Related papers: The multiplicative inequality for class degrees vi…
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…
Higher-dimensional analogs of the predictable degree property and column reducedness are defined, and it is proved that the two properties are equivalent. It is shown that every multidimensional convolutional code has, what is called, a…
The partition function of a factor graph can sometimes be accurately estimated by Monte Carlo methods. In this paper, such methods are extended to factor graphs with negative and complex factors.
We give lower bounds on the number of effective divisors of degree $\leq g-1$ with respect to the number of places of certain degrees of an algebraic function field of genus $g$ defined over a finite field. We deduce lower bounds and…
In this paper we study probabilistic aspects such as subgroup commutativity degree and cyclic subgroup commutativity degree of the (generalized) dicyclic groups. We find explicit formulas for these concepts and we provide another example of…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
If a linear differential operator with rational function coefficients is reducible, its factors may have coefficients with numerators and denominatorsof very high degree. When the base field is $\mathbb C$, we give a completely explicit…
We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function…
Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify…
Imbalance learning is a subfield of machine learning that focuses on learning tasks in the presence of class imbalance. Nearly all existing studies refer to class imbalance as a proportion imbalance, where the proportion of training samples…
Let $G$ be a finite group, and let $d$ be the degree of an irreducible character of $G$ such that $|G|=d(d+e)$ for some $e>1$. Consider the case when $G$ is solvable, $d$ is square-free, and $(d,d+e)=1$. We wish to explore an equivalent…
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…
We investigate how the metric dimension of infinite graphs change when we add edges to the graph. Our two main results: (1) there exists a growing sequence of graphs (under the subgraph relation, but without adding vertices) for which the…
There is a way of assigning a realizability notion to each degree of incomputability. In our setting, we make use of Weihrauch degrees (degrees of incomputability/discontinuity of partial multi-valued functions) to obtain Lifschitz-like…
Expressions for the derivatives with respect to order of modified Bessel functions evaluated at integer orders and certain integral representations of associated Legendre functions with modulus argument greater than unity are used to…
In engineering practice one often encounters planar problems, where the corresponding vector space of forces, velocities or (infinitesimal) displacements is three dimensional. This paper shows how these spaces can be factorized, such that…
We describe the isomorphism classes of infinite-dimensional graded Lie algebras of maximal class, generated by elements of weight one, over fields of odd characteristic.
We consider the problem of producing fair probabilistic classifiers for multi-class classification tasks. We formulate this problem in terms of "projecting" a pre-trained (and potentially unfair) classifier onto the set of models that…
The degree of commutativity of a group $G$ measures the probability of choosing two elements in $G$ which commute. There are many results studying this for finite groups. In [AMV17], this was generalised to infinite groups. In this note, we…
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…