Next Issue
Volume 9, March
Previous Issue
Volume 8, September

Axioms, Volume 8, Issue 4 (December 2019) – 34 articles

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
Order results
Result details
Select all
Export citation of selected articles as:
Open AccessArticle
Separability of Nonassociative Algebras with Metagroup Relations
Axioms 2019, 8(4), 139; https://doi.org/10.3390/axioms8040139 - 12 Dec 2019
Cited by 1 | Viewed by 606
Abstract
This article is devoted to a class of nonassociative algebras with metagroup relations. This class includes, in particular, generalized Cayley–Dickson algebras. The separability of the nonassociative algebras with metagroup relations is investigated. For this purpose the cohomology theory is utilized. Conditions are found [...] Read more.
This article is devoted to a class of nonassociative algebras with metagroup relations. This class includes, in particular, generalized Cayley–Dickson algebras. The separability of the nonassociative algebras with metagroup relations is investigated. For this purpose the cohomology theory is utilized. Conditions are found under which such algebras are separable. Algebras satisfying these conditions are described. Full article
Open AccessArticle
Repeated Derivatives of Hyperbolic Trigonometric Functions and Associated Polynomials
Axioms 2019, 8(4), 138; https://doi.org/10.3390/axioms8040138 - 06 Dec 2019
Cited by 1 | Viewed by 681
Abstract
Elementary problems as the evaluation of repeated derivatives of ordinary transcendent functions can usefully be treated with the use of special polynomials and of a formalism borrowed from combinatorial analysis. Motivated by previous researches in this field, we review the results obtained by [...] Read more.
Elementary problems as the evaluation of repeated derivatives of ordinary transcendent functions can usefully be treated with the use of special polynomials and of a formalism borrowed from combinatorial analysis. Motivated by previous researches in this field, we review the results obtained by other authors and develop a complementary point of view for the repeated derivatives of sec ( . ) , tan ( . ) and for their hyperbolic counterparts. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II) Printed Edition available
Open AccessArticle
Solutions of the Generalized Abel’s Integral Equations of the Second Kind with Variable Coefficients
Axioms 2019, 8(4), 137; https://doi.org/10.3390/axioms8040137 - 05 Dec 2019
Cited by 2 | Viewed by 629
Abstract
Applying Babenko’s approach, we construct solutions for the generalized Abel’s integral equations of the second kind with variable coefficients on R and Rn, and show their convergence and stability in the spaces of Lebesgue integrable functions, with several illustrative examples. [...] Read more.
Applying Babenko’s approach, we construct solutions for the generalized Abel’s integral equations of the second kind with variable coefficients on R and R n , and show their convergence and stability in the spaces of Lebesgue integrable functions, with several illustrative examples. Full article
Open AccessArticle
GRSA Enhanced for Protein Folding Problem in the Case of Peptides
Axioms 2019, 8(4), 136; https://doi.org/10.3390/axioms8040136 - 04 Dec 2019
Viewed by 791
Abstract
Protein folding problem (PFP) consists of determining the functional three-dimensional structure of a target protein. PFP is an optimization problem where the objective is to find the structure with the lowest Gibbs free energy. It is significant to solve PFP for use in [...] Read more.
Protein folding problem (PFP) consists of determining the functional three-dimensional structure of a target protein. PFP is an optimization problem where the objective is to find the structure with the lowest Gibbs free energy. It is significant to solve PFP for use in medical and pharmaceutical applications. Hybrid simulated annealing algorithms (HSA) use a kind of simulated annealing or Monte Carlo method, and they are among the most efficient for PFP. The instances of PFP can be classified as follows: (a) Proteins with a large number of amino acids and (b) peptides with a small number of amino acids. Several HSA have been positively applied for the first case, where I-Tasser has been one of the most successful in the CASP competition. PEP-FOLD3 and golden ratio simulated annealing (GRSA) are also two of these algorithms successfully applied to peptides. This paper presents an enhanced golden simulated annealing (GRSA2) where soft perturbations (collision operators), named “on-wall ineffective collision” and “intermolecular ineffective collision”, are applied to generate new solutions in the metropolis cycle. GRSA2 is tested with a dataset for peptides previously proposed, and a comparison with PEP-FOLD3 and I-Tasser is presented. According to the experimentation, GRSA2 has an equivalent performance to those algorithms. Full article
(This article belongs to the Special Issue Softcomputing: Theories and Applications)
Show Figures

Figure 1

Open AccessArticle
A Fast Multilevel Fuzzy Transform Image Compression Method
Axioms 2019, 8(4), 135; https://doi.org/10.3390/axioms8040135 - 03 Dec 2019
Viewed by 612
Abstract
We present a fast algorithm that improves on the performance of the multilevel fuzzy transform image compression method. The multilevel F-transform (for short, MF-tr) algorithm is an image compression method based on fuzzy transforms that, compared to the classic fuzzy transform (F-transform) image [...] Read more.
We present a fast algorithm that improves on the performance of the multilevel fuzzy transform image compression method. The multilevel F-transform (for short, MF-tr) algorithm is an image compression method based on fuzzy transforms that, compared to the classic fuzzy transform (F-transform) image compression method, has the advantage of being able to reconstruct an image with the required quality. However, this method can be computationally expensive in terms of execution time since, based on the compression ratio used, different iterations may be necessary in order to reconstruct the image with the required quality. To solve this problem, we propose a fast variation of the multilevel F-transform algorithm in which the optimal compression ratio is found in order to reconstruct the image in as few iterations as possible. Comparison tests show that our method reconstructs the image in at most half of the CPU time used by the MF-tr algorithm. Full article
(This article belongs to the Special Issue Fuzzy Transforms and Their Applications)
Show Figures

Graphical abstract

Open AccessArticle
Exact Solutions for a Class of Wick-Type Stochastic (3+1)-Dimensional Modified Benjamin–Bona–Mahony Equations
Axioms 2019, 8(4), 134; https://doi.org/10.3390/axioms8040134 - 03 Dec 2019
Cited by 12 | Viewed by 731
Abstract
In this paper, we investigate the Wick-type stochastic (3+1)-dimensional modified Benjamin–Bona–Mahony (BBM) equations. We present a generalised version of the modified tanh–coth method. Using the generalised, modified tanh–coth method, white noise theory, and Hermite transform, we produce a new set of exact travelling [...] Read more.
In this paper, we investigate the Wick-type stochastic (3+1)-dimensional modified Benjamin–Bona–Mahony (BBM) equations. We present a generalised version of the modified tanh–coth method. Using the generalised, modified tanh–coth method, white noise theory, and Hermite transform, we produce a new set of exact travelling wave solutions for the (3+1)-dimensional modified BBM equations. This set includes solutions of exponential, hyperbolic, and trigonometric types. With the help of inverse Hermite transform, we obtained stochastic travelling wave solutions for the Wick-type stochastic (3+1)-dimensional modified BBM equations. Eventually, by application example, we show how the stochastic solutions can be given as white noise functional solutions. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Optimization with Applications)
Open AccessArticle
Synthetic Tableaux with Unrestricted Cut for First-Order Theories
Axioms 2019, 8(4), 133; https://doi.org/10.3390/axioms8040133 - 29 Nov 2019
Cited by 1 | Viewed by 677
Abstract
The method of synthetic tableaux is a cut-based tableau system with synthesizing rules introducing complex formulas. In this paper, we present the method of synthetic tableaux for Classical First-Order Logic, and we propose a strategy of extending the system to first-order theories axiomatized [...] Read more.
The method of synthetic tableaux is a cut-based tableau system with synthesizing rules introducing complex formulas. In this paper, we present the method of synthetic tableaux for Classical First-Order Logic, and we propose a strategy of extending the system to first-order theories axiomatized by universal axioms. The strategy was inspired by the works of Negri and von Plato. We illustrate the strategy with two examples: synthetic tableaux systems for identity and for partial order. Full article
Show Figures

Figure 1

Open AccessArticle
General Linear Recurrence Sequences and Their Convolution Formulas
Axioms 2019, 8(4), 132; https://doi.org/10.3390/axioms8040132 - 19 Nov 2019
Cited by 3 | Viewed by 636
Abstract
We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by 11+at+bt2x. The case of generating functions containing [...] Read more.
We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by 1 1 + a t + b t 2 x . The case of generating functions containing parameters, even in the numerator is considered. Convolution formulas and general recurrence relations are derived. Many illustrative examples and a straightforward extension to the case of matrix polynomials are shown. Full article
Open AccessArticle
Global Analysis and the Periodic Character of a Class of Difference Equations
Axioms 2019, 8(4), 131; https://doi.org/10.3390/axioms8040131 - 15 Nov 2019
Cited by 1 | Viewed by 687
Abstract
In biology, difference equations is often used to understand and describe life phenomenon through mathematical models. So, in this work, we study a new class of difference equations by focusing on the periodicity character, stability (local and global) and boundedness of its solutions. [...] Read more.
In biology, difference equations is often used to understand and describe life phenomenon through mathematical models. So, in this work, we study a new class of difference equations by focusing on the periodicity character, stability (local and global) and boundedness of its solutions. Furthermore, this equation involves a May’s Host Parasitoid Model, as a special case. Full article
(This article belongs to the Special Issue Numerical Computation and Nonlinear Dynamical Systems)
Show Figures

Figure 1

Open AccessArticle
Measure of Weak Noncompactness and Fixed Point Theorems in Banach Algebras with Applications
Axioms 2019, 8(4), 130; https://doi.org/10.3390/axioms8040130 - 14 Nov 2019
Viewed by 741
Abstract
In this paper, we prove some fixed point theorems for the nonlinear operator A·B+C in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the [...] Read more.
In this paper, we prove some fixed point theorems for the nonlinear operator A · B + C in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the application of our results to a nonlinear integral equation in Banach algebra. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Topics) Printed Edition available
Open AccessArticle
Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem
Axioms 2019, 8(4), 129; https://doi.org/10.3390/axioms8040129 - 14 Nov 2019
Cited by 5 | Viewed by 618
Abstract
In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our results. [...] Read more.
In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our results. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Topics) Printed Edition available
Open AccessReview
A Short Survey and Open Questions on Compact Q-Groups
Axioms 2019, 8(4), 128; https://doi.org/10.3390/axioms8040128 - 13 Nov 2019
Viewed by 697
Abstract
Finite Q-groups have been recently studied and form a class of solvable groups, which satisfy interesting structural conditions. We survey some of their main properties and introduce the idea of Q-group for compact p-groups (p prime). A list of [...] Read more.
Finite Q -groups have been recently studied and form a class of solvable groups, which satisfy interesting structural conditions. We survey some of their main properties and introduce the idea of Q -group for compact p-groups (p prime). A list of open questions is presented, along with several connections of arithmetic nature on a problem originally due to Frobenius. Full article
(This article belongs to the collection Topological Groups) Printed Edition available
Open AccessArticle
Smashed and Twisted Wreath Products of Metagroups
Axioms 2019, 8(4), 127; https://doi.org/10.3390/axioms8040127 - 11 Nov 2019
Cited by 3 | Viewed by 571
Abstract
In this article, nonassociative metagroups are studied. Different types of smashed products and smashed twisted wreath products are scrutinized. Extensions of central metagroups are studied. Full article
Open AccessArticle
Informal Complete Metric Space and Fixed Point Theorems
Axioms 2019, 8(4), 126; https://doi.org/10.3390/axioms8040126 - 07 Nov 2019
Viewed by 697
Abstract
The concept of informal vector space is introduced in this paper. In informal vector space, the additive inverse element does not necessarily exist. The reason is that an element in informal vector space which subtracts itself cannot be a zero element. An informal [...] Read more.
The concept of informal vector space is introduced in this paper. In informal vector space, the additive inverse element does not necessarily exist. The reason is that an element in informal vector space which subtracts itself cannot be a zero element. An informal vector space can also be endowed with a metric to define a so-called informal metric space. The completeness of informal metric space can be defined according to the similar concept of a Cauchy sequence. A new concept of fixed point and the related results are studied in informal complete metric space. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Topics) Printed Edition available
Open AccessArticle
Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches
Axioms 2019, 8(4), 125; https://doi.org/10.3390/axioms8040125 - 07 Nov 2019
Cited by 7 | Viewed by 773
Abstract
The fractional traveling wave solution of important Whitham–Broer–Kaup equations was investigated by using the q-homotopy analysis transform method and natural decomposition method. The Caputo definition of fractional derivatives is used to describe the fractional operator. The obtained results, using the suggested methods are [...] Read more.
The fractional traveling wave solution of important Whitham–Broer–Kaup equations was investigated by using the q-homotopy analysis transform method and natural decomposition method. The Caputo definition of fractional derivatives is used to describe the fractional operator. The obtained results, using the suggested methods are compared with each other as well as with the exact results of the problems. The comparison shows the best agreement of solutions with each other and with the exact solution as well. Moreover, the proposed methods are found to be accurate, effective, and straightforward while dealing with the fractional-order system of partial differential equations and therefore can be generalized to other fractional order complex problems from engineering and science. Full article
Show Figures

Figure 1

Open AccessArticle
Regularized Solution of Singularly Perturbed Cauchy Problem in the Presence of Rational “Simple” Turning Point in Two-Dimensional Case
Axioms 2019, 8(4), 124; https://doi.org/10.3390/axioms8040124 - 01 Nov 2019
Cited by 2 | Viewed by 597
Abstract
By Lomov’s S.A. regularization method, we constructed an asymptotic solution of the singularly perturbed Cauchy problem in a two-dimensional case in the case of violation of stability conditions of the limit-operator spectrum. In particular, the problem with a ”simple” turning point was considered, [...] Read more.
By Lomov’s S.A. regularization method, we constructed an asymptotic solution of the singularly perturbed Cauchy problem in a two-dimensional case in the case of violation of stability conditions of the limit-operator spectrum. In particular, the problem with a ”simple” turning point was considered, i.e., one eigenvalue vanishes for t = 0 and has the form t m / n a ( t ) (limit operator is discretely irreversible). The regularization method allows us to construct an asymptotic solution that is uniform over the entire segment [ 0 , T ] , and under additional conditions on the parameters of the singularly perturbed problem and its right-hand side, the exact solution. Full article
Open AccessArticle
Advanced Control Strategies to Improve Nonlinear Automotive Dynamical Systems Consumption
Axioms 2019, 8(4), 123; https://doi.org/10.3390/axioms8040123 - 01 Nov 2019
Viewed by 542
Abstract
Electric motors and Internal Combustion Engine test benches allow for testing, under various conditions, the behavior of the Electric Vehicles and they are essential in the automotive field development. In this paper, we introduce the state-of-art of the control algorithms and their validation [...] Read more.
Electric motors and Internal Combustion Engine test benches allow for testing, under various conditions, the behavior of the Electric Vehicles and they are essential in the automotive field development. In this paper, we introduce the state-of-art of the control algorithms and their validation over different test runs, on the standard driving cycles. Ad-hoc simulations and test benches designed for the issue offer a significant opportunity to reduce costs. The modelling of automotive systems is a non-trivial problem due to the non-linearities. The paper presents a linearized solution and an adaptive control scheme to improve model performances starting from real data, and also discusses the behavior of the proposed system and the control law reporting emissions of the considered virtual vehicle when compared with the target emission regulations. Full article
(This article belongs to the Special Issue Numerical Computation and Nonlinear Dynamical Systems)
Show Figures

Figure 1

Open AccessArticle
A Versatile Integral in Physics and Astronomy and Fox’s H-Function
Axioms 2019, 8(4), 122; https://doi.org/10.3390/axioms8040122 - 01 Nov 2019
Cited by 2 | Viewed by 630
Abstract
This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in physics and astronomy. Nuclear reaction rate probability integrals in nuclear physics, Krätzel integrals in applied mathematical analysis, inverse Gaussian distributions, generalized type-1, type-2, [...] Read more.
This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in physics and astronomy. Nuclear reaction rate probability integrals in nuclear physics, Krätzel integrals in applied mathematical analysis, inverse Gaussian distributions, generalized type-1, type-2, and gamma families of distributions in statistical distribution theory, Tsallis statistics and Beck–Cohen superstatistics in statistical mechanics, and Mathai’s pathway model are all shown to be connected to the integral under consideration. Representations of the integral in terms of Fox’s H-function are pointed out. Full article
(This article belongs to the Special Issue Special Functions and Their Applications)
Open AccessArticle
Best Proximity Points for Monotone Relatively Nonexpansive Mappings in Ordered Banach Spaces
Axioms 2019, 8(4), 121; https://doi.org/10.3390/axioms8040121 - 01 Nov 2019
Viewed by 656
Abstract
In this paper, we give sufficient conditions to ensure the existence of the best proximity point of monotone relatively nonexpansive mappings defined on partially ordered Banach spaces. An example is given to illustrate our results. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Optimization with Applications)
Open AccessReview
A Comprehensive Survey on Parallel Submanifolds in Riemannian and Pseudo-Riemannian Manifolds
Axioms 2019, 8(4), 120; https://doi.org/10.3390/axioms8040120 - 30 Oct 2019
Viewed by 735
Abstract
A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden–Bortolotti connection. From submanifold point of view, parallel submanifolds are the simplest Riemannian submanifolds next to totally geodesic ones. [...] Read more.
A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden–Bortolotti connection. From submanifold point of view, parallel submanifolds are the simplest Riemannian submanifolds next to totally geodesic ones. Parallel submanifolds form an important class of Riemannian submanifolds since extrinsic invariants of a parallel submanifold do not vary from point to point. In this paper, we provide a comprehensive survey on this important class of submanifolds. Full article
(This article belongs to the Special Issue Geometric Analysis and Mathematical Physics)
Open AccessArticle
Numerical Solutions of Coupled Burgers’ Equations
Axioms 2019, 8(4), 119; https://doi.org/10.3390/axioms8040119 - 23 Oct 2019
Cited by 15 | Viewed by 1466
Abstract
In this article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers’ equations. These modifications are made with the help of auxiliary parameters to speed up the convergence rate of the series solutions. Three numerical test problems [...] Read more.
In this article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers’ equations. These modifications are made with the help of auxiliary parameters to speed up the convergence rate of the series solutions. Three numerical test problems are given to judge the behavior of the modified algorithms, and error norms are used to evaluate the accuracy of the method. Numerical simulations are carried out for different values of parameters. The results are also compared with the existing methods in the literature. Full article
Show Figures

Graphical abstract

Open AccessArticle
Hybrid Deduction–Refutation Systems
Axioms 2019, 8(4), 118; https://doi.org/10.3390/axioms8040118 - 21 Oct 2019
Cited by 2 | Viewed by 704
Abstract
Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. [...] Read more.
Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system of natural deduction for classical propositional logic, for which I show soundness and completeness for both deductions and refutations. Full article
Open AccessArticle
On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order
Axioms 2019, 8(4), 117; https://doi.org/10.3390/axioms8040117 - 18 Oct 2019
Cited by 1 | Viewed by 797
Abstract
The present paper is devoted to the spectral analysis of operators induced by fractional differential equations and boundary conditions of Sturm-Liouville type. It should be noted that these operators are non-self-adjoint. The spectral structure of such operators has been insufficiently explored. In particular, [...] Read more.
The present paper is devoted to the spectral analysis of operators induced by fractional differential equations and boundary conditions of Sturm-Liouville type. It should be noted that these operators are non-self-adjoint. The spectral structure of such operators has been insufficiently explored. In particular, a study of the completeness of systems of eigenfunctions and associated functions has begun relatively recently. In this paper, the completeness of the system of eigenfunctions and associated functions of one class of non-self-adjoint integral operators corresponding boundary value problems for fractional differential equations is established. The proof is based on the well-known Theorem of M.S. Livshits on the spectral decomposition of linear non-self-adjoint operators, as well as on the sectoriality of the fractional differentiation operator. The results of Dzhrbashian-Nersesian on the asymptotics of the zeros of the Mittag-Leffler function are used. Full article
Open AccessReview
A Study Concerning Soft Computing Approaches for Stock Price Forecasting
Axioms 2019, 8(4), 116; https://doi.org/10.3390/axioms8040116 - 18 Oct 2019
Cited by 2 | Viewed by 717
Abstract
Financial time-series are well known for their non-linearity and non-stationarity nature. The application of conventional econometric models in prediction can incur significant errors. The fast advancement of soft computing techniques provides an alternative approach for estimating and forecasting volatile stock prices. Soft computing [...] Read more.
Financial time-series are well known for their non-linearity and non-stationarity nature. The application of conventional econometric models in prediction can incur significant errors. The fast advancement of soft computing techniques provides an alternative approach for estimating and forecasting volatile stock prices. Soft computing approaches exploit tolerance for imprecision, uncertainty, and partial truth to progressively and adaptively solve practical problems. In this study, a comprehensive review of latest soft computing tools is given. Then, examples incorporating a series of machine learning models, including both single and hybrid models, to predict prices of two representative indexes and one stock in Hong Kong’s market are undertaken. The prediction performances of different models are evaluated and compared. The effects of the training sample size and stock patterns (viz. momentum and mean reversion) on model prediction are also investigated. Results indicate that artificial neural network (ANN)-based models yield the highest prediction accuracy. It was also found that the determination of optimal training sample size should take the pattern and volatility of stocks into consideration. Large prediction errors could be incurred when stocks exhibit a transition between mean reversion and momentum trend. Full article
(This article belongs to the Special Issue Softcomputing: Theories and Applications)
Show Figures

Figure 1

Open AccessArticle
Deduction in Non-Fregean Propositional Logic SCI
Axioms 2019, 8(4), 115; https://doi.org/10.3390/axioms8040115 - 17 Oct 2019
Cited by 2 | Viewed by 740
Abstract
We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI. The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that [...] Read more.
We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI . The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side, SCI is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for SCI known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for SCI and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper. Full article
Show Figures

Figure 1

Open AccessArticle
Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity
Axioms 2019, 8(4), 114; https://doi.org/10.3390/axioms8040114 - 14 Oct 2019
Cited by 3 | Viewed by 775
Abstract
We continue the presentation of new results in the calculus for interval-valued functions of a single real variable. We start here with the results presented in part I of this paper, namely, a general setting of partial orders in the space of compact [...] Read more.
We continue the presentation of new results in the calculus for interval-valued functions of a single real variable. We start here with the results presented in part I of this paper, namely, a general setting of partial orders in the space of compact intervals (in midpoint-radius representation) and basic results on convergence and limits, continuity, gH-differentiability, and monotonicity. We define different types of (local) minimal and maximal points and develop the basic theory for their characterization. We then consider some interesting connections with applied geometry of curves and the convexity of interval-valued functions is introduced and analyzed in detail. Further, the periodicity of interval-valued functions is described and analyzed. Several examples and pictures accompany the presentation. Full article
Show Figures

Figure 1

Open AccessArticle
Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable. Part I: Partial Orders, gH-Derivative, Monotonicity
Axioms 2019, 8(4), 113; https://doi.org/10.3390/axioms8040113 - 14 Oct 2019
Cited by 4 | Viewed by 687
Abstract
We present new results in interval analysis (IA) and in the calculus for interval-valued functions of a single real variable. Starting with a recently proposed comparison index, we develop a new general setting for partial order in the (semi linear) space of compact [...] Read more.
We present new results in interval analysis (IA) and in the calculus for interval-valued functions of a single real variable. Starting with a recently proposed comparison index, we develop a new general setting for partial order in the (semi linear) space of compact real intervals and we apply corresponding concepts for the analysis and calculus of interval-valued functions. We adopt extensively the midpoint-radius representation of intervals in the real half-plane and show its usefulness in calculus. Concepts related to convergence and limits, continuity, gH-differentiability and monotonicity of interval-valued functions are introduced and analyzed in detail. Graphical examples and pictures accompany the presentation. A companion Part II of the paper will present additional properties (max and min points, convexity and periodicity). Full article
Show Figures

Figure 1

Open AccessArticle
Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function
Axioms 2019, 8(4), 112; https://doi.org/10.3390/axioms8040112 - 11 Oct 2019
Cited by 3 | Viewed by 643
Abstract
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new families, but also derive many new [...] Read more.
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new families, but also derive many new identities, relations, derivative formulas, and combinatorial sums with the inclusion of binomials coefficients, falling factorial, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), the Poisson–Charlier polynomials, combinatorial numbers and polynomials, the Bersntein basis functions, and the probability distribution functions. Furthermore, by applying the p-adic integrals and Riemann integral, we obtain some combinatorial sums including the binomial coefficients, falling factorial, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), and the Cauchy numbers (or the Bernoulli numbers of the second kind). Finally, we give some remarks and observations on our results related to some probability distributions such as the binomial distribution and the Poisson distribution. Full article
Open AccessArticle
Approximation Properties of an Extended Family of the Szász–Mirakjan Beta-Type Operators
Axioms 2019, 8(4), 111; https://doi.org/10.3390/axioms8040111 - 10 Oct 2019
Cited by 4 | Viewed by 641
Abstract
Approximation and some other basic properties of various linear and nonlinear operators are potentially useful in many different areas of researches in the mathematical, physical, and engineering sciences. Motivated essentially by this aspect of approximation theory, our present study systematically investigates the approximation [...] Read more.
Approximation and some other basic properties of various linear and nonlinear operators are potentially useful in many different areas of researches in the mathematical, physical, and engineering sciences. Motivated essentially by this aspect of approximation theory, our present study systematically investigates the approximation and other associated properties of a class of the Szász-Mirakjan-type operators, which are introduced here by using an extension of the familiar Beta function. We propose to establish moments of these extended Szász-Mirakjan Beta-type operators and estimate various convergence results with the help of the second modulus of smoothness and the classical modulus of continuity. We also investigate convergence via functions which belong to the Lipschitz class. Finally, we prove a Voronovskaja-type approximation theorem for the extended Szász-Mirakjan Beta-type operators. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications II) Printed Edition available
Open AccessArticle
A New Approach to the Interpolative Contractions
Axioms 2019, 8(4), 110; https://doi.org/10.3390/axioms8040110 - 10 Oct 2019
Cited by 4 | Viewed by 628
Abstract
We propose a refinement in the interpolative approach in fixed-point theory. In particular, using this method, we prove the existence of fixed points and common fixed points for Kannan-type contractions and provide examples to support our results. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Topics) Printed Edition available
Previous Issue
Next Issue
Back to TopTop