The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this  graph. Also we give a relation between the order graph and prime  graph of a group.

The melting parameter Gamma(m) of a classical one-component plasma is estimated using a relation between the melting temperature, density, shear modulus, and a crystal coordination number that follows from our model of dislocation-mediated melting. We obtain gamma(m)=172+/-35, in good agreement with the results of numerous Monte Carlo calculations.

This study aimed to assess effects of chronic occupational exposure on immune status in Mayak workers chronically exposed to ionizing radiation (IR). The study cohort consists of 77 workers occupationally exposed to external gamma-rays at total dose from 0.5 to 3.0 Gy (14 individuals) and workers with combined exposure (external gamma-rays at total dose range 0.7-5.1 Gy and internal alpha-radia...

In this paper, some recursive relations of the derivatives of the gamma function Γ(α) and incomplete gamma function Γ(α, z) are obtained for complex number α ̸= 0,−1,−2, · · ·. Moreover, the recurrence relation of the derivative of the k−gamma function Γk(x) are also given. Thus, the partial derivative ∂ p+q ∂νp∂μq B(ν, μ) of the Beta function B(ν, μ) can also be represented for p, q = 0, 1, 2, ...

Ioka and Nakamura (2001) proposed a simple jet model which is compatible with the peak luminosity-spectral lag relation, the peak luminosity-variability relation and various other relations in the Gamma-Ray Bursts. If the viewing angle is much larger than the collimation angle of the jet in the model by Ioka and Nakamura, for appropriate model parameters we obtain the observational characterist...

Using measurements obtained by the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite, relationships between layer-integrated depolarization ratio (delta) and layer-integrated attenuated backscatter (gamma) are established for moderately thick clouds of both ice and water. A new and simple form of the delta-gamma relation for spherical particles, developed fr...

A flat solvmanifold is a compact quotient $$\Gamma \backslash G$$ where G simply-connected solvable Lie group endowed with left invariant metric and $$ lattice of G. Any such can be written as $$G={\mathbb {R}}^k < imes _{\phi } {\mathbb {R}}^m$$ $${\mathbb the nilradical. In this article we focus on 6-dimensional splittable solvmanifolds, which are obtained quotienting by that decomposed =\Gam...

A theory for the vibrational dynamics in disordered solids [W. Schirmacher, Europhys. Lett. 73, 892 (2006), based on the random spatial variation of the shear modulus, has been applied to determine the wave vector (k) dependence of the Brillouin peak position (Omega(k)) and width (Gamma(k)), as well as the density of vibrational states [g(omega)], in disordered systems. As a result, we give a f...