Journal Menu

E-Mail Alert

Journal Browser

Highly Accessed

Latest Books

Mathematics — Open Access Journal

Mathematics (ISSN 2227-7390) is a peer-reviewed open access journal which provides an advanced forum for studies related to mathematics, and is published monthly online by MDPI.

Open Access - free for readers, with article processing charges (APC) paid by authors or their institutions.
High visibility: Indexed in the Science Citation Indexed Expanded - SCIE (Web of Science) from Vol. 4 (2016), Scopus from Vol. 5 (2017) and Zentralblatt MATH from Vol. 3 (2015).
Rapid publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 22 days after submission; acceptance to publication is undertaken in 7.6 days (median values for papers published in the first six months of 2018).
Recognition of reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.

Full Imprint Information | Download Journal Flyer

Latest Articles

Open AccessArticle

Fractional Modeling for Quantitative Inversion of Soil-Available Phosphorus Content

by Chengbiao Fu, Heigang Xiong and Anhong Tian

Mathematics 2018, 6(12), 330; https://doi.org/10.3390/math6120330 (registering DOI) - 14 December 2018

Abstract

[...] Read more.

The study of field spectra based on fractional-order differentials has rarely been reported, and traditional integer-order differentials only perform the derivative calculation for 1st-order or 2nd-order spectrum signals, ignoring the spectral transformation details between 0th-order to 1st-order and 1st-order to 2nd-order, resulting in the problem of low-prediction accuracy. In this paper, a spectral quantitative analysis model of soil-available phosphorus content based on a fractional-order differential is proposed. Firstly, a fractional-order differential was used to perform a derivative calculation of original spectral data from 0th-order to 2nd-order using 0.2-order intervals, to obtain 11 fractional-order spectrum data. Afterwards, seven bands with absolute correlation coefficient greater than 0.5 were selected as sensitive bands. Finally, a stepwise multiple linear regression algorithm was used to establish a spectral estimation model of soil-available phosphorus content under different orders, then the prediction effect of the model under different orders was compared and analyzed. Simulation results show that the best order for a soil-available phosphorus content regression model is a 0.6 fractional-order, the coefficient of determination (), root mean square error (RMSE), and ratio of performance to deviation (RPD) of the best model are 0.7888, 3.348878, and 2.001142, respectively. Since the RPD value is greater than 2, the optimal fractional model established in this study has good quantitative predictive ability for soil-available phosphorus content. Full article

Open AccessArticle

Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials

by Yuan He, Serkan Araci, Hari M. Srivastava and Mahmoud Abdel-Aty

Mathematics 2018, 6(12), 329; https://doi.org/10.3390/math6120329 (registering DOI) - 14 December 2018

Abstract

In this paper, we present a systematic and unified investigation for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. By applying the generating-function methods and summation-transform techniques, we establish some higher-order convolutions for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the

[...] Read more.

Open AccessArticle

Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

by Yanli Ma, Jia-Bao Liu and Haixia Li

Mathematics 2018, 6(12), 328; https://doi.org/10.3390/math6120328 (registering DOI) - 14 December 2018

Abstract

In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number

R_{0}

, which

[...] Read more.

R_{0}

, which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when

R_{0} < 1

, and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when

R_{0} > 1

. Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when

R_{0} > 1

. Finally, some numerical simulations are presented to illustrate the analysis results. Full article

► Figures

Figure 1

Open AccessArticle

Symmetric Radial Basis Function Method for Simulation of Elliptic Partial Differential Equations

by Phatiphat Thounthong, Muhammad Nawaz Khan, Iltaf Hussain, Imtiaz Ahmad and Poom Kumam

Mathematics 2018, 6(12), 327; https://doi.org/10.3390/math6120327 - 14 December 2018

Abstract

[...] Read more.

In this paper, the symmetric radial basis function method is utilized for the numerical solution of two- and three-dimensional elliptic PDEs. Numerical results are obtained by using a set of uniform or random points. Numerical tests are accomplished to demonstrate the efficacy and accuracy of the method on both regular and irregular domains. Furthermore, the proposed method is tested for the solution of elliptic PDE in the case of various frequencies. Full article

► Figures

Figure 1

Open AccessArticle

A Parameter-Based Ostrowski–Grüss Type Inequalities with Multiple Points for Derivatives Bounded by Functions on Time Scales

by Seth Kermausuor and Eze R. Nwaeze

Mathematics 2018, 6(12), 326; https://doi.org/10.3390/math6120326 - 14 December 2018

Abstract

[...] Read more.

In this paper, we present some Ostrowski–Grüss-type inequalities on time scales for functions whose derivatives are bounded by functions for k points via a parameter. The 2D versions of these inequalities are also presented. Our results generalize some of the results in the literature. As a by-product, we apply our results to the continuous and discrete calculus to obtain some interesting inequalities in this direction. Full article

Open AccessArticle

A Model and an Algorithm for a Large-Scale Sustainable Supplier Selection and Order Allocation Problem

by Jong Soo Kim, Eunhee Jeon, Jiseong Noh and Jun Hyeong Park

Mathematics 2018, 6(12), 325; https://doi.org/10.3390/math6120325 - 13 December 2018

Abstract

[...] Read more.

We consider a buyer’s decision problem of sustainable supplier selection and order allocation (SSS & OA) among multiple heterogeneous suppliers who sell multiple types of items. The buyer periodically orders items from chosen suppliers to refill inventory to preset levels. Each supplier is differentiated from others by the types of items supplied, selling price, and order-related costs, such as transportation cost. Each supplier also has a preset requirement for minimum order quantity or minimum purchase amount. In the beginning of each period, the buyer constructs an SSS & OA plan considering various information from both parties. The buyer’s planning problem is formulated as a mathematical model, and an efficient algorithm to solve larger instances of the problem is developed. The algorithm is designed to take advantage of the branch-and-bound method, and the special structure of the model. We perform computer experiments to test the accuracy of the proposed algorithm. The test result confirmed that the algorithm can find a near-optimal solution with only 0.82 percent deviation on average. We also observed that the use of the algorithm can increase solvable problem size by about 2.4 times. Full article

Open AccessArticle

New Existence of Fixed Point Results in Generalized Pseudodistance Functions with Its Application to Differential Equations

by Sujitra Sanhan, Winate Sanhan and Chirasak Mongkolkeha

Mathematics 2018, 6(12), 324; https://doi.org/10.3390/math6120324 - 12 December 2018

Abstract

The purpose of this article is to prove some existences of fixed point theorems for generalized

F

-contraction mapping in metric spaces by using the concept of generalized pseudodistance. In addition, we give some examples to illustrate our main results. As the application,

[...] Read more.

The purpose of this article is to prove some existences of fixed point theorems for generalized

F

-contraction mapping in metric spaces by using the concept of generalized pseudodistance. In addition, we give some examples to illustrate our main results. As the application, the existence of the solution of the second order differential equation is given. Full article

► Figures

Figure 1

Open AccessArticle

Soft Neutrosophic Modules

by Mikail Bal and Necati Olgun

Mathematics 2018, 6(12), 323; https://doi.org/10.3390/math6120323 - 12 December 2018

Abstract

[...] Read more.

In this study, for the first time, we study some basic definitions of soft neutrosophic modules in algebra being generalized and its several related properties, structural characteristics are investigated with suitable examples. In this paper, we utilized neutrosophic soft sets and neutrosophic modules. As a result, we defined soft neutrosophic modules. After weak soft neutrosophic modules and strong soft neutrosophic modules are described and illustrated by examples. Finally soft neutrosophic module homomorphism is defined and soft neutrosophic module isomorphism is explained. Full article

Open AccessArticle

Coopetitive Games for Management of Marine Transportation Activity: A Study Case

by Alessia Donato, David Carfì and Beatrice Blandina

Mathematics 2018, 6(12), 322; https://doi.org/10.3390/math6120322 - 12 December 2018

Abstract

[...] Read more.

In this paper, we will use coopetitive game theory to analyze a case of real coopetition among port companies, for what concerns loading and unloading of goods, within a competitive management scenario of marine transportation activities. Our research consists of the analysis of a study case involving coopetition between two real companies from which we obtained the financial and contractual data allowing us to define two modeling payoff functions, both of them based on real agreements and tariffs. We recognize actual coopetition and an asymmetric R&D alliance in this type of agreement, where a bigger enterprise deals with a smaller competitor, in order to capture more value from their activities. In particular, our model will show a precise coopetitive bi-dimensional trajectory within which we suggest, after a quantitative analysis, different kinds of solutions: the purely coopetitive solution, a Kalai-Smorodinsky solution and, finally, a transferable utility Kalai-Smorodinsky solution. Our methods provide specific strategy procedures determining win-win solutions for both. Full article

► Figures

Figure 1

Open AccessArticle

Serret-Frenet Frame and Curvatures of Bézier Curves

by Esra Erkan and Salim Yüce

Mathematics 2018, 6(12), 321; https://doi.org/10.3390/math6120321 (registering DOI) - 12 December 2018

Abstract

The aim of this study is to view the role of Bézier curves in both the Euclidean plane

E^{2}

and Euclidean space

E^{3}

with the help of the fundamental algorithm which is commonly used in Computer Science and Applied Mathematics and

[...] Read more.

The aim of this study is to view the role of Bézier curves in both the Euclidean plane

E^{2}

and Euclidean space

E^{3}

with the help of the fundamental algorithm which is commonly used in Computer Science and Applied Mathematics and without this algorithm. The Serret-Frenet elements of non-unit speed curves in the Euclidean plane

E^{2}

and Euclidean space

E^{3}

are given by Gray et al. in 2016. We used these formulas to find Serret-Frenet elements of planar Bézier curve at the end points and for every parameter t. Moreover, we reconstruct these elements for a planar Bézier curve, which is defined by the help of the algorithm based on intermediate points. Finally, in the literature, the spatial Bézier curve only mentioned at the end points, so we improve these elements for all parameters t. Additionally, we calculate these elements for all parameters t using algorithm above mentioned for spatial Bézier curve. Full article

► Figures

Figure 1

Open AccessArticle

Double Controlled Metric Type Spaces and Some Fixed Point Results

by Thabet Abdeljawad, Nabil Mlaiki, Hassen Aydi and Nizar Souayah

Mathematics 2018, 6(12), 320; https://doi.org/10.3390/math6120320 - 12 December 2018

Abstract

In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions

α (x, y)

and

μ (x, y)

on the right-hand side of the

b -

triangle

[...] Read more.

In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions

α (x, y)

and

μ (x, y)

on the right-hand side of the

b -

triangle inequality, that is,

d (x, y) \leq α (x, z) d (x, z) + μ (z, y) d (z, y), for all x, y, z \in X .

Some examples of a double controlled metric type space by two incomparable functions, which is not a controlled metric type by one of the given functions, are presented. We also provide some fixed point results involving Banach type, Kannan type and

ϕ

-nonlinear type contractions in the setting of double controlled metric type spaces. Full article

Open AccessArticle

Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample

by Xuehua Hu and Wenhao Gui

Mathematics 2018, 6(12), 319; https://doi.org/10.3390/math6120319 - 11 December 2018

Abstract

[...] Read more.

In this paper, first we consider the maximum likelihood estimators for two unknown parameters, reliability and hazard functions of the generalized Pareto distribution under progressively Type II censored sample. Next, we discuss the asymptotic confidence intervals for two unknown parameters, reliability and hazard functions by using the delta method. Then, based on the bootstrap algorithm, we obtain another two pairs of approximate confidence intervals. Furthermore, by applying the Markov Chain Monte Carlo techniques, we derive the Bayesian estimates of the two unknown parameters, reliability and hazard functions under various balanced loss functions and the corresponding confidence intervals. A simulation study was conducted to compare the performances of the proposed estimators. A real dataset analysis was carried out to illustrate the proposed methods. Full article

Open AccessArticle

Classification Theorems of Ruled Surfaces in Minkowski Three-Space

by Miekyung Choi and Young Ho Kim

Mathematics 2018, 6(12), 318; https://doi.org/10.3390/math6120318 - 11 December 2018

Abstract

By generalizing the notion of the pointwise 1-type Gauss map, the generalized 1-type Gauss map has been recently introduced. Without any assumption, we classified all possible ruled surfaces with the generalized 1-type Gauss map in a 3-dimensional Minkowski space. In particular, null scrolls

[...] Read more.

Open AccessArticle

Statistical Analysis of Maximally Similar Sets in Ecological Research

by David W. Roberts

Mathematics 2018, 6(12), 317; https://doi.org/10.3390/math6120317 - 11 December 2018

Abstract

[...] Read more.

Maximally similar sets (MSSs) are sets of elements that share a neighborhood in a high-dimensional space defined by a symmetric, reflexive similarity relation. Each element of the universe is employed as the kernel of a neighborhood of a given size (number of members), and elements are added to the neighborhood in order of similarity to the current members of the set until the desired neighborhood size is achieved. The set of neighborhoods is then reduced to the set of unique, maximally similar sets by eliminating all sets that are permutations of an existing set. Subsequently, the within-MSS variability of candidate explanatory variables associated with the elements is compared to random sets of the same size to estimate the probability of obtaining variability as low as was observed. Explanatory variables can be compared for effect size by the rank order of within-MSS variability and random set variability, correcting for statistical power as necessary. The analyses performed identify constraints, as opposed to determinants, in the triangular distribution of pair-wise element similarity. In the example given here, the variability in spring temperature, summer temperature, and the growing degree days of forest vegetation sample units shows the greatest constraint on forest composition of a large set of candidate environmental variables. Full article

► Figures

Figure 1

Open AccessReview

On the Riemann Function

by Peter J. Zeitsch

Mathematics 2018, 6(12), 316; https://doi.org/10.3390/math6120316 - 10 December 2018

Abstract

[...] Read more.

Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E.T. Copson in 1958. This study extends that work. Firstly, three solution methods were overlooked in Copson’s original paper. Secondly, several new approaches for finding Riemann functions have been developed since 1958. Those techniques are included here and placed in the context of Copson’s original study. There are also numerous equivalences between Riemann functions that have not previously been identified in the literature. Those links are clarified here by showing that many known Riemann functions are often equivalent due to the governing equation admitting a symmetry algebra isomorphic to

S L (2, R)

. Alternatively, the equation admits a Lie-Bäcklund symmetry algebra. Combining the results from several methods, a new class of Riemann functions is then derived which admits no symmetries whatsoever. Full article

► Figures

Figure 1

Open AccessReview

Scaling Laws in the Fine-Scale Structure of Range Margins

by Beáta Oborny

Mathematics 2018, 6(12), 315; https://doi.org/10.3390/math6120315 - 9 December 2018

Abstract

[...] Read more.

Margins of the geographic distributions of species are important regions in terms of ecological and evolutionary processes, including the species’ response to climate change. This paper reviews some spatially explicit metapopulation models of range margins across environmental gradients (e.g., across latitudes or altitudes). These models share some robust results, which allow for generalizations within a broad variety of species and environments: (1) sharp edges can emerge even across relatively smooth environmental gradients; (2) intraspecific competition combined with dispersal limitation is a sufficient condition for the sharpening; (3) at the margin, the “mainland” of continuous occurrence splits into “islands”. Computer simulations pointed out some characteristic scaling laws in the size distribution of the islands, and in the structure of the hull of the mainland. The hull is a fractal with a dimension 7/4. Its width and length scale with the gradient according to characteristic scaling laws (with exponents 3/7 and 4/7, respectively). These general features follow from a second-order phase transition from a connected to a fragmented state. The results contribute to understanding the origin of vegetation zones and the spatial pattern of ecotones. Full article

► Figures

Figure 1

Open AccessArticle

The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition

by Alessandra Bernardi, Enrico Carlini, Maria Virginia Catalisano, Alessandro Gimigliano and Alessandro Oneto

Mathematics 2018, 6(12), 314; https://doi.org/10.3390/math6120314 - 8 December 2018

Abstract

[...] Read more.

We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety X. The case we concentrate on is when X is a Veronese variety, a Grassmannian or a Segre variety. Not only these varieties are among the ones that have been most classically studied, but a strong motivation in taking them into consideration is the fact that they parameterize, respectively, symmetric, skew-symmetric and general tensors, which are decomposable, and their secant varieties give a stratification of tensors via tensor rank. We collect here most of the known results and the open problems on this fascinating subject. Full article

Open AccessFeature PaperArticle

A Note on the Classical Gauss Sums

by Tingting Wang and Guohui Chen

Mathematics 2018, 6(12), 313; https://doi.org/10.3390/math6120313 - 8 December 2018

Abstract

The main purpose of this paper is to study the computational problem of one kind rational polynomials of the classical Gauss sums, and using the purely algebraic methods and the properties of the character sums

mod p

( a prime with

p \equiv

[...] Read more.

mod p

( a prime with

p \equiv 1 mod 12

) to give an exact evaluation formula for it. Full article

Open AccessArticle

On the Generalization of a Class of Harmonic Univalent Functions Defined by Differential Operator

by Aqeel Ketab AL-khafaji, Waggas Galib Atshan and Salwa Salman Abed

Mathematics 2018, 6(12), 312; https://doi.org/10.3390/math6120312 - 7 December 2018

Abstract

In this article, a new class of harmonic univalent functions, defined by the differential operator, is introduced. Some geometric properties, like, coefficient estimates, extreme points, convex combination and convolution (Hadamard product) are obtained. Full article

Open AccessArticle

A Lichnerowicz–Obata–Cheng Type Theorem on Finsler Manifolds

by Songting Yin and Pan Zhang

Mathematics 2018, 6(12), 311; https://doi.org/10.3390/math6120311 - 7 December 2018

Abstract

Let

(M, F, d μ)

[...] Read more.

Let

(M, F, d μ)

be a Finsler manifold with the Ricci curvature bounded below by a positive number and constant S-curvature. We prove that, if the first eigenvalue of the Finsler–Laplacian attains its lower bound, then M is isometric to a Finsler sphere. Moreover, we establish a comparison result on the Hessian trace of the distance function. Full article

» More Articles

Submit to Mathematics Review for Mathematics