Displaying similar documents to “Dissipative Euler flows and Onsager's conjecture”

On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function

Ke-Pao Lin, Xue Luo, Stephen S.-T. Yau, Huaiqing Zuo (2014)

Journal of the European Mathematical Society

Similarity:

It is well known that getting the estimate of integral points in right-angled simplices is equivalent to getting the estimate of Dickman-De Bruijn function ψ ( x , y ) which is the number of positive integers x and free of prime factors > y . Motivating from the Yau Geometry Conjecture, the third author formulated the Number Theoretic Conjecture which gives a sharp polynomial upper estimate that counts the number of positive integral points in n-dimensional ( n 3 ) real right-angled simplices. In this...

On the Brocard-Ramanujan problem and generalizations

Andrzej Dąbrowski (2012)

Colloquium Mathematicae

Similarity:

Let p i denote the ith prime. We conjecture that there are precisely 28 solutions to the equation n ² - 1 = p α p k α k in positive integers n and α₁,..., α k . This conjecture implies an explicit description of the set of solutions to the Brocard-Ramanujan equation. We also propose another variant of the Brocard-Ramanujan problem: describe the set of solutions in non-negative integers of the equation n! + A = x₁²+x₂²+x₃² (A fixed).

On the uniqueness of periodic decomposition

Viktor Harangi (2011)

Fundamenta Mathematicae

Similarity:

Let a , . . . , a k be arbitrary nonzero real numbers. An ( a , . . . , a k ) -decomposition of a function f:ℝ → ℝ is a sum f + + f k = f where f i : is an a i -periodic function. Such a decomposition is not unique because there are several solutions of the equation h + + h k = 0 with h i : a i -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the ( a , . . . , a k ) -decomposition is essentially unique. We characterize those periods for which essential...

Eigenspaces of the ideal class group

Cornelius Greither, Radan Kučera (2014)

Annales de l’institut Fourier

Similarity:

The aim of this paper is to prove an analog of Gras’ conjecture for an abelian field F and an odd prime p dividing the degree [ F : ] assuming that the p -part of Gal ( F / ) group is cyclic.

The CR Yamabe conjecture the case n = 1

Najoua Gamara (2001)

Journal of the European Mathematical Society

Similarity:

Let ( M , θ ) be a compact CR manifold of dimension 2 n + 1 with a contact form θ , and L = ( 2 + 2 / n ) Δ b + R its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form θ ˜ on M conformal to θ which has a constant Webster curvature. This problem is equivalent to the existence of a function u such that L u = u 1 + 2 / n , u > 0 on M . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where n 2 and ( M , θ ) is not locally CR equivalent to the sphere S 2 n + 1 of 𝐂 n . In a join work with R. Yacoub, the CR Yamabe...

Existence and uniqueness of periodic solutions for odd-order ordinary differential equations

Yongxiang Li, He Yang (2011)

Annales Polonici Mathematici

Similarity:

The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation u ( 2 n + 1 ) = f ( t , u , u ' , . . . , u ( 2 n ) ) , where f : × 2 n + 1 is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity f ( t , x , x , . . . , x 2 n ) to guarantee the existence and uniqueness are presented. These conditions extend and improve the ones presented by Cong [Appl. Math. Lett. 17 (2004), 727-732].

Characterization of the alternating groups by their order and one conjugacy class length

Alireza Khalili Asboei, Reza Mohammadyari (2016)

Czechoslovak Mathematical Journal

Similarity:

Let G be a finite group, and let N ( G ) be the set of conjugacy class sizes of G . By Thompson’s conjecture, if L is a finite non-abelian simple group, G is a finite group with a trivial center, and N ( G ) = N ( L ) , then L and G are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation)....

The generalized Hodge and Bloch conjectures are equivalent for general complete intersections

Claire Voisin (2013)

Annales scientifiques de l'École Normale Supérieure

Similarity:

We prove that Bloch’s conjecture is true for surfaces with p g = 0 obtained as 0 -sets X σ of a section σ of a very ample vector bundle on a variety X with “trivial” Chow groups. We get a similar result in presence of a finite group action, showing that if a projector of the group acts as 0 on holomorphic 2 -forms of  X σ , then it acts as 0 on  0 -cycles of degree 0 of  X σ . In higher dimension, we also prove a similar but conditional result showing that the generalized Hodge conjecture for general X σ ...

On a conjecture of Dekking : The sum of digits of even numbers

Iurie Boreico, Daniel El-Baz, Thomas Stoll (2014)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let q 2 and denote by s q the sum-of-digits function in base q . For j = 0 , 1 , , q - 1 consider # { 0 n < N : s q ( 2 n ) j ( mod q ) } . In 1983, F. M. Dekking conjectured that this quantity is greater than N / q and, respectively, less than N / q for infinitely many N , thereby claiming an absence of a drift (or Newman) phenomenon. In this paper we prove his conjecture.

Recent progress on the Jacobian Conjecture

Michiel de Bondt, Arno van den Essen (2005)

Annales Polonici Mathematici

Similarity:

We describe some recent developments concerning the Jacobian Conjecture (JC). First we describe Drużkowski’s result in [6] which asserts that it suffices to study the JC for Drużkowski mappings of the form x + ( A x ) * 3 with A² = 0. Then we describe the authors’ result of [2] which asserts that it suffices to study the JC for so-called gradient mappings, i.e. mappings of the form x - ∇f, with f k [ n ] homogeneous of degree 4. Using this result we explain Zhao’s reformulation of the JC which asserts the...

Stability of periodic stationary solutions of scalar conservation laws with space-periodic flux

Anne-Laure Dalibard (2011)

Journal of the European Mathematical Society

Similarity:

This article investigates the long-time behaviour of parabolic scalar conservation laws of the type t u + div y A ( y , u ) - Δ y u = 0 , where y N and the flux A is periodic in y . More specifically, we consider the case when the initial data is an L 1 disturbance of a stationary periodic solution. We show, under polynomial growth assumptions on the flux, that the difference between u and the stationary solution behaves in L 1 norm like a self-similar profile for large times. The proof uses a time and space change of variables...

The L p -Helmholtz projection in finite cylinders

Tobias Nau (2015)

Czechoslovak Mathematical Journal

Similarity:

In this article we prove for 1 < p < the existence of the L p -Helmholtz projection in finite cylinders Ω . More precisely, Ω is considered to be given as the Cartesian product of a cube and a bounded domain V having C 1 -boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in Ω is solved, which implies existence and a representation of the L p -Helmholtz projection...

Singularities of 2 Θ -divisors in the jacobian

Christian Pauly, Emma Previato (2001)

Bulletin de la Société Mathématique de France

Similarity:

We consider the linear system | 2 Θ 0 | of second order theta functions over the Jacobian J C of a non-hyperelliptic curve C . A result by J.Fay says that a divisor D | 2 Θ 0 | contains the origin 𝒪 J C with multiplicity 4 if and only if D contains the surface C - C = { 𝒪 ( p - q ) p , q C } J C . In this paper we generalize Fay’s result and some previous work by R.C.Gunning. More precisely, we describe the relationship between divisors containing 𝒪 with multiplicity 6 , divisors containing the fourfold C 2 - C 2 = { 𝒪 ( p + q - r - s ) p , q , r , s C } , and divisors singular along C - C , using...

Some remarks on the interpolation spaces A θ , A θ

Mohammad Daher (2016)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let ( A 0 , A 1 ) be a regular interpolation couple. Under several different assumptions on a fixed A β , we show that A θ = A θ for every θ ( 0 , 1 ) . We also deal with assumptions on A ¯ β , the closure of A β in the dual of ( A 0 * , A 1 * ) β .

On geodesics of phyllotaxis

Roland Bacher (2014)

Confluentes Mathematici

Similarity:

Seeds of sunflowers are often modelled by n ϕ θ ( n ) = n e 2 i π n θ leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance 2 π θ for θ the golden ratio. We associate to such a map ϕ θ a geodesic path γ θ : &gt; 0 PSL 2 ( ) of the modular curve and use it for local descriptions of the image ϕ θ ( ) of the phyllotactic map ϕ θ .