Let G = (V,E) be a graph of order n. A distance magic labeling of G is a bijection l : V → {1, 2, . . . , n} for which there exists a positive integer k such that ∑ x∈N(v) l(x) = k for all v ∈ V , where N(v) is the open neighborhood of v. In this paper we deal with circulant graphs C(1, p). The circulant graph Cn(1, p) is the graph on the vertex set V = {x0, x1, . . . , xn−1} with edges (xi, xi...

A positive integer is called a (Ore’s) harmonic number if its positive divisors have integral harmonic mean. Ore conjectured that every harmonic number greater than 1 is even. If Ore’s conjecture is true, there exist no odd perfect numbers. In this paper, we prove that every odd harmonic number greater than 1 must be divisible by a prime greater than 105.

Self-consistent mean field calculations with the SLy4 interaction and a densitydependent pairing force are presented for nuclei in the Nobelium mass region. Predicted quasi-particle spectra are compared with experiment for the heaviest known odd N and odd Z nuclei. Spectra and rotational bands are presented for nuclei around 252,4No for which experiments are either planned or already running.

Let G be a graph with its vertices and edges. On defining bijective function ρ:V(G) →{0,1,...,p}. For each edge assign the label 1 if ρ*(ab)= | ρ(a) 2 −ρ(b) /ρ(a)−ρ(b) is odd or 0 otherwise such that |eρ(1) − eρ(0)| ≤ then labeling called as divided square difference cordial graph. We prove in this paper for relatively possible set of spider graphs atmost one legs greater than namely J(SP(1 m ,...

Abstract By using a jump transformation associated to the Romik map, we define new continued fraction algorithm called odd-odd fraction, whose principal convergents are rational numbers of odd denominators and numerators. Among others, it is proved that all best approximating rationals numerators an irrational number given by vice versa.

Elasticity typically refers to a material's ability store energy, whereas viscosity tendency dissipate it. In this review, we discuss fluids and solids for which is not the case. These materials display additional linear response coefficients known as odd elasticity. We first introduce elasticity from continuum perspective, with an emphasis on their rich phenomenology, including transverse resp...

BACKGROUND This study was designed to assess the prevalence of Attention-Deficit/Hyperactivity Disorder (ADHD) and Oppositional Defiant Disorder (ODD) in a representative sample of second grade students from a country in a region where no previous rates are available (Turkey). The second aim is to evaluate the differences in ADHD and ODD prevalence rates among four different waves with one-year...

The mean-square charge radii of $^{207,208}$Hg ($Z=80, N=127,128$) have been studied for the first time and those $^{202,203,206}$Hg ($N=122,123,126$) remeasured by application in-source resonance-ionization laser spectroscopy at ISOLDE (CERN). characteristic \textit{kink} in $N=126$ neutron shell closure has revealed, providing information on its behavior below $Z=82$ proton closure. A theoret...