Positivity of quadratic base change -functions
Hervé Jacquet, Chen Nan (2001)
Bulletin de la Société Mathématique de France
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We show that certain quadratic base change -functions for are non-negative at their center of symmetry.
Hervé Jacquet, Chen Nan (2001)
Bulletin de la Société Mathématique de France
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We show that certain quadratic base change -functions for are non-negative at their center of symmetry.
G. L. Watson
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CONTENTSIntroduction.......................................................................................61. Definition of certain special forms...........................................62. Statement of results...................................................................83. Proof of Theorem 2.....................................................................94. Preliminaries for Theorem 1.....................................................105. Further preliminaries for Theorem...
Malkhaz Ashordia (2016)
Mathematica Bohemica
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The Cauchy problem for the system of linear generalized ordinary differential equations in the J. Kurzweil sense , with a unique solution is considered. Necessary and sufficient conditions are obtained for a sequence of the Cauchy problems , to have a unique solution for any sufficiently large such that uniformly on . Presented results are analogous to the sufficient conditions due to Z. Opial for linear ordinary differential systems....
Clemens Heuberger, Daniel Krenn (2013)
Journal de Théorie des Nombres de Bordeaux
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We consider digit expansions with an endomorphism of an Abelian group. In such a numeral system, the -NAF condition (each block of consecutive digits contains at most one nonzero) is shown to minimise the Hamming weight over all expansions with the same digit set if and only if it fulfills the subadditivity condition (the sum of every two expansions of weight admits an optimal -NAF). This result is then applied to imaginary quadratic bases, which are used for scalar...
N. Ch. Wass
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This thesis is concerned with the problem of determining a measure of algebraic independence for a particular m-tuple θ₁,..., of complex numbers. Specifically, let K be a number field and let f₁(z),..., be elements of K[[z]] algebraically independent over K(z) satisfying equations of the form(*) (j = i,...,m)for b ≥ 2, , in K(z). Suppose finally that α ∈ K is such that 0 < |α| < 1, the ) converge at z = α and the , are analytic at Then the are algebraically independent...
Takao Komatsu (2002)
Bulletin de la Société Mathématique de France
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Let be irrational. Several authors studied the numbers where is a positive integer and denotes the set of all real numbers of the form with restricted integer coefficients . The value of was determined for many particular Pisot numbers and for the golden number. In this paper the value of is determined for irrational numbers , satisfying with a positive integer .
Somjate Chaiya, Aimo Hinkkanen (2013)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let denote the unit disk in the complex plane . In this paper, we study a family of polynomials with only one zero lying outside . We establish criteria for to satisfy implying that each of and has exactly one critical point outside .
Carlos Alexis Ruiz Gómez, Florian Luca (2015)
Acta Arithmetica
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We consider the Tribonacci sequence given by T₀ = 0, T₁ = T₂ = 1 and for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent.
Emmanuel Hebey, Pierre-Damien Thizy (2013-2014)
Séminaire Laurent Schwartz — EDP et applications
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We report on results we recently obtained in Hebey and Thizy [11, 12] for critical stationary Kirchhoff systems in closed manifolds. Let be a closed -manifold, . The critical Kirchhoff systems we consider are written as for all , where is the Laplace-Beltrami operator, is a -map from into the space of symmetric matrices with real entries, the ’s are the components of , , is the Euclidean norm of , is the critical Sobolev exponent, and...
G. Letac, J. Wesołowski (2011)
Bulletin de la Société Mathématique de France
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If the space of quadratic forms in is splitted in a direct sum and if and are independent random variables of , assume that there exist a real number such that and real distinct numbers such that for any in We prove that this happens only when , when can be structured in a Euclidean Jordan algebra and when and have Wishart distributions corresponding to this structure.