Let G = (V,E) be a simple graph. An edge labeling f : E → {0, 1} induces a vertex labeling f : V → Z2 defined by f(v) ≡ ∑ uv∈E f(uv) (mod 2) for each v ∈ V , where Z2 = {0, 1} is the additive group of order 2. For i ∈ {0, 1}, let ef (i) = |f−1(i)| and vf (i) = |(f+)−1(i)|. A labeling f is called edge-friendly if |ef (1) − ef (0)| ≤ 1. If (G) = vf (1) − vf (0) is called the edge-friendly index o...

FOOD REFORMULATION: Reformulation of foods is considered one of the key options to achieve population nutrient goals. The compositions of many foods are modified to assist the consumer bring his or her daily diet more in line with dietary recommendations. INITIATIVES ON FOOD REFORMULATION: Over the past few years the number of reformulated foods introduced on the European market has increased e...

We establish a characterization of adequate knots in terms of the degree of their colored Jones polynomial. We show that, assuming the Strong Slope conjecture, our characterization can be reformulated in terms of “Jones slopes” of knots and the essential surfaces that realize the slopes. For alternating knots the reformulated characterization follows by recent work of J. Greene and J. Howie. 20...

Community structures detection is one of the fundamental problems in complex network analysis towards understanding the topology structures of the network and the functions of it. Nonnegative matrix factorization (NMF) is a widely used method for community detection, and modularity Q and modularity density D are criteria to evaluate the quality of community structures. In this paper, we establi...

LetG=(V ,E) be a graph, a vertex labeling f : V → Z2 induces an edge labeling f ∗ : E → Z2 defined by f ∗(xy)=f (x)+f (y) for each xy ∈ E. For each i ∈ Z2, define vf (i)=|f−1(i)| and ef (i)=|f ∗−1(i)|. We call f friendly if |vf (1)− vf (0)| 1. The full friendly index set of G is the set of all possible values of ef (1)− ef (0), where f is friendly. In this note, we study the full friendly index...

Standard H2 optimal control of networked dynamic systems tend to become unscalable with network size. Structural constraints can be imposed on the design to counteract this problem albeit at the risk of making the solution nonconvex. In this paper, we present a special class of structural constraints such that the H2 design satisfies a quadratic invariance condition, and therefore can be reform...

The Riemann mapping theorem asserts that the open unit disk D = {z| |z| < 1} is conformally equivalent to each simply connected domain G in the complex plane, whose boundary consists of at least two points, i.e., there exists a function f , analytic and univalent function on D , such that f maps D onto G . More precisely, if do is an arbitrary point in D and go is an arbitrary point in G, then ...

In this paper, the concept of Abramov's method for transferring boundary conditions posed for regular ordinary diierential equations is applied to index 1 DAEs. Having discussed the reduction of inhomogeneous problems to homogeneous ones and analyzed the underlying ideas of Abramov's method, we consider boundary value problems for index 1 linear DAEs both with constant and varying leading matri...

Falcaria vulgaris is a member of Umbelliferae family and is used for treatment of stomach disorders in the folk medicines of the west of Iran. This study was designed to evaluate the gastroprotective effect of F. vulgaris extract on ethanol (%50) induced gastric ulcers in rat. Thirty five young white male rats were divided to five groups (7rats/ group).Three case groups received plant extract (...

Fast algorithms for high-speed divider design in finite fields GF(2) are very crucial in applications like cryptosystems. In this paper, we reformulated the conventional iterative division algorithm by changing the pre-defined variable and then updating its initial value accordingly. The reformulated division algorithm allows a restructuring of the divider architecture to further improve its op...