Displaying similar documents to “Computation of linear algebraic equations with solvability verification over multi-agent networks”

The adaptation of the k -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm

Rudolf Scitovski, Kristian Sabo (2019)

Applications of Mathematics

Similarity:

We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse E is viewed as a Mahalanobis circle with center S , radius r , and some positive definite matrix Σ . A very efficient method for solving this problem is proposed. The method uses a modification of the k -means algorithm for Mahalanobis-circle centers. The initial approximation consists of the set of circles whose centers...

Algebraic independence of the values at algebraic points of a class of functions considered by Mahler

N. Ch. Wass

Similarity:

This thesis is concerned with the problem of determining a measure of algebraic independence for a particular m-tuple θ₁,..., θ m of complex numbers. Specifically, let K be a number field and let f₁(z),..., f m ( z ) be elements of K[[z]] algebraically independent over K(z) satisfying equations of the form(*) f j ( z b ) = i = 1 m f i ( z ) a i j ( z ) + b j ( z ) (j = i,...,m)for b ≥ 2, a i j ( z ) , b j ( z ) in K(z). Suppose finally that α ∈ K is such that 0 < |α| < 1, the f j ( z ) converge at z = α and the a i j ( z ) , b j ( z ) are analytic at z = α , α b , α b ² , . . . Then the θ i = f i ( α ) are algebraically independent...

Diagonalization and rationalization of algebraic Laurent series

Boris Adamczewski, Jason P. Bell (2013)

Annales scientifiques de l'École Normale Supérieure

Similarity:

We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime p the reduction modulo p of the diagonal of a multivariate algebraic power series f with integer coefficients is an algebraic power series of degree at most p A and height at most A p A , where A is an effective constant that only...

Seasonal time-series imputation of gap missing algorithm (STIGMA)

Eduardo Rangel-Heras, Pavel Zuniga, Alma Y. Alanis, Esteban A. Hernandez-Vargas, Oscar D. Sanchez (2023)

Kybernetika

Similarity:

This work presents a new approach for the imputation of missing data in weather time-series from a seasonal pattern; the seasonal time-series imputation of gap missing algorithm (STIGMA). The algorithm takes advantage from a seasonal pattern for the imputation of unknown data by averaging available data. We test the algorithm using data measured every 10 minutes over a period of 365 days during the year 2010; the variables include global irradiance, diffuse irradiance, ultraviolet irradiance,...

The R₂ measure for totally positive algebraic integers

V. Flammang (2016)

Colloquium Mathematicae

Similarity:

Let α be a totally positive algebraic integer of degree d, i.e., all of its conjugates α = α , . . . , α d are positive real numbers. We study the set ₂ of the quantities ( i = 1 d ( 1 + α ² i ) 1 / 2 ) 1 / d . We first show that √2 is the smallest point of ₂. Then, we prove that there exists a number l such that ₂ is dense in (l,∞). Finally, using the method of auxiliary functions, we find the six smallest points of ₂ in (√2,l). The polynomials involved in the auxiliary function are found by a recursive algorithm.

Isomorphisms of algebraic number fields

Mark van Hoeij, Vivek Pal (2012)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let ( α ) and ( β ) be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, ( β ) ( α ) . The algorithm is particularly efficient if there is only one isomorphism.

Sum of squares and the Łojasiewicz exponent at infinity

Krzysztof Kurdyka, Beata Osińska-Ulrych, Grzegorz Skalski, Stanisław Spodzieja (2014)

Annales Polonici Mathematici

Similarity:

Let V ⊂ ℝⁿ, n ≥ 2, be an unbounded algebraic set defined by a system of polynomial equations h ( x ) = = h r ( x ) = 0 and let f: ℝⁿ→ ℝ be a polynomial. It is known that if f is positive on V then f | V extends to a positive polynomial on the ambient space ℝⁿ, provided V is a variety. We give a constructive proof of this fact for an arbitrary algebraic set V. Precisely, if f is positive on V then there exists a polynomial h ( x ) = i = 1 r h ² i ( x ) σ i ( x ) , where σ i are sums of squares of polynomials of degree at most p, such that f(x) + h(x) >...

Multiplicatively dependent triples of Tribonacci numbers

Carlos Alexis Ruiz Gómez, Florian Luca (2015)

Acta Arithmetica

Similarity:

We consider the Tribonacci sequence T : = T n n 0 given by T₀ = 0, T₁ = T₂ = 1 and T n + 3 = T n + 2 + T n + 1 + T n for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent.

Cycles on algebraic models of smooth manifolds

Wojciech Kucharz (2009)

Journal of the European Mathematical Society

Similarity:

Every compact smooth manifold M is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of M . We study modulo 2 homology classes represented by algebraic subsets of X , as X runs through the class of all algebraic models of M . Our main result concerns the case where M is a spin manifold.

Uniform convergence of the greedy algorithm with respect to the Walsh system

Martin Grigoryan (2010)

Studia Mathematica

Similarity:

For any 0 < ϵ < 1, p ≥ 1 and each function f L p [ 0 , 1 ] one can find a function g L [ 0 , 1 ) with mesx ∈ [0,1): g ≠ f < ϵ such that its greedy algorithm with respect to the Walsh system converges uniformly on [0,1) and the sequence | c k ( g ) | : k s p e c ( g ) is decreasing, where c k ( g ) is the sequence of Fourier coefficients of g with respect to the Walsh system.

Exceptional sets in Waring's problem: two squares and s biquadrates

Lilu Zhao (2014)

Acta Arithmetica

Similarity:

Let R s ( n ) denote the number of representations of the positive number n as the sum of two squares and s biquadrates. When s = 3 or 4, it is established that the anticipated asymptotic formula for R s ( n ) holds for all n X with at most O ( X ( 9 - 2 s ) / 8 + ε ) exceptions.

On the principle of real moduli flexibility: perfect parametrizations

Edoardo Ballico, Riccardo Ghiloni (2014)

Annales Polonici Mathematici

Similarity:

Let V be a real algebraic manifold of positive dimension. The aim of this paper is to show that, for every integer b (arbitrarily large), there exists a trivial Nash family = V y y R b of real algebraic manifolds such that V₀ = V, is an algebraic family of real algebraic manifolds over y R b 0 (possibly singular over y = 0) and is perfectly parametrized by R b in the sense that V y is birationally nonisomorphic to V z for every y , z R b with y ≠ z. A similar result continues to hold if V is a singular real algebraic...

Algorithm for the complement of orthogonal operations

Iryna V. Fryz (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a k -tuple of orthogonal n -ary operations, where k < n , to an n -tuple of orthogonal n -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a k -tuple of orthogonal n -ary operations to an n -tuple of orthogonal n -ary operations and an algorithm for complementing a k -tuple of orthogonal k -ary operations to an n -tuple of orthogonal n -ary operations. Also...