Axioms doi: 10.3390/axioms9030111

Authors: George Tsintsifas

The paper concerns inequalities between fundamental quantities as area, perimeter, diameter and width for convex plane fugures.

]]>Axioms doi: 10.3390/axioms9030110

Authors: Kifayat Ullah Junaid Ahmad Manuel de la Sen

The purpose of this research work is to prove some weak and strong convergence results for maps satisfying (E)-condition through three-step Thakur (J. Inequal. Appl.2014, 2014:328.) iterative process in Banach spaces. We also present a new example of maps satisfying (E)-condition, and prove that its three-step Thakur iterative process is more efficient than the other well-known three-step iterative processes. At the end of the paper, we apply our results for finding solutions of split feasibility problems. The presented research work updates some of the results of the current literature.

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Authors: Omar Benslimane Ahmed Aberqi Jaouad Bennouna

The purpose of this work is to prove the existence and uniqueness of a class of nonlinear unilateral elliptic problem (P) in an arbitrary domain, managed by a low-order term and non-polynomial growth described by an N-uplet of N-function satisfying the &Delta;2-condition. The source term is merely integrable.

]]>Axioms doi: 10.3390/axioms9030108

Authors: Alex Citkin Urszula Wybraniec-Skardowska

Since its inception, logic has studied the acceptable rules of reasoning, the rules that allow us to pass from certain statements, serving as premises or assumptions, to a statement taken as a conclusion [...]

]]>Axioms doi: 10.3390/axioms9030107

Authors: Kyoung Ja Lee Seok-Zun Song Young Bae Jun

The notions of (quasi, pseudo) star-shaped sets are introduced, and several related properties are investigated. Characterizations of (quasi) star-shaped sets are considered. The translation of (quasi, pseudo) star-shaped sets are discussed. Unions and intersections of quasi star-shaped sets are conceived. Conditions for a quasi (or, pseudo) star-shaped set to be a star-shaped set are provided.

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Authors: Abdessamad Dehaj Mohamed Guessous

We give a geometrical proof of Koml&oacute;s&rsquo; theorem for sequences of random variables with values in super-reflexive Banach space. Our approach is inspired by the elementary proof given by Guessous in 1996 for the Hilbert case and uses some geometric properties of smooth spaces.

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Authors: Meryeme El Harrak Ahmed Hajji

In the present paper, we propose a common fixed point theorem for three commuting mappings via a new contractive condition which generalizes fixed point theorems of Darbo, Hajji and Aghajani et al. An application is also given to illustrate our main result. Moreover, several consequences are derived, which are generalizations of Darbo&rsquo;s fixed point theorem and a Hajji&rsquo;s result.

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Authors: Irvanizam Zi Zuhra Amrusi Sofyan

In this manuscript, we extend the traditional multi-attributive border approximation area comparison (MABAC) method for the multiple-criteria group decision-making (MCGDM) with triangular fuzzy neutrosophic numbers (TFNNs) to propose the TFNNs-MABAC method. In the proposed method, we utilize the TFNNs to express the values of criteria for each alternative in MCGDM problems. First, we briefly acquaint the basic concept of TFNNs and describe its corresponding some operation laws, the functions of score and accuracy, and the normalized hamming distance. We then review two aggregation operators of TFNNs. Afterward, we combine the traditional MABAC method with the triangular fuzzy neutrosophic evaluation and provide a sequence of calculation procedures of the TFNNs-MABAC method. After comparing it with some TFNNs aggregation operators and another method, the results showed that our extended MABAC method can not only effectively handle the conflicting attributes, but also practically deal with incomplete and indeterminate information in the MCGDM problem. Therefore, the extended MABAC method is more effective, conformable, and reasonable. Finally, an investment selection problem is demonstrated as a practice to verify the reasonability of our MABAC method.

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Authors: Chinda Chaichuay Atid Kangtunyakarn

There are many methods for finding a common solution of a system of variational inequalities, a split equilibrium problem, and a hierarchical fixed-point problem in the setting of real Hilbert spaces. They proved the strong convergence theorem. Many split feasibility problems are generated in real Hillbert spaces. The open problem is proving a strong convergence theorem of three Hilbert spaces with different methods from the lasted method. In this research, a new split variational inequality in three Hilbert spaces is proposed. Important tools which are used to solve classical problems will be developed. The convergence theorem for finding a common element of the set of solution of such problems and the sets of fixed-points of discontinuous mappings has been proved.

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Authors: Pradip Debnath Hari Mohan Srivastava

In this paper, we study a problem of global optimization using common best proximity point of a pair of multivalued mappings. First, we introduce a multivalued Banach-type contractive pair of mappings and establish criteria for the existence of their common best proximity point. Next, we put forward the concept of multivalued Kannan-type contractive pair and also the concept of weak &Delta;-property to determine the existence of common best proximity point for such a pair of maps.

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Authors: Nopparat Wairojjana Habib ur Rehman Manuel De la Sen Nuttapol Pakkaranang

A plethora of applications from mathematical programming, such as minimax, and mathematical programming, penalization, fixed point to mention a few can be framed as equilibrium problems. Most of the techniques for solving such problems involve iterative methods that is why, in this paper, we introduced a new extragradient-like method to solve equilibrium problems in real Hilbert spaces with a Lipschitz-type condition on a bifunction. The advantage of a method is a variable stepsize formula that is updated on each iteration based on the previous iterations. The method also operates without the previous information of the Lipschitz-type constants. The weak convergence of the method is established by taking mild conditions on a bifunction. For application, fixed-point theorems that involve strict pseudocontraction and results for pseudomonotone variational inequalities are studied. We have reported various numerical results to show the numerical behaviour of the proposed method and correlate it with existing ones.

]]>Axioms doi: 10.3390/axioms9030100

Authors: Henrique Antunes Walter Carnielli Andreas Kapsner Abilio Rodrigues

In this paper, we propose Kripke-style models for the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson&rsquo;s logic N4 and the logic of first-degree entailment (FDE) with a classicality operator ∘ that recovers classical logic for formulas in its scope. According to the intended interpretation here proposed, these models represent a database that receives information as time passes, and such information can be positive, negative, non-reliable, or reliable, while a formula ∘A means that the information about A, either positive or negative, is reliable. This proposal is in line with the interpretation of N4 and FDE as information-based logics, but adds to the four scenarios expressed by them two new scenarios: reliable (or conclusive) information (i) for the truth and (ii) for the falsity of a given proposition.

]]>Axioms doi: 10.3390/axioms9030099

Authors: Nopparat Wairojjana Habib ur Rehman Ioannis K. Argyros Nuttapol Pakkaranang

Several methods have been put forward to solve equilibrium problems, in which the two-step extragradient method is very useful and significant. In this article, we propose a new extragradient-like method to evaluate the numerical solution of the pseudomonotone equilibrium in real Hilbert space. This method uses a non-monotonically stepsize technique based on local bifunction values and Lipschitz-type constants. Furthermore, we establish the weak convergence theorem for the suggested method and provide the applications of our results. Finally, several experimental results are reported to see the performance of the proposed method.

]]>Axioms doi: 10.3390/axioms9030098

Authors: Maria Letizia Guerra Laerte Sorini

Value at Risk (VaR) has become a crucial measure for decision making in risk management over the last thirty years and many estimation methodologies address the finding of the best performing measure at taking into account unremovable uncertainty of real financial markets. One possible and promising way to include uncertainty is to refer to the mathematics of fuzzy numbers and to its rigorous methodologies which offer flexible ways to read and to interpret properties of real data which may arise in many areas. The paper aims to show the effectiveness of two distinguished models to account for uncertainty in VaR computation; initially, following a non parametric approach, we apply the Fuzzy-transform approximation function to smooth data by capturing fundamental patterns before computing VaR. As a second model, we apply the Average Cumulative Function (ACF) to deduce the quantile function at point p as the potential loss VaRp for a fixed time horizon for the 100p% of the values. In both cases a comparison is conducted with respect to the identification of VaR through historical simulation: twelve years of daily S&amp;P500 index returns are considered and a back testing procedure is applied to verify the number of bad VaR forecasting in each methodology. Despite the preliminary nature of the research, we point out that VaR estimation, when modelling uncertainty through fuzzy numbers, outperforms the traditional VaR in the sense that it is the closest to the right amount of capital to allocate in order to cover future losses in normal market conditions.

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Authors: P. Njionou Sadjang S. Mboutngam

In this paper, we introduce a fractional q-extension of the q-differential operator Dq&minus;1 and prove some of its main properties. Next, fractional q-extensions of some classical q-orthogonal polynomials are introduced and some of the main properties of the newly-defined functions are given. Finally, a fractional q-difference equation of Gaussian type is introduced and solved by means of the power series method.

]]>Axioms doi: 10.3390/axioms9030096

Authors: Omar Bazighifan Rami Ahmad El-Nabulsi Osama Moaaz

The aim of this work is to study oscillatory behavior of solutions for even-order neutral nonlinear differential equations. By using the Riccati substitution, a new oscillation conditions is obtained which insures that all solutions to the studied equation are oscillatory. The obtained results complement the well-known oscillation results present in the literature. Some example are illustrated to show the applicability of the obtained results.

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Authors: Yazid Gouari Zoubir Dahmani Shan E. Farooq Farooq Ahmad

A coupled system of singular fractional differential equations involving Riemann&ndash;Liouville integral and Caputo derivative is considered in this paper. The question of existence and uniqueness of solutions is studied using Banach contraction principle. Furthermore, the question of existence of at least one solution is discussed. At the end, an illustrative example is given in details.

]]>Axioms doi: 10.3390/axioms9030094

Authors: José Luis Carmona Jiménez Marco Castrillón López

We study the reduction procedure applied to pseudo-K&auml;hler manifolds by a one dimensional Lie group acting by isometries and preserving the complex tensor. We endow the quotient manifold with an almost contact metric structure. We use this fact to connect pseudo-K&auml;hler homogeneous structures with almost contact metric homogeneous structures. This relation will have consequences in the class of the almost contact manifold. Indeed, if we choose a pseudo-K&auml;hler homogeneous structure of linear type, then the reduced, almost contact homogeneous structure is of linear type and the reduced manifold is of type C5&oplus;C6&oplus;C12 of Chinea-Gonz&aacute;lez classification.

]]>Axioms doi: 10.3390/axioms9030093

Authors: Thomas Ernst

The Horn&ndash;Karlsson approach to find convergence regions is applied to find convergence regions for triple q-hypergeometric functions. It turns out that the convergence regions are significantly increased in the q-case; just as for q-Appell and q-Lauricella functions, additions are replaced by Ward q-additions. Mostly referring to Krishna Srivastava 1956, we give q-integral representations for these functions.

]]>Axioms doi: 10.3390/axioms9030092

Authors: Shaima M. Dsouza Tittu Mathew Varghese P. R. Budarapu S. Natarajan

A non-intrusive approach coupled with non-uniform rational B-splines based isogeometric finite element method is proposed here. The developed methodology was employed to study the stochastic static bending and free vibration characteristics of functionally graded material plates with inhered material randomness. A first order shear deformation theory with an artificial shear correction factor was used for spatial discretization. The output randomness is represented by polynomial chaos expansion. The robustness and accuracy of the framework were demonstrated by comparing the results with Monte Carlo simulations. A systematic parametric study was carried out to bring out the sensitivity of the input randomness on the stochastic output response using Sobol&rsquo; indices. Functionally graded plates made up of Aluminium (Al) and Zirconium Oxide (ZrO2) were considered in all the numerical examples.

]]>Axioms doi: 10.3390/axioms9030091

Authors: Romeo Pascone Cathryn Callahan

A novel method for generating and providing quadrature solutions to families of linear, second-order, ordinary differential equations is presented in this paper. It is based upon a comparison of control system feedback diagrams&mdash;one representing the system and equation under study and a second equalized to it and providing solutions. The resulting Riccati equation connection between them is utilized to generate and solve groups of equations parameterized by arbitrary functions and constants. This method also leads to a formal solution mechanism for all second-order linear differential equations involving an infinite series of integrals of each equation&rsquo;s Schwarzian derivative. The practicality of this mechanism is strongly dependent on the series rates of and allowed regions for convergence. The feedback diagram method developed is shown to be equivalent to a comparable method based on the differential equation&rsquo;s normal form and another relying upon the grouping of terms for a reduction of the equation order, but augmenting their results. Applications are also made to the Helmholtz equation.

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Authors: Kazuki Yamaga

It is known that, in quantum theory, measurements may suppress Hamiltonian dynamics of a system. A famous example is the &lsquo;Quantum Zeno Effect&rsquo;. This is the phenomena that, if one performs the measurements M times asking whether the system is in the same state as the one at the initial time until the fixed measurement time t, then survival probability tends to 1 by taking the limit M&rarr;&infin;. This is the case for fixed measurement time t. It is known that, if one takes measurement time infinite at appropriate scaling, the &lsquo;Quantum Zeno Effect&rsquo; does not occur and the effect of Hamiltonian dynamics emerges. In the present paper, we consider the long time repeated measurements and the dynamics of quantum many body systems in the scaling where the effect of measurements and dynamics are balanced. We show that the stochastic process, called the symmetric simple exclusion process (SSEP), is obtained from the repeated and long time measurements of configuration of particles in finite lattice fermion systems. The emerging stochastic process is independent of potential and interaction of the underlying Hamiltonian of the system.

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Authors: Konstantinos Kalimeris Athanassios S. Fokas

Using the unified transform, also known as the Fokas method, we analyse the modified Helmholtz equation in the regular hexagon with symmetric Dirichlet boundary conditions; namely, the boundary value problem where the trace of the solution is given by the same function on each side of the hexagon. We show that if this function is odd, then this problem can be solved in closed form; numerical verification is also provided.

]]>Axioms doi: 10.3390/axioms9030088

Authors: David Levin

In some applications, one is interested in reconstructing a function f from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we suggest a method for deriving high order approximation to f using a Pad&eacute;-like method. Namely, we do this by fitting some Fourier coefficients of the approximant to the given Fourier coefficients of f. Given the Fourier series coefficients of a function on a rectangular domain in Rd, assuming the function is piecewise smooth, we approximate the function by piecewise high order spline functions. First, the singularity structure of the function is identified. For example in the 2D case, we find high accuracy approximation to the curves separating between smooth segments of f. Secondly, simultaneously we find the approximations of all the different segments of f. We start by developing and demonstrating a high accuracy algorithm for the 1D case, and we use this algorithm to step up to the multidimensional case.

]]>Axioms doi: 10.3390/axioms9030087

Authors: Julio César Hernández Arzusa

In this paper, we give conditions under which a commutative topological semigroup can be embedded algebraically and topologically into a compact topological Abelian group. We prove that every feebly compact regular first countable cancellative commutative topological semigroup with open shifts is a topological group, as well as every connected locally compact Hausdorff cancellative commutative topological monoid with open shifts. Finally, we use these results to give sufficient conditions on a commutative topological semigroup that guarantee it to have countable cellularity.

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Authors: Alexander Yeliseev

An asymptotic solution of the linear Cauchy problem in the presence of a &ldquo;weak&rdquo; turning point for the limit operator is constructed by the method of S. A. Lomov regularization. The main singularities of this problem are written out explicitly. Estimates are given for &epsilon; that characterize the behavior of singularities for ϵ&rarr;0. The asymptotic convergence of a regularized series is proven. The results are illustrated by an example. Bibliography: six titles.

]]>Axioms doi: 10.3390/axioms9030085

Authors: Kyung-Tae Kang Seok-Zun Song Eun Hwan Roh Young Bae Jun

The notion of hybrid ideals in B C K / B C I -algebras is introduced, and related properties are investigated. Characterizations of hybrid ideals are discussed. Relations between hybrid ideals and hybrid subalgebras are considered. Characterizations of hybrid ideals are considered. Based on a hybrid structure, properties of special sets are investigated, and conditions for the special sets to be ideals are displayed.

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Authors: Sopo Pkhakadze Hans Tompits

Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we introduce sequent-type calculi for two variants of default logic, viz., on the one hand, for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default logic, due to Gelfond, Lifschitz, Przymusinska, and Truszczyński. The first variant of default logic employs Łukasiewicz&rsquo;s three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults. Both versions have been introduced to address certain representational shortcomings of standard default logic. The calculi we introduce axiomatise brave reasoning for these versions of default logic, which is the task of determining whether a given formula is contained in some extension of a given default theory. Our approach follows the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a rejection calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

]]>Axioms doi: 10.3390/axioms9030083

Authors: David W. Pravica Njinasoa Randriampiry Michael J. Spurr

A family of Schwartz functions W ( t ) are interpreted as eigensolutions of MADEs in the sense that W ( &delta; ) ( t ) = E W ( q &gamma; t ) where the eigenvalue E &isin; R is independent of the advancing parameter q &gt; 1 . The parameters &delta; , &gamma; &isin; N are characteristics of the MADE. Some issues, which are related to corresponding q-advanced PDEs, are also explored. In the limit that q &rarr; 1 + we show convergence of MADE eigenfunctions to solutions of ODEs, which involve only simple exponentials and trigonometric functions. The limit eigenfunctions ( q = 1 + ) are not Schwartz, thus convergence is only uniform in t &isin; R on compact sets. An asymptotic analysis is provided for MADEs which indicates how to extend solutions in a neighborhood of the origin t = 0 . Finally, an expanded table of Fourier transforms is provided that includes Schwartz solutions to MADEs.

]]>Axioms doi: 10.3390/axioms9030082

Authors: Fateme Ghomanjani Stanford Shateyi

An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograph delay differential equations (MPDDEs), and optimal control systems (OCSs) with pantograph delays is presented in this paper. This technique is based on Genocchi polynomials (GPs). The properties of Genocchi polynomials are stated, and operational matrices of derivative are constructed. A collocation method based on this operational matrix is used. The findings show that the technique is accurate and simple to use.

]]>Axioms doi: 10.3390/axioms9030081

Authors: Maksim V. Kukushkin

In this paper, we continue our study of the Abel equation with the right-hand side belonging to the Lebesgue weighted space. We have improved the previously known result&mdash; the existence and uniqueness theorem formulated in terms of the Jacoby series coefficients that gives us an opportunity to find and classify a solution by virtue of an asymptotic of some relation containing the Jacobi series coefficients of the right-hand side. The main results are the following&mdash;the conditions imposed on the parameters, under which the Abel equation has a unique solution represented by the series, are formulated; the relationship between the values of the parameters and the solution smoothness is established. The independence between one of the parameters and the smoothness of the solution is proved.

]]>Axioms doi: 10.3390/axioms9030080

Authors: Abdukomil Risbekovich Khashimov Dana Smetanová

The paper is devoted to solutions of the third order pseudo-elliptic type equations. An energy estimates for solutions of the equations considering transformation&rsquo;s character of the body form were established by using of an analog of the Saint-Venant principle. In consequence of this estimate, the uniqueness theorems were obtained for solutions of the first boundary value problem for third order equations in unlimited domains. The energy estimates are illustrated on two examples.

]]>Axioms doi: 10.3390/axioms9030079

Authors: G. Muhiuddin D. Al-Kadi M. Balamurugan

The notion of anti-intuitionistic fuzzy soft a-ideals of B C I -algebras is introduced and several related properties are investigated. Furthermore, the operations, namely; AND, extended intersection, restricted intersection, and union on anti-intuitionistic fuzzy soft a-ideals are discussed. Finally, characterizations of anti-intuitionistic fuzzy soft a-ideals of B C I -algebras are given.

]]>Axioms doi: 10.3390/axioms9030078

Authors: Olga Grigorenko Juan Jose Miñana Alexander Šostak Oscar Valero

We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare them with &ldquo;classic&rdquo; fuzzy (pseudo)metrics. A method for construction CB-fuzzy (pseudo)metrics from ordinary metrics is elaborated and topology induced by CB-fuzzy (pseudo)metrics is studied. We establish interrelations between CB-fuzzy metrics and modulars, and in the process of this study, a particular role of Hamacher t-(co)norm in the theory of (CB)-fuzzy metrics is revealed. Finally, an intuitionistic version of a CB-fuzzy metric is introduced and applied in order to emphasize the roles of t-norms and a t-conorm in this context.

]]>Axioms doi: 10.3390/axioms9030077

Authors: Sanjib Biswas Dragan Pamucar

Facility location is one of the critical strategic decisions for any organization. It not only carries the organization’s identity but also connects the point of origin and point of consumption. In the case of higher educational institutions, specifically B-Schools, location is one of the primary concerns for potential students and their parents while selecting an institution for pursuing higher education. There has been a plethora of research conducted to investigate the factors influencing the B-School selection decision-making. However, location as a standalone factor has not been widely studied. This paper aims to explore various location selection criteria from the viewpoint of the candidates who aspire to enroll in B-Schools. We apply an integrated group decision-making framework of pivot pairwise relative criteria importance assessment (PIPRECIA), and level-based weight assessment LBWA is used wherein a group of student counselors, admission executives, and educators from India has participated. The factors which influence the location decision are identified through qualitative opinion analysis. The results show that connectivity and commutation are the dominant issues.

]]>Axioms doi: 10.3390/axioms9030076

Authors: Senee Suwandee Arumona Edward Arumona Kanad Ray Phichai Youplao Preecha Yupapin

We have proposed that human life is formed on a space and time function relationship basis, which is distorted after fertilization in the ovum, from which growth is generated by a space&ndash;time distortion against the universe&rsquo;s gravity. A space&ndash;time distortion&rsquo;s reduction can be managed by space and time separation, which is known as mindfulness. A space&ndash;time distortion in human cells is configured by a polariton traveling in a gold grating film, which can be employed to investigate mindfulness characteristics. Mindfulness is the steady state of the time function of energy after the separation. Energy levels of mindfulness based on polariton aspects are categorized by a quantum number (n), which can be reduced to be a two-level system called Rabi oscillation by a successive filtering method. We have assumed a cell space&ndash;time distortion can reduce to reach the original state, which is the stopping state. Mindfulness with a certain frequency energy level of n = 2 was achieved. Several techniques in the practice of mindfulness based on successive filtering called meditation are given and explained, where the required levels of the mindfulness state can be achieved. The criteria of the proposed method are a low energy level (n) and high frequency (f) outputs, which can apply to having a working performance improvement.

]]>Axioms doi: 10.3390/axioms9030074

Authors: Ilya Boykov Vladimir Roudnev Alla Boykova

We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides. We investigate hypersingular integral equations with second order singularities. Today, hypersingular integral equations of this type are widely used in physics and technology. The convergence of the proposed method is based on the Lyapunov stability theory of solutions of ordinary differential equation systems. The advantage of the method for linear equations is in simplicity of unique solvability verification for the approximate equations system in terms of the operator logarithmic norm. This makes it possible to estimate the norm of the inverse matrix for an approximating system. The advantage of the method for nonlinear equations is that neither the existence or reversibility of the nonlinear operator derivative is required. Examples are given illustrating the effectiveness of the proposed method.

]]>Axioms doi: 10.3390/axioms9030075

Authors: Osama Moaaz Hamida Mahjoub Ali Muhib

In this paper, we are interested in studying the periodic behavior of solutions of nonlinear difference equations. We used a new method to find the necessary and sufficient conditions for the existence of periodic solutions. Through examples, we compare the results of this method with the usual method.

]]>Axioms doi: 10.3390/axioms9030073

Authors: Diego Caratelli Pierpaolo Natalini Paolo Emilio Ricci

After recalling the most important properties of the Bell polynomials, we show how to approximate a positive compact operator by a suitable matrix. Then, we derive a representation formula for functions of the obtained matrix, which can be considered as an approximate value for the functions of the corresponding operator.

]]>Axioms doi: 10.3390/axioms9030072

Authors: Mohamed Tahar Kadaoui Abbassi Noura Amri

In this paper, we study natural paracontact magnetic trajectories in the unit tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza&ndash;Klein type metrics on their unit tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics).

]]>Axioms doi: 10.3390/axioms9020071

Authors: Maxim Khlopov Biplab Paik Saibal Ray

Primordial black holes (PBHs) are the sensitive probe for physics and cosmology of very early Universe. The observable effect of their existence depends on the PBH mass. Mini PBHs evaporate and do not survive to the present time, leaving only background effect of products of their evaporation, while PBHs evaporating now can be new exotic sources of energetic particles and gamma rays in the modern Universe. Here we revisit the history of evolution of mini PBHs. We follow the aspects associated with growth versus evaporation rate of &ldquo;a mini PBH being trapped inside intense local cosmological matter inhomogeneity&rdquo;. We show that the existence of baryon accretion forbidden black hole regime enables constraints on mini PBHs with the mass M &le; 5.5 &times; 10 13 g. On the other hand, we propose the mechanism of delay of evaporation of primordial population of PBHs of primordial mass range 5.5 &times; 10 13 g &le; M &le; 5.1 &times; 10 14 g. It can provide their evaporation to be the main contributor to &gamma; -ray flux distribution in the current Universe. At the final stage of evaporation these PBHs can be the source of ultrahigh energy cosmic rays and gamma radiation challenging probe for their existence in the LHAASO experiment.

]]>Axioms doi: 10.3390/axioms9020070

Authors: Bashir Ahmad Najla Alghamdi Ahmed Alsaedi Sotiris K. Ntouyas

In this paper, we discuss the existence and uniqueness of solutions for a new class of multi-point and integral boundary value problems of multi-term fractional differential equations by using standard fixed point theorems. We also demonstrate the application of the obtained results with the aid of examples.

]]>Axioms doi: 10.3390/axioms9020069

Authors: Paulo Guzman Luciano Lugo Juan Nápoles Valdés Miguel Vivas-Cortez

In this paper, we present a general definition of a generalized integral operator which contains as particular cases, many of the well-known, fractional and integer order integrals.

]]>Axioms doi: 10.3390/axioms9020068

Authors: Tursun K. Yuldashev Bakhtiyor J. Kadirkulov

In this paper, we consider a boundary value problem for a nonlinear partial differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. With respect to the first variable, this equation is a nonlinear fractional differential equation in the positive part of the considering segment and is a second-order nonlinear differential equation with spectral parameter in the negative part of this segment. Using the Fourier series method, the solutions of nonlinear boundary value problems are constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the classical solution of the problem are proved for regular values of the spectral parameter. For irregular values of the spectral parameter, an infinite number of solutions of the mixed equation in the form of a Fourier series are constructed.

]]>Axioms doi: 10.3390/axioms9020067

Authors: Dariusz Surowik

The article discusses minimal temporal logic systems built on the basis of classical logic as well as intuitionistic logic. The constructions of these systems are discussed as well as their basic properties. The K t system was discussed as the minimal temporal logic system built based on classical logic, while the IK t system and its modification were discussed as the minimal temporal logic system built based on intuitionistic logic.

]]>Axioms doi: 10.3390/axioms9020066

Authors: Sergey V. Ludkowski

In this article, the structure of topological metagroups was investigated. Relations between topological and algebraic properties of metagroups were scrutinized. A uniform continuity of functions on them was studied. Smashed products of topological metagroups were investigated.

]]>Axioms doi: 10.3390/axioms9020065

Authors: R. Leelavathi G. Suresh Kumar Ravi P. Agarwal Chao Wang M.S.N. Murty

This paper mainly deals with introducing and studying the properties of generalized nabla differentiability for fuzzy functions on time scales via Hukuhara difference. Further, we obtain embedding results on E n for generalized nabla differentiable fuzzy functions. Finally, we prove a fundamental theorem of a nabla integral calculus for fuzzy functions on time scales under generalized nabla differentiability. The obtained results are illustrated with suitable examples.

]]>Axioms doi: 10.3390/axioms9020064

Authors: Giovanni Calvaruso

We study and solve the Ricci soliton equation for an arbitrary locally conformally flat Siklos metric, proving that such spacetimes are always Ricci solitons.

]]>Axioms doi: 10.3390/axioms9020063

Authors: Jiří Močkoř

Various types of topological and closure operators are significantly used in fuzzy theory and applications. Although they are different operators, in some cases it is possible to transform an operator of one type into another. This in turn makes it possible to transform results relating to an operator of one type into results relating to another operator. In the paper relationships among 15 categories of modifications of topological L-valued operators, including Čech closure or interior L-valued operators, L-fuzzy pretopological and L-fuzzy co-pretopological operators, L-valued fuzzy relations, upper and lower F-transforms and spaces with fuzzy partitions are investigated. The common feature of these categories is that their morphisms are various L-fuzzy relations and not only maps. We prove the existence of 23 functors among these categories, which represent transformation processes of one operator into another operator, and we show how these transformation processes can be mutually combined.

]]>Axioms doi: 10.3390/axioms9020062

Authors: Ravi P. Agarwal Petio S. Kelevedjiev Todor Z. Todorov

Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] &mdash;solutions to various two-point boundary value problems for the equation x ‴ = f ( t , x , x &prime; , x &Prime; ) . We give also some results guaranteeing positive or non-negative, monotone, convex or concave solutions.

]]>Axioms doi: 10.3390/axioms9020061

Authors: Francesca Pitolli

Boundary value problems having fractional derivative in space are used in several fields, like biology, mechanical engineering, control theory, just to cite a few. In this paper we present a new numerical method for the solution of boundary value problems having Caputo derivative in space. We approximate the solution by the Schoenberg-Bernstein operator, which is a spline positive operator having shape-preserving properties. The unknown coefficients of the approximating operator are determined by a collocation method whose collocation matrices can be constructed efficiently by explicit formulas. The numerical experiments we conducted show that the proposed method is efficient and accurate.

]]>Axioms doi: 10.3390/axioms9020060

Authors: Kristof Dekimpe Joeri Van der Veken

A marginally trapped surface in a spacetime is a Riemannian surface whose mean curvature vector is lightlike at every point. In this paper we give an up-to-date overview of the differential geometric study of these surfaces in Minkowski, de Sitter, anti-de Sitter and Robertson-Walker spacetimes. We give the general local descriptions proven by Anciaux and his coworkers as well as the known classifications of marginally trapped surfaces satisfying one of the following additional geometric conditions: having positive relative nullity, having parallel mean curvature vector field, having finite type Gauss map, being invariant under a one-parameter group of ambient isometries, being isotropic, being pseudo-umbilical. Finally, we provide examples of constant Gaussian curvature marginally trapped surfaces and state some open questions.

]]>Axioms doi: 10.3390/axioms9020059

Authors: Ahmed Salem Mohammad Alnegga

In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann&ndash;Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo&rsquo;s fixed point theorem. A numerical example is presented to clarify our outcomes.

]]>Axioms doi: 10.3390/axioms9020058

Authors: Gwang Hui Kim Themistocles M. Rassias

In this paper, we investigate the generalized Hyers&ndash;Ulam stability for the generalized psi functional equation f ( x + p ) = f ( x ) + &phi; ( x ) by the direct method in the sense of P. Gǎvruta and the Hyers&ndash;Ulam&ndash;Rassias stability.

]]>Axioms doi: 10.3390/axioms9020057

Authors: Choukri Derbazi Zidane Baitiche Mouffak Benchohra Alberto Cabada

In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the &psi; -Caputo derivative. Moreover, some uniqueness results are obtained. Our results rely on the standard tools of functional analysis. More precisely we apply the monotone iterative technique combined with the method of upper and lower solutions to establish sufficient conditions for existence as well as the uniqueness of extremal solutions to the initial value problem. An illustrative example is presented to point out the applicability of our main results.

]]>Axioms doi: 10.3390/axioms9020056

Authors: Piotr Kulicki

Aristotle&rsquo;s syllogistic is the first ever deductive system. After centuries, Aristotle&rsquo;s ideas are still interesting for logicians who develop Aristotle&rsquo;s work and draw inspiration from his results and even more from his methods. In the paper we discuss the essential elements of the Aristotelian system of syllogistic and Łukasiewicz&rsquo;s reconstruction of it based on the tools of modern formal logic. We pay special attention to the notion of completeness of a deductive system as discussed by both authors. We describe in detail how completeness can be defined and proved with the use of an axiomatic refutation system. Finally, we apply this methodology to different axiomatizations of syllogistic presented by Łukasiewicz, Lemmon and Shepherdson.

]]>Axioms doi: 10.3390/axioms9020055

Authors: Jan L. Cieśliński Artur Kobus

Scator set, introduced by Fern&aacute;ndez-Guasti and Zald&iacute;var, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension 1 + 2 and the so called fundamental embedding which maps the subset of scators with non-zero scalar component into 4-dimensional space endowed with a natural distributive product. The original definition of the scator product is induced in a straightforward way. Moreover, we propose an extension of the scator product on the whole scator space, including all scators with vanishing scalar component.

]]>Axioms doi: 10.3390/axioms9020054

Authors: Claudio Corianò Matteo Maria Maglio

We review the emergence of hypergeometric structures (of F4 Appell functions) from the conformal Ward identities (CWIs) in conformal field theories (CFTs) in dimensions d &gt; 2. We illustrate the case of scalar 3- and 4-point functions. 3-point functions are associated to hypergeometric systems with four independent solutions. For symmetric correlators, they can be expressed in terms of a single 3K integral&mdash;functions of quadratic ratios of momenta&mdash;which is a parametric integral of three modified Bessel K functions. In the case of scalar 4-point functions, by requiring the correlator to be conformal invariant in coordinate space as well as in some dual variables (i.e., dual conformal invariant), its explicit expression is also given by a 3K integral, or as a linear combination of Appell functions which are now quartic ratios of momenta. Similar expressions have been obtained in the past in the computation of an infinite class of planar ladder (Feynman) diagrams in perturbation theory, which, however, do not share the same (dual conformal/conformal) symmetry of our solutions. We then discuss some hypergeometric functions of 3 variables, which define 8 particular solutions of the CWIs and correspond to Lauricella functions. They can also be combined in terms of 4K integral and appear in an asymptotic description of the scalar 4-point function, in special kinematical limits.

]]>Axioms doi: 10.3390/axioms9020053

Authors: Ruba Almahasneh Boldizsár Tüű-Szabó László T. Kóczy Péter Földesi

This study proposes a new model and approach for solving a realistic extension of the Time-Dependent Traveling Salesman Problem, by using the concept of distance between interval-valued intuitionistic fuzzy sets. For this purpose, we developed an interval-valued fuzzy degree repository based on the relations between rush hour periods and traffic regions in the &ldquo;city center areas&rdquo;, and then we utilized the interval-valued intuitionistic fuzzy weighted arithmetic average to aggregate fuzzy information to be able to quantify the delay in any given trip between two nodes (cities). The proposed method is illustrated by a simple numerical example.

]]>Axioms doi: 10.3390/axioms9020052

Authors: Aroonkumar Beesham

The cosmic censorship hypothesis is regarded as one of the most important unsolved problems in classical general relativity; viz., will generic gravitational collapse of a star after it has exhausted its nuclear fuel lead to black holes only, under reasonable physical conditions. We discuss the collapse of a fluid with nonzero radial pressure within the context of the Vaidya spacetime considering a decaying cosmological parameter as well as nonzero charge. Previously, a similar analysis was done, but without considering charge. A decaying cosmological parameter may also be associated with dark energy. We found that both black holes and naked singularities can form, depending upon the initial conditions. Hence, charge does not restore the validity of the hypothesis. This provides another example of the violation of the cosmic censorship hypothesis. We also discuss some radiating rotating solutions, arriving at the same conclusion.

]]>Axioms doi: 10.3390/axioms9020051

Authors: Godwin Amechi Okeke Mujahid Abbas Manuel de la Sen

We propose two new iterative algorithms for solving K-pseudomonotone variational inequality problems in the framework of real Hilbert spaces. These newly proposed methods are obtained by combining the viscosity approximation algorithm, the Picard Mann algorithm and the inertial subgradient extragradient method. We establish some strong convergence theorems for our newly developed methods under certain restriction. Our results extend and improve several recently announced results. Furthermore, we give several numerical experiments to show that our proposed algorithms performs better in comparison with several existing methods.

]]>Axioms doi: 10.3390/axioms9020050

Authors: Ahmed Alsaedi Abrar Broom Sotiris K. Ntouyas Bashir Ahmad

In this paper, we study the existence of solutions for nonlocal single and multi-valued boundary value problems involving right-Caputo and left-Riemann&ndash;Liouville fractional derivatives of different orders and right-left Riemann&ndash;Liouville fractional integrals. The existence of solutions for the single-valued case relies on Sadovskii&rsquo;s fixed point theorem. The first existence results for the multi-valued case are proved by applying Bohnenblust-Karlin&rsquo;s fixed point theorem, while the second one is based on Martelli&rsquo;s fixed point theorem. We also demonstrate the applications of the obtained results.

]]>Axioms doi: 10.3390/axioms9020049

Authors: Anton Romanov Valeria Voronina Gleb Guskov Irina Moshkina Nadezhda Yarushkina

The development of the economy and the transition to industry 4.0 creates new challenges for artificial intelligence methods. Such challenges include the processing of large volumes of data, the analysis of various dynamic indicators, the discovery of complex dependencies in the accumulated data, and the forecasting of the state of processes. The main point of this study is the development of a set of analytical and prognostic methods. The methods described in this article based on fuzzy logic, statistic, and time series data mining, because data extracted from dynamic systems are initially incomplete and have a high degree of uncertainty. The ultimate goal of the study is to improve the quality of data analysis in industrial and economic systems. The advantages of the proposed methods are flexibility and orientation to the high interpretability of dynamic data. The high level of the interpretability and interoperability of dynamic data is achieved due to a combination of time series data mining and knowledge base engineering methods. The merging of a set of rules extracted from the time series and knowledge base rules allow for making a forecast in case of insufficiency of the length and nature of the time series. The proposed methods are also based on the summarization of the results of processes modeling for diagnosing technical systems, forecasting of the economic condition of enterprises, and approaches to the technological preparation of production in a multi-productive production program with the application of type 2 fuzzy sets for time series modeling. Intelligent systems based on the proposed methods demonstrate an increase in the quality and stability of their functioning. This article contains a set of experiments to approve this statement.

]]>Axioms doi: 10.3390/axioms9020048

Authors: Elisabetta Barletta Sorin Dragomir Francesco Esposito

We review several results in the theory of weighted Bergman kernels. Weighted Bergman kernels generalize ordinary Bergman kernels of domains &Omega; &sub; C n but also appear locally in the attempt to quantize classical states of mechanical systems whose classical phase space is a complex manifold, and turn out to be an efficient computational tool that is useful for the calculation of transition probability amplitudes from a classical state (identified to a coherent state) to another. We review the weighted version (for weights of the form &gamma; = | &phi; | m on strictly pseudoconvex domains &Omega; = { &phi; &lt; 0 } &sub; C n ) of Fefferman&rsquo;s asymptotic expansion of the Bergman kernel and discuss its possible extensions (to more general classes of weights) and implications, e.g., such as related to the construction and use of Fefferman&rsquo;s metric (a Lorentzian metric on &part; &Omega; &times; S 1 ). Several open problems are indicated throughout the survey.

]]>Axioms doi: 10.3390/axioms9020047

Authors: Davor Dragičević Ciprian Preda

For linear skew-product three-parameter semiflows with discrete time acting on an arbitrary Hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate Lyapunov functions. As a nontrivial application of our work, we prove that the notion of an exponential stability persists under sufficiently small linear perturbations.

]]>Axioms doi: 10.3390/axioms9020046

Authors: Juan Pedro Lucanera Laura Fabregat-Aibar Valeria Scherger Hernán Vigier

The paper aims to identify which variables related to capital structure theory predict business failure in the Spanish construction sector during the subprime crisis. An artificial neural network (ANN) approach based on Self-Organizing Maps (SOM) is proposed, which allows one to cluster between default and active firms&rsquo; groups. The similarities and differences between the main features in each group determine the variables that explain the capacities of failure of the analyzed firms. The network tests whether the factors that explain leverage, such as profitability, growth opportunities, size of the company, risk, asset structure, and age of the firm, can be suitable to predict business failure. The sample is formed by 152 construction firms (76 default and 76 active) in the Spanish market. The results show that the SOM correctly predicts 97.4% of firms in the construction sector and classifies the firms in five groups with clear similarities inside the clusters. The study proves the suitability of the SOM for predicting business bankruptcy situations using variables related to capital structure theory and financial crises.

]]>Axioms doi: 10.3390/axioms9020045

Authors: Tursun K. Yuldashev

The questions of solvability of a nonlocal inverse boundary value problem for a mixed pseudohyperbolic-pseudoelliptic integro-differential equation with spectral parameters are considered. Using the method of the Fourier series, a system of countable systems of ordinary integro-differential equations is obtained. To determine arbitrary integration constants, a system of algebraic equations is obtained. From this system regular and irregular values of the spectral parameters were calculated. The unique solvability of the inverse boundary value problem for regular values of spectral parameters is proved. For irregular values of spectral parameters is established a criterion of existence of an infinite set of solutions of the inverse boundary value problem. The results are formulated as a theorem.

]]>Axioms doi: 10.3390/axioms9020044

Authors: Subramanian Muthaiah Dumitru Baleanu

This article deals with the solutions of the existence and uniqueness for a new class of boundary value problems (BVPs) involving nonlinear fractional differential equations (FDEs), inclusions, and boundary conditions involving the generalized fractional integral. The nonlinearity relies on the unknown function and its fractional derivatives in the lower order. We use fixed-point theorems with single-valued and multi-valued maps to obtain the desired results, through the support of illustrations, the main results are well explained. We also address some variants of the problem.

]]>Axioms doi: 10.3390/axioms9020043

Authors: Serena Doria Radko Mesiar Adam Šeliga

Coherent lower previsions generalize the expected values and they are defined on the class of all real random variables on a finite non-empty set. Well known construction of coherent lower previsions by means of lower probabilities, or by means of super-modular capacities-based Choquet integrals, do not cover this important class of functionals on real random variables. In this paper, a new approach to the construction of coherent lower previsions acting on a finite space is proposed, exemplified and studied. It is based on special decomposition integrals recently introduced by Even and Lehrer, in our case the considered decomposition systems being single collections and thus called collection integrals. In special case when these integrals, defined for non-negative random variables only, are shift-invariant, we extend them to the class of all real random variables, thus obtaining so called super-additive integrals. Our proposed construction can be seen then as a normalized super-additive integral. We discuss and exemplify several particular cases, for example, when collections determine a coherent lower prevision for any monotone set function. For some particular collections, only particular set functions can be considered for our construction. Conjugated coherent upper previsions are also considered.

]]>Axioms doi: 10.3390/axioms9020042

Authors: Rabha W. Ibrahim Rafida M. Elobaid Suzan J. Obaiys

A class of Briot&ndash;Bouquet differential equations is a magnificent part of investigating the geometric behaviors of analytic functions, using the subordination and superordination concepts. In this work, we aim to formulate a new differential operator with complex connections (coefficients) in the open unit disk and generalize a class of Briot&ndash;Bouquet differential equations (BBDEs). We study and generalize new classes of analytic functions based on the new differential operator. Consequently, we define a linear operator with applications.

]]>Axioms doi: 10.3390/axioms9020041

Authors: J.-Martín Castro-Manzano

The concept of distribution is a concept within traditional logic that has been fundamental for the syntactic development of Sommers and Englebretsen&rsquo;s term functor logic, a logic that recovers the term syntax of traditional logic. The issue here, however, is that the semantic counterpart of distribution for this logic is still in the making. Consequently, given this disparity between syntax and semantics, in this contribution we adapt some ideas of term functor logic tableaux to develop models of distribution, thus providing some alternative formal semantics to help close this breach.

]]>Axioms doi: 10.3390/axioms9020040

Authors: Florin F. Nichita

In January 2019, MDPI published a book titled Hopf Algebras, Quantum Groups and Yang&ndash;Baxter Equations, based on a successful special issue [...]

]]>Axioms doi: 10.3390/axioms9020039

Authors: Omar Bazighifan Feliz Minhos Osama Moaaz

Some new sufficient conditions are established for the oscillation of fourth order neutral differential equations with continuously distributed delay of the form r t N x ‴ t &alpha; &prime; + &int; a b q t , &thetasym; x &beta; &delta; t , &thetasym; d &thetasym; = 0 , where t &ge; t 0 and N x t : = x t + p t x &phi; t . An example is provided to show the importance of these results.

]]>Axioms doi: 10.3390/axioms9020038

Authors: Marcin Bartkowiak Aleksandra Rutkowska

In a real market, the quantity of information and recommendations is constantly increasing. However, recommendations are often in linguistic form and no one recommendation is based on a single piece of information. Predictions of individuals and their confidence can vary greatly. Thus, a problem arises concerning different (disjointed or partially coherent) vague opinions of various experts or information from multiple sources. In this paper, we introduce extensions of the Black&mdash;Litterman model with linguistic expressed views from different experts/many sources. The study focuses on empirical analysis of proposed fuzzy approach results. In the presented modification every expert presents its opinion about particular assets according to intervals, and then an experton for each asset is built. In the portfolio optimization, we use aggregated views presented by interval, which is the mean value of the experton built on particular views. In an empirical study, we built and tested 10,000 portfolios based on recommendation from EquityRT, which was made by 14&ndash;49 experts monthly between November 2017 and June 2019 for the 29 biggest companies from the US market and different sectors. The annual average return from portfolios is 9.5&ndash;11.8%, depending on the width of the intervals and additional constraints. This approach allows people to formulate intuitive views and view the opinions of a group of experts.

]]>Axioms doi: 10.3390/axioms9020037

Authors: Donal O’Regan

This paper considers the topological transversality theorem for general multivalued maps which have selections in a given class of maps.

]]>Axioms doi: 10.3390/axioms9020036

Authors: Mujahid Abbas Fatemeh Lael Naeem Saleem

In this paper we introduce the concepts of ψ -contraction and monotone ψ -contraction correspondence in “fuzzy b -metric spaces” and obtain fixed point results for these contractive mappings. The obtained results generalize some existing ones in fuzzy metric spaces and “fuzzy b -metric spaces”. Further we address an open problem in b -metric and “fuzzy b -metric spaces”. To elaborate the results obtained herein we provide an example that shows the usability of the obtained results.

]]>Axioms doi: 10.3390/axioms9020035

Authors: Janusz Ciuciura

A logic is called explosive if its consequence relation validates the so-called principle of ex contradictione sequitur quodlibet. A logic is called paraconsistent so long as it is not explosive. Sette&rsquo;s calculus P 1 is widely recognized as one of the most important paraconsistent calculi. It is not surprising then that the calculus was a starting point for many research studies on paraconsistency. Fern&aacute;ndez&ndash;Coniglio&rsquo;s hierarchy of paraconsistent systems is a good example of such an approach. The hierarchy is presented in Newton da Costa&rsquo;s style. Therefore, the law of non-contradiction plays the main role in its negative axioms. The principle of ex contradictione sequitur quodlibet has been marginalized: it does not play any leading role in the hierarchy. The objective of this paper is to present an alternative axiomatization for the hierarchy. The main idea behind it is to focus explicitly on the (in)validity of the principle of ex contradictione sequitur quodlibet. This makes the hierarchy less complex and more transparent, especially from the viewpoint of paraconsistency.

]]>Axioms doi: 10.3390/axioms9010034

Authors: Juan Carlos Ferrando Salvador López-Alfonso Manuel López-Pellicer

We call a subset M of an algebra of sets A a Grothendieck set for the Banach space b a ( A ) of bounded finitely additive scalar-valued measures on A equipped with the variation norm if each sequence &mu; n n = 1 &infin; in b a ( A ) which is pointwise convergent on M is weakly convergent in b a ( A ) , i.e., if there is &mu; &isin; b a A such that &mu; n A &rarr; &mu; A for every A &isin; M then &mu; n &rarr; &mu; weakly in b a ( A ) . A subset M of an algebra of sets A is called a Nikod&yacute;m set for b a ( A ) if each sequence &mu; n n = 1 &infin; in b a ( A ) which is pointwise bounded on M is bounded in b a ( A ) . We prove that if &Sigma; is a &sigma; -algebra of subsets of a set &Omega; which is covered by an increasing sequence &Sigma; n : n &isin; N of subsets of &Sigma; there exists p &isin; N such that &Sigma; p is a Grothendieck set for b a ( A ) . This statement is the exact counterpart for Grothendieck sets of a classic result of Valdivia asserting that if a &sigma; -algebra &Sigma; is covered by an increasing sequence &Sigma; n : n &isin; N of subsets, there is p &isin; N such that &Sigma; p is a Nikod&yacute;m set for b a &Sigma; . This also refines the Grothendieck result stating that for each &sigma; -algebra &Sigma; the Banach space ℓ &infin; &Sigma; is a Grothendieck space. Some applications to classic Banach space theory are given.

]]>Axioms doi: 10.3390/axioms9010033

Authors: Grigoris Panotopoulos

We compute the quasinormal frequencies for scalar perturbations of charged black holes in five-dimensional Einstein-power-Maxwell theory. The impact on the spectrum of the electric charge of the black holes, of the angular degree, of the overtone number, and of the mass of the test scalar field is investigated in detail. The quasinormal spectra in the eikonal limit are computed as well for several different space-time dimensionalities.

]]>Axioms doi: 10.3390/axioms9010032

Authors: Abdeljabbar Talal Yousef Zabidin Salleh

In this paper, a subclass of complex-valued harmonic univalent functions defined by a generalized linear operator is introduced. Some interesting results such as coefficient bounds, compactness, and other properties of this class are obtained.

]]>Axioms doi: 10.3390/axioms9010031

Authors: Ataollah Arabnia Firozjah Hamidreza Rahimi Manuel De la Sen Ghasem Soleimani Rad

In this work, we define the concept of a generalized c-distance in cone b-metric spaces over a Banach algebra and introduce some its properties. Then, we prove the existence and uniqueness of fixed points for mappings satisfying weak contractive conditions such as Han&ndash;Xu-type contraction and Cho-type contraction with respect to this distance. Our assertions are useful, since we remove the continuity condition of the mapping and the normality condition for the cone. Several examples are given to support the main results.

]]>Axioms doi: 10.3390/axioms9010030

Authors: Nikolaos Kalogeropoulos

We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3 + 1)-dimensional spacetimes. We ascribe this entropy to the non-trivial topology of the space-like sections &Sigma; of the horizon. This is not forbidden by topological censorship, since all the known energy inequalities needed to prove the spherical topology of &Sigma; are violated in quantum theory. We choose the systoles of &Sigma; to encode its complexity, which gives rise to the black hole entropy. We present hand-waving reasons why the entropy of the black hole can be considered as a function of the volume entropy of &Sigma; . We focus on the limiting case of &Sigma; having a large genus.

]]>Axioms doi: 10.3390/axioms9010029

Authors: Nita H Shah Nisha Sheoran Yash Shah

According to World Health Organization (WHO), the population suffering from human immunodeficiency virus (HIV) infection over a period of time may suffer from TB infection which increases the death rate. There is no cure for acquired immunodeficiency syndrome (AIDS) to date but antiretrovirals (ARVs) can slow down the progression of disease as well as prevent secondary infections or complications. This is considered as a medication in this paper. This scenario of HIV-TB co-infection is modeled using a system of non-linear differential equations. This model considers HIV-infected individual as the initial stage. Four equilibrium points are found. Reproduction number R0 is calculated. If R0 &gt;1 disease persists uniformly, with reference to the reproduction number, backward bifurcation is computed for pre-AIDS (latent) stage. Global stability is established for the equilibrium points where there is no Pre-AIDS TB class, point without co-infection and for the endemic point. Numerical simulation is carried out to validate the data. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics.

]]>Axioms doi: 10.3390/axioms9010028

Authors: Xin Sun Feifei He Quanlong Wang

Bit commitment is a cryptographic task in which Alice commits a bit to Bob such that she cannot change the value of the bit after her commitment and Bob cannot learn the value of the bit before Alice opens her commitment. According to the Mayers&ndash;Lo&ndash;Chau (MLC) no-go theorem, ideal bit commitment is impossible within quantum theory. In the information theoretic-reconstruction of quantum theory, the impossibility of quantum bit commitment is one of the three information-theoretic constraints that characterize quantum theory. In this paper, we first provide a very simple proof of the MLC no-go theorem and its quantitative generalization. Then, we formalize bit commitment in the theory of dagger monoidal categories. We show that in the setting of dagger monoidal categories, the impossibility of bit commitment is equivalent to the unitary equivalence of purification.

]]>Axioms doi: 10.3390/axioms9010027

Authors: Gilberto Rivera Luis Cisneros Patricia Sánchez-Solís Nelson Rangel-Valdez Jorge Rodas-Osollo

In this paper, we develop and apply a genetic algorithm to solve surgery scheduling cases in a Mexican Public Hospital. Here, one of the most challenging issues is to process containers with heterogeneous capacity. Many scheduling problems do not share this restriction; because of this reason, we developed and implemented a strategy for the processing of heterogeneous containers in the genetic algorithm. The final product was named &ldquo;genetic algorithm for scheduling optimization&rdquo; (GAfSO). The results of GAfSO were tested with real data of a local hospital. Said hospital assigns different operational time to the operating rooms throughout the week. Also, the computational complexity of GAfSO is analyzed. Results show that GAfSO can assign the corresponding capacity to the operating rooms while optimizing their use.

]]>Axioms doi: 10.3390/axioms9010026

Authors: Samuel Swire Elizabeth Pasipanodya Manuel A. Morales Enrique Peacock-López

This paper presents the first five variable model of mutualism motivated by the interaction between ants and homopterans. In this mutualism, homopterans benefit both directly through increased feeding rates and indirectly through predator protection. Results of our analyses show oscillatory, complex, and chaotic dynamic behavior. In addition, we show that intraspecies interactions are crucial for closing trophic levels and stabilizing the dynamic system from potential &ldquo;chaotic&rdquo; behavior.

]]>Axioms doi: 10.3390/axioms9010025

Authors: Hans G. Feichtinger

The Banach Gelfand Triple ( S 0 , L 2 , S 0 &prime; ) ( R d ) consists of S 0 ( R d ) , ∥ &middot; ∥ S 0 , a very specific Segal algebra as algebra of test functions, the Hilbert space L 2 ( R d ) , ∥ &middot; ∥ 2 and the dual space S 0 &prime; ( R d ) , whose elements are also called &ldquo;mild distributions&rdquo;. Together they provide a universal tool for Fourier Analysis in its many manifestations. It is indispensable for a proper formulation of Gabor Analysis, but also useful for a distributional description of the classical (generalized) Fourier transform (with Plancherel&rsquo;s Theorem and the Fourier Inversion Theorem as core statements) or the foundations of Abstract Harmonic Analysis, as it is not difficult to formulate this theory in the context of locally compact Abelian (LCA) groups. A new approach presented recently allows to introduce S 0 ( R d ) , ∥ &middot; ∥ S 0 and hence ( S 0 &prime; ( R d ) , ∥ &middot; ∥ S 0 &prime; ) , the space of &ldquo;mild distributions&rdquo;, without the use of the Lebesgue integral or the theory of tempered distributions. The present notes will describe an alternative, even more elementary approach to the same objects, based on the idea of completion (in an appropriate sense). By drawing the analogy to the real number system, viewed as infinite decimals, we hope that this approach is also more interesting for engineers. Of course it is very much inspired by the Lighthill approach to the theory of tempered distributions. The main topic of this article is thus an outline of the sequential approach in this concrete setting and the clarification of the fact that it is just another way of describing the Banach Gelfand Triple. The objects of the extended domain for the Short-Time Fourier Transform are (equivalence classes) of so-called mild Cauchy sequences (in short ECmiCS). Representatives are sequences of bounded, continuous functions, which correspond in a natural way to mild distributions as introduced in earlier papers via duality theory. Our key result shows how standard functional analytic arguments combined with concrete properties of the Segal algebra S 0 ( R d ) , ∥ &middot; ∥ S 0 can be used to establish this natural identification.

]]>Axioms doi: 10.3390/axioms9010024

Authors: Leonid Shaikhet

The known mathematical model of rumor spreading, which is described by a system of four nonlinear differential equations and is very popular in research, is considered. It is supposed that the considered model is influenced by stochastic perturbations that are of the type of white noise and are proportional to the deviation of the system state from its equilibrium point. Sufficient conditions of stability in probability for each from the five equilibria of the considered model are obtained by virtue of the Routh&ndash;Hurwitz criterion and the method of linear matrix inequalities (LMIs). The obtained results are illustrated by numerical analysis of appropriate LMIs and numerical simulations of solutions of the considered system of stochastic differential equations. The research method can also be used in other applications for similar nonlinear models with the order of nonlinearity higher than one.

]]>Axioms doi: 10.3390/axioms9010023

Authors: Mikhail Tkachenko

We study the factorization properties of continuous homomorphisms defined on a (dense) submonoid S of a Tychonoff product D = &prod; i &isin; I D i of topological or even topologized monoids. In a number of different situations, we establish that every continuous homomorphism f : S &rarr; K to a topological monoid (or group) K depends on at most finitely many coordinates. For example, this is the case if S is a subgroup of D and K is a first countable left topological group without small subgroups (i.e., K is an NSS group). A stronger conclusion is valid if S is a finitely retractable submonoid of D and K is a regular quasitopological NSS group of a countable pseudocharacter. In this case, every continuous homomorphism f of S to K has a finite type, which means that f admits a continuous factorization through a finite subproduct of D. A similar conclusion is obtained for continuous homomorphisms of submonoids (or subgroups) of products of topological monoids to Lie groups. Furthermore, we formulate a number of open problems intended to delimit the validity of our results.

]]>Axioms doi: 10.3390/axioms9010022

Authors: Carlo Cattani

In this paper, local fractional cylindrical wave solutions on Signorini hyperelastic materials are studied. In particular, we focus on the so-called Signorini potential. Cantor-type cylindrical coordinates are used to analyze, both from dynamical and geometrical point of view, wave solutions, so that the nonlinear fundamental equations of the fractional model are explicitly given. In the special case of linear approximation we explicitly compute the fractional wave profile.

]]>Axioms doi: 10.3390/axioms9010021

Authors: Laura Vall-Llosera Salvador Linares-Mustarós Andrea Bikfalvi Germà Coenders

This article presents an empirical comparative assessment of the measurement quality of two instruments commonly used to measure fuzzy characteristics in computer-assisted questionnaires: a graphic scale (a line production scale using a slider bar) and an endecanary scale (a 0&ndash;10 rating scale using radio buttons). Data are analyzed by means of multitrait&ndash;multimethod models estimated as structural equation models with a mean and covariance structure. For the first time in such research, the results include bias, valid variance, method variance, and random error variance. The data are taken from a program that assesses entrepreneurial competences in undergraduate Economics and Business students by means of questionnaires administered on desktop computers. Neither of the measurement instruments was found to be biased with respect to the other, meaning that their scores are comparable. While both instruments achieve valid and reliable measurements, the reliability and validity are higher for the endecanary scale. This study contributes to the still scarce literature on fuzzy measurement instruments and on the comparability and relative merits of graphic and discrete rating scales on computer-assisted questionnaires.

]]>Axioms doi: 10.3390/axioms9010020

Authors: Diego G. Bussandri Tristán M. Osán Pedro W. Lamberti Ana P. Majtey

We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.

]]>Axioms doi: 10.3390/axioms9010019

Authors: Erdal Karapınar Mujahid Abbas Sadia Farooq

In this paper, we investigate the existence of best proximity points that belong to the zero set for the &alpha; p -admissible weak ( F , &phi; ) -proximal contraction in the setting of M-metric spaces. For this purpose, we establish &phi; -best proximity point results for such mappings in the setting of a complete M-metric space. Some examples are also presented to support the concepts and results proved herein. Our results extend, improve and generalize several comparable results on the topic in the related literature.

]]>Axioms doi: 10.3390/axioms9010018

Authors: Peter Simons

The predominant form of logic before Frege, the logic of terms has been largely neglected since. Terms may be singular, empty or plural in their denotation. This article, presupposing propositional logic, provides an axiomatization based on an identity predicate, a predicate of non-existence, a constant empty term, and term conjunction and negation. The idea of basing term logic on existence or non-existence, outlined by Brentano, is here carried through in modern guise. It is shown how categorical syllogistic reduces to just two forms of inference. Tree and diagram methods of testing validity are described. An obvious translation into monadic predicate logic shows the system is decidable, and additional expressive power brought by adding quantifiers enables numerical predicates to be defined. The system&rsquo;s advantages for pedagogy are indicated.

]]>Axioms doi: 10.3390/axioms9010017

Authors: Irina Georgescu Jani Kinnunen

This paper studies an optimal saving model in which risk is represented by a fuzzy number and the total utility function of the model is defined by an expected utility operator. This model generalizes some existing possibilistic saving models and from them, by a particularization, one can obtain new saving models. In the paper, sufficient conditions are set for the presence of potential risk to increase optimal saving levels and an approximation formula for optimal saving is demonstrated. Particular models for a few concrete expected utility operators are analyzed for triangular fuzzy numbers and CRRA-utility functions.

]]>Axioms doi: 10.3390/axioms9010016

Authors: Hari M. Srivastava

Web Site: http://www [...]

]]>Axioms doi: 10.3390/axioms9010015

Authors: Davide Radi Laerte Sorini Luciano Stefanini

An interesting property of the inverse F-transform f ^ of a continuous function f on a given interval [ a , b ] says that the integrals of f ^ and f on [ a , b ] coincide. Furthermore, the same property can be established for the restrictions of the functions to all subintervals [ a , p k ] of the fuzzy partition of [ a , b ] used to define the F-transform. Based on this fact, we propose a new method for the numerical solution of ordinary differential equations (initial-value ordinary differential equation (ODE)) obtained by approximating the derivative x &middot; ( t ) via F-transform, then computing (an approximation of) the solution x ( t ) by exact integration. For an ODE, a global second-order approximation is obtained. A similar construction is then applied to interval-valued and (level-wise) fuzzy differential equations in the setting of generalized differentiability (gH-derivative). Properties of the new method are analyzed and a computational section illustrates the performance of the obtained procedures, in comparison with well-known efficient algorithms.

]]>Axioms doi: 10.3390/axioms9010014

Authors: Choonkil Park Osama Moaaz Omar Bazighifan

The objective of our research was to study asymptotic properties of the class of higher order differential equations with a p-Laplacian-like operator. Our results supplement and improve some known results obtained in the literature. An illustrative example is provided.

]]>Axioms doi: 10.3390/axioms9010013

Authors: Kateryna Marynets

We present some new results on the approximation of solutions of a special type of fractional boundary-value problem. The focus of our research is a system of three fractional differential equations of the mixed order, subjected to the so-called &ldquo;interpolation&rdquo; type boundary restrictions. Under certain conditions, the aforementioned problem is simplified via a proper parametrization technique, and with the help of the numerical-analytic method, the approximate solutions are constructed.

]]>Axioms doi: 10.3390/axioms9010012

Authors: Miguel J. Vivas-Cortez Artion Kashuri Rozana Liko Jorge E. Hernández

In this work, a study is conducted on the Hermite&ndash;Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found for functions such as the hypergeometric function and the classical Mittag&ndash;Leffler function. The method used to obtain the results is classic in the study of quantum integral inequalities.

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