Axioms doi: 10.3390/axioms10010029

Authors: Ugur Duran Serkan Araci Mehmet Acikgoz

In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind. Then, we introduce Bell-based Bernoulli polynomials of order α and investigate multifarious correlations and formulas including some summation formulas and derivative properties. Also, we acquire diverse implicit summation formulas and symmetric identities for Bell-based Bernoulli polynomials of order α. Moreover, we attain several interesting formulas of Bell-based Bernoulli polynomials of order α arising from umbral calculus.

]]>Axioms doi: 10.3390/axioms10010028

Authors: Anil Kumar Aysegul Tas

In the present paper, we pointed out that there is a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012). Then after, utilizing the concept of (E.A.) property in convex metric space, we obtained an alternative and correct version of this result. Finally, it is clarified that in the theory of common fixed point, the notion of (E.A.) property in the set up of convex metric space develops some new dimensions in comparison to the hypothesis that a range set of one map is contained in the range set of another map.

]]>Axioms doi: 10.3390/axioms10010027

Authors: Hari Mohan Srivastava Ahmad Motamednezhad Safa Salehian

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

]]>Axioms doi: 10.3390/axioms10010026

Authors: Hassan Almusawa Hasanen A. Hammad Nisha Sharma

In this manuscript, a new three-step iterative scheme to approximate fixed points in the setting of Busemann spaces is introduced. The proposed algorithms unify and extend most of the existing iterative schemes. Thereafter, by making consequent use of this method, strong and Δ-convergence results of mappings that satisfy the condition (Eμ) in the framework of uniformly convex Busemann space are obtained. Our results generalize several existing results in the same direction.

]]>Axioms doi: 10.3390/axioms10010025

Authors: Ehab Almetwally Randa Alharbi Dalia Alnagar Eslam Hafez

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

]]>Axioms doi: 10.3390/axioms10010024

Authors: Pradip Debnath Zoran D. Mitrović Hari Mohan Srivastava

In this paper, we establish some existence of fixed-point results for some asymptotically regular multivalued mappings satisfying Kannan-type contractive condition without assuming compactness of the underlying metric space or continuity of the mapping.

]]>Axioms doi: 10.3390/axioms10010023

Authors: Eleonora Messina Antonia Vecchio

In this paper, the asymptotic behaviour of the numerical solution to the Volterra integral equations is studied. In particular, a technique based on an appropriate splitting of the kernel is introduced, which allows one to obtain vanishing asymptotic (transient) behaviour in the numerical solution, consistently with the properties of the analytical solution, without having to operate restrictions on the integration steplength.

]]>Axioms doi: 10.3390/axioms10010022

Authors: Anastassios K. Lazopoulos Dimitrios Karaoulanis

Λ-Fractional Derivative (Λ-FD) is a new groundbreaking Fractional Derivative (FD) introduced recently in mechanics. This derivative, along with Λ-Transform (Λ-T), provides a reliable alternative to fractional differential equations’ current solving. To put it straightforwardly, Λ-Fractional Derivative might be the only authentic non-local derivative that exists. In the present article, Λ-Fractional Derivative is used to describe the phenomenon of viscoelasticity, while the whole methodology is demonstrated meticulously. The fractional viscoelastic Zener model is studied, for relaxation as well as for creep. Interesting results are extracted and compared to other methodologies showing the value of the pre-mentioned method.

]]>Axioms doi: 10.3390/axioms10010021

Authors: Nil Orhan Ertaş

In this note, we investigate the relationship between almost projective modules and generalized projective modules. These concepts are useful for the study on the finite direct sum of lifting modules. It is proved that; if M is generalized N-projective for any modules M and N, then M is almost N-projective. We also show that if M is almost N-projective and N is lifting, then M is im-small N-projective. We also discuss the question of when the finite direct sum of lifting modules is again lifting.

]]>Axioms doi: 10.3390/axioms10010020

Authors: Helga Fetter Nathansky Jeimer Villada Bedoya

In this work, we introduce the notion of cascading non-expansive mappings in the setting of CAT(0) spaces. This family of mappings properly contains the non-expansive maps, but it differs from other generalizations of this class of maps. Considering the concept of Δ-convergence in metric spaces, we prove a principle of demiclosedness for this type of mappings and a Δ-convergence theorem for a Mann iteration process defined using cascading operators.

]]>Axioms doi: 10.3390/axioms10010019

Authors: Ramin Bazrafshan Sarfaraz Hashemkhani Hashemkhani Zolfani S. Mohammad J. Mirzapour Al-e-hashem

There are many sub-tour elimination constraint (SEC) formulations for the traveling salesman problem (TSP). Among the different methods found in articles, usually three apply more than others. This study examines the Danzig–Fulkerson–Johnson (DFJ), Miller–Tucker–Zemlin (MTZ), and Gavish–Graves (GG) formulations to select the best asymmetric traveling salesman problem (ATSP) formulation. The study introduces five criteria as the number of constraints, number of variables, type of variables, time of solving, and differences between the optimum and the relaxed value for comparing these constraints. The reason for selecting these criteria is that they have the most significant impact on the mathematical problem-solving complexity. A new and well-known multiple-criteria decision making (MCDM) method, the simultaneous evaluation of the criteria and alternatives (SECA) method was applied to analyze these criteria. To use the SECA method for ranking the alternatives and extracting information about the criteria from constraints needs computational computing. In this research, we use CPLEX 12.8 software to compute the criteria value and LINGO 11 software to solve the SECA method. Finally, we conclude that the Gavish–Graves (GG) formulation is the best. The new web-based software was used for testing the results.

]]>Axioms doi: 10.3390/axioms10010018

Authors: Marouane Mahrouf Adnane Boukhouima Houssine Zine El Mehdi Lotfi Delfim F. M. Torres Noura Yousfi

The novel coronavirus disease (COVID-19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID-19 in Morocco was reported on 2 March 2020, and the number of reported cases has increased day by day. In this work, we extend the well-known SIR compartmental model to deterministic and stochastic time-delayed models in order to predict the epidemiological trend of COVID-19 in Morocco and to assess the potential role of multiple preventive measures and strategies imposed by Moroccan authorities. The main features of the work include the well-posedness of the models and conditions under which the COVID-19 may become extinct or persist in the population. Parameter values have been estimated from real data and numerical simulations are presented for forecasting the COVID-19 spreading as well as verification of theoretical results.

]]>Axioms doi: 10.3390/axioms10010017

Authors: Maria Laura Delle Delle Monache Karen Chi Yong Chen Paola Goatin Ke Han Jing-mei Qiu Benedetto Piccoli

This paper uses empirical traffic data collected from three locations in Europe and the US to reveal a three-phase fundamental diagram with two phases located in the uncongested regime. Model-based clustering, hypothesis testing and regression analyses are applied to the speed–flow–occupancy relationship represented in the three-dimensional space to rigorously validate the three phases and identify their gaps. The finding is consistent across the aforementioned different geographical locations. Accordingly, we propose a three-phase macroscopic traffic flow model and a characterization of solutions to the Riemann problems. This work identifies critical structures in the fundamental diagram that are typically ignored in first- and higher-order models and could significantly impact travel time estimation on highways.

]]>Axioms doi: 10.3390/axioms10010016

Authors: Olawale Kazeem Oyewole Oluwatosin Temitope Mewomo

In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves the split null point problem and also solves a generalized mixed equilibrium problem. We prove a strong convergence of the proposed algorithm to a common solution of the two problems. We display some numerical examples to illustrate our method. Our result improves some existing results in the literature.

]]>Axioms doi: 10.3390/axioms10010015

Authors: Kengo Kasahara Yasunori Kimura

We consider Halpern&rsquo;s and Mann&rsquo;s types of iterative schemes to find a common minimizer of a finite number of proper lower semicontinuous convex functions defined on a complete geodesic space with curvature bounded above.

]]>Axioms doi: 10.3390/axioms10010014

Authors: André H. Erhardt

We study the stability of a unique weak solution to certain parabolic systems with nonstandard growth condition, which are additionally dependent on a cross-diffusion term. More precisely, we show that two unique weak solutions of the considered system with different initial values are controlled by their initial values.

]]>Axioms doi: 10.3390/axioms10010013

Authors: Axioms Editorial Office Axioms Editorial Office

Peer review is the driving force of journal development, and reviewers are gatekeepers who ensure that Axioms maintains its standards for the high quality of its published papers [...]

]]>Axioms doi: 10.3390/axioms10010012

Authors: Simone Göttlich Michael Herty Gediyon Weldegiyorgis

In this paper, we study input-to-state stability (ISS) of an equilibrium for a scalar conservation law with nonlocal velocity and measurement error arising in a highly re-entrant manufacturing system. By using a suitable Lyapunov function, we prove sufficient and necessary conditions on ISS. We propose a numerical discretization of the scalar conservation law with nonlocal velocity and measurement error. A suitable discrete Lyapunov function is analyzed to provide ISS of a discrete equilibrium for the proposed numerical approximation. Finally, we show computational results to validate the theoretical findings.

]]>Axioms doi: 10.3390/axioms10010011

Authors: Junjian Zhao Wei-Shih Du

In this paper, by applying the abstract maximal element principle of Lin and Du, we present some new existence theorems related with critical point theorem, maximal element theorem, generalized Ekeland&rsquo;s variational principle and common (fuzzy) fixed point theorem for essential distances.

]]>Axioms doi: 10.3390/axioms10010010

Authors: Amirul Aizad Ahmad Fuad Tahir Ahmad

This paper explores how electroencephalography (EEG) signals in the Krohn-Rhodes form can be decomposed further using the Jordan-Chevalley decomposition technique. First, the recorded EEG signals of a seizure were transformed into a set of matrices. Each of these matrices was decomposed into its elementary components using the Krohn-Rhodes decomposition method. The components were then further decomposed into semisimple and nilpotent matrices using the Jordan-Chevalley decomposition. These matrices&mdash;which are the extended building blocks of elementary EEG signals&mdash;provide evidence that the EEG signals recorded during a seizure contain patterns similar to that of prime numbers.

]]>Axioms doi: 10.3390/axioms10010009

Authors: Iryna Banakh Taras Banakh Serhii Bardyla

A subset A of a semigroup S is called a chain (antichain) if ab&isin;{a,b} (ab&notin;{a,b}) for any (distinct) elements a,b&isin;A. A semigroup S is called periodic if for every element x&isin;S there exists n&isin;N such that xn is an idempotent. A semigroup S is called (anti)chain-finite if S contains no infinite (anti)chains. We prove that each antichain-finite semigroup S is periodic and for every idempotent e of S the set e&infin;={x&isin;S:&exist;n&isin;N(xn=e)} is finite. This property of antichain-finite semigroups is used to prove that a semigroup is finite if and only if it is chain-finite and antichain-finite. Furthermore, we present an example of an antichain-finite semilattice that is not a union of finitely many chains.

]]>Axioms doi: 10.3390/axioms10010008

Authors: Giulia Dileo

We introduce a new class of almost 3-contact metric manifolds, called 3-(0,&delta;)-Sasaki manifolds. We show fundamental geometric properties of these manifolds, analyzing analogies and differences with the known classes of 3-(&alpha;,&delta;)-Sasaki (&alpha;&ne;0) and 3-&delta;-cosymplectic manifolds.

]]>Axioms doi: 10.3390/axioms10010007

Authors: Ion Mihai Radu-Ioan Mihai

We give a simple proof of the Chen inequality for the Chen invariant &delta;(2,&hellip;,2)︸k&nbsp;terms of submanifolds in Riemannian space forms.

]]>Axioms doi: 10.3390/axioms10010006

Authors: Mohammed Hamed Alshbool Osman Isik Ishak Hashim

In the present paper, we introduce the fractional Bernstein series solution (FBSS) to solve the fractional diffusion equation, which is a generalization of the classical diffusion equation. The Bernstein polynomial method is a promising one and can be generalized to more complicated problems in fractional partial differential equations. To get the FBSS, we first convert all terms in the problem to matrix forms. Then, the fundamental matrix equation is obtained and thus, the solution is obtained. Two error estimation methods based on a residual correction procedure and the consecutive approximations are incorporated to find the estimate and bound of the absolute error. The perturbation and stability analysis of the method is given. We apply the method to some illustrative examples. The numerical results are compared with the exact solutions and known second-order methods. The outcomes of the numerical examples are very encouraging and show that the FBSS is highly useful in solving fractional partial problems. The results show the accuracy and effectiveness of the method.

]]>Axioms doi: 10.3390/axioms10010005

Authors: Hsien-Chung Wu

This paper investigates the common coupled coincidence points and common coupled fixed points in fuzzy semi-metric spaces. The symmetric condition is not necessarily satisfied in fuzzy semi-metric space. Therefore, four kinds of triangle inequalities are taken into account in order to study the Cauchy sequences. Inspired by the intuitive observations, the concepts of rational condition and distance condition are proposed for the purpose of simplifying the discussions.

]]>Axioms doi: 10.3390/axioms10010004

Authors: Andriy Bandura Maria Martsinkiv Oleh Skaskiv

Let b&isin;Cn\{0} be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e., we study functions that are analytic in the intersection of every slice {z0+tb:t&isin;C} with the unit ball Bn={z&isin;C:|z|:=|z|12+&hellip;+|zn|2&lt;1} for any z0&isin;Bn. For this class of functions, there is introduced a concept of boundedness of L-index in the direction b, where L:Bn&rarr;R+ is a positive continuous function such that L(z)&gt;&beta;|b|1&minus;|z|, where &beta;&gt;1 is some constant. For functions from this class, we describe a local behavior of modulus of directional derivatives on every &rsquo;circle&rsquo; {z+tb:|t|=r/L(z)} with r&isin;(0;&beta;],t&isin;C,z&isin;Cn. It is estimated by the value of the function at the center of the circle. Other propositions concern a connection between the boundedness of L-index in the direction b of the slice holomorphic function F and the boundedness of lz-index of the slice function gz(t)=F(z+tb) with lz(t)=L(z+tb). In addition, we show that every slice holomorphic and joint continuous function in the unit ball has a bounded L-index in direction in any domain compactly embedded in the unit ball and for any continuous function L:Bn&rarr;R+.

]]>Axioms doi: 10.3390/axioms10010003

Authors: Ehsan Lotfali Ghasab Hamid Majani Manuel De la Sen Ghasem Soleimani Rad

The main purpose of the present paper is to define the concept of an e-distance (as a generalization of r-distance) on a Menger PGM space and to introduce some of its properties. Moreover, some coupled fixed point results, in terms of this distance on a complete PGM space, are proved. To support our definitions and main results, several examples and an application are considered.

]]>Axioms doi: 10.3390/axioms10010002

Authors: Jaeyoo Choy Hahng-Yun Chu Ahyoung Kim

In this article, we deal with stabilities of several functional equations in n-Banach spaces. For a surjective mapping f into a n-Banach space, we prove the generalized Hyers&ndash;Ulam stabilities of the cubic functional equation and the quartic functional equation for f in n-Banach spaces.

]]>Axioms doi: 10.3390/axioms10010001

Authors: Hammed Anuoluwapo Abass Lateef Olakunle Jolaoso

In this paper, we propose a generalized viscosity iterative algorithm which includes a sequence of contractions and a self adaptive step size for approximating a common solution of a multiple-set split feasibility problem and fixed point problem for countable families of k-strictly pseudononspeading mappings in the framework of real Hilbert spaces. The advantage of the step size introduced in our algorithm is that it does not require the computation of the Lipschitz constant of the gradient operator which is very difficult in practice. We also introduce an inertial process version of the generalize viscosity approximation method with self adaptive step size. We prove strong convergence results for the sequences generated by the algorithms for solving the aforementioned problems and present some numerical examples to show the efficiency and accuracy of our algorithm. The results presented in this paper extends and complements many recent results in the literature.

]]>Axioms doi: 10.3390/axioms9040144

Authors: Radu Iordanescu Florin Felix Nichita Ovidiu Pasarescu

The main concepts in this paper are the means and Euler type formulas; the generalized mean which incorporates the harmonic mean, the geometric mean, the arithmetic mean, and the quadratic mean can be further generalized. Results on the Euler&rsquo;s formula, the (modified) Yang&ndash;Baxter equation, coalgebra structures, and non-associative structures are also included in the current paper.

]]>Axioms doi: 10.3390/axioms9040143

Authors: Kazeem Olalekan Aremu Chinedu Izuchukwu Hammed Anuolwupo Abass Oluwatosin Temitope Mewomo

In this paper, we propose and study an iterative algorithm that comprises of a finite family of inverse strongly monotone mappings and a finite family of Lipschitz demicontractive mappings in an Hadamard space. We establish that the proposed algorithm converges strongly to a common solution of a finite family of variational inequality problems, which is also a common fixed point of the demicontractive mappings. Furthermore, we provide a numerical experiment to demonstrate the applicability of our results. Our results generalize some recent results in literature.

]]>Axioms doi: 10.3390/axioms9040142

Authors: Janusz Ciuciura

In this paper, we consider some paraconsistent calculi in a Hilbert-style formulation with the rule of detachment as the sole rule of interference. Each calculus will be expected to contain all axiom schemas of the positive fragment of classical propositional calculus and respect the principle of gentle explosion.

]]>Axioms doi: 10.3390/axioms9040141

Authors: Yaé Ulrich Gaba Erdal Karapınar Adrian Petruşel Stojan Radenović

In this manuscript we investigate the existence of start-points for the generalized weakly contractive multi-valued mappings in the setting of left K-complete quasi-pseudo metric space. We provide an example to support the given result.

]]>Axioms doi: 10.3390/axioms9040140

Authors: Chibueze Christian Okeke Lateef Olakunle Jolaoso Regina Nwokoye

In this paper, we present a new self-adaptive inertial projection method for solving split common null point problems in p-uniformly convex and uniformly smooth Banach spaces. The algorithm is designed such that its convergence does not require prior estimate of the norm of the bounded operator and a strong convergence result is proved for the sequence generated by our algorithm under mild conditions. Moreover, we give some applications of our result to split convex minimization and split equilibrium problems in real Banach spaces. This result improves and extends several other results in this direction in the literature.

]]>Axioms doi: 10.3390/axioms9040139

Authors: Maria Letizia Guerra Laerte Sorini Luciano Stefanini

Sentiment analysis to characterize the properties of Bitcoin prices and their forecasting is here developed thanks to the capability of the Fuzzy Transform (F-transform for short) to capture stylized facts and mutual connections between time series with different natures. The recently proposed Lp-norm F-transform is a powerful and flexible methodology for data analysis, non-parametric smoothing and for fitting and forecasting. Its capabilities are illustrated by empirical analyses concerning Bitcoin prices and Google Trend scores (six years of daily data): we apply the (inverse) F-transform to both time series and, using clustering techniques, we identify stylized facts for Bitcoin prices, based on (local) smoothing and fitting F-transform, and we study their time evolution in terms of a transition matrix. Finally, we examine the dependence of Bitcoin prices on Google Trend scores and we estimate short-term forecasting models; the Diebold&ndash;Mariano (DM) test statistics, applied for their significance, shows that sentiment analysis is useful in short-term forecasting of Bitcoin cryptocurrency.

]]>Axioms doi: 10.3390/axioms9040138

Authors: Tatiana Ratnikova

The aim of the research is to develop the regularization method. By Lomov&rsquo;s regularization method, we constructed a uniform asymptotic solution of the singularly perturbed Cauchy problem for a parabolic equation in the case of violation of stability conditions of the limit-operator spectrum. The problem with a &ldquo;simple&rdquo; turning point is considered in the case, when the eigenvalue vanishes at t=0 and has the form tm/na(t). The asymptotic convergence of the regularized series is proved.

]]>Axioms doi: 10.3390/axioms9040137

Authors: Wiyada Kumam Kanikar Muangchoo

A plethora of applications in non-linear analysis, including minimax problems, mathematical programming, the fixed-point problems, saddle-point problems, penalization and complementary problems, may be framed as a problem of equilibrium. Most of the methods used to solve equilibrium problems involve iterative methods, which is why the aim of this article is to establish a new iterative method by incorporating an inertial term with a subgradient extragradient method to solve the problem of equilibrium, which includes a bifunction that is strongly pseudomonotone and meets the Lipschitz-type condition in a real Hilbert space. Under certain mild conditions, a strong convergence theorem is proved, and a required sequence is generated without the information of the Lipschitz-type cost bifunction constants. Thus, the method operates with the help of a slow-converging step size sequence. In numerical analysis, we consider various equilibrium test problems to validate our proposed results.

]]>Axioms doi: 10.3390/axioms9040136

Authors: Shyam Sundar Santra Taher A. Nofal Hammad Alotaibi Omar Bazighifan

In this work, we consider a type of second-order functional differential equations and establish qualitative properties of their solutions. These new results complement and improve a number of results reported in the literature. Finally, we provide an example that illustrates our results.

]]>Axioms doi: 10.3390/axioms9040135

Authors: Sotiris K. Ntouyas

Differential and difference equations play an important role in many branches of mathematics [...]

]]>Axioms doi: 10.3390/axioms9040134

Authors: Shyam Sundar Santra Ioannis Dassios Tanusri Ghosh

In this work, we present some new sufficient conditions for the oscillation of a class of second-order neutral delay differential equation. Our oscillation results, complement, simplify and improve recent results on oscillation theory of this type of non-linear neutral differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

]]>Axioms doi: 10.3390/axioms9040133

Authors: Andriy Zagorodnyuk Anna Hihliuk

In this paper we investigate analytic functions of unbounded type on a complex infinite dimensional Banach space X. The main question is: under which conditions is there an analytic function of unbounded type on X such that its Taylor polynomials are in prescribed subspaces of polynomials? We obtain some sufficient conditions for a function f to be of unbounded type and show that there are various subalgebras of polynomials that support analytic functions of unbounded type. In particular, some examples of symmetric analytic functions of unbounded type are constructed.

]]>Axioms doi: 10.3390/axioms9040132

Authors: Youssef Errai El Miloudi Marhrani Mohamed Aamri

We use interpolation to obtain a common fixed point result for a new type of Ćirić&ndash;Reich&ndash;Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić&ndash;Reich&ndash;Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.

]]>Axioms doi: 10.3390/axioms9040131

Authors: Burkhan Kalimbetov Valeriy Safonov

In this paper, we consider a system with rapidly oscillating coefficients, which includes an integral operator with an exponentially varying kernel. The main goal of the work is to develop an algorithm for the regularization method for such systems and to identify the influence of the integral term on the asymptotic behavior of the solution of the original problem.

]]>Axioms doi: 10.3390/axioms9040130

Authors: Tommi Huotari Jyrki Savolainen Mikael Collan

This study investigated the performance of a trading agent based on a convolutional neural network model in portfolio management. The results showed that with real-world data the agent could produce relevant trading results, while the agent&rsquo;s behavior corresponded to that of a high-risk taker. The data used were wide in comparison with earlier reported research and was based on the full set of the S&amp;P 500 stock data for twenty-one years supplemented with selected financial ratios. The results presented are new in terms of the size of the data set used and with regards to the model used. The results provide direction and offer insight into how deep learning methods may be used in constructing automatic trading systems.

]]>Axioms doi: 10.3390/axioms9040129

Authors: Reny George Zoran D. Mitrović Stojan Radenović

Common coupled fixed point theorems for generalized T-contractions are proved for a pair of mappings S:X&times;X&rarr;X and g:X&rarr;X in a bv(s)-metric space, which generalize, extend, and improve some recent results on coupled fixed points. As an application, we prove an existence and uniqueness theorem for the solution of a system of nonlinear integral equations under some weaker conditions and given a convergence criteria for the unique solution, which has been properly verified by using suitable example.

]]>Axioms doi: 10.3390/axioms9040128

Authors: Kazuki Yamaga

In this paper, Non-Equilibrium Steady State that is induced by electric field and the conductivity of non-interacting fermion systems under the dissipative dynamics is discussed. The dissipation is taken into account within a framework of the quantum dynamical semigroup introduced by Davies (1977). We obtain a formula of the conductivity for the stationary state, which is applicable to arbitrary potentials. Our formula gives a justification of an adiabatic factor that is often introduced in practical calculation while using the Kubo formula. In addition, the conductivity of crystals (i.e., periodic potentials) is also discussed.

]]>Axioms doi: 10.3390/axioms9040127

Authors: Wiyada Kumam Kanikar Muangchoo

A number of applications from mathematical programmings, such as minimization problems, variational inequality problems and fixed point problems, can be written as equilibrium problems. Most of the schemes being used to solve this problem involve iterative methods, and for that reason, in this paper, we introduce a modified iterative method to solve equilibrium problems in real Hilbert space. This method can be seen as a modification of the paper titled &ldquo;A new two-step proximal algorithm of solving the problem of equilibrium programming&rdquo; by Lyashko et al. (Optimization and its applications in control and data sciences, Springer book pp. 315&ndash;325, 2016). A weak convergence result has been proven by considering the mild conditions on the cost bifunction. We have given the application of our results to solve variational inequality problems. A detailed numerical study on the Nash&ndash;Cournot electricity equilibrium model and other test problems is considered to verify the convergence result and its performance.

]]>Axioms doi: 10.3390/axioms9040126

Authors: Simon Gluzman

We develop nonlinear approximations to critical and relaxation phenomena, complemented by the optimization procedures. In the first part, we discuss general methods for calculation of critical indices and amplitudes from the perturbative expansions. Several important examples of the Stokes flow through 2D channels are brought up. Power series for the permeability derived for small values of amplitude are employed for calculation of various critical exponents in the regime of large amplitudes. Special nonlinear approximations valid for arbitrary values of the wave amplitude are derived from the expansions. In the second part, the technique developed for critical phenomena is applied to relaxation phenomena. The concept of time-translation invariance is discussed, and its spontaneous violation and restoration considered. Emerging probabilistic patterns correspond to a local breakdown of time-translation invariance. Their evolution leads to the time-translation invariance complete (or partial) restoration. We estimate the typical time extent, amplitude and direction for such a restorative process. The new technique is based on explicit introduction of origin in time as an optimization parameter. After some transformations, we arrive at the exponential and generalized exponential-type solutions (Gompertz approximants), with explicit finite time scale, which is only implicit in the initial parameterization with polynomial approximation. The concept of crash as a fast relaxation phenomenon, consisting of time-translation invariance breaking and restoration, is advanced. Several COVID-related crashes in the time series for Shanghai Composite and Dow Jones Industrial are discussed as an illustration.

]]>Axioms doi: 10.3390/axioms9040125

Authors: Richard Cushman Jędrzej Śniatycki

The original Bohr-Sommerfeld theory of quantization did not give operators of transitions between quantum quantum states. This paper derives these operators, using the first principles of geometric quantization.

]]>Axioms doi: 10.3390/axioms9040124

Authors: Faïçal Ndaïrou Delfim F. M. Torres

Distributed-order fractional non-local operators were introduced and studied by Caputo at the end of the 20th century. They generalize fractional order derivatives/integrals in the sense that such operators are defined by a weighted integral of different orders of differentiation over a certain range. The subject of distributed-order non-local derivatives is currently under strong development due to its applications in modeling some complex real world phenomena. Fractional optimal control theory deals with the optimization of a performance index functional, subject to a fractional control system. One of the most important results in classical and fractional optimal control is the Pontryagin Maximum Principle, which gives a necessary optimality condition that every solution to the optimization problem must verify. In our work, we extend the fractional optimal control theory by considering dynamical system constraints depending on distributed-order fractional derivatives. Precisely, we prove a weak version of Pontryagin&rsquo;s maximum principle and a sufficient optimality condition under appropriate convexity assumptions.

]]>Axioms doi: 10.3390/axioms9040123

Authors: Mehmet Yavuz Ndolane Sene

This paper addresses the solution of the incompressible second-grade fluid models. Fundamental qualitative properties of the solution are primarily studied for proving the adequacy of the physical interpretations of the proposed model. We use the Liouville-Caputo fractional derivative with its generalized version that gives more comprehensive physical results in the analysis and investigations. In this work, both the &rho;-Laplace homotopy transform method (&rho;-LHTM) and the heat balance integral method (HBIM) are successfully combined to solve the fractional incompressible second-grade fluid differential equations. Numerical simulations and their physical interpretations of the mentioned incompressible second-grade fluid model are ensured to illustrate the main findings. It is also proposed that one can recognize the differences in physical analysis of diffusions such as ballistic diffusion, super diffusion, and subdiffusion cases by considering the impact of the orders &rho; and &phi;.

]]>Axioms doi: 10.3390/axioms9040122

Authors: Hasan S. Panigoro Agus Suryanto Wuryansari Muharini Kusumawinahyu Isnani Darti

The harvesting management is developed to protect the biological resources from over-exploitation such as harvesting and trapping. In this article, we consider a predator&ndash;prey interaction that follows the fractional-order Rosenzweig&ndash;MacArthur model where the predator is harvested obeying a threshold harvesting policy (THP). The THP is applied to maintain the existence of the population in the prey&ndash;predator mechanism. We first consider the Rosenzweig&ndash;MacArthur model using the Caputo fractional-order derivative (that is, the operator with the power-law kernel) and perform some dynamical analysis such as the existence and uniqueness, non-negativity, boundedness, local stability, global stability, and the existence of Hopf bifurcation. We then reconsider the same model involving the Atangana&ndash;Baleanu fractional derivative with the Mittag&ndash;Leffler kernel in the Caputo sense (ABC). The existence and uniqueness of the solution of the model with ABC operator are established. We also explore the dynamics of the model with both fractional derivative operators numerically and confirm the theoretical findings. In particular, it is shown that models with both Caputo operator and ABC operator undergo a Hopf bifurcation that can be controlled by the conversion rate of consumed prey into the predator birth rate or by the order of fractional derivative. However, the bifurcation point of the model with the Caputo operator is different from that of the model with the ABC operator.

]]>Axioms doi: 10.3390/axioms9040121

Authors: Tursun K. Yuldashev Erkinjon T. Karimov

The questions of the one-value solvability of an inverse boundary value problem for a mixed type integro-differential equation with Caputo operators of different fractional orders and spectral parameters are considered. The mixed type integro-differential equation with respect to the main unknown function is an inhomogeneous partial integro-differential equation of fractional order in both positive and negative parts of the multidimensional rectangular domain under consideration. This mixed type of equation, with respect to redefinition functions, is a nonlinear Fredholm type integral equation. The fractional Caputo operators&rsquo; orders are smaller in the positive part of the domain than the orders of Caputo operators in the negative part of the domain under consideration. Using the method of Fourier series, two systems of countable systems of ordinary fractional integro-differential equations with degenerate kernels and different orders of integro-differentation are obtained. Furthermore, a method of degenerate kernels is used. In order to determine arbitrary integration constants, a linear system of functional algebraic equations is obtained. From the solvability condition of this system are calculated the regular and irregular values of the spectral parameters. The solution of the inverse problem under consideration is obtained in the form of Fourier series. The unique solvability of the problem for regular values of spectral parameters is proved. During the proof of the convergence of the Fourier series, certain properties of the Mittag&ndash;Leffler function of two variables, the Cauchy&ndash;Schwarz inequality and Bessel inequality, are used. We also studied the continuous dependence of the solution of the problem on small parameters for regular values of spectral parameters. The existence and uniqueness of redefined functions have been justified by solving the systems of two countable systems of nonlinear integral equations. The results are formulated as a theorem.

]]>Axioms doi: 10.3390/axioms9040120

Authors: Salvatore Triolo

In this paper, we analyze local spectral properties of operators R,S and RS which satisfy the operator equations RnSRn=Rj and SnRSn=Sj for same integers j&ge;n&ge;0. We also continue to study the relationship between the local spectral properties of an operator R and the local spectral properties of S. Thus, we investigate the transmission of some local spectral properties from R to S and we illustrate our results with an example. The theory is exemplified in some cases.

]]>Axioms doi: 10.3390/axioms9040119

Authors: Nallapu Vijender Vasileios Drakopoulos

In this article, firstly, an overview of affine fractal interpolation functions using a suitable iterated function system is presented and, secondly, the construction of Bernstein affine fractal interpolation functions in two and three dimensions is introduced. Moreover, the convergence of the proposed Bernstein affine fractal interpolation functions towards the data generating function does not require any condition on the scaling factors. Consequently, the proposed Bernstein affine fractal interpolation functions possess irregularity at any stage of convergence towards the data generating function.

]]>Axioms doi: 10.3390/axioms9040118

Authors: Nopparat Wairojjana Mudasir Younis Habib ur Rehman Nuttapol Pakkaranang Nattawut Pholasa

Variational inequality theory is an effective tool for engineering, economics, transport and mathematical optimization. Some of the approaches used to resolve variational inequalities usually involve iterative techniques. In this article, we introduce a new modified viscosity-type extragradient method to solve monotone variational inequalities problems in real Hilbert space. The result of the strong convergence of the method is well established without the information of the operator&rsquo;s Lipschitz constant. There are proper mathematical studies relating our newly designed method to the currently state of the art on several practical test problems.

]]>Axioms doi: 10.3390/axioms9040117

Authors: Miguel Vivas-Cortez Artion Kashuri Rozana Liko Jorge Eliecer Hernández Hernández

In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite&ndash;Hadamard inequality for generalized coordinate ϕ-convex functions via an extension of the Riemann&ndash;Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina&rsquo;s special function via generalized coordinate ϕ-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well.

]]>Axioms doi: 10.3390/axioms9040116

Authors: Nipon Waiyaworn Kamsing Nonlaopon Somsak Orankitjaroen

In this paper, we present the distributional solutions of the modified spherical Bessel differential equations t2y&Prime;(t)+2ty&prime;(t)&minus;[t2+&nu;(&nu;+1)]y(t)=0 and the linear differential equations of the forms t2y&Prime;(t)+3ty&prime;(t)&minus;(t2+&nu;2&minus;1)y(t)=0, where &nu;&isin;N&cup;{0} and t&isin;R. We find that the distributional solutions, in the form of a finite series of the Dirac delta function and its derivatives, depend on the values of &nu;. The results of several examples are also presented.

]]>Axioms doi: 10.3390/axioms9040115

Authors: Nopparat Wairojjana Nuttapol Pakkaranang Habib ur Rehman Nattawut Pholasa Tiwabhorn Khanpanuk

A number of applications from mathematical programmings, such as minimax problems, penalization methods and fixed-point problems can be formulated as a variational inequality model. Most of the techniques used to solve such problems involve iterative algorithms, and that is why, in this paper, we introduce a new extragradient-like method to solve the problems of variational inequalities in real Hilbert space involving pseudomonotone operators. The method has a clear advantage because of a variable stepsize formula that is revised on each iteration based on the previous iterations. The key advantage of the method is that it works without the prior knowledge of the Lipschitz constant. Strong convergence of the method is proved under mild conditions. Several numerical experiments are reported to show the numerical behaviour of the method.

]]>Axioms doi: 10.3390/axioms9040114

Authors: Somayeh Nemati Delfim F. M. Torres

We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann&ndash;Liouville integral operator is used in our new techniques. An accurate operational matrix of variable-order fractional integration for Bernoulli polynomials is introduced. Our methods proceed as follows. First, a specific approximation of the differentiation order of the state function is considered, in terms of Bernoulli polynomials. Such approximation, together with the initial conditions, help us to obtain some approximations for the other existing functions in the dynamical control-affine system. Using these approximations, and the Gauss&mdash;Legendre integration formula, the problem is reduced to a system of nonlinear algebraic equations. Some error bounds are then given for the approximate optimal state and control functions, which allow us to obtain an error bound for the approximate value of the performance index. We end by solving some test problems, which demonstrate the high accuracy of our results.

]]>Axioms doi: 10.3390/axioms9040113

Authors: George D. Verros

In this work comprehensive criteria for detecting the extrema in entropy production rate for heat transfer by conduction in a uniform body under a constant volume in the linear region of Extended Thermodynamics Framework are developed. These criteria are based on calculating the time derivative of entropy production rate with the aid of well-established engineering principles, such as the local heat transfer coefficients. By using these coefficients, the temperature gradient is replaced by the difference of this quantity. It is believed that the result of this work could be used to further elucidate irreversible processes.

]]>Axioms doi: 10.3390/axioms9030112

Authors: Noureddine Sabiri Mohamed Guessous

Let (&Omega;,F,&mu;) be a complete probability space, E a separable Banach space and E&prime; the topological dual vector space of E. We present some compactness results in LE&prime;1E, the Banach space of weak*-scalarly integrable E&prime;-valued functions. As well we extend the classical theorem of Koml&oacute;s to the bounded sequences in LE&prime;1E.

]]>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.

]]>Axioms doi: 10.3390/axioms9030109

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 Lee Seok-Zun Song Young 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.

]]>Axioms doi: 10.3390/axioms9030106

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.

]]>Axioms doi: 10.3390/axioms9030105

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.

]]>Axioms doi: 10.3390/axioms9030104

Authors: Irvanizam Irvanizam Nawar Nabila Zi Rahma Zuhra Amrusi Amrusi Hizir 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.

]]>Axioms doi: 10.3390/axioms9030103

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.

]]>Axioms doi: 10.3390/axioms9030102

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.

]]>Axioms doi: 10.3390/axioms9030101

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.

]]>Axioms doi: 10.3390/axioms9030097

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.

]]>Axioms doi: 10.3390/axioms9030095

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.

]]>Axioms doi: 10.3390/axioms9030090

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.

]]>Axioms doi: 10.3390/axioms9030089

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.

]]>Axioms doi: 10.3390/axioms9030086

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.

]]>Axioms doi: 10.3390/axioms9030084

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.

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