Related papers: A Class of Orthogonal Sequences
Sigmoid functions play an important role in many areas of applied mathematics, including machine learning, population dynamics and probability. We place the study of sigmoid functions in the context of the derivative sub-group of the group…
We introduce characteristic classes for the spectral sequence associated to a split short exact sequence of Hopf algebras. We show that these characteristic classes can be seen as obstructions for the vanishing of differentials in the…
Homogeneous random fractals form a probabilistic extension of self-similar sets with more dependencies than in random recursive constructions. For such random fractals we consider mean values of the Lipschitz-Killing curvatures of their…
Properties of the recently reported homogeneous Hilbert curves are deduced and reported. The nature of the affine transformations involved in the construction of the Hilbert curves is explored. The analytical representation of proper and…
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…
In a classical case, orthogonal polynomial sequences are in such a way that the $ n $th polynomial has the exact degree $n$. Such sequences are complete and form a basis of the space for any arbitrary polynomial. In this paper, we introduce…
Orthogonal polynomials appear naturally in the study of compositions of M\"obius transformations. In this paper, we consider several classes of orthogonal polynomials associated to non-autonomous perturbations of a parabolic M\"obius map.…
We carry out some algebraic and analytic properties of a new class of orthogonal polyanalytic polynomials, including their operational formulas, recurrence relations, generating functions, integral representations and different…
A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…
We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necessary conditions for Koszulity of such algebras in terms of…
The classical Fibonacci sequence is known to exhibit many fascinating properties. In this paper, we explore the Fibonacci sequence and integer sequences generated by second order linear recurrence relations with positive integer…
Binary sequences with lower autocorrelation values have important applications in cryptography and communications. In this paper, we present all possible parameters for binary periodical sequences with a 2-level autocorrelation values. For…
We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle given in terms of the exponential of Gaussian Free Field. We conjecture that our curves are locally…
We introduce several classes of pseudorandom sequences which represent a natural extension of classical methods in random number generation. The sequences are obtained from constructions on labeled binary trees, generalizing the well-known…
A new method of composition orthogonality is introduced. It is applied to generate new sequences of orthogonal polynomials and functions. In particular, classical orthogonal polynomials are interpreted in the sense of composition…
We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the result for the symplectic group where all classes have normal closure, there is…
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…
In this article, the reproducing kernel Hilbert space [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast…
A rigorous derivation is provided for canonical correlations and partial canonical correlations for certain Hilbert space indexed stochastic processes. The formulation relies on a key congruence mapping between the space spanned by a second…
For the family of the orthogonal quantum matrix algebras we investigate the structure of their characteristic subalgebras -- special commutative subalgebras, which for the subfamily of the reflection equation algebras appear to be central.…