Mathematics

17 pages, 1083 KiB

Open AccessArticle

The Relation between the Probability of Collision-Free Broadcast Transmission in a Wireless Network and the Stirling Number of the Second Kind

by Prakash Veeraraghavan, Golnar Khomami and Fernando Perez Fontan

Mathematics 2018, 6(7), 127; https://doi.org/10.3390/math6070127 - 21 Jul 2018

Cited by 3 | Viewed by 3346

Abstract

The broadcast performance of the 802.11 wireless protocol depends on several factors. One of the important factor is the number of nodes simultaneously contending for the shared channel. The Medium Access Control (MAC) technique of 802.11 is called the Distributed Coordination [...] Read more.

The broadcast performance of the 802.11 wireless protocol depends on several factors. One of the important factor is the number of nodes simultaneously contending for the shared channel. The Medium Access Control (MAC) technique of 802.11 is called the Distributed Coordination Function (DCF). DCF is a Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) scheme with binary slotted exponential backoff. A collision is the result of two or more stations transmitting simultaneously. Given the simplicity of the DCF scheme, it was adapted for Dedicated Short Range Communication (DSRC) based vehicular communication. A broadcast mechanism is used to disseminate emergency and safety related messages in a vehicular network. Emergency and safety related messages have a strict end-to-end latency of 100 ms and a Packet Delivery Ratio (PDR) of 90% and above. The PDR can be evaluated through the packet loss probability. The packet loss probability

P_{L}

is given by,

P_{L}

= 1 − (

1 - P_{e}

)(

1 - P_{C}

), where

P_{e}

is the probability of channel error and

P_{C}

is the probability of collision.

P_{e}

depends on several environmental and operating factors and thus cannot be improved. The only way to reduce

P_{L}

is by reducing

P_{C}

. Currently, expensive radio hardware are used to measure

P_{L}

. Several adaptive algorithms are available to reduce

P_{C}

. In this paper, we establish a closed relation between

P_{C}

and the Stirling number of the second kind. Simulation results are presented and compared with the analytical model for accuracy. Our simulation results show an accuracy of 99.9% compared with the analytical model. Even on a smaller sample size, our simulation results show an accuracy of 95% and above. Based on our analytical model, vehicles can precisely estimate these real-time requirements with the least expensive hardware available. Also, once the distribution of

P_{C}

and

P_{L}

are known, one can precisely determine the distribution of

P_{e}

. Full article

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13 pages, 7628 KiB

Open AccessArticle

Eccentricity Based Topological Indices of an Oxide Network

by Muhammad Imran, Muhammad Kamran Siddiqui, Amna A. E. Abunamous, Dana Adi, Saida Hafsa Rafique and Abdul Qudair Baig

Mathematics 2018, 6(7), 126; https://doi.org/10.3390/math6070126 - 18 Jul 2018

Cited by 23 | Viewed by 6043

Abstract

Graph theory has much great advances in the field of mathematical chemistry. Chemical graph theory has become very popular among researchers because of its wide applications in mathematical chemistry. The molecular topological descriptors are the numerical invariants of a molecular graph and are [...] Read more.

Graph theory has much great advances in the field of mathematical chemistry. Chemical graph theory has become very popular among researchers because of its wide applications in mathematical chemistry. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. A great variety of such indices are studied and used in theoretical chemistry, pharmaceutical researchers, in drugs and in different other fields. In this article, we study the chemical graph of an oxide network and compute the total eccentricity, average eccentricity, eccentricity based Zagreb indices, atom-bond connectivity (

A B C

) index and geometric arithmetic index of an oxide network. Furthermore, we give analytically closed formulas of these indices which are helpful in studying the underlying topologies. Full article

(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)

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37 pages, 838 KiB

Open AccessArticle

Soft Rough Neutrosophic Influence Graphs with Application

by Hafsa Masood Malik, Muhammad Akram and Florentin Smarandache

Mathematics 2018, 6(7), 125; https://doi.org/10.3390/math6070125 - 18 Jul 2018

Cited by 6 | Viewed by 3139

Abstract

In this paper, we apply the notion of soft rough neutrosophic sets to graph theory. We develop certain new concepts, including soft rough neutrosophic graphs, soft rough neutrosophic influence graphs, soft rough neutrosophic influence cycles and soft rough neutrosophic influence trees. We illustrate [...] Read more.

In this paper, we apply the notion of soft rough neutrosophic sets to graph theory. We develop certain new concepts, including soft rough neutrosophic graphs, soft rough neutrosophic influence graphs, soft rough neutrosophic influence cycles and soft rough neutrosophic influence trees. We illustrate these concepts with examples, and investigate some of their properties. We solve the decision-making problem by using our proposed algorithm. Full article

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13 pages, 456 KiB

Open AccessArticle

Decomposition of Dynamical Signals into Jumps, Oscillatory Patterns, and Possible Outliers

by Elena Barton, Basad Al-Sarray, Stéphane Chrétien and Kavya Jagan

Mathematics 2018, 6(7), 124; https://doi.org/10.3390/math6070124 - 16 Jul 2018

Cited by 3 | Viewed by 3475

Abstract

In this note, we present a component-wise algorithm combining several recent ideas from signal processing for simultaneous piecewise constants trend, seasonality, outliers, and noise decomposition of dynamical time series. Our approach is entirely based on convex optimisation, and our decomposition is guaranteed to [...] Read more.

In this note, we present a component-wise algorithm combining several recent ideas from signal processing for simultaneous piecewise constants trend, seasonality, outliers, and noise decomposition of dynamical time series. Our approach is entirely based on convex optimisation, and our decomposition is guaranteed to be a global optimiser. We demonstrate the efficiency of the approach via simulations results and real data analysis. Full article

(This article belongs to the Special Issue Chaos and Randomness of Discrete Dynamical Systems: Their Use in Applied Science)

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10 pages, 220 KiB

Open AccessArticle

On the Most Extended Modal Operator of First Type over Interval-Valued Intuitionistic Fuzzy Sets

by Krassimir Atanassov

Mathematics 2018, 6(7), 123; https://doi.org/10.3390/math6070123 - 13 Jul 2018

Cited by 5 | Viewed by 3633

Abstract

The definition of the most extended modal operator of first type over interval-valued intuitionistic fuzzy sets is given, and some of its basic properties are studied. Full article

(This article belongs to the Special Issue Fuzzy Mathematics)

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16 pages, 312 KiB

Open AccessArticle

A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results

by Shin Min Kang, Ghulam Abbas, Ghulam Farid and Waqas Nazeer

Mathematics 2018, 6(7), 122; https://doi.org/10.3390/math6070122 - 11 Jul 2018

Cited by 15 | Viewed by 3450

Abstract

In this paper, we obtain a version of the Fejér–Hadamard inequality for harmonically convex functions via generalized fractional integral operator. In addition, we establish an integral identity and some Fejér–Hadamard type integral inequalities for harmonically convex functions via a generalized fractional integral operator. [...] Read more.

In this paper, we obtain a version of the Fejér–Hadamard inequality for harmonically convex functions via generalized fractional integral operator. In addition, we establish an integral identity and some Fejér–Hadamard type integral inequalities for harmonically convex functions via a generalized fractional integral operator. Being generalizations, our results reproduce some known results. Full article

16 pages, 298 KiB

Open AccessArticle

Some Generalized Dice Measures for Double-Valued Neutrosophic Sets and Their Applications

by Qaisar Khan, Peide Liu and Tahir Mahmood

Mathematics 2018, 6(7), 121; https://doi.org/10.3390/math6070121 - 10 Jul 2018

Cited by 14 | Viewed by 2888

Abstract

Neutrosophic sets (NSs) are used to illustrate uncertain, inconsistent, and indeterminate information existing in real-world problems. Double-valued neutrosophic sets (DVNSs) are an alternate form of NSs, in which the indeterminacy has two distinct parts: indeterminacy leaning toward truth membership, and indeterminacy leaning toward [...] Read more.

Neutrosophic sets (NSs) are used to illustrate uncertain, inconsistent, and indeterminate information existing in real-world problems. Double-valued neutrosophic sets (DVNSs) are an alternate form of NSs, in which the indeterminacy has two distinct parts: indeterminacy leaning toward truth membership, and indeterminacy leaning toward falsity membership. The aim of this article is to propose novel Dice measures and generalized Dice measures for DVNSs, and to specify Dice measures and asymmetric measures (projection measures) as special cases of generalized Dice measures via specific parameter values. Finally, the proposed generalized Dice measures and generalized weighted Dice measures were applied to pattern recognition and medical diagnosis to show their effectiveness. Full article

10 pages, 271 KiB

Open AccessArticle

A Characterization of Projective Special Unitary Group PSU(3,3) and Projective Special Linear Group PSL(3,3) by NSE

by Farnoosh Hajati, Ali Iranmanesh and Abolfazl Tehranian

Mathematics 2018, 6(7), 120; https://doi.org/10.3390/math6070120 - 10 Jul 2018

Cited by 1 | Viewed by 3382

Abstract

Let G be a finite group and

ω (G)

be the set of element orders of G. Let

k \in ω (G)

and

m_{k}

be the number of elements of order k in G. Let [...] Read more.

Let G be a finite group and

ω (G)

be the set of element orders of G. Let

k \in ω (G)

and

m_{k}

be the number of elements of order k in G. Let

n s e (G) = {m_{k} | k \in ω (G)}

. In this paper, we prove that if G is a finite group such that nse(G) = nse(H), where

H = P S U (3, 3)

or

P S L (3, 3)

, then

G ≅ H

. Full article

(This article belongs to the Special Issue Computer Algebra in Scientific Computing)

28 pages, 614 KiB

Open AccessReview

Ecological Diversity: Measuring the Unmeasurable

by Aisling J. Daly, Jan M. Baetens and Bernard De Baets

Mathematics 2018, 6(7), 119; https://doi.org/10.3390/math6070119 - 10 Jul 2018

Cited by 188 | Viewed by 23055

Abstract

Diversity is a concept central to ecology, and its measurement is essential for any study of ecosystem health. But summarizing this complex and multidimensional concept in a single measure is problematic. Dozens of mathematical indices have been proposed for this purpose, but these [...] Read more.

Diversity is a concept central to ecology, and its measurement is essential for any study of ecosystem health. But summarizing this complex and multidimensional concept in a single measure is problematic. Dozens of mathematical indices have been proposed for this purpose, but these can provide contradictory results leading to misleading or incorrect conclusions about a community’s diversity. In this review, we summarize the key conceptual issues underlying the measurement of ecological diversity, survey the indices most commonly used in ecology, and discuss their relative suitability. We advocate for indices that: (i) satisfy key mathematical axioms; (ii) can be expressed as so-called effective numbers; (iii) can be extended to account for disparity between types; (iv) can be parameterized to obtain diversity profiles; and (v) for which an estimator (preferably unbiased) can be found so that the index is useful for practical applications. Full article

(This article belongs to the Special Issue Progress in Mathematical Ecology)

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19 pages, 517 KiB

Open AccessArticle

Global Stability of Within-Host Virus Dynamics Models with Multitarget Cells

by Ahmed M. Elaiw, Taofeek O. Alade and Saud M. Alsulami

Mathematics 2018, 6(7), 118; https://doi.org/10.3390/math6070118 - 10 Jul 2018

Cited by 13 | Viewed by 3204

Abstract

In this paper, we study the stability analysis of two within-host virus dynamics models with antibody immune response. We assume that the virus infects n classes of target cells. The second model considers two types of infected cells: (i) latently infected cells; and [...] Read more.

In this paper, we study the stability analysis of two within-host virus dynamics models with antibody immune response. We assume that the virus infects n classes of target cells. The second model considers two types of infected cells: (i) latently infected cells; and (ii) actively infected cells that produce the virus particles. For each model, we derive a biological threshold number

R_{0}

. Using the method of Lyapunov function, we establish the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations. Full article

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11 pages, 240 KiB

Open AccessArticle

Some Simultaneous Generalizations of Well-Known Fixed Point Theorems and Their Applications to Fixed Point Theory

by Wei-Shih Du, Erdal Karapınar and Zhenhua He

Mathematics 2018, 6(7), 117; https://doi.org/10.3390/math6070117 - 9 Jul 2018

Cited by 7 | Viewed by 3253

Abstract

In this paper, we first establish a new fixed point theorem that generalizes and unifies a number of well-known fixed point results, including the Banach contraction principle, Kannan’s fixed point theorem, Chatterjea fixed point theorem, Du-Rassias fixed point theorem and many others. The [...] Read more.

In this paper, we first establish a new fixed point theorem that generalizes and unifies a number of well-known fixed point results, including the Banach contraction principle, Kannan’s fixed point theorem, Chatterjea fixed point theorem, Du-Rassias fixed point theorem and many others. The presented results not only unify and generalize the existing results, but also yield several new fixed point theorems, which are different from the well-known results in the literature. Full article

(This article belongs to the Special Issue Fixed Point Theory)

11 pages, 263 KiB

Open AccessArticle

On p-Cyclic Orbital M-K Contractions in a Partial Metric Space

by Tharmalingam Gunasekar, Saravanan Karpagam and Boyan Zlatanov

Mathematics 2018, 6(7), 116; https://doi.org/10.3390/math6070116 - 9 Jul 2018

Cited by 4 | Viewed by 2920

Abstract

A cyclic map with a contractive type of condition called p-cyclic orbital M-Kcontraction is introduced in a partial metric space. Sufficient conditions for the existence and uniqueness of fixed points and the best proximity points for these maps in complete partial metric [...] Read more.

A cyclic map with a contractive type of condition called p-cyclic orbital M-Kcontraction is introduced in a partial metric space. Sufficient conditions for the existence and uniqueness of fixed points and the best proximity points for these maps in complete partial metric spaces are obtained. Furthermore, a necessary and sufficient condition for the completeness of partial metric spaces is given. The results are illustrated with an example. Full article

11 pages, 268 KiB

Open AccessArticle

Boundary Value Problem of the Operator ⊕^k Related to the Biharmonic Operator and the Diamond Operator

by Chalermpon Bunpog

Mathematics 2018, 6(7), 115; https://doi.org/10.3390/math6070115 - 5 Jul 2018

Cited by 1 | Viewed by 2534

Abstract

This paper presents an alternative methodology for finding the solution of the boundary value problem (BVP) for the linear partial differential operator. We are particularly interested in the linear operator

\oplus^{k}

, where

\oplus^{k} = ♡^{k} ♢^{k}

, [...] Read more.

This paper presents an alternative methodology for finding the solution of the boundary value problem (BVP) for the linear partial differential operator. We are particularly interested in the linear operator

\oplus^{k}

, where

\oplus^{k} = ♡^{k} ♢^{k}

,

♡^{k}

is the biharmonic operator iterated k-times and

♢^{k}

is the diamond operator iterated k-times. The solution is built on the Green’s identity of the operators

♡^{k}

and

\oplus^{k}

, in which their derivations are also provided. To illustrate our findings, the example with prescribed boundary conditions is exhibited. Full article

10 pages, 245 KiB

Open AccessArticle

Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials

by George Livadiotis

Mathematics 2018, 6(7), 114; https://doi.org/10.3390/math6070114 - 3 Jul 2018

Cited by 6 | Viewed by 6895

Abstract

Maxwell equations have two types of asymmetries between the electric and magnetic fields. The first asymmetry is the inhomogeneity induced by the absence of magnetic charge sources. The second asymmetry is due to parity. We show how both asymmetries are naturally resolved under [...] Read more.

Maxwell equations have two types of asymmetries between the electric and magnetic fields. The first asymmetry is the inhomogeneity induced by the absence of magnetic charge sources. The second asymmetry is due to parity. We show how both asymmetries are naturally resolved under an alternative formulation of Maxwell equations for fields or potentials that uses a compact complex vector operator representation. The developed complex symmetric operator formalism can be easily applied to performing the continuity equation, the field wave equations, the Maxwell equations for potentials, the gauge transformations, and the 4-momentum representation; in general, the developed formalism constitutes a simple way of unfolding the Maxwell theory. Finally, we provide insights for extending the presented analysis within the context of (i) bicomplex numbers and tessarine algebra; and (ii) L^p-spaces in nonlinear Maxwell equations. Full article

21 pages, 709 KiB

Open AccessFeature PaperArticle

Analysis of the Incidence of Poxvirus on the Dynamics between Red and Grey Squirrels

by Fadi Barbara, Valentina La Morgia, Valerio Parodi, Giuseppe Toscano and Ezio Venturino

Mathematics 2018, 6(7), 113; https://doi.org/10.3390/math6070113 - 1 Jul 2018

Cited by 12 | Viewed by 4775

Abstract

A model for the interactions of the invasive grey squirrel species as asymptomatic carriers of the poxvirus with the native red squirrel is presented and analyzed. Equilibria of the dynamical system are assessed, and their sensitivity in terms of the ecosystem parameters is [...] Read more.

A model for the interactions of the invasive grey squirrel species as asymptomatic carriers of the poxvirus with the native red squirrel is presented and analyzed. Equilibria of the dynamical system are assessed, and their sensitivity in terms of the ecosystem parameters is investigated through numerical simulations. The findings are in line with both field and theoretical research. The results indicate that mainly the reproduction rate of the alien population should be drastically reduced to repel the invasion, and to achieve disease eradication, actions must be performed to reduce the intraspecific transmission rate; also, the native species mortality plays a role: if grey squirrels are controlled, increasing it may help in the red squirrel preservation, while the invaders vanish; on the contrary, decreasing it in favorable situations, the coexistence of the two species may occur. Preservation or restoration of the native red squirrel requires removal of the grey squirrels or keeping them at low values. Wildlife managers should exert a constant effort to achieve a harsh reduction of the grey squirrel growth rate and to protect the remnant red squirrel population. Full article

(This article belongs to the Special Issue Progress in Mathematical Ecology)

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8 pages, 235 KiB

Open AccessArticle

On Generalized Roughness in LA-Semigroups

by Noor Rehman, Choonkil Park, Syed Inayat Ali Shah and Abbas Ali

Mathematics 2018, 6(7), 112; https://doi.org/10.3390/math6070112 - 27 Jun 2018

Cited by 11 | Viewed by 3096

Abstract

The generalized roughness in LA-semigroups is introduced, and several properties of lower and upper approximations are discussed. We provide examples to show that the lower approximation of a subset of an LA-semigroup may not be an LA-subsemigroup/ideal of LA-semigroup under a set valued [...] Read more.

The generalized roughness in LA-semigroups is introduced, and several properties of lower and upper approximations are discussed. We provide examples to show that the lower approximation of a subset of an LA-semigroup may not be an LA-subsemigroup/ideal of LA-semigroup under a set valued homomorphism. Full article

(This article belongs to the Special Issue Fuzzy Mathematics)

8 pages, 262 KiB

Open AccessFeature PaperArticle

Symmetries and Invariants for Non-Hermitian Hamiltonians

by Miguel Ángel Simón, Álvaro Buendía and J. G. Muga

Mathematics 2018, 6(7), 111; https://doi.org/10.3390/math6070111 - 27 Jun 2018

Cited by 14 | Viewed by 4020

Abstract

We discuss Hamiltonian symmetries and invariants for quantum systems driven by non-Hermitian Hamiltonians. For time-independent Hermitian Hamiltonians, a unitary or antiunitary transformation

A H A^{†}

that leaves the Hamiltonian H unchanged represents a symmetry of the Hamiltonian, which implies the commutativity [...] Read more.

We discuss Hamiltonian symmetries and invariants for quantum systems driven by non-Hermitian Hamiltonians. For time-independent Hermitian Hamiltonians, a unitary or antiunitary transformation

A H A^{†}

that leaves the Hamiltonian H unchanged represents a symmetry of the Hamiltonian, which implies the commutativity

[H, A] = 0

and, if A is linear and time-independent, a conservation law, namely the invariance of expectation values of A. For non-Hermitian Hamiltonians,

H^{†}

comes into play as a distinct operator that complements H in generalized unitarity relations. The above description of symmetries has to be extended to include also A-pseudohermiticity relations of the form

A H = H^{†} A

. A superoperator formulation of Hamiltonian symmetries is provided and exemplified for Hamiltonians of a particle moving in one-dimension considering the set of A operators that form Klein’s 4-group: parity, time-reversal, parity&time-reversal, and unity. The link between symmetry and conservation laws is discussed and shown to be richer and subtler for non-Hermitian than for Hermitian Hamiltonians. Full article

(This article belongs to the Special Issue Time and Time Dependence in Quantum Mechanics)

20 pages, 4797 KiB

Open AccessArticle

The Emergence of Fuzzy Sets in the Decade of the Perceptron—Lotfi A. Zadeh’s and Frank Rosenblatt’s Research Work on Pattern Classification

by Rudolf Seising

Mathematics 2018, 6(7), 110; https://doi.org/10.3390/math6070110 - 26 Jun 2018

Cited by 11 | Viewed by 7255

Abstract

In the 1950s, the mathematically oriented electrical engineer, Lotfi A. Zadeh, investigated system theory, and in the mid-1960s, he established the theory of Fuzzy sets and systems based on the mathematical theorem of linear separability and the pattern classification problem. Contemporaneously, the psychologist, [...] Read more.

In the 1950s, the mathematically oriented electrical engineer, Lotfi A. Zadeh, investigated system theory, and in the mid-1960s, he established the theory of Fuzzy sets and systems based on the mathematical theorem of linear separability and the pattern classification problem. Contemporaneously, the psychologist, Frank Rosenblatt, developed the theory of the perceptron as a pattern recognition machine based on the starting research in so-called artificial intelligence, and especially in research on artificial neural networks, until the book of Marvin L. Minsky and Seymour Papert disrupted this research program. In the 1980s, the Parallel Distributed Processing research group requickened the artificial neural network technology. In this paper, we present the interwoven historical developments of the two mathematical theories which opened up into fuzzy pattern classification and fuzzy clustering. Full article

(This article belongs to the Special Issue Fuzzy Mathematics)

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11 pages, 2458 KiB

Open AccessArticle

An Implicit Hybrid Method for Solving Fractional Bagley-Torvik Boundary Value Problem

by Muhammed I. Syam, Azza Alsuwaidi, Asia Alneyadi, Safa Al Refai and Sondos Al Khaldi

Mathematics 2018, 6(7), 109; https://doi.org/10.3390/math6070109 - 25 Jun 2018

Cited by 6 | Viewed by 3560

Abstract

In this article, a modified implicit hybrid method for solving the fractional Bagley-Torvik boundary (BTB) value problem is investigated. This approach is of a higher order. We study the convergence, zero stability, consistency, and region of absolute stability of the modified implicit hybrid [...] Read more.

In this article, a modified implicit hybrid method for solving the fractional Bagley-Torvik boundary (BTB) value problem is investigated. This approach is of a higher order. We study the convergence, zero stability, consistency, and region of absolute stability of the modified implicit hybrid method. Three of our numerical examples are presented. Full article

(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications)

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27 pages, 336 KiB

Open AccessArticle

Near Fixed Point Theorems in the Space of Fuzzy Numbers

by Hsien-Chung Wu

Mathematics 2018, 6(7), 108; https://doi.org/10.3390/math6070108 - 25 Jun 2018

Cited by 3 | Viewed by 2733

Abstract

The fuzzy numbers are fuzzy sets owning some elegant mathematical structures. The space consisting of all fuzzy numbers cannot form a vector space because it lacks the concept of the additive inverse element. In other words, the space of fuzzy numbers cannot be [...] Read more.

The fuzzy numbers are fuzzy sets owning some elegant mathematical structures. The space consisting of all fuzzy numbers cannot form a vector space because it lacks the concept of the additive inverse element. In other words, the space of fuzzy numbers cannot be a normed space even though the normed structure can be defined on this space. This also says that the fixed point theorems established in the normed space cannot apply directly to the space of fuzzy numbers. The purpose of this paper is to propose the concept of near fixed point in the space of fuzzy numbers and to study its existence. In order to consider the contraction of fuzzy-number-valued function, the concepts of near metric space and near normed space of fuzzy numbers are proposed based on the almost identical concept. The concepts of Cauchy sequences in near metric space and near normed space of fuzzy numbers are also proposed. Under these settings, the existence of near fixed points of fuzzy-number-valued contraction function in complete near metric space and near Banach space of fuzzy numbers are established. Full article

(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)

7 pages, 257 KiB

Open AccessArticle

Recognition of M × M by Its Complex Group Algebra Where M Is a Simple K₃-Group

by Morteza Baniasad Azad and Behrooz Khosravi

Mathematics 2018, 6(7), 107; https://doi.org/10.3390/math6070107 - 25 Jun 2018

Cited by 1 | Viewed by 2879

Abstract

In this paper we prove that if M is a simple

K_{3}

-group, then

M \times M

is uniquely determined by its order and some information on irreducible character degrees and as a consequence of our results we show that [...] Read more.

In this paper we prove that if M is a simple

K_{3}

-group, then

M \times M

is uniquely determined by its order and some information on irreducible character degrees and as a consequence of our results we show that

M \times M

is uniquely determined by the structure of its complex group algebra. Full article

19 pages, 287 KiB

Open AccessArticle

Fuzzy Semi-Metric Spaces

by Hsien-Chung Wu

Mathematics 2018, 6(7), 106; https://doi.org/10.3390/math6070106 - 22 Jun 2018

Cited by 5 | Viewed by 3470

Abstract

The

T_{1}

-spaces induced by the fuzzy semi-metric spaces endowed with the special kind of triangle inequality are investigated in this paper. The limits in fuzzy semi-metric spaces are also studied to demonstrate the consistency of limit concepts in the induced topologies. Full article

(This article belongs to the Special Issue Fuzzy Mathematics)

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