An extended formulation of a polytope P is a system of linear inequalities and equations that describe some polyhedron which can be projected onto P. Extended formulations of small size (i.e., number of inequalities) are of interest, as they allow to model corresponding optimization problems as linear programs of small sizes. In this paper, we describe several aspects and new results on the mai...

We describe the general class of N -extended D = (2 + 1) Galilean supersymmetries obtained, respectively, from the N -extended D = 3 Poincaré superalgebras with maximal sets of central charges. We confirm the consistency of supersymmetry with the presence of the ‘exotic’ second central charge θ. We show further how to introduce a N = 2 Galilean superfield equation describing nonrelativistic spi...

This study was conducted to reveal the phylogenetic background, to detect the genes encoding TEM, SHV and CTX-M-15 extended-spectrum β-lactamases (ESBL), and to analyze their distribution in phylo-groups of 150 Escherichia coli isolates from broiler chickens in Ahvaz (Southwest of Iran). Seventy- five cloacal swabs from healthy birds (fecal isolates), and 75 heart blood samples from bi...

The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

Given a digraph D=(V(D),A(D)), let ∂D+(v)={vw|w∈ND+(v)} and ∂D−(v)={uv|u∈ND−(v)} be semi-cuts of v. A mapping φ:A(D)→[k] is called weak-odd k-edge coloring D if it satisfies the condition: for each v∈V(D), there at least one color with an odd number occurrences on non-empty semi-cut We call minimum integer k chromatic index D. When limit to 2 colors, def(D) denote defect D, i.e vertices in whic...

Let D be an integral domain and X an indeterminate over D. It is well known that (a) D is quasi-Prüfer (i.e, its integral closure is a Prüfer domain) if and only if each upper to zero Q in D[X] contains a polynomial g ∈ D[X] with content cD(g) = D; (b) an upper to zero Q in D[X] is a maximal t-ideal if and only if Q contains a nonzero polynomial g ∈ D[X] with cD(g) v = D. Using these facts, the...

We study the effect of site diagonal, non-magnetic, disorder on the a pairing amplitude in an extended Hubbard model with the intersite attraction. Analyzing fluctuations of a pairing potential we discuss the instability of mixed solutions, ’s + d’ and ’s + id’, in presence of disorder. The influence of disorder on extended s– and d–wave superconductors appear to be comparable but in certain re...

The exceptional superalgebra D(2, 1;α) has been classified as a candidate conformal supersymmetry algebra in two dimensions. We propose an alternative interpretation of it as extended BFV-BRST quantisation superalgebras in 2D (D(2, 1; 1) ≃ osp(2, 2|2)). A superfield realization is presented wherein the standard extended phase space coordinates can be identified. The physical states are studied ...

We construct a one-to-one mapping between binary vectors of length n and preorder codewords of regular, ordered, oriented, rooted, binary trees having N ≈ n+2 log n nodes. The mappings in both directions can be organized in such a way that complexities of all transformations are measured by linear functions of n. The approach is then completely extended to non-regular binary trees and partially...