Given a matrix, the Null Space Problem asks for a basis of its null space having the fewest nonzeros. This problem is known to be NP-complete and even hard to approximate. The null space of a forest is the null space of its adjacency matrix. Sander and Sander (2005) and Akbari et al. (2006), independently, proved that the null space of each forest admits a {−1, 0, 1}-basis. We devise an algorit...

ABSTRACT: In this paper, sorting of two Iranian varieties of pistachio, “Akbari” (Ak) and “Kaleghouchi” (Ka), by the decision tree and fuzzy logic classifier is investigated. 240 Ak and 120 Ka pistachio nuts impacted to a stainless steel plate through a chute, and the acoustic signal of these impacts picked up using a microphone and saved on a computer via a sound card. Further analysis has bee...

BACKGROUND It is evident that infant's umbilical cord is essential for its survival and growth. In the past, it was not considered as a necessary tissue. However, nowadays, it has attracted lots of attention and its relation to different diseases has been demonstrated. In Iranian traditional medicine, caring for newborn's umbilical cord has been frequently recommended and it has been associated...

Let G be a connected graph of chromatic number k. For a k-coloring f of G, a full f -rainbow path is a path of order k in G whose vertices are all colored differently by f . We show that G has a k-coloring f such that every vertex of G lies on a full f -rainbow path, which provides a positive answer to a question posed by Lin (Simple proofs of results on paths representing all colors in proper ...

A dynamic coloring of a graph is a proper coloring of its vertices such that every vertex of degree more than one has at least two neighbors with distinct colors. The least number of colors in a dynamic coloring of G, denoted by χ2(G), is called the dynamic chromatic number of G. The least integer k, such that if every vertex of G is assigned a list of k colors, then G has a proper (resp. dynam...

A vertex-coloring of a hypergraph is conflict-free, if each edge contains a vertex whose color is not repeated on any other vertex of that edge. Let f(r,∆) be the smallest integer k such that each r-uniform hypergraph of maximum vertex degree ∆ has a conflict-free coloring with at most k colors. As shown by Tardos and Pach, similarly to a classical Brooks’ type theorem for hypergraphs, f(r,∆) ≤...

INTRODUCTION At present, about 1% of newborns are delivered through assisted reproductive technologies (ART) worldwide. This study aimed to evaluate and compare the growth parameters of children born in assisted and natural conception at 5 years of age. MATERIALS AND METHODS In a cross-sectional case control study, weight, height and head circumference of 5-year old children were assessed. Th...

Motivated by breakthroughs in the synthesis of faceted nano- and colloidal particles, as well as theoretical and computational studies of their packings, we investigate a family of truncated triangular bipyramids. We report dense periodic packings with small unit cells that were obtained via numerical and analytical optimization. The maximal packing fraction φ(max) changes continuously with the...

This paper analyzed the model of swinging oscillation a solid circular sector arising in hydrodynamical machines, electrical engineering, heat transfer applications, and civil engineering. Nonlinear differential equations govern mathematical for frequency system. Furthermore, computational strength Cascade neural networks (CNNs) is utilized with backpropagated Levenberg–Marquardt (BLM) algorith...