Related papers: On a generalized $k$-FL sequence and its applicati…
In this paper, we propose a general model for plane-based clustering. The general model contains many existing plane-based clustering methods, e.g., k-plane clustering (kPC), proximal plane clustering (PPC), twin support vector clustering…
We study a generalisation of the set-theoretic Yang-Baxter equation and investigate the connection between its solutions and matrix refactorisation problems. We refer to such solutions as scalene Yang-Baxter maps. Moreover, we construct…
We interpret a formula established by Lapid-M\'{\i}nguez on real regular representations of ${\rm GL}_n$ over a local non-archimedean field as a matrix determinant. We use the Lewis Carroll determinant identity to prove new relations…
We create a sequence version of calculus. First, we define equivalence, some fundamental operations, differential, and integral for sequences. Then, we propose sequence versions of identity function, power function, exponential function,…
We introduce a generalized similarity analysis which grants a qualitative description of the localised solutions of any nonlinear differential equation. This procedure provides relations between amplitude, width, and velocity of the…
We introduce and study a generalized Parikh matrix mapping based on tracking the occurrence counts of special types of subsequences. These matrices retain more information about a word than the original Parikh matrix mapping while…
In this paper we introduce I^K-convergence which is a common generalization of the I^K-convergence of sequences, double sequences and nets. We show that many results that were shown before for these special cases are true for the…
We introduce the notion of $GL(n)$-dependence of matrices, which is a generalization of linear dependence taking into account the matrix structure. Then we prove a theorem, which generalizes, on the one hand, the fact that $n+1$ vectors in…
Under certain mild assumption, we establish a one-to-one correspondence between solutions of the Nehari-Takagi problem and solutions of some Takagi-Sarason interpolation problem. The resolvent matrix of the Nehari-Takagi problem is shown to…
We use ring-theoretic methods and methods from the theory of skew braces to produce set-theoretic solutions to the reflection equation. We also use set-theoretic solutions to construct solutions to the parameter-dependent reflection…
This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. We briefly summarize results developed over the last 30 years, as well as more recent discoveries.…
We give a general formula for the equivariant complex $K$-theory $K_G^*(V)$ of a finite dimensional real linear space $V$ equipped with a linear action of a compact group $G$ in terms of the representation theory of a certain double cover…
In this article, we define a very important sequence of functions, all the functions of this sequence present behaviors very close to that of the Collatz function. The study of such functions allows us to obtain very interesting results…
Consider $k\ge 2$ distinct, linearly independent, homogeneous linear recurrences of order $k$ satisfying the same recurrence relation. We prove that the recurrences are related to a decomposable form of degree $k$, and there is a very broad…
The theory of the functional sequences and series is presented; uniformly convergent, convergent in the sense of a mean square and weakly convergent sequences and series are considered. Sequential approach to constructing generalized…
We study symplectic linear algebra over the ring $\Rt$ of Colombeau generalized numbers. Due to the algebraic properties of $\Rt$ it is possible to preserve a number of central results of classical symplectic linear algebra. In particular,…
Subsequently to the author's preceding paper, we give full proofs of some explicit formulas about factorizations of $K$-$k$-Schur functions associated with any multiple $k$-rectangles.
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…
We extend the validity domain of the conjecture about the average generalized integral means spectrum of whole-plane SLE introduced in [7, 8]. Thence we improve the results obtained in [7, 8] on the average generalized integral means…