Related papers: 2-adic Valuations of Quadratic Sequences
We study the periodic properties of sequences of quantum channels sampled from an ergodic stochastic process satisfying a natural irreducibility condition. We relate these periodic properties to certain global spectral data defined by the…
For a d-dimensional polyhedral complex P, the dimension of the space of piecewise polynomial functions (splines) on P of smoothness r and degree k is given, for k sufficiently large, by a polynomial f(P,r,k) of degree d. When d=2 and P is…
In this paper, we define a q-adic factorial and we demonstrate some properties of a generalized p-adic gamma function. Also, some numerical examples have been given
We count with a smooth weight the number of $2 \times 2$ integer matrices with a fixed characteristic polynomial with a main term and an error term using bounds for sums of Weyl sums for quadratic roots.
The normalized Yamada polynomial is a polynomial invariant in variable A for theta-curves. In this work, we show that the coefficients of the power series obtained from this polynomial by the substitution A=e^x=1+x+x^2/2+x^3/6+... are…
We consider a sequence of sums of powers of the the roots of the cubic equation characterizing the Tribonacci sequences and derive its relationship with a particular Tribonacci sequence. Then we make a conjecture on the possible…
We explicitly determine the values of reduced cyclotomic periods of order $2^m$, $m\ge 4$, for finite fields of characteristic $p\equiv 3$ or $5\pmod{8}$. These evaluations are applied to obtain explicit factorizations of the corresponding…
The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees…
In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also…
An overview of the basic results on Macdonald(-Koornwinder) polynomials and double affine Hecke algebras is given. We develop the theory in such a way that it naturally encompasses all known cases. Among the basic properties of the…
In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
In this article, we show that the algebraic degree in semidefinite programming can be expressed in terms of the coefficient of a certain monomial in a doubly symmetric polynomial. This characterization of the algebraic degree allows us to…
When the Euclidean algorithm produces a symmetric sequence of quotients, we give explicit formulas for the remainders that allow the analysis of two families of quadratic forms in the remainders.
This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…
Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is…
We study monic univariate polynomials whose coefficients are analytic functions of a real variable and whose roots lie in a specified analytic curve. These include characteristic polynomials of unitary and hermitian matrices whose entries…
In this paper, we consider sequences of polynomials that satisfy differential--difference recurrences. Our interest is motivated by the fact that polynomials satisfying such recurrences frequently appear as generating polynomials of integer…
We explore parameterizations by radicals of low genera algebraic curves. We prove that for $q$ a prime power that is large enough and prime to $6$, a fixed positive proportion of all genus 2 curves over the field with $q$ elements can be…
We establish a valuative version of Grothendieck's section conjecture for curves over p-adic local fields. The image of every section is contained in the decomposition subgroup of a valuation which prolongs the p-adic valuation to the…