Foreword on the special issue dedicated to the 70th anniversary of prof. Peter Tallos

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A special oligopoly model is considered when the firms compete on the factor market, and the used factor volumes determine their outputs. In the <italic>N</italic>firm case conditions are given for the existence of the Nash equilibrium, and in the cooperative case, sufficient conditions are derived for the existence and uniqueness of the joint profit maximizer. In the case of a linear duopoly the dynamic extensions are introduced in both cases based on gradient adjustments. Conditions are given for the local asymptotic stability of the equilibrium and the joint profit maximizer without and with information delays.
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Department of Industrial and Systems Engineering

Some notes on dynamic oligopsonies

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A short proof is given for the Cayley-Hamilton theorem using the concept of the subminimal polynomial.
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The subminimal polynomial and the Cayley-Hamilton theorem

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In this paper we discuss structural Ramsey theory and how it relates to the understanding of extremely amenable groups with an emphasis on the measure theoretic nature of this problem. We discuss the problem within Blass-Ramsey actions on discrete spaces and and more general group actions on compact spaces and explore how we can look at these problems by looking at Gelfand duals of commutative <italic>C</italic>*-algebras.
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Ramsey actions and Gelfand duality

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In this paper we determine the asymptotic behavior of the Non-dictatorship Index (NDI) introduced in Bednay, Moskalenko and Tasnádi (2019). We show that if <italic>m</italic> denotes the number of alternatives, then as the number of voters tends to infinity the NDI of any anonymous voting rule tends to (<italic>m</italic> − 1)/<italic>m</italic>, which equals the NDI of the constant rule.
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The Limit of the Non-dictatorship Index

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We establish that the local viability for a convex and compact valued upper Hausdorff continuous map on a convex and compact domain in a Banach space, implies the existence of an equilibrium.
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Viability and equilibrium in Banach spaces

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Bonus-malus system is an often used risk management tool in the insurance industry, and it is usually modeled with Markov chains. Under mild conditions it can be stated that the bonus-malus system converges to a unique stationary distribution in the long run. The maximum likelihood ratio property is a well-known statistical concept and we define it for the stationary distribution of a bonus-malus system. For two special cases we could justify it algebraically. For other cases we describe a numerical method with which we can test this property in any case. With the help of the described method, we checked this property for cases that appear in actuarial practice.
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On monotone likelihood ratio of stationary probabilities in bonus-malus systems

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The article discusses the construction of the elementary trigonometric functions. It discusses several approaches, but the main message is that to construct the trigonometric functions one needs to follow the same approach as one should use during the construction of the real exponential function, but one should use complex numbers. The key point is that one must construct the complex square root function to define the trigonometric functions on the binary numbers and then one should use some convexity argument to prove their differentiability. This approach, as the power series approach, based on the intimate relation between the trigonometric and the exponential functions.
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On the construction of the elementary trigonometric functions

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We consider several concepts of computability (recursiveness) for sets in Euclidean space. A list of four ideal properties for such sets is proposed and it is shown in a very elementary way that no notion can satisfy all four desiderata. Most notions introduced here are essentially based on separability of ℝ<italic>n</italic> and this is natural when thinking about operations on an actual digital computer where, in fact, rational numbers are the basis of everything. We enumerate some properties of some naïve but practical notions of recursive sets and contrast these with others, including the widely used and accepted notion of <italic>computable</italic> set developed by Weihrauch, Brattka and others which is based on the “Polish school” notion of a computable real function. We also offer a conjecture about the Mandelbrot set.
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Computability of sets in Euclidean space

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This is a <italic>selected overview</italic> of a research line initiated and mostly developed by the three authors over the last three decades. Applying the state space paradigm of Mathematical Systems Theory, monitoring means that from the observation (a transform) of an unknown state process, the latter should be recovered. Since most of the dynamic models of population biology are nonlinear, for solving the monitoring problem, tools of nonlinear analysis are applied in different contexts. This approach to monitoring has found different applications ranging from population ecology to radiotherapy, from stock estimation in fisheries to monitoring of solar thermal heating systems.
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Hungarian University of Agriculture and Life Sciences

Monitoring of population systems

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The class of ABS methods was originally developed for solving systems of linear equations in a finite number of iterations. Later it was shown that methods for solving nonlinear systems of equations, linear programming algorithms, quadratic programming, etc. are also members of the ABS class. In this paper, we show that QR factorization can also be derived from three ABS subclasses, which is an essential step in methods solving eigenvalue problems. Another possibility to use the ABS class in the eigenvalue problems is to transform a matrix to Hessenberg form which is an important initial step when solving eigenvalue problems by QR-type methods. Here we study versions of the plain QR-method which are based on the QR factorization computed by the ABS methods and compare them with the MATLAB eig () function. We also compare the ABS Hessenberg method to the MATLAB hess() function. The preliminary results show the competitiveness of 3 ABS eigenvalue solving methods with the MATLAB eig () function.
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Solution of the real and complex eigenvalue problems in the ABS class

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We investigate the relationship between numerical semigroups and Dyck paths discovered by Bras-Amorós and de Mier. More specifically, we consider some classes of Dyck paths and characterize those paths giving rise to numerical semigroups.
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Dipartimento di Matematica e Informatica “U. Dini”

Classes of Dyck paths associated with numerical semigroups

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The paper investigates an one-product reverse logistics system. The aim is to analyze the functioning of such a system with continuous time and linear cost structure. The costs consist of linear holding costs for both warehouse, and the linear remanufacturing, manufacturing, and disposal costs. The demand and return rates are known deterministic parameters. The problem is solved with the Pontyagin’s maximum principle. Solving the control problem, it is corrected an earlier paper [1].
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Production-inventory strategies for a linear reverse logistics system

AHEAD OF PRINT

Volume 30 (2022): Issue 4 (December 2022)

Volume 30 (2022): Issue 3 (October 2022) Special issue dedicated to 70th anniversary of prof. Peter Tallos

Volume 30 (2022): Issue 2 (August 2022)

Volume 30 (2022): Issue 1 (June 2022)

Volume 29 (2020): Issue 1 (December 2020)

Volume 28 (2019): Issue 1 (October 2019)

Volume 27 (2018): Issue 2 (August 2018)

Volume 27 (2018): Issue 1 (July 2018)

Volume 26 (2017): Issue 1 (June 2017)

Volume 25 (2015): Issue 2 (December 2015)

Volume 25 (2015): Issue 1 (September 2015)

Pure Mathematics and Applications

 Pure Mathematics and Applications - section Algebra and Theoretical Computer Science - publishes original high quality articles of international relevance in the two disciplines of algebra and theoretical computer science. Specific topics include (but are not limited to) group and semigroup theory, commutative algebra, computational algebra, poset and lattice theory, linear algebra, theory of automata and formal languages, computational complexity, analysis of algorithms, game theory. In particular, articles in which interactions between algebra and theoretical computer science play a relevant role (i.e. techniques of either discipline are fundamental in obtaining results of the other) will be privileged. As a natural consequence of this fact, one of the disciplines which are more relevant to the journal is discrete mathematics, and more specifically enumerative and algebraic combinatorics, graph theory, discrete tomography, random and exhaustive generation, combinatorial order theory, bioinformatics, matroid theory, combinatorics on words.Papers about high quality applications of combinatorial methods to computer science (especially algorithms, data structures, and criptography), or special issues, completely devoted to a certain contemporary topic of high interest, are also published.  Pure Mathematics and Applications - section Mathematics of Optimization - publishes original research works, surveys, historical and biographical articles primarily on mathematics of optimization. Papers about high quality applications of mathematical methods to decision sciences (especially operations research, economics, games and control theory, actuarial and financial mathematics), or special issues, completely devoted to a certain contemporary topic of high interest are also published.  The journal contains two sections - one devoted to Algebra and Theoretical Computer Science, and second to Mathematics of Optimization. The published articles of the first section focus on algebra and theoretical computer science, with interactions between algebra and theoretical computer science in particular. The second section publishes research works, surveys, historical and biographical articles primarily on mathematics of optimization.  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.  Target group  researchers in the fields of algebra and theoretical computer science 

Volume 30 (2022): Issue 3 (October 2022) - Special issue dedicated to 70th anniversary of prof. Peter Tallos