Any relational hypersubstitution for algebraic systems of type (τ, τ ′ ) = ((m i ) i∈I , (n j ) j∈J ) is a mapping which maps any m i -ary operation symbol to an m i -ary term and maps any n j -ary relational symbol to an n j -ary relational term preserving arities, where I, J are indexed sets.The set of all relational hypersubstitutions for algebraic systems of type (τ, τ ′ ) together with a binary operation defined on the set and its identity forms a monoid.The properties of this structure are expressed by terms and formulas.Some algebraic properties of the monoid of a special type, especially the set of all unit-regular elements, were studied.In this paper, we determine all maximal unit-regular submonoids of this monoid of type ((m), (n)) for arbitrary natural numbers m, n ≥ 2.
In their previous paper [4], Künzi and Olela Otafudu constructed the ultra-quasi-metric hull of a T 0 -ultra-quasi-metric space.In this article, we continue these studies by investigating the tightness and essentiality of extension maps in the category of ultra-quasi-metric spaces and nonexpansive maps.We show, for instance, that q-spherical completeness is preserved by a retraction map.Furthermore, we point out some categorical aspects of ultra-quasi-metrically injective hulls.
. The paper deals with a certain trinomial with two strictly complex coef- ficients. The root locus technique is utilized to obtain a distribution of roots with respect to a unit circle in the complex plane. A number of roots inside the unit disk is described in a relation with the two parameter values. Several appropriate graphs illustrate the trinomial roots distribution in particular cases.
This paper is devoted to the study of the T 0 separation axiom for a neutrosophic topological space.We give a categorical study of these spaces in a special case of neutrosophic topological spaces called neutrosophic saturated topological spaces.
Many theoretically beautiful conclusions of the producer theory were derived on the common assumption that every firm attempts to maximize its profit and minimize its cost, while all firms employ the same methodology in their optimization efforts.By losing up these two behavioral assumptions and by introducing the concept of value-belief systems for individual firms, this paper reestablishes a few well-known results of the producer theory for the general case of not specifying what criteria of priority a firm holds.At the same time, this paper shows by using counterexamples, among others, that generally, (i) except for a specific scenario, the optimal production correspondence does not satisfy the homogeneity of degree zero, and (ii) even when individuals act in their own best self-interests, they may not collectively produce unintended greater social benefits and public goods.In the end, several topics of expected significance are suggested for future research.MSC (2020)
The geometric product represents a core concept for establishing geometric algebras and in case of vectors matches the formal sum of their inner product and their wedge product.The geometric product is reconsidered for the case of 3-vectors by means of usual matrix algebra in this article.Therefore, a symmetric matrix product and an antisymmetric matrix product are introduced, whose matrix sum yields a third product that renders the information of a vector pair's geometric product in terms of a matrix associated to the vectors.The three matrices -that correspond to inner product, wedge product, and geometric product, respectively -are named wheel product, curl product, and full product.The observation about the structural correspondence of the geometric product with matrix theory may be used for future practical computations and unveils connections of geometric algebra with related disciplines.MSC (2020)
This paper presents a method of constructing topologies on vertex set of a graph G induced by chromatic partition of vertex set of the graph. It introduces colour lower approximation and colour upper approximation of vertex induced subgraphs and acquaints the open and closed sets of the topology generated by chromatic partition on the vertex set of graphs. It explores some of the properties of colour lower approximation and colour upper approximation of vertex induced subgraphs. It also establishes some new subgraphs based on the colour lower approximation and colour upper approximation and some of their properties have been studied.
Electric circuit analysis under non-sinusoidal, non-linear situationshas been a hot topic for a long time. Many scientific communities holdopposing viewpoints on the additional analysis tool and domain,resulting in a variety of standards and definitions. With the advent ofPower Electronic equipment, converters, and Renewable Energy sources,the electric power system has become increasingly sophisticated sinceits inception. Electronic equipment has transformed the electricalsystem and provided a slew of advantages to industrial applications.Unfortunately, this comes at the expense of power system distortion(voltage and current). Understanding power flow in non-sinusoidal linearand non-linear circuit circumstances is required for this. As a result,a novel mathematical framework to analyze the circuit in such anenvironment is always required. Finally, in sinusoidal conditions, aconsensus can be reached on norms that comply with well-known,established standards. The work provided here compares the use ofharmonic domain and geometric algebra in circuits with disturbances forsinusoidal and non-sinusoidal excitations in order to demonstrate theaccuracy of geometrical algebra in power flow calculations.
In this paper, we consider the nabla fractional order boundary value problemand derive sufficient conditions for the existence of positive solutions by an application of Krasnoselskii's fixed point theorem on a Banach space.Later, we derive sufficient conditions for the existence of a unique solution by applying Rus's contraction mapping theorem in a metric space, where two metrics are employed.
In this paper, we express a new subcollection of bi-close-to-convex functions by means of Gegenbauer polynomials in the open unit disc U. Further, several related outcomes such as coefficient bounds and Fekete–Szegő inequalities are obtained.
In this paper, we propose a method that balances between variable selection and variable shrinkage in linear regression.A diagonal matrix G is injected to the covariance matrix of prior distribution of the coefficient vector β, with each g j , bounded between 0 and 1, on the diagonal serving as a stabilizer of the corresponding β j .Mathematically, a g j value close to 0 indicates that the β j is nonzero, and hence the corresponding variable should be selected, whereas the value of g j close to 1 indicates otherwise.We prove this property under orthogonality.Computationally, the proposed method is easy to fit using automated programs such as JAGS.We provide three examples to verify the capability of this methodology in variable selection and shrinkage.
Using the admissibility condition, we obtain certain third order differential subordination results for an analytic function p with p(0) = 1 belonging to the class of Janowski functions, P[A, B].As an application, certain second order differential inequalities involving special functions are obtained.∞ n=0 Γ(a + n) Γ(c + n) z n n! , MSC (2020):
A pre-topological space equipped with an order is called an ordered pretopological space.These spaces form the objects of a category which will be denoted by OVPT.The arrows of this category are certain increasing maps called V -continuous.Essentially, we will prove that the subcategory of ordered pretopological spaces of type T 0 , OVPT 0 , is reflective in OVPT.We introduce and study some new separation axioms and characterize the class of morphisms orthogonal to the objects of OVPT 0 . MSC (2020)
The 50th anniversary of the McClintock effect deserves a new view on the subject.This paper applies (evolutionary) game theory to gain further insight.Among interesting results are strong indications of Nash equilibria in mixed strategies, indicating that the effect depends on parameters characterizing both females and males in the group.As such, much of the empirical research conducted on the subject over the last 50 years may be questioned.Furthermore, the article predicts that the effect's potential presence depends strongly on female envy/jealousy as well as male preferences on female attractiveness. MSC (2020):
In this paper, we provide the exact expressions (not found in the literature) for the curved surface area of revolution (about the x-axis and y-axis) of horizontal and oblique hyperbolas.Closed-form expressions for the curved surface area are obtained in terms of Gauss function, Clausen function, and Appell's hypergeometric function of the first kind.
Based on an assumption of an existing scoring probability difference between two teams engaged in a football match, the conditional probability distribution given the number of goals in the match for the low quality team beating the high quality team, is derived.Furthermore, similar distributions for the high quality team beating the low quality team as well as a draw are also derived.Based on a Poisson distribution of goals, we discuss a potential for optimizing expected uncertainty of outcome (UO) by adjusting intra-match rules or league rules for team sports.The main variables in this regard are (i) the typical number of goals scored, and (ii) the evenness of competing teams.We identify a curve defining the optimal expected number of goals as a function of team quality difference. MSC (2020):
Let D ∈ Z and let C D be the set of all monic cubic polynomials with integer coefficients and with the discriminant equal to D. In this paper we devise a method for determining the set C D .Our method is closely related to integer solutions of Mordell's equation.A complete discussion of the case D = 0 is also included.
. In metric spaces, a set is Bourbaki-bounded if and only if every real- valued uniformily continuous function on it is bounded. In this article, we study Bourbaki-boundedness on quasi-pseudometric spaces. It turns out that if a set is Bourbaki-bounded on a symmetrized quasi-pseudometric space, then it is Bourbaki-bounded in the quasi-metric space but the converse need not to be true. We show that an asymmetric normed space is Bourbaki-bounded if and only if it is bounded. Consequently, we prove that every real-valued semi-Lipschitz in the small function on a quasi-metric space is bounded if and only if the quasi-metric is Bourbaki-bounded. This article extends some results from Beer and Garrido’s paper [2] from the metric point of view to the context of quasi-metric spaces.
We employ some known critical point theorems to establish results on the existence of weak solutions for an impulsive boundary value problem depending on two real parameters.One of the results ensures the existence of at least three weak solutions, while another one proves the existence of at least one.j u ′ (t) -lim t→t - j u ′ (t).Moreover, I j : R → R is continuous for every j ∈ {1, 2, . . ., m}, and g, kWe emphasize that in [1], under assumptions similar to those of our results, the authors established the existence of infinitely many solutions for (1.1).MSC (2020)
The purpose of this paper is to introduce the notion of a µ-proximity base and to explore some properties and results of µ-proximity spaces.We show that the collection of all µ-proximities constitutes a complete lattice. MSC (2020): primary 54E05
