An edge-magic total labeling on G is a one-to-one map λ from V (G) ∪ E(G) onto the integers 1, 2, . . . , |V (G) ∪ E(G)| with the property that, given any edge (x, y), λ(x) + λ(x, y) + λ(y) = k for some constant k. The labeling is strong if all the smallest labels are assigned to the vertices. Enomoto et al. proved that a graph admitting a strong labeling can have at most 2|V (G)| − 3 edges. In...

The directed acyclic word graph (DAWG) of a string y is the smallest (partial) DFA which recognizes all suffixes of y and has only O(n) nodes and edges. We present the first O(n)-time algorithm for computing the DAWG of a given string y of length n over an integer alphabet of polynomial size in n. We also show that a straightforward modification to our DAWG construction algorithm leads to the f...

In this paper, we establish a multiplicative decomposition formula for nonnegative local martingales and use it to characterize the set of continuous local submartingales Y of the form Y = N + A, where the measure dA is carried by the set of zeros of Y. In particular, we shall see that in the set of all local submartingales with the same martingale part in the multiplicative decomposition, thes...

In this paper, we establish a multiplicative decomposition formula for nonnegative local martingales and use it to characterize the set of continuous local submartingales Y of the form Y = N +A, where the measure dA is carried by the set of zeros of Y . In particular, we shall see that in the set of all local submartingales with the same martingale part in the multiplicative decomposition, thes...

This paper presents a method for optimal encoding of a given set of partial orders so that a Conditional Partial Order Graph containing all of them has the least possible total count of literals in all of its vertex and arc conditions, thus leading to the smallest and fastest controller. The presented method is implemented in a software tool for automated CPOG synthesis.

and Applied Analysis 3 Remark 2.3. If x, y : 0, ∞ → R with order α > 0, then Dt ( x t y t ) Dtx t Dty t . 2.3 Proposition 2.4 see 18, 19 . 1 If x ∈ L1 0, 1 , ν > σ > 0, then IIx t I x t , DtIx t Iν−σx t , DtIx t x t . 2.4 2 If ν > 0, σ > 0, then Dttσ−1 Γ σ Γ σ − ν t σ−ν−1. 2.5 Proposition 2.5 see 18, 19 . Let α > 0, and f x is integrable, then IDtf x f x c1xα−1 c2xα−2 · · · cnxα−n, 2.6 where ci...

background:isolates of staphylococcus aureus express a myriad of adhesive surface proteins that play important role in colonization of the bacteria on nasal and skin surfaces, beginning the process of pathogenesis. the aim of this study was to screen several of the microbial surface components recognizing adhesive matrix molecules (mscramms) genes among the isolate of s. aureus from hospitalize...

AnL(2, 1)-labeling of a graphG is defined as a function f from the vertex setV (G) into the nonnegative integers such that for any two vertices x, y, |f (x)−f (y)| ≥ 2 if d(x, y) = 1 and |f (x)− f (y)| ≥ 1 if d(x, y) = 2, where d(x, y) is the distance between x and y in G. The L(2, 1)-labeling number λ2,1(G) of G is the smallest number k such that G has an L(2, 1)-labeling with k = max{f (x)|x ...