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Axioms, Volume 6, Issue 4 (December 2017)

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Research

Open AccessArticle Computing the Scale of an Endomorphism of a totally Disconnected Locally Compact Group
Axioms 2017, 6(4), 27; doi:10.3390/axioms6040027
Received: 28 August 2017 / Revised: 9 October 2017 / Accepted: 9 October 2017 / Published: 20 October 2017
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Abstract
The scale of an endomorphism of a totally disconnected, locally compact group G is defined and an example is presented which shows that the scale function is not always continuous with respect to the Braconnier topology on the automorphism group of G.
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The scale of an endomorphism of a totally disconnected, locally compact group G is defined and an example is presented which shows that the scale function is not always continuous with respect to the Braconnier topology on the automorphism group of G. Methods for computing the scale, which is a positive integer, are surveyed and illustrated by applying them in diverse cases, including when G is compact; an automorphism group of a tree; Neretin’s group of almost automorphisms of a tree; and a p-adic Lie group. The information required to compute the scale is reviewed from the perspective of the, as yet incomplete, general theory of totally disconnected, locally compact groups. Full article
(This article belongs to the collection Topological Groups)
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Open AccessArticle Large Sets in Boolean and Non-Boolean Groups and Topology
Axioms 2017, 6(4), 28; doi:10.3390/axioms6040028
Received: 1 September 2017 / Revised: 20 October 2017 / Accepted: 23 October 2017 / Published: 24 October 2017
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Abstract
Various notions of large sets in groups, including the classical notions of thick, syndetic, and piecewise syndetic sets and the new notion of vast sets in groups, are studied with emphasis on the interplay between such sets in Boolean groups. Natural topologies closely
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Various notions of large sets in groups, including the classical notions of thick, syndetic, and piecewise syndetic sets and the new notion of vast sets in groups, are studied with emphasis on the interplay between such sets in Boolean groups. Natural topologies closely related to vast sets are considered; as a byproduct, interesting relations between vast sets and ultrafilters are revealed. Full article
(This article belongs to the collection Topological Groups)
Open AccessArticle Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness
Axioms 2017, 6(4), 29; doi:10.3390/axioms6040029
Received: 6 October 2017 / Revised: 23 October 2017 / Accepted: 26 October 2017 / Published: 28 October 2017
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Abstract
Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy
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Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
Open AccessArticle Mild Solutions to the Cauchy Problem for Some Fractional Differential Equations with Delay
Axioms 2017, 6(4), 30; doi:10.3390/axioms6040030
Received: 5 October 2017 / Revised: 9 November 2017 / Accepted: 14 November 2017 / Published: 20 November 2017
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Abstract
In this paper, we present new existence theorems of mild solutions to Cauchy problem for some fractional differential equations with delay. Our main tools to obtain our results are the theory of analytic semigroups and compact semigroups, the Kuratowski measure of non-compactness, and
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In this paper, we present new existence theorems of mild solutions to Cauchy problem for some fractional differential equations with delay. Our main tools to obtain our results are the theory of analytic semigroups and compact semigroups, the Kuratowski measure of non-compactness, and fixed point theorems, with the help of some estimations. Examples are also given to illustrate the applicability of our results. Full article
(This article belongs to the Special Issue Fractional Differential Equations)
Open AccessArticle A Dynamic Ticket Pricing Approach for Soccer Games
Axioms 2017, 6(4), 31; doi:10.3390/axioms6040031
Received: 3 November 2017 / Revised: 14 November 2017 / Accepted: 15 November 2017 / Published: 19 November 2017
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Abstract
This study proposes a mathematical model of dynamic pricing for soccer game tickets. The logic behind the dynamic ticket pricing model is price change based on multipliers which reflect the effects of time and inventory. Functions are formed for the time and inventory
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This study proposes a mathematical model of dynamic pricing for soccer game tickets. The logic behind the dynamic ticket pricing model is price change based on multipliers which reflect the effects of time and inventory. Functions are formed for the time and inventory multipliers. The optimization algorithm attempts to find optimal values of these multipliers in order to maximize revenue. By multiplying the mean season ticket price (used as the reference price) by the multipliers, dynamic ticket prices are obtained. Demand rates at different prices are needed for the model, and they are provided by a unique fuzzy logic model. The results of this model are compared with real data to test the model’s effectiveness. According to the results of the dynamic pricing model, the total revenue generated is increased by 8.95% and 0.76% compared with the static pricing strategy in the first and second cases, respectively. The results of the fuzzy logic model are also found to be competitive and effective. This is the first time a fuzzy logic model has been designed to forecast the attendance of soccer games. It is also the first time this type of mathematical model of dynamic pricing for soccer game tickets has been designed. Full article
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Open AccessArticle Factorization of Graded Traces on Nichols Algebras
Axioms 2017, 6(4), 32; doi:10.3390/axioms6040032
Received: 27 October 2017 / Revised: 23 November 2017 / Accepted: 25 November 2017 / Published: 4 December 2017
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Abstract
A ubiquitous observation for finite-dimensional Nichols algebras is that as a graded algebra the Hilbert series factorizes into cyclotomic polynomials. For Nichols algebras of diagonal type (e.g., Borel parts of quantum groups), this is a consequence of the existence of a root system
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A ubiquitous observation for finite-dimensional Nichols algebras is that as a graded algebra the Hilbert series factorizes into cyclotomic polynomials. For Nichols algebras of diagonal type (e.g., Borel parts of quantum groups), this is a consequence of the existence of a root system and a Poincare-Birkhoff-Witt (PBW) basis basis, but, for nondiagonal examples (e.g., Fomin–Kirillov algebras), this is an ongoing surprise. In this article, we discuss this phenomenon and observe that it continues to hold for the graded character of the involved group and for automorphisms. First, we discuss thoroughly the diagonal case. Then, we prove factorization for a large class of nondiagonal Nichols algebras obtained by the folding construction. We conclude empirically by listing all remaining examples, which were in size accessible to the computer algebra system GAP and find that again all graded characters factorize. Full article
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang–Baxter Equations 2017)
Open AccessArticle Universal Enveloping Commutative Rota–Baxter Algebras of Pre- and Post-Commutative Algebras
Axioms 2017, 6(4), 33; doi:10.3390/axioms6040033
Received: 2 October 2017 / Revised: 22 November 2017 / Accepted: 4 December 2017 / Published: 7 December 2017
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Abstract
Universal enveloping commutative Rota–Baxter algebras of pre- and post-commutative algebras are constructed. The pair of varieties (RBλCom, postCom) is proved to be a Poincaré–Birkhoff–Witt-pair (PBW)-pair and the pair (RBCom, preCom) is proven not to be. Full article
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang–Baxter Equations 2017)
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