scholarly journals Some More New Properties of Consecutive Odd Numbers

2017 ◽  
Vol 9 (5) ◽  
pp. 61
Author(s):  
Xingbo Wang
Keyword(s):  
Symmetric Distribution ◽  
Composite Number

The article proves several new properties of consecutive odd integers. The proved properties reveal divisors’ transition by subtracting two terms of an odd sequence, divisors’ stationary with adding or subtracting an item to the terms and pseudo-symmetric distribution of a divisor’s power in an odd sequence. The new properties are helpful for finding a divisor of an odd composite number in an odd sequence.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

On estimating a symmetric distribution

Biometrika ◽  
1976 ◽  
Vol 63 (3) ◽  
pp. 680-681 ◽  
Author(s):  
DAVID HINKLEY
Keyword(s):  
Symmetric Distribution

THE KORSELT SET OF pq

2012 ◽  
Vol 08 (02) ◽  
pp. 299-309 ◽  
Author(s):  
OTHMAN ECHI ◽  
NEJIB GHANMI
Keyword(s):  
Positive Integer ◽  
Prime Divisor ◽  
Prime Numbers ◽  
Composite Number

Let α ∈ ℤ\{0}. A positive integer N is said to be an α-Korselt number (Kα-number, for short) if N ≠ α and N - α is a multiple of p - α for each prime divisor p of N. By the Korselt set of N, we mean the set of all α ∈ ℤ\{0} such that N is a Kα-number; this set will be denoted by [Formula: see text]. Given a squarefree composite number, it is not easy to provide its Korselt set and Korselt weight both theoretically and computationally. The simplest kind of squarefree composite number is the product of two distinct prime numbers. Even for this kind of numbers, the Korselt set is far from being characterized. Let p, q be two distinct prime numbers. This paper sheds some light on [Formula: see text].

Quelques reflexions sur l'unite de plan de l'orogenie terrestre

1950 ◽  
Vol S5-XX (1-3) ◽  
pp. 25-32
Author(s):  
Philibert Russo
Keyword(s):  
Mediterranean Region ◽  
Symmetric Distribution ◽  
The Mediterranean

Abstract Zones of orogenic activity exhibit a symmetric distribution, with crescent-shaped orientation, relative to the poles and the Mediterranean region.

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