Next Issue
Previous Issue

Table of Contents

Mathematics, Volume 6, Issue 11 (November 2018)

  • 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.
Cover Story (view full-size image) The power means (Hölder means and Lehmer means) of a number of variables have traditionally been [...] Read more.
View options order results:
result details:
Displaying articles 1-58
Export citation of selected articles as:
Open AccessArticle Universe of Discourse and Existence
Mathematics 2018, 6(11), 272; https://doi.org/10.3390/math6110272
Received: 25 August 2018 / Revised: 28 September 2018 / Accepted: 17 November 2018 / Published: 21 November 2018
Viewed by 158 | PDF Full-text (311 KB) | HTML Full-text | XML Full-text
Abstract
There is a fairly widespread belief that the problem of existence is not an essential issue for logic. Logic, though formal, must deal with the problem of existence. However, logic should be limited to describing “formal existence” or “existence of
[...] Read more.
There is a fairly widespread belief that the problem of existence is not an essential issue for logic. Logic, though formal, must deal with the problem of existence. However, logic should be limited to describing “formal existence” or “existence of a formal system”. However, the logical problem of existence and how to treat and resolve this problem differ completely from the corresponding metaphysical problem. It is possible to deduce that formal existence is nothing other than belonging to the universe of discourse, so proposing a solution to the logical problem of existence in an epistemological, rather than a metaphysical, context. In this paper, we conclude, from a formal point of view, no universe of discourse is given in advance; any universe of discourse that satisfies the necessary conditions can be used. The extended epistemological belief that there is a universe of discourse defined rigorously, which would be the true and should be “the universe of discourse of logic”, cannot be justified. Full article
Open AccessArticle The Extremal Graphs of Some Topological Indices with Given Vertex k-Partiteness
Mathematics 2018, 6(11), 271; https://doi.org/10.3390/math6110271
Received: 12 October 2018 / Revised: 16 November 2018 / Accepted: 16 November 2018 / Published: 21 November 2018
Viewed by 160 | PDF Full-text (261 KB) | HTML Full-text | XML Full-text
Abstract
The vertex k-partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb index, the
[...] Read more.
The vertex k-partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb index, the general Laplacian-energy-like invariant, the general zeroth-order Randić index, and the modified-Wiener index among graphs of order n with vertex k-partiteness not more than m . Full article
(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)
Open AccessArticle Efficient Solutions of Interval Programming Problems with Inexact Parameters and Second Order Cone Constraints
Mathematics 2018, 6(11), 270; https://doi.org/10.3390/math6110270
Received: 1 October 2018 / Revised: 5 November 2018 / Accepted: 13 November 2018 / Published: 20 November 2018
Viewed by 181 | PDF Full-text (639 KB) | HTML Full-text | XML Full-text
Abstract
In this article, a methodology is developed to solve an interval and a fractional interval programming problem by converting into a non-interval form for second order cone constraints, with the objective function and constraints being interval valued functions. We investigate the parametric and
[...] Read more.
In this article, a methodology is developed to solve an interval and a fractional interval programming problem by converting into a non-interval form for second order cone constraints, with the objective function and constraints being interval valued functions. We investigate the parametric and non-parametric forms of the interval valued functions along with their convexity properties. Two approaches are developed to obtain efficient and properly efficient solutions. Furthermore, the efficient solutions or Pareto optimal solutions of fractional and non-fractional programming problems over R + n { 0 } are also discussed. The main idea of the present article is to introduce a new concept for efficiency, called efficient space, caused by the lower and upper bounds of the respective intervals of the objective function which are shown in different figures. Finally, some numerical examples are worked through to illustrate the methodology and affirm the validity of the obtained results. Full article
Figures

Figure 1

Open AccessArticle Identifying the Informational/Signal Dimension in Principal Component Analysis
Mathematics 2018, 6(11), 269; https://doi.org/10.3390/math6110269
Received: 23 October 2018 / Revised: 11 November 2018 / Accepted: 14 November 2018 / Published: 20 November 2018
Viewed by 187 | PDF Full-text (1161 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
The identification of a reduced dimensional representation of the data is among the main issues of exploratory multidimensional data analysis and several solutions had been proposed in the literature according to the method. Principal Component Analysis (PCA) is the method that
[...] Read more.
The identification of a reduced dimensional representation of the data is among the main issues of exploratory multidimensional data analysis and several solutions had been proposed in the literature according to the method. Principal Component Analysis (PCA) is the method that has received the largest attention thus far and several identification methods—the so-called stopping rules—have been proposed, giving very different results in practice, and some comparative study has been carried out. Some inconsistencies in the previous studies led us to try to fix the distinction between signal from noise in PCA—and its limits—and propose a new testing method. This consists in the production of simulated data according to a predefined eigenvalues structure, including zero-eigenvalues. From random populations built according to several such structures, reduced-size samples were extracted and to them different levels of random normal noise were added. This controlled introduction of noise allows a clear distinction between expected signal and noise, the latter relegated to the non-zero eigenvalues in the samples corresponding to zero ones in the population. With this new method, we tested the performance of ten different stopping rules. Of every method, for every structure and every noise, both power (the ability to correctly identify the expected dimension) and type-I error (the detection of a dimension composed only by noise) have been measured, by counting the relative frequencies in which the smallest non-zero eigenvalue in the population was recognized as signal in the samples and that in which the largest zero-eigenvalue was recognized as noise, respectively. This way, the behaviour of the examined methods is clear and their comparison/evaluation is possible. The reported results show that both the generalization of the Bartlett’s test by Rencher and the Bootstrap method by Pillar result much better than all others: both are accounted for reasonable power, decreasing with noise, and very good type-I error. Thus, more than the others, these methods deserve being adopted. Full article
(This article belongs to the Special Issue New Paradigms and Trends in Quantitative Ecology)
Figures

Figure 1

Open AccessArticle On Domain of Nörlund Matrix
Mathematics 2018, 6(11), 268; https://doi.org/10.3390/math6110268
Received: 24 October 2018 / Revised: 14 November 2018 / Accepted: 16 November 2018 / Published: 20 November 2018
Viewed by 164 | PDF Full-text (308 KB) | HTML Full-text | XML Full-text
Abstract
In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f
[...] Read more.
In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f0 and f in 2016. Additionally, Tuğ defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in 2017. In this article, we defined new space b s ( N t ) and c s ( N t ) and examined the domain of the Nörlund mean on the bs and cs, which are bounded and convergent series, respectively. We also examined their inclusion relations. We defined the norms over them and investigated whether these new spaces provide conditions of Banach space. Finally, we determined their α-, β-, γ-duals, and characterized their matrix transformations on this space and into this space. Full article
Open AccessArticle Some PPF Dependent Fixed Point Theorems for Generalized α-F-Contractions in Banach Spaces and Applications
Mathematics 2018, 6(11), 267; https://doi.org/10.3390/math6110267
Received: 25 October 2018 / Revised: 14 November 2018 / Accepted: 15 November 2018 / Published: 19 November 2018
Viewed by 154 | PDF Full-text (280 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we introduce the concepts of an α-admissible nonself-mapping, an α-F-contractive nonself-mapping, a weak α-F-contractive nonself-mapping, and a generalized α-F-contractive nonself-mapping and prove some PPF (past-present-future)-dependent fixed point theorems
[...] Read more.
In this paper, we introduce the concepts of an α -admissible nonself-mapping, an α -F-contractive nonself-mapping, a weak α -F-contractive nonself-mapping, and a generalized α -F-contractive nonself-mapping and prove some P P F (past-present-future)-dependent fixed point theorems for the proposed contractive nonself-mappings in certain Razumikhin classes. By using our results, we derive some P P F -dependent fixed point theorems for an α -F-contractive nonself-mapping endowed with a graph or a partial order. Finally, we give some applications to illustrate the main results. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
Open AccessArticle On a Length Problem for Univalent Functions
Mathematics 2018, 6(11), 266; https://doi.org/10.3390/math6110266
Received: 11 October 2018 / Revised: 14 November 2018 / Accepted: 16 November 2018 / Published: 19 November 2018
Viewed by 142 | PDF Full-text (747 KB) | HTML Full-text | XML Full-text
Abstract
Let g be an analytic function with the normalization in the open unit disk. Let L(r) be the length of g({z:|z|=r}). In this paper we present a correspondence
[...] Read more.
Let g be an analytic function with the normalization in the open unit disk. Let L ( r ) be the length of g ( { z : | z | = r } ) . In this paper we present a correspondence between g and L ( r ) for the case when g is not necessary univalent. Furthermore, some other results related to the length of analytic functions are also discussed. Full article
Open AccessArticle Scheduling and Planning in Service Systems with Goal Programming: Literature Review
Mathematics 2018, 6(11), 265; https://doi.org/10.3390/math6110265
Received: 1 November 2018 / Revised: 13 November 2018 / Accepted: 14 November 2018 / Published: 19 November 2018
Viewed by 222 | PDF Full-text (273 KB) | HTML Full-text | XML Full-text
Abstract
Background: People want to be able to evaluate different kinds of information in a good way. There are various methods that they develop in such situations. Among the optimization methods, the goal programming method is often used when there are multiple objectives that
[...] Read more.
Background: People want to be able to evaluate different kinds of information in a good way. There are various methods that they develop in such situations. Among the optimization methods, the goal programming method is often used when there are multiple objectives that decision makers want to accomplish. Because scheduling and planning problems have multiple objectives that are desired to be achieved, the goal programming method helps the researcher in contradictory situations between these goals. Methods: This study includes, examines, and analyzes recent research on service scheduling and planning. In the literature, service scheduling and planning studies have been examined using goal programming method from past to today. Results: The studies are detailed according to the type of goal programming, according to scheduling types, the purpose used in the studies, and the methods integrated with the goal programming. There are 142 studies in Emerald, Science Direct, Jstor, Springer, Taylor and Francis, Google Scholar, etc. databases that are examined in detail. For readers, diversification has been made to facilitate the identification of these studies and a detailed overview has been presented. Conclusion: As a result of the study, studies with the goal programming in the literature have been seen. The readers’ perspectives for planning and scheduling are discussed. Full article
(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)
Open AccessFeature PaperArticle Tsallis Entropy of Fuzzy Dynamical Systems
Mathematics 2018, 6(11), 264; https://doi.org/10.3390/math6110264
Received: 1 November 2018 / Accepted: 14 November 2018 / Published: 18 November 2018
Viewed by 242 | PDF Full-text (360 KB) | HTML Full-text | XML Full-text
Abstract
This article deals with the mathematical modeling of Tsallis entropy in fuzzy dynamical systems. At first, the concepts of Tsallis entropy and Tsallis conditional entropy of order q, where q is a positive real number not equal to 1, of fuzzy partitions
[...] Read more.
This article deals with the mathematical modeling of Tsallis entropy in fuzzy dynamical systems. At first, the concepts of Tsallis entropy and Tsallis conditional entropy of order q , where q is a positive real number not equal to 1, of fuzzy partitions are introduced and their mathematical behavior is described. As an important result, we showed that the Tsallis entropy of fuzzy partitions of order q > 1 satisfies the property of sub-additivity. This property permits the definition of the Tsallis entropy of order q > 1 of a fuzzy dynamical system. It was shown that Tsallis entropy is an invariant under isomorphisms of fuzzy dynamical systems; thus, we acquired a tool for distinguishing some non-isomorphic fuzzy dynamical systems. Finally, we formulated a version of the Kolmogorov–Sinai theorem on generators for the case of the Tsallis entropy of a fuzzy dynamical system. The obtained results extend the results provided by Markechová and Riečan in Entropy, 2016, 18, 157, which are particularized to the case of logical entropy. Full article
Open AccessArticle The Coefficients of Powers of Bazilević Functions
Mathematics 2018, 6(11), 263; https://doi.org/10.3390/math6110263
Received: 30 September 2018 / Revised: 12 November 2018 / Accepted: 13 November 2018 / Published: 18 November 2018
Viewed by 178 | PDF Full-text (280 KB) | HTML Full-text | XML Full-text
Abstract
In the present work, a sharp bound on the modulus of the initial coefficients for powers of strongly Bazilević functions is obtained. As an application of these results, certain conditions are investigated under which the Littlewood-Paley conjecture holds for strongly Bazilević functions for
[...] Read more.
In the present work, a sharp bound on the modulus of the initial coefficients for powers of strongly Bazilević functions is obtained. As an application of these results, certain conditions are investigated under which the Littlewood-Paley conjecture holds for strongly Bazilević functions for large values of the parameters involved therein. Further, sharp estimate on the generalized Fekete-Szegö functional is also derived. Relevant connections of our results with the existing ones are also made. Full article
(This article belongs to the Special Issue Special Functions and Applications)
Open AccessArticle Random Best Proximity Points for α-Admissible Mappings via Simulation Functions
Mathematics 2018, 6(11), 262; https://doi.org/10.3390/math6110262
Received: 29 September 2018 / Revised: 9 November 2018 / Accepted: 9 November 2018 / Published: 18 November 2018
Viewed by 228 | PDF Full-text (771 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we introduce a new concept of random α-proximal admissible and random α-Z-contraction. Then we establish random best proximity point theorems for such mapping in complete separable metric spaces.
[...] Read more.
In this paper, we introduce a new concept of random α -proximal admissible and random α - Z -contraction. Then we establish random best proximity point theorems for such mapping in complete separable metric spaces. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
Open AccessArticle Common Fixed Points for Mappings under Contractive Conditions of (α,β,ψ)-Admissibility Type
Mathematics 2018, 6(11), 261; https://doi.org/10.3390/math6110261
Received: 20 October 2018 / Revised: 11 November 2018 / Accepted: 14 November 2018 / Published: 18 November 2018
Viewed by 218 | PDF Full-text (260 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we introduce the notion of (α,β,ψ)-contraction for a pair of mappings (S,T) defined on a set X. We use our new notion to create and prove a common
[...] Read more.
In this paper, we introduce the notion of ( α , β , ψ ) -contraction for a pair of mappings ( S , T ) defined on a set X. We use our new notion to create and prove a common fixed point theorem for two mappings defined on a metric space ( X , d ) under a set of conditions. Furthermore, we employ our main result to get another new result. Our results are modifications of many existing results in the literature. An example is included in order to show the authenticity of our main result. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
Open AccessArticle Ball Convergence of an Efficient Eighth Order Iterative Method Under Weak Conditions
Mathematics 2018, 6(11), 260; https://doi.org/10.3390/math6110260
Received: 15 October 2018 / Revised: 13 November 2018 / Accepted: 15 November 2018 / Published: 17 November 2018
Viewed by 151 | PDF Full-text (249 KB) | HTML Full-text | XML Full-text
Abstract
The convergence order of numerous iterative methods is obtained using derivatives of a higher order, although these derivatives are not involved in the methods. Therefore, these methods cannot be used to solve equations with functions that do not have such high-order derivatives, since
[...] Read more.
The convergence order of numerous iterative methods is obtained using derivatives of a higher order, although these derivatives are not involved in the methods. Therefore, these methods cannot be used to solve equations with functions that do not have such high-order derivatives, since their convergence is not guaranteed. The convergence in this paper is shown, relying only on the first derivative. That is how we expand the applicability of some popular methods. Full article
(This article belongs to the Special Issue Computational Methods in Analysis and Applications)
Open AccessArticle Inequalities on Sasakian Statistical Manifolds in Terms of Casorati Curvatures
Mathematics 2018, 6(11), 259; https://doi.org/10.3390/math6110259
Received: 13 September 2018 / Revised: 14 November 2018 / Accepted: 15 November 2018 / Published: 17 November 2018
Viewed by 173 | PDF Full-text (248 KB) | HTML Full-text | XML Full-text
Abstract
A statistical structure is considered as a generalization of a pair of a Riemannian metric and its Levi-Civita connection. With a pair of conjugate connections ∇ and * in the Sasakian statistical structure, we provide the normalized scalar curvature which is bounded
[...] Read more.
A statistical structure is considered as a generalization of a pair of a Riemannian metric and its Levi-Civita connection. With a pair of conjugate connections ∇ and * in the Sasakian statistical structure, we provide the normalized scalar curvature which is bounded above from Casorati curvatures on C-totally real (Legendrian and slant) submanifolds of a Sasakian statistical manifold of constant φ -sectional curvature. In addition, we give examples to show that the total space is a sphere. Full article
(This article belongs to the Special Issue Differential Geometry)
Open AccessArticle Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials
Mathematics 2018, 6(11), 258; https://doi.org/10.3390/math6110258
Received: 26 October 2018 / Revised: 12 November 2018 / Accepted: 13 November 2018 / Published: 17 November 2018
Viewed by 171 | PDF Full-text (359 KB) | HTML Full-text | XML Full-text
Abstract
The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of q-Hermite-Appell polynomials such as determinant definitions, q-recurrence relations and q-difference equations
[...] Read more.
The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of q-Hermite-Appell polynomials such as determinant definitions, q-recurrence relations and q-difference equations are established. Examples providing the corresponding results for certain members belonging to this q-Hermite-Appell family are considered. In addition, graphs of certain q-special polynomials are demonstrated using computer experiment. Thereafter, distribution of zeros of these q-special polynomials is displayed. Full article
(This article belongs to the Special Issue Special Functions and Applications)
Figures

Figure 1

Open AccessArticle Strong Convergence Theorems for Fixed Point Problems for Nonexpansive Mappings and Zero Point Problems for Accretive Operators Using Viscosity Implicit Midpoint Rules in Banach Spaces
Mathematics 2018, 6(11), 257; https://doi.org/10.3390/math6110257
Received: 13 October 2018 / Revised: 11 November 2018 / Accepted: 14 November 2018 / Published: 16 November 2018
Viewed by 156 | PDF Full-text (1085 KB) | HTML Full-text | XML Full-text
Abstract
This paper uses the viscosity implicit midpoint rule to find common points of the fixed point set of a nonexpansive mapping and the zero point set of an accretive operator in Banach space. Under certain conditions, this paper obtains the strong convergence results
[...] Read more.
This paper uses the viscosity implicit midpoint rule to find common points of the fixed point set of a nonexpansive mapping and the zero point set of an accretive operator in Banach space. Under certain conditions, this paper obtains the strong convergence results of the proposed algorithm and improves the relevant results of researchers in this field. In the end, this paper gives numerical examples to support the main results. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
Figures

Figure 1

Open AccessArticle Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces
Mathematics 2018, 6(11), 256; https://doi.org/10.3390/math6110256
Received: 23 October 2018 / Revised: 13 November 2018 / Accepted: 14 November 2018 / Published: 16 November 2018
Viewed by 168 | PDF Full-text (237 KB) | HTML Full-text | XML Full-text
Abstract
By giving a counter-example, we point out a gap in the paper by Karapinar (Adv. Theory Nonlinear Anal. Its Appl. 2018, 2, 85–87) where the given fixed point may be not unique and we present the corrected version. We also state the celebrated
[...] Read more.
By giving a counter-example, we point out a gap in the paper by Karapinar (Adv. Theory Nonlinear Anal. Its Appl. 2018, 2, 85–87) where the given fixed point may be not unique and we present the corrected version. We also state the celebrated fixed point theorem of Reich–Rus–Ćirić in the framework of complete partial metric spaces, by taking the interpolation theory into account. Some examples are provided where the main result in papers by Reich (Can. Math. Bull. 1971, 14, 121–124; Boll. Unione Mat. Ital. 1972, 4, 26–42 and Boll. Unione Mat. Ital. 1971, 4, 1–11.) is not applicable. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
Open AccessArticle Interval-Valued Cores and Interval-Valued Dominance Cores of Cooperative Games Endowed with Interval-Valued Payoffs
Mathematics 2018, 6(11), 255; https://doi.org/10.3390/math6110255
Received: 25 October 2018 / Revised: 14 November 2018 / Accepted: 14 November 2018 / Published: 16 November 2018
Viewed by 136 | PDF Full-text (313 KB) | HTML Full-text | XML Full-text
Abstract
Cooperative games endowed with interval-valued payoffs are studied in this paper. Based on the interval-valued payoff and the different types of orderings, we can propose many types of so-called interval-valued cores and interval-valued dominance cores. The main issue of this paper is to
[...] Read more.
Cooperative games endowed with interval-valued payoffs are studied in this paper. Based on the interval-valued payoff and the different types of orderings, we can propose many types of so-called interval-valued cores and interval-valued dominance cores. The main issue of this paper is to establish the equalities of different types of interval-valued cores and interval-valued dominance cores under a mild assumption. Without considering the individual rationality, we also establish the equalities of different types of interval-valued pre-cores and interval-valued dominance pre-cores without any extra assumptions. Full article
Open AccessArticle Rule-Based Production of Mathematical Expressions
Mathematics 2018, 6(11), 254; https://doi.org/10.3390/math6110254
Received: 11 October 2018 / Revised: 9 November 2018 / Accepted: 12 November 2018 / Published: 15 November 2018
Viewed by 203 | PDF Full-text (2299 KB) | HTML Full-text | XML Full-text
Abstract
There are situations in which one needs to write various kinds of mathematical expressions, such as practicing tests and school exams. There is a variety of methods to produce such expressions, but they are usually based on a database. This paper addresses the
[...] Read more.
There are situations in which one needs to write various kinds of mathematical expressions, such as practicing tests and school exams. There is a variety of methods to produce such expressions, but they are usually based on a database. This paper addresses the production of new expressions using the template ones that can be derived from the evaluation process or entered by users. With special limitations on the values of parameters, some templates can be dynamically constructed for the automatic generation of mathematical expressions and represented in the form of classes. For this purpose, a new type of grammar is proposed. This grammar is similar to Context-Free Grammar, but it empowers the producer to gain control over the generation of rules for different expressions. Our work mainly focuses on generating mathematical expressions in a user-oriented way, using a predefined set of templates of production rules. The production of expressions is not completely random, and is based on the defined subject. Full article
Figures

Figure 1

Open AccessArticle Inverse Multiquadratic Functions as the Basis for the Rectangular Collocation Method to Solve the Vibrational Schrödinger Equation
Mathematics 2018, 6(11), 253; https://doi.org/10.3390/math6110253
Received: 28 September 2018 / Revised: 12 November 2018 / Accepted: 13 November 2018 / Published: 15 November 2018
Cited by 1 | Viewed by 202 | PDF Full-text (1067 KB) | HTML Full-text | XML Full-text
Abstract
We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions
[...] Read more.
We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large, and for a range of IMQ exponents. The IMQ functions are; however, advantageous when a small number of functions is used or with a small number of collocation points (e.g., when using square collocation). Full article
(This article belongs to the Special Issue Computational Spectroscopy)
Figures

Figure 1

Open AccessCorrection Correction: Kuniya, T. Stability Analysis of an Age-Structured SIR Epidemic Model with a Reduction Method to ODEs. Mathematics 2018, 6, 147
Mathematics 2018, 6(11), 252; https://doi.org/10.3390/math6110252
Received: 13 November 2018 / Accepted: 14 November 2018 / Published: 15 November 2018
Viewed by 152 | PDF Full-text (160 KB) | HTML Full-text | XML Full-text
Abstract
I have found an error in Equation (17) in my paper [1] [...] Full article
(This article belongs to the Special Issue Applied Analysis of Ordinary Differential Equations)
Open AccessArticle Geometric Construction of Some Lehmer Means
Mathematics 2018, 6(11), 251; https://doi.org/10.3390/math6110251
Received: 2 October 2018 / Revised: 7 November 2018 / Accepted: 8 November 2018 / Published: 14 November 2018
Viewed by 164 | PDF Full-text (1377 KB) | HTML Full-text | XML Full-text
Abstract
The main aim of this paper is to contribute to the recently initiated research concerning geometric constructions of means, where the variables are appearing as line segments. The present study shows that all Lehmer means of two variables for integer power k and
[...] Read more.
The main aim of this paper is to contribute to the recently initiated research concerning geometric constructions of means, where the variables are appearing as line segments. The present study shows that all Lehmer means of two variables for integer power k and for k = m 2 , where m is an integer, can be geometrically constructed, that Lehmer means for power k = 0 , 1 and 2 can be geometrically constructed for any number of variables and that Lehmer means for power k = 1 / 2 and 1 can be geometrically constructed, where the number of variables is n = 2 m and m is a positive integer. Full article
Figures

Figure 1

Open AccessArticle A Generalized Framework for Analyzing Taxonomic, Phylogenetic, and Functional Community Structure Based on Presence–Absence Data
Mathematics 2018, 6(11), 250; https://doi.org/10.3390/math6110250
Received: 17 October 2018 / Revised: 5 November 2018 / Accepted: 6 November 2018 / Published: 12 November 2018
Viewed by 252 | PDF Full-text (1415 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Community structure as summarized by presence–absence data is often evaluated via diversity measures by incorporating taxonomic, phylogenetic and functional information on the constituting species. Most commonly, various dissimilarity coefficients are used to express these aspects simultaneously such that the results are not comparable
[...] Read more.
Community structure as summarized by presence–absence data is often evaluated via diversity measures by incorporating taxonomic, phylogenetic and functional information on the constituting species. Most commonly, various dissimilarity coefficients are used to express these aspects simultaneously such that the results are not comparable due to the lack of common conceptual basis behind index definitions. A new framework is needed which allows such comparisons, thus facilitating evaluation of the importance of the three sources of extra information in relation to conventional species-based representations. We define taxonomic, phylogenetic and functional beta diversity of species assemblages based on the generalized Jaccard dissimilarity index. This coefficient does not give equal weight to species, because traditional site dissimilarities are lowered by taking into account the taxonomic, phylogenetic or functional similarity of differential species in one site to the species in the other. These, together with the traditional, taxon- (species-) based beta diversity are decomposed into two additive fractions, one due to taxonomic, phylogenetic or functional excess and the other to replacement. In addition to numerical results, taxonomic, phylogenetic and functional community structure is visualized by 2D simplex or ternary plots. Redundancy with respect to taxon-based structure is expressed in terms of centroid distances between point clouds in these diagrams. The approach is illustrated by examples coming from vegetation surveys representing different ecological conditions. We found that beta diversity decreases in the following order: taxon-based, taxonomic (Linnaean), phylogenetic and functional. Therefore, we put forward the beta-redundancy hypothesis suggesting that this ordering may be most often the case in ecological communities, and discuss potential reasons and possible exceptions to this supposed rule. Whereas the pattern of change in diversity may be indicative of fundamental features of the particular community being studied, the effect of the choice of functional traits—a more or less subjective element of the framework—remains to be investigated. Full article
(This article belongs to the Special Issue New Paradigms and Trends in Quantitative Ecology)
Figures

Figure 1

Open AccessArticle The Combination Projection Method for Solving Convex Feasibility Problems
Mathematics 2018, 6(11), 249; https://doi.org/10.3390/math6110249
Received: 17 October 2018 / Revised: 4 November 2018 / Accepted: 7 November 2018 / Published: 12 November 2018
Viewed by 169 | PDF Full-text (337 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we propose a new method, which is called the combination projection method (CPM), for solving the convex feasibility problem (CFP) of finding some x*C:=i=1m{xH|c
[...] Read more.
In this paper, we propose a new method, which is called the combination projection method (CPM), for solving the convex feasibility problem (CFP) of finding some x * C : = i = 1 m { x H | c i ( x ) 0 } , where m is a positive integer, H is a real Hilbert space, and { c i } i = 1 m are convex functions defined as H . The key of the CPM is that, for the current iterate x k , the CPM firstly constructs a new level set H k through a convex combination of some of { c i } i = 1 m in an appropriate way, and then updates the new iterate x k + 1 only by using the projection P H k . We also introduce the combination relaxation projection methods (CRPM) to project onto half-spaces to make CPM easily implementable. The simplicity and easy implementation are two advantages of our methods since only one projection is used in each iteration and the projections are also easy to calculate. The weak convergence theorems are proved and the numerical results show the advantages of our methods. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
Figures

Figure 1

Open AccessArticle Bounds of Riemann-Liouville Fractional Integrals in General Form via Convex Functions and Their Applications
Mathematics 2018, 6(11), 248; https://doi.org/10.3390/math6110248
Received: 15 September 2018 / Revised: 6 November 2018 / Accepted: 7 November 2018 / Published: 12 November 2018
Viewed by 159 | PDF Full-text (225 KB) | HTML Full-text | XML Full-text
Abstract
In this article, we establish bounds of sum of the left and right sided Riemann Liouville (RL) fractional integrals and related inequalities in general form. A new and novel approach is followed to obtain these results for general Riemann Liouville (RL) fractional integrals.
[...] Read more.
In this article, we establish bounds of sum of the left and right sided Riemann Liouville (RL) fractional integrals and related inequalities in general form. A new and novel approach is followed to obtain these results for general Riemann Liouville (RL) fractional integrals. Monotonicity and convexity of functions are used with some usual and straight forward inequalities. The presented results are also have connection with some known and already published results. Applications and motivations of presented results are briefly discussed. Full article
Open AccessArticle Seeking for the Maximum Symmetric Rank
Mathematics 2018, 6(11), 247; https://doi.org/10.3390/math6110247
Received: 9 October 2018 / Revised: 2 November 2018 / Accepted: 3 November 2018 / Published: 12 November 2018
Viewed by 134 | PDF Full-text (352 KB) | HTML Full-text | XML Full-text
Abstract
We present the state-of-the-art on maximum symmetric tensor rank, for each given dimension and order. After a general discussion on the interplay between symmetric tensors, polynomials and divided powers, we introduce the technical environment and the methods that have been set up in
[...] Read more.
We present the state-of-the-art on maximum symmetric tensor rank, for each given dimension and order. After a general discussion on the interplay between symmetric tensors, polynomials and divided powers, we introduce the technical environment and the methods that have been set up in recent times to find new lower and upper bounds. Full article
(This article belongs to the Special Issue Decomposability of Tensors)
Open AccessArticle Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator
Mathematics 2018, 6(11), 246; https://doi.org/10.3390/math6110246
Received: 19 September 2018 / Revised: 3 November 2018 / Accepted: 6 November 2018 / Published: 9 November 2018
Viewed by 163 | PDF Full-text (214 KB) | HTML Full-text | XML Full-text
Abstract
Let M be a three-dimensional trans-Sasakian manifold of type (α,β). In this paper, we obtain that the Ricci operator of M is invariant along Reeb flow if and only if M is an α-Sasakian manifold, cosymplectic manifold
[...] Read more.
Let M be a three-dimensional trans-Sasakian manifold of type ( α , β ) . In this paper, we obtain that the Ricci operator of M is invariant along Reeb flow if and only if M is an α -Sasakian manifold, cosymplectic manifold or a space of constant sectional curvature. Applying this, we give a new characterization of proper trans-Sasakian 3-manifolds. Full article
(This article belongs to the Special Issue Differential Geometry)
Open AccessArticle New Numerical Method for Solving Tenth Order Boundary Value Problems
Mathematics 2018, 6(11), 245; https://doi.org/10.3390/math6110245
Received: 21 September 2018 / Revised: 4 November 2018 / Accepted: 5 November 2018 / Published: 8 November 2018
Viewed by 197 | PDF Full-text (241 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied to get approximate solutions of such problems. We obtain some useful reproducing kernel functions to get approximate
[...] Read more.
In this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied to get approximate solutions of such problems. We obtain some useful reproducing kernel functions to get approximate solutions. We obtain very efficient results by this method. We show our numerical results by tables. Full article
Open AccessArticle A New Identity Involving the Chebyshev Polynomials
Mathematics 2018, 6(11), 244; https://doi.org/10.3390/math6110244
Received: 18 October 2018 / Revised: 24 October 2018 / Accepted: 5 November 2018 / Published: 7 November 2018
Viewed by 204 | PDF Full-text (724 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, firstly, we introduced a second order non-linear recursive sequence, then we use this sequence and the combinatorial methods to perform a deep study on the computational problem concerning one kind sums, which includes the Chebyshev polynomials. This makes it possible
[...] Read more.
In this paper, firstly, we introduced a second order non-linear recursive sequence, then we use this sequence and the combinatorial methods to perform a deep study on the computational problem concerning one kind sums, which includes the Chebyshev polynomials. This makes it possible to simplify a class of complex computations involving the second type Chebyshev polynomials into a very simple problem. Finally, we give a new and interesting identity for it. Full article
Open AccessArticle Edge Version of Metric Dimension and Doubly Resolving Sets of the Necklace Graph
Mathematics 2018, 6(11), 243; https://doi.org/10.3390/math6110243
Received: 23 September 2018 / Revised: 27 October 2018 / Accepted: 29 October 2018 / Published: 7 November 2018
Viewed by 213 | PDF Full-text (297 KB) | HTML Full-text | XML Full-text
Abstract
Consider an undirected and connected graph G=(VG,EG), where VG and EG represent the set of vertices and the set of edges respectively. The concept of edge version of metric dimension and doubly
[...] Read more.
Consider an undirected and connected graph G = ( V G , E G ) , where V G and E G represent the set of vertices and the set of edges respectively. The concept of edge version of metric dimension and doubly resolving sets is based on the distances of edges in a graph. In this paper, we find the edge version of metric dimension and doubly resolving sets for the necklace graph. Full article
(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)
Figures

Figure 1

Back to Top