Displaying similar documents to “High Frequency limit of the Helmholtz Equations”

Sumsets in quadratic residues

I. D. Shkredov (2014)

Acta Arithmetica

Similarity:

We describe all sets A p which represent the quadratic residues R p in the sense that R = A + A or R = A ⨣ A. Also, we consider the case of an approximate equality R ≈ A + A and R ≈ A ⨣ A and prove that A is then close to a perfect difference set.

Positivity of quadratic base change L -functions

Hervé Jacquet, Chen Nan (2001)

Bulletin de la Société Mathématique de France

Similarity:

We show that certain quadratic base change L -functions for Gl ( 2 ) are non-negative at their center of symmetry.

Another look at real quadratic fields of relative class number 1

Debopam Chakraborty, Anupam Saikia (2014)

Acta Arithmetica

Similarity:

The relative class number H d ( f ) of a real quadratic field K = ℚ (√m) of discriminant d is defined to be the ratio of the class numbers of f and K , where K denotes the ring of integers of K and f is the order of conductor f given by + f K . R. Mollin has shown recently that almost all real quadratic fields have relative class number 1 for some conductor. In this paper we give a characterization of real quadratic fields with relative class number 1 through an elementary approach considering the...

Capturing forms in dense subsets of finite fields

Brandon Hanson (2013)

Acta Arithmetica

Similarity:

An open problem of arithmetic Ramsey theory asks if given an r-colouring c:ℕ → 1,...,r of the natural numbers, there exist x,y ∈ ℕ such that c(xy) = c(x+y) apart from the trivial solution x = y = 2. More generally, one could replace x+y with a binary linear form and xy with a binary quadratic form. In this paper we examine the analogous problem in a finite field q . Specifically, given a linear form L and a quadratic form Q in two variables, we provide estimates on the necessary size...

Minimal 𝒮 -universality criteria may vary in size

Noam D. Elkies, Daniel M. Kane, Scott Duke Kominers (2013)

Journal de Théorie des Nombres de Bordeaux

Similarity:

In this note, we give simple examples of sets 𝒮 of quadratic forms that have minimal 𝒮 -universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh [KKO05] in the negative.

Quadratic differentials ( A ( z - a ) ( z - b ) / ( z - c ) 2 ) d z 2 and algebraic Cauchy transform

Mohamed Jalel Atia, Faouzi Thabet (2016)

Czechoslovak Mathematical Journal

Similarity:

We discuss the representability almost everywhere (a.e.) in of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. This brings us to the study of trajectories of the particular family of quadratic differentials A ( z - a ) ( z - b ) ( z - c ) - 2 d z 2 . More precisely, we give a necessary and sufficient condition on the complex numbers a and b for these quadratic differentials to have finite critical...

Isometries of quadratic spaces

Eva Bayer-Fluckiger (2015)

Journal of the European Mathematical Society

Similarity:

Let k be a global field of characteristic not 2, and let f k [ X ] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the completions of k . This gives a partial answer to a question of Milnor.

Tameness criterion for posets with zero-relations and three-partite subamalgams of tiled orders

Stanisław Kasjan (2002)

Colloquium Mathematicae

Similarity:

A criterion for tame prinjective type for a class of posets with zero-relations is given in terms of the associated prinjective Tits quadratic form and a list of hypercritical posets. A consequence of this result is that if Λ is a three-partite subamalgam of a tiled order then it is of tame lattice type if and only if the reduced Tits quadratic form q Λ associated with Λ in [26] is weakly non-negative. The result generalizes a criterion for tameness of such orders given by Simson [28]...

Some properties of stationary sets

C. A. Di Prisco, W. Marek

Similarity:

CONTENTSIntroduction..................................................................51. Derivative of a stationary set...................................72. Stationary degrees ...............................................133. Subsets of P ϰ ( λ ) ..............................................194. Stationary subsets of P ϰ ( λ ) .............................255. Superstationary substes of P ϰ ( λ ) ....................326. End-stationary subsets of P ϰ ( λ ) ......................34References................................................................37 ...

Porous Medium Type Equations with a Quadratic Gradient Term

Daniela Giachetti, Giulia Maroscia (2007)

Bollettino dell'Unione Matematica Italiana

Similarity:

We show an existence result for the Cauchy-Dirichlet problem in Q T = Ω × ( 0 , T ) for parabolic equations with degenerate principal part (of porous medium type) with a lower order term having a quadratic growth with respect to the gradient. The right hand side of the equation f and the initial datum u 0 are bounded nonnegative functions.

Grothendieck and Witt groups in the reduced theory of quadratic forms

Andrzej Sładek (1980)

Annales Polonici Mathematici

Similarity:

Abstract. Let F be a formally real field. Denote by G(F) and G t ( F ) the Grothen-dieck group of quadratic forms over F and its torsion subgroup, respectively. In this paper we study the structure of the factor group G ( F ) / G t ( F ) . This reduced Grothendieck group is a free Abelian group. The main results of the paper describe some sets of generators for G ( F ) / G t ( F ) , which in many cases allow us to find a basis for the group. Throughout the paper we use the language of the reduced theory of quadratic forms. In the...

The sum of divisors of a quadratic form

Lilu Zhao (2014)

Acta Arithmetica

Similarity:

We study the sum τ of divisors of the quadratic form m₁² + m₂² + m₃². Let S ( X ) = 1 m , m , m X τ ( m ² + m ² + m ² ) . We obtain the asymptotic formula S₃(X) = C₁X³logX + C₂X³ + O(X²log⁷X), where C₁,C₂ are two constants. This improves upon the error term O ε ( X 8 / 3 + ε ) obtained by Guo and Zhai (2012).

On some identities involving spherical means

Gianfranco Cimmino (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

For every positive definite quadratic form in n variables the reciprocal of the square root of the discriminant is equal to the arithmetic mean of the values assumed by the form on the n - 1 sphere centered at 0 and with radius 1 raised to the ( - n 2 )-th. power. Various consequences are deduced from this, in particular a simplification of some calculations from which one obtains the possibility of solving linear systems using spherical means rather than determinants.

High-order phase transitions in the quadratic family

Daniel Coronel, Juan Rivera-Letelier (2015)

Journal of the European Mathematical Society

Similarity:

We give the first example of a transitive quadratic map whose real and complex geometric pressure functions have a high-order phase transition. In fact, we show that this phase transition resembles a Kosterlitz-Thouless singularity: Near the critical parameter the geometric pressure function behaves as x exp ( x 2 ) near x = 0 , before becoming linear. This quadratic map has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.

Large data local solutions for the derivative NLS equation

Ioan Bejenaru, Daniel Tataru (2008)

Journal of the European Mathematical Society

Similarity:

We consider the derivative NLS equation with general quadratic nonlinearities. In [2] the first author has proved a sharp small data local well-posedness result in Sobolev spaces with a decay structure at infinity in dimension n = 2 . Here we prove a similar result for large initial data in all dimensions n 2 .

On some identities involving spherical means

Gianfranco Cimmino (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

For every positive definite quadratic form in n variables the reciprocal of the square root of the discriminant is equal to the arithmetic mean of the values assumed by the form on the n - 1 sphere centered at 0 and with radius 1 raised to the ( - n 2 )-th. power. Various consequences are deduced from this, in particular a simplification of some calculations from which one obtains the possibility of solving linear systems using spherical means rather than determinants.