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        <title>Pure Mathematics and Applications Feed</title>
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            <title>Pure Mathematics and Applications Feed</title>
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        <copyright>All rights reserved 2026, Corvinus University of Budapest</copyright>
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            <title><![CDATA[Enumeration of inversion sequences according to the outer and inner perimeter]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2023-0004</link>
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            <pubDate>Tue, 31 Dec 2024 00:00:00 GMT</pubDate>
            <description><![CDATA[The integer sequence π = π1 ‧‧‧ πn is said to be an inversion sequence if 0 ≤ πi ≤ i – 1 for all i. Let ℐn denote the set of inversion sequences of length n, represented using positive instead of non-negative integers. We consider here two new statistics defined on the bargraph representation b(π) of an inversion sequence π which record the number of unit squares touching the boundary of b(π) and that are either exterior or interior to b(π). We denote these statistics on ℐn recording the number of outer and inner perimeter squares respectively by oper and iper. In this paper, we study the distribution of oper and iper on ℐn and also on members of ℐn that end in a particular letter. We find explicit formulas for the maximum and minimum values of oper and iper achieved by a member of ℐn as well as for the average value of these parameters. We make use of both algebraic and combinatorial arguments in establishing our results.]]></description>
            <category>ARTICLE</category>
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        <item>
            <title><![CDATA[Comparison of disposal strategies in linear reverse logistics models]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2023-0002</link>
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            <pubDate>Wed, 24 Jul 2024 00:00:00 GMT</pubDate>
            <description><![CDATA[In this paper we investigate disposal activities in a reverse logistics models with linear costs structure. The two models have different disposal strategy. The first model analyzes a continuous disposal strategy, i.e. disposal can happen in every time in the planning horizon. This type of models was investigated in earlier works. The second possible disposal strategy assumes that disposal is only at the end of the planning horizon. After characterization of the optimal strategies of the two models we compare the costs and the trajectories of the optimal paths. The result of the paper is that the relevant costs are higher in case of disposal at the end of the planning horizon. It is cost efficient to dispose off the not necessary products inside of the planning horizon.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Controlling a demographic wave in defined contribution pension systems]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2023-0001</link>
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            <pubDate>Wed, 24 Jul 2024 00:00:00 GMT</pubDate>
            <description><![CDATA[A common problem in systems and control theory is to provide an approximation to non-linear systems. We provide a novel approach as a general solution to this problem originally conceived by Gamkrelidze. We consider and solve a general approximation problem which provides the fundamentals for various switching-type systems thus encompassing a wide range of systems theory problems.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Results on E-quasiconvex Functions for a linear map E]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2023-0003</link>
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            <pubDate>Wed, 24 Jul 2024 00:00:00 GMT</pubDate>
            <description><![CDATA[It is well known that convexity theory and its generalization play an important role and have many applications in mathematical programming. In the previous article [2], the authors studied E-convex and semi-E-convex functions. In the present article, we deal with a class of E-quasiconvex functions and give a weak condition for a lower semi-continuous function on ℝn to be an E-quasiconvex function.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[The longest increasing subsequence in involutions avoiding 3412 and another pattern]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0032</link>
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            <pubDate>Mon, 13 Feb 2023 00:00:00 GMT</pubDate>
            <description><![CDATA[In this note, we study the mean length of the longest increasing subsequence of a uniformly sampled involution that avoids the pattern 3412 and another pattern.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[The expected number of distinct consecutive patterns in a random permutation]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0031</link>
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            <pubDate>Mon, 13 Feb 2023 00:00:00 GMT</pubDate>
            <description><![CDATA[Let πn be a uniformly chosen random permutation on [n]. Using an analysis of the probability that two overlapping consecutive k-permutations are order isomorphic, we show that the expected number of distinct consecutive patterns of all lengths k ∈ {1, 2,…, n} in πn is 


n22(1-o(1))
{{{n^2}} \over 2}\left( {1 - o\left( 1 \right)} \right)

 as n → ∞. This exhibits the fact that random permutations pack consecutive patterns near-perfectly.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Foreword on the special issue dedicated to the 70th anniversary of prof. Peter Tallos]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0027</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Ramsey actions and Gelfand duality]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0020</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[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 C*-algebras.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Classes of Dyck paths associated with numerical semigroups]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0029</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[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.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Monitoring of population systems]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0026</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[This is a selected overview 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.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Computability of sets in Euclidean space]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0025</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[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 ℝn 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 computable 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.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[The subminimal polynomial and the Cayley-Hamilton theorem]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0019</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[A short proof is given for the Cayley-Hamilton theorem using the concept of the subminimal polynomial.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Solution of the real and complex eigenvalue problems in the ABS class]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0028</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[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.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[The Limit of the Non-dictatorship Index]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0021</link>
            <guid isPermaLink="false">/article/10.2478/puma-2022-0021</guid>
            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[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 m denotes the number of alternatives, then as the number of voters tends to infinity the NDI of any anonymous voting rule tends to (m − 1)/m, which equals the NDI of the constant rule.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Production-inventory strategies for a linear reverse logistics system]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0030</link>
            <guid isPermaLink="false">/article/10.2478/puma-2022-0030</guid>
            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[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].]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Viability and equilibrium in Banach spaces]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0022</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[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.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[On monotone likelihood ratio of stationary probabilities in bonus-malus systems]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0023</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[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.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[On the construction of the elementary trigonometric functions]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0024</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[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.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Some notes on dynamic oligopsonies]]></title>
            <link>https://reference-global.com/article/10.2478/puma-2022-0018</link>
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            <pubDate>Mon, 07 Nov 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[A special oligopoly model is considered when the firms compete on the factor market, and the used factor volumes determine their outputs. In the Nfirm 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.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Finiteness of the criss-cross algorithm for the linear programming problem with s-monotone index selection rules]]></title>
            <link>https://reference-global.com/article/10.1515/puma-2015-0041</link>
            <guid isPermaLink="false">/article/10.1515/puma-2015-0041</guid>
            <pubDate>Wed, 17 Aug 2022 00:00:00 GMT</pubDate>
            <description><![CDATA[The traditional criss-cross algorithm for the linear programming problem is shown to be finite when s-monotone index selection rules are used. The set of s-monotone index selection rules, among others, include the Last In First Out (LIFO) and the Most Often Selected Variable rule (MOSV). The advantage of applying the s-monotone index selection rule is the flexibility it provides in selecting the pivot element while still preserving the guarantee for finiteness. Such flexibility may be used to improve the numerical stability of the algorithm.]]></description>
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