منابع مشابه
3D Euler about a 2D symmetry plane
Initial results from new calculations of interacting anti-parallel Euler vortices are presented with the objective of understanding the origins of singular scaling presented by Kerr [R.M. Kerr, Evidence for a singularity of the three-dimensional, incompressible Euler equations, Phys. Fluids 5 (1993) 1725–1746] and the lack thereof by Hou and Li [T.Y. Hou, R. Li, Dynamic depletion of vortex stre...
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متن کاملArithmetic Functions and the Euler Phi Function
• An arithmetic function takes positive integers as inputs and produces real or complex numbers as outputs. • If f is an arithmetic function, the divisor sum Df(n) is the sum of the values of f at the positive divisors of n. • τ (n) is the number of positive divisors of n; σ(n) is the sum of the positive divisors of n. • The Möbius function μ(n) is 1 if n = 1 and 0 if n has a repeated prime fac...
متن کاملEuler Systems in Global Function Fields
In this paper, the construction of Euler systems of cyclotomic units in a general global function fields is explained. As an application, an analogue of Gras' conjecture in a global function field is proved. 1. I n t r o d u c t i o n and n o t a t i o n s Kolyvagin [7] introduced his remarkable Euler systems to prove important new results on ideal class groups of nmnber felds. This method was ...
متن کاملSome Divisibility Properties of the Euler Function
Let φ(·) denote the Euler function, and let a > 1 be a fixed integer. We study several divisibility conditions which exhibit typographical similarity with the standard formulation of the Euler theorem, such as an ≡ 1 (mod φ(n)), and we estimate the number of positive integers n ≤ x satisfying these conditions. 2000 Mathematics Subject Classification. 11A07, 11N37.
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ژورنال
عنوان ژورنال: Polythematic Online Scientific Journal of Kuban State Agrarian University
سال: 2017
ISSN: 1990-4665
DOI: 10.21515/1990-4665-127-004