Torsion points on curves and common divisors of and
Nir Ailon, Zéev Rudnick (2004)
Acta Arithmetica
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Nir Ailon, Zéev Rudnick (2004)
Acta Arithmetica
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Jeffrey L. Stuart (2015)
Czechoslovak Mathematical Journal
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Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the - and -factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse -matrices with symmetric, irreducible, tridiagonal inverses.
Kevin Ford, Richard H. Hudson (2001)
Acta Arithmetica
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Hacène Belbachir, Farid Bencherif (2008)
Discussiones Mathematicae - General Algebra and Applications
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Letting (resp. ) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences and for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also and admit remarkableness integer coordinates on each of the two basis.
Aleksander Grytczuk, Izabela Kurzydło (2009)
Discussiones Mathematicae - General Algebra and Applications
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Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) with d ∈ N for nonsingular , i=1,...,n.
Brian Jefferies (2001)
Studia Mathematica
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It is shown that a finite system T of matrices whose real linear combinations have real spectrum satisfies a bound of the form . The proof appeals to the monogenic functional calculus.
S. Gurak (2007)
Acta Arithmetica
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Castelli, Roberto, Lessard, Jean-Philippe
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In this paper, a rigorous computational method to enclose eigenpairs of complex interval matrices is proposed. Each eigenpair is found by solving a nonlinear equation of the form via a contraction argument. The set-up of the method relies on the notion of , which provide an efficient mean of determining a domain on which the contraction mapping theorem is applicable.
Z. Cylkowski (1966)
Applicationes Mathematicae
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Johannes F. Morgenbesser (2011)
Acta Arithmetica
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Jean Schmets, Manuel Valdivia (2005)
Annales Polonici Mathematici
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We deal with projective limits of classes of functions and prove that: (a) the Chebyshev polynomials constitute an absolute Schauder basis of the nuclear Fréchet spaces ; (b) there is no continuous linear extension map from into ; (c) under some additional assumption on , there is an explicit extension map from into by use of a modification of the Chebyshev polynomials. These results extend the corresponding ones obtained by Beaugendre in [1] and [2].
Roland Coghetto (2016)
Formalized Mathematics
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In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26]) of [...] ℰTn and in [20] he has formalized that [...] ℰTn is second-countable, we build (in the topological sense defined in [23]) a denumerable base of [...] ℰTn . Then we introduce the n-dimensional intervals (interval in n-dimensional Euclidean space, pavé (borné) de ℝn [16], semi-intervalle (borné) de ℝn [22]). We conclude with the definition of Chebyshev distance [11]. ...
Harold G. Diamond, Wen-Bin Zhang (2013)
Acta Arithmetica
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If the counting function N(x) of integers of a Beurling generalized number system satisfies both and , then the counting function π(x) of the primes of this system is known to satisfy the Chebyshev bound π(x) ≪ x/logx. Let f(x) increase to infinity arbitrarily slowly. We give a construction showing that and do not imply the Chebyshev bound.
Roswitha Hofer, Harald Niederreiter (2014)
Acta Arithmetica
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The second-named author recently suggested identifying the generating matrices of a digital (t,m,s)-net over the finite field with an s × m matrix C over . More exactly, the entries of C are determined by interpreting the rows of the generating matrices as elements of . This paper introduces so-called Vandermonde nets, which correspond to Vandermonde-type matrices C, and discusses the quality parameter and the discrepancy of such nets. The methods that have been successfully used...
Frank J. Hall, Miroslav Rozložník (2016)
Czechoslovak Mathematical Journal
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A real matrix is a G-matrix if is nonsingular and there exist nonsingular diagonal matrices and such that , where denotes the transpose of the inverse of . Denote by a diagonal (signature) matrix, each of whose diagonal entries is or . A nonsingular real matrix is called -orthogonal if . Many connections are established between these matrices. In particular, a matrix is a G-matrix if and only if is diagonally (with positive diagonals) equivalent to a column permutation...
Caroline Sweezy (2004)
Studia Mathematica
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For two strictly elliptic operators L₀ and L₁ on the unit ball in ℝⁿ, whose coefficients have a difference function that satisfies a Carleson-type condition, it is shown that a pointwise comparison concerning Lusin area integrals is valid. This result is used to prove that if L₁u₁ = 0 in B₁(0) and then lies in the exponential square class whenever L₀ is an operator so that L₀u₀ = 0 and implies is in the exponential square class; here S is the Lusin area integral. The exponential...
Marcin Gąsiorek, Daniel Simson (2012)
Colloquium Mathematicae
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A complete list of positive Tits-sincere one-peak posets is provided by applying combinatorial algorithms and computer calculations using Maple and Python. The problem whether any square integer matrix is ℤ-congruent to its transpose is also discussed. An affirmative answer is given for the incidence matrices and the Tits matrices of positive one-peak posets I.
Bruno de Malafosse (2006)
Studia Mathematica
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We give some new properties of the space and we apply them to the σ-core theory. These results generalize those by Choudhary and Yardimci.
Teodor Banica, Ion Nechita, Jean-Marc Schlenker (2014)
Annales mathématiques Blaise Pascal
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We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for the quantity satisfies , with equality if and only if is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of , (2) the study of the critical points of , and (3) the computation of the moments of . We explore here...
Trung Hoa Dinh, Sima Ahsani, Tin-Yau Tam (2016)
Czechoslovak Mathematical Journal
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We study some geometric properties associated with the -geometric means of two positive definite matrices and . Some geodesical convexity results with respect to the Riemannian structure of the positive definite matrices are obtained. Several norm inequalities with geometric mean are obtained. In particular, we generalize a recent result of Audenaert (2015). Numerical counterexamples are given for some inequality questions. A conjecture on the geometric mean inequality regarding...