Related papers: On a generalized $k$-FL sequence and its applicati…
In this paper we obtain explicit estimates and existence results on the number of $\mathbb{F}_q$-rational solutions of certain systems defined by families of diagonal equations over finite fields. Our approach relies on the study of the…
We generalize the notion of linear chord diagrams to the case of matched sets of size $k$, which we call $k$-chord diagrams. We provide formal generating functions and recurrence relations enumerating these $k$-chord diagrams by the number…
Family of replica matrices, related to general ultrametric spaces, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed.
This note generalizes $\mathrm{SL}(k)$-friezes to configurations of numbers in which one of the boundary rows has been replaced by a ragged edge (described by a juggling function). We provide several equivalent definitions/characterizations…
This work is dedicated to a new completely algebraic approach to Arakelov geometry, which doesn't require the variety under consideration to be generically smooth or projective. In order to construct such an approach we develop a theory of…
In this note we derive some interesting definite integrals involving Malmsten logarithm forms, reciprocal logarithm forms and K\"{o}lbig type integrals in terms of special functions.
We derive new formulas for the number of unordered (distinct) factorizations with $k$ parts of a positive integer $n$ as sums over the partitions of $k$ and an auxiliary function, the number of partitions of the prime exponents of $n$,…
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.
By means of the derivative operator and Whipple-type $_3F_2$-series identities, two families of summation formulae involving generalized harmonic numbers are established.
Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…
We establish certain fundamental properties of $f$-vectors and $F$-matrices for generalized cluster algebras, including the initial and final seed mutation formulas, the compatibility property and the symmetry property. Along the way, we…
In the theory of generalized cluster algebras, we build the so-called cluster formula and $D$-matrix pattern. Then as applications, some fundamental conjectures of generalized cluster algebras are solved affirmatively.
The general linear group acts on $m$-tuples of $N\times N$ matrices by simultaneous conjugation. Quantum deformations of the corresponding rings of invariants and the so-called trace rings are investigated.
$k$-diagonal circulant matrices and cyclic banded matrices are widely used in numerical simulations and signal processing of circular linear systems. Algorithms that directly involve or specify linear or quadratic complexity for the…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
This paper is dedicated to compute Pfaffian and determinant of one type of skew centrosymmetric matrices in terms of general number sequence of second order.
This paper presents a family of rapidly convergent summation formulas for various finite sums of the form $\sum_{k=0}^{\lfloor x\rfloor}f(k)$, where $x$ is a positive real number.
In this work, the authors provide closed forms and recurrence expressions for computing the $k$th power of the formal power series, some of them in terms of a determinant of some matrices. As a consequence, we obtain the reciprocal of the…
The modified Bessel function of the second kind K$\nu$ appears in a wide variety of applied scientific fields. While its use is greatly facilitated by an implementation in most numerical libraries, overflow issues can be encountered…
We obtain the Mellin transforms of the generalized fractional integrals and derivatives that generalize the Riemann-Liouville and the Hadamard fractional integrals and derivatives. We also obtain interesting results, which combine…