Jakub Jan Ludew
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Jakub Jan Ludew has a total of 11 co-authors. Here are the top co-authors by number of shared publications:
- Roman Wituła
Department of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
5 shared publications - Michał Różański
Department of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
4 shared publications - Adrian Smuda
Department of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
3 shared publications - Alicja Samulewicz
Department of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
1 shared publication - Barbara Smoleń-Duda
Silesian Tech Univ, Dept Math, Kaszubska 23, PL-44100 Gliwice, Poland
1 shared publication - Beata Bajorska
Department of Mathematics, Silesian Univesity of Technology, Kaszubska 23 , 44-100 Gliwice , Poland
1 shared publication
Latest Publications
- Open Access
Asymptotics of Riemann Sums for Uniform Partitions of Intervals of Integration
Our goal is to prove the Euler–Maclaurin summation formula using only the Taylor formula. Furthermore, the Euler–Maclaurin summation formula will be considered for the case of functions of the class . A stronger version of the estimation of the rest for functions of class is given. We will also present the application of the obtained Euler–Maclaurin summation formulas to determine the asymptotics of Riemann sums for uniform partitions of intervals of integration. This paper also introduces the concepts of the asymptotic smoothing of the graph of a given function, as well as the asymptotic uniform distribution of the positive and negative values of the given function (generalizing the concept of the symmetric distribution of these values with respect to the x-axis, as in the case of the Peano–Jordan measure).Open AccessAsymptotics of Riemann Sums for Uniform Partitions of Intervals of Integration
Our goal is to prove the Euler–Maclaurin summation formula using only the Taylor formula. Furthermore, the Euler–Maclaurin summation formula will be considered for the case of functions of the class . A stronger version of the estimation of the rest for functions of class is given. We will also present the application of the obtained Euler–Maclaurin summation formulas to determine the asymptotics of Riemann sums for uniform partitions of intervals of integration. This paper also introduces the concepts of the asymptotic smoothing of the graph of a given function, as well as the asymptotic uniform distribution of the positive and negative values of the given function (generalizing the concept of the symmetric distribution of these values with respect to the x-axis, as in the case of the Peano–Jordan measure). - Open Access
A New Proof of Ramsey’s Theorem
Ramsey’s theorem states that for any natural numbers n, m there exists a natural number N such that any red–blue coloring of the graph contains either a red or blue as a subgraph. The smallest such N is called the Ramsey number, denoted as . In this paper, we reformulate this theorem and present a proof of Ramsey’s theorem that is novel as far as we are aware.Open AccessA New Proof of Ramsey’s Theorem
Ramsey’s theorem states that for any natural numbers n, m there exists a natural number N such that any red–blue coloring of the graph contains either a red or blue as a subgraph. The smallest such N is called the Ramsey number, denoted as . In this paper, we reformulate this theorem and present a proof of Ramsey’s theorem that is novel as far as we are aware. - Open Access
Improper Integrals of Type II—A New Look and Some Surprising Facts
The goal of this work is to present a new theoretical and simultaneously practical approach to the conception of improper integrals of type II and, consequently, to improper integrals of type I. Seven distinct definitions of improper integrals of type II are presented, each illustrated by suitable examples. Among them, particularly important are those defined on nets composed of sets symmetric with respect to points belonging to a given finite family of points. Connections between improper integrals of type II defined here are described in two main theorems. It should be emphasized that all definitions of improper integrals presented here are special cases of a very general definition of improper integrals on non-compact sets, which is presented at the end of this work. This definition is inspired by a concept introduced by Maurin.
Open AccessImproper Integrals of Type II—A New Look and Some Surprising Facts
The goal of this work is to present a new theoretical and simultaneously practical approach to the conception of improper integrals of type II and, consequently, to improper integrals of type I. Seven distinct definitions of improper integrals of type II are presented, each illustrated by suitable examples. Among them, particularly important are those defined on nets composed of sets symmetric with respect to points belonging to a given finite family of points. Connections between improper integrals of type II defined here are described in two main theorems. It should be emphasized that all definitions of improper integrals presented here are special cases of a very general definition of improper integrals on non-compact sets, which is presented at the end of this work. This definition is inspired by a concept introduced by Maurin.
- Open Access
- 25 February 2023
- Published by Springer Nature in Results in Mathematics
- Vol. 78 (3) , 1-6
A New Description of the Complex Roots Using Zeros of Some Polynomials
Inspired by a problem found in a textbook of Faddeev and Sominsky we propose a new form of roots of an arbitrary complex number. Our idea uses the zeros of some polynomials connected with the modified Chebyshev polynomials.
- 25 February 2023
- Published by Springer Nature in Results in Mathematics
- Vol. 78 (3) , 1-6
Open AccessA New Description of the Complex Roots Using Zeros of Some Polynomials
Inspired by a problem found in a textbook of Faddeev and Sominsky we propose a new form of roots of an arbitrary complex number. Our idea uses the zeros of some polynomials connected with the modified Chebyshev polynomials.
- Open Access
- 1 January 2021
- Published by Walter de Gruyter GmbH in Open Mathematics
- Vol. 19 (1) , 583-599
On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras. Explicit and recurrent formulae for Split Quaternacci sequences are given, as well as generating functions. Also, matrices related to Split Quaternaccis sequences are investigated. Moreover, new identities connecting Horadam sequences with other known sequences are generated. Analogous identities for Horadam quaternions and split Horadam quaternions are proved.
- 1 January 2021
- Published by Walter de Gruyter GmbH in Open Mathematics
- Vol. 19 (1) , 583-599
Open AccessOn split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis
In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras. Explicit and recurrent formulae for Split Quaternacci sequences are given, as well as generating functions. Also, matrices related to Split Quaternaccis sequences are investigated. Moreover, new identities connecting Horadam sequences with other known sequences are generated. Analogous identities for Horadam quaternions and split Horadam quaternions are proved.
- 1 January 2011
- Published by Walter de Gruyter GmbH in Journal of Applied Analysis
- Vol. 17 (2)
On Nemytskij operator in the space of absolutely continuous set-valued functions
We consider the Nemytskij operator, defined by (Nφ)(x) ≔ G(x, φ(x)), where G is a given set-valued function. It is shown that if N maps AC(I, C), the space of all absolutely continuous functions on the interval I ≔ [0, 1] with values in a cone C in a reflexive Banach space, into AC(I,
- 1 January 2011
- Published by Walter de Gruyter GmbH in Journal of Applied Analysis
- Vol. 17 (2)
On Nemytskij operator in the space of absolutely continuous set-valued functions
We consider the Nemytskij operator, defined by (Nφ)(x) ≔ G(x, φ(x)), where G is a given set-valued function. It is shown that if N maps AC(I, C), the space of all absolutely continuous functions on the interval I ≔ [0, 1] with values in a cone C in a reflexive Banach space, into AC(I,
- Open Access
- 1 January 2008
- Published by Walter de Gruyter GmbH in Demonstratio Mathematica
- Vol. 41 (2) , 403-414
On Nemytskij operator of substitution in the C1 space of set-valued functions
We consider the Nemytskij operator, i.e., the operator of substitution, defined by (
- 1 January 2008
- Published by Walter de Gruyter GmbH in Demonstratio Mathematica
- Vol. 41 (2) , 403-414
Open AccessOn Nemytskij operator of substitution in the C1 space of set-valued functions
We consider the Nemytskij operator, i.e., the operator of substitution, defined by (