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.
Noam D. Elkies, Daniel M. Kane, Scott Duke Kominers (2013)
Journal de Théorie des Nombres de Bordeaux
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In this note, we give simple examples of sets of quadratic forms that have minimal -universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh [KKO05] in the negative.
Lifeng Li, Jianke Zhang, Chang Zhou (2019)
Kybernetika
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For a t-norm T on a bounded lattice , a partial order was recently defined and studied. In [11], it was pointed out that the binary relation is a partial order on , but may not be a lattice in general. In this paper, several sufficient conditions under which is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on such that is a lattice are presented.
I. D. Shkredov (2014)
Acta Arithmetica
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We describe all sets which represent the quadratic residues 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.
Zbigniew Leszczyński, Daniel Simson (2015)
Colloquium Mathematicae
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The incidence coalgebras of interval finite posets I and their comodules are studied by means of the reduced Euler integral quadratic form , where K is an algebraically closed field. It is shown that for any such coalgebra the tameness of the category of finite-dimensional left -modules is equivalent to the tameness of the category of finitely copresented left -modules. Hence, the tame-wild dichotomy for the coalgebras is deduced. Moreover, we prove that for an interval finite...
Gábor Czédli (2024)
Mathematica Bohemica
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Following G. Grätzer and E. Knapp (2007), a slim planar semimodular lattice, SPS lattice for short, is a finite planar semimodular lattice having no as a sublattice. An SPS lattice is a slim rectangular lattice if it has exactly two doubly irreducible elements and these two elements are complements of each other. A finite poset is said to be JConSPS-representable if there is an SPS lattice such that is isomorphic to the poset of join-irreducible congruences of . We prove that...
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...
Gianfranco Cimmino (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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For every positive definite quadratic form in 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 sphere centered at and with radius raised to the ()-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.
Ivan Chajda, Helmut Länger (2022)
Mathematica Bohemica
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We investigate the lattice of subspaces of an -dimensional vector space over a finite field with a prime power together with the unary operation of orthogonality. It is well-known that this lattice is modular and that the orthogonality is an antitone involution. The lattice satisfies the chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when is orthomodular....
Xiaoli Liu, Zhishan Yang (2022)
Czechoslovak Mathematical Journal
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Let be a quadratic field over the rational field and be the number of nonzero integral ideals with norm . We establish Erdős-Kac type theorems weighted by and of quadratic field in short intervals with . We also get asymptotic formulae for the average behavior of and in short intervals.
Gül Deniz Çaylı, Funda Karaçal (2017)
Kybernetika
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In this paper, we propose the general methods, yielding uninorms on the bounded lattice , with some additional constraints on for a fixed neutral element based on underlying an arbitrary triangular norm on and an arbitrary triangular conorm on . And, some illustrative examples are added for clarity.
Kamila Kliś-Garlicka (2016)
Czechoslovak Mathematical Journal
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The notion of a bilattice was introduced by Shulman. A bilattice is a subspace analogue for a lattice. In this work the definition of hyperreflexivity for bilattices is given and studied. We give some general results concerning this notion. To a given lattice we can construct the bilattice . Similarly, having a bilattice we may consider the lattice . In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples...
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...