The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing...

When learning the meaning of symbolic numbers, children learn numbers up to 4 sequentially. A prominent account this process proposes that increasing sensitivity preverbal approximate number system (ANS) allows for reliable discrimination increasingly large neighboring which, consequently, leads sequential acquisition first numbers. In work, a more complete quantitative description is provided....

introduction: : low level laser therapy (lllt) is gaining acceptance in clinical applications. for example, it is used as therapeutic modality in the repair of diabetic foot ulcer when conventional therapy was not effective, separately. the aim of this study is to determine the effect of local and travenous lllt for the healing of diabetic foot ulcer. methods:   this study contains 74 diabetic ...

These are meant to be a rough set of notes and so could have some informal language. They give a quick reference to the background and material for the course but are not meant to be comprehensive. We will provide proofs for certain results but for most details we will refer the reader to the appropriate book or article. Notation: N = {1, 2, . . . } is the set of natural numbers, Z = {. . . ,−1...

in this paper, a novel method for ranking of fuzzy numbers are proposed. in this method, decision maker is defined based on the center of mass at some cuts of a pair of fuzzy numbers in discreet version and center of mass on all of cuts of a pair of fuzzy numbers in continuous version. our method can rank more than two fuzzy numbers simultaneously. also, some properties of methods are described...