), where the elements of the tuple represent, respectively, the vocabulary of terminal and nontermi...

Let K be a compact set of Rn and t ? 0. In this paper, we discuss the relation between t-dimensional Hewitt-Stromberg premeasure measure denoted by H?t Ht respectively. We prove : if (K) &lt; +? then = Ht(K) +?, there exists subset F such that (F) Ht(F) is close as like to Ht(K).

For a graph G, an L(2, 1)-labeling of G with span k is a mapping L → {0, 1, 2, . . . , k} such that adjacent vertices are assigned integers which differ by at least 2, vertices at distance two are assigned integers which differ by at least 1, and the image of L includes 0 and k. The minimum span over all L(2, 1)-labelings of G is denoted λ(G), and each L(2, 1)-labeling with span λ(G) is called ...