Mathematics

8 pages, 206 KiB

Open AccessFeature PaperArticle

Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

by Adela Mihai and Ion Mihai

Mathematics 2018, 6(3), 44; https://doi.org/10.3390/math6030044 - 15 Mar 2018

Cited by 35 | Viewed by 4394

We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold. Full article

(This article belongs to the Special Issue Differential Geometry)

29 pages, 9169 KiB

Open AccessArticle

Acquisition War-Gaming Technique for Acquiring Future Complex Systems: Modeling and Simulation Results for Cost Plus Incentive Fee Contract

by Tien M. Nguyen, Hien T. Tran, Andy T. Guillen, Tung X. Bui and Sumner S. Matsunaga

Mathematics 2018, 6(3), 43; https://doi.org/10.3390/math6030043 - 14 Mar 2018

Cited by 3 | Viewed by 5640

Abstract

This paper provides a high-level discussion and propositions of frameworks and models for acquisition strategy of complex systems. In particular, it presents an innovative system engineering approach to model the Department of Defense (DoD) acquisition process and offers several optimization modules including simulation [...] Read more.

This paper provides a high-level discussion and propositions of frameworks and models for acquisition strategy of complex systems. In particular, it presents an innovative system engineering approach to model the Department of Defense (DoD) acquisition process and offers several optimization modules including simulation models using game theory and war-gaming concepts. Our frameworks employ Advanced Game-based Mathematical Framework (AGMF) and Unified Game-based Acquisition Framework (UGAF), and related advanced simulation and mathematical models that include a set of War-Gaming Engines (WGEs) implemented in MATLAB statistical optimization models. WGEs are defined as a set of algorithms, characterizing the Program and Technical Baseline (PTB), technology enablers, architectural solutions, contract type, contract parameters and associated incentives, and industry bidding position. As a proof of concept, Aerospace, in collaboration with the North Carolina State University (NCSU) and University of Hawaii (UH), successfully applied and extended the proposed frameworks and decision models to determine the optimum contract parameters and incentives for a Cost Plus Incentive Fee (CPIF) contract. As a result, we can suggest a set of acquisition strategies that ensure the optimization of the PTB. Full article

(This article belongs to the Special Issue Recent Advances in Game and Decision Theory: Structures, Models, Applications and Software Implementation)

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12 pages, 3102 KiB

Open AccessFeature PaperArticle

Certain Algorithms for Modeling Uncertain Data Using Fuzzy Tensor Product Bézier Surfaces

by Musavarah Sarwar and Muhammad Akram

Mathematics 2018, 6(3), 42; https://doi.org/10.3390/math6030042 - 9 Mar 2018

Cited by 2 | Viewed by 4705

Abstract

Real data and measures are usually uncertain and cannot be satisfactorily described by accurate real numbers. The imprecision and vagueness should be modeled and represented in data using the concept of fuzzy numbers. Fuzzy splines are proposed as an integrated approach to uncertainty [...] Read more.

Real data and measures are usually uncertain and cannot be satisfactorily described by accurate real numbers. The imprecision and vagueness should be modeled and represented in data using the concept of fuzzy numbers. Fuzzy splines are proposed as an integrated approach to uncertainty in mathematical interpolation models. In the context of surface modeling, fuzzy tensor product Bézier surfaces are suitable for representing and simplifying both crisp and imprecise surface data with fuzzy numbers. The framework of this research paper is concerned with various properties of fuzzy tensor product surface patches by means of fuzzy numbers including fuzzy parametric curves, affine invariance, fuzzy tangents, convex hull and fuzzy iso-parametric curves. The fuzzification and defuzzification processes are applied to obtain the crisp Beziér curves and surfaces from fuzzy data points. The degree elevation and de Casteljau’s algorithms for fuzzy Bézier curves and fuzzy tensor product Bézier surfaces are studied in detail with numerical examples. Full article

(This article belongs to the Special Issue Fuzzy Mathematics)

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13 pages, 2076 KiB

Open AccessArticle

Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey

by Malay Banerjee, Nayana Mukherjee and Vitaly Volpert

Mathematics 2018, 6(3), 41; https://doi.org/10.3390/math6030041 - 8 Mar 2018

Cited by 18 | Viewed by 5891

Abstract

Spatiotemporal pattern formation in integro-differential equation models of interacting populations is an active area of research, which has emerged through the introduction of nonlocal intra- and inter-specific interactions. Stationary patterns are reported for nonlocal interactions in prey and predator populations for models with [...] Read more.

Spatiotemporal pattern formation in integro-differential equation models of interacting populations is an active area of research, which has emerged through the introduction of nonlocal intra- and inter-specific interactions. Stationary patterns are reported for nonlocal interactions in prey and predator populations for models with prey-dependent functional response, specialist predator and linear intrinsic death rate for predator species. The primary goal of our present work is to consider nonlocal consumption of resources in a spatiotemporal prey-predator model with bistable reaction kinetics for prey growth in the absence of predators. We derive the conditions of the Turing and of the spatial Hopf bifurcation around the coexisting homogeneous steady-state and verify the analytical results through extensive numerical simulations. Bifurcations of spatial patterns are also explored numerically. Full article

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

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12 pages, 259 KiB

Open AccessArticle

Existence of Solution, Filippov’s Theorem and Compactness of the Set of Solutions for a Third-Order Differential Inclusion with Three- Point Boundary Conditions

by Ali Rezaiguia and Smail Kelaiaia

Mathematics 2018, 6(3), 40; https://doi.org/10.3390/math6030040 - 8 Mar 2018

Cited by 2 | Viewed by 3279

Abstract

In this paper, we study a third-order differential inclusion with three-point boundary conditions. We prove the existence of a solution under convexity conditions on the multi-valued right-hand side; the proof is based on a nonlinear alternative of Leray-Schauder type. We also study the [...] Read more.

In this paper, we study a third-order differential inclusion with three-point boundary conditions. We prove the existence of a solution under convexity conditions on the multi-valued right-hand side; the proof is based on a nonlinear alternative of Leray-Schauder type. We also study the compactness of the set of solutions and establish some Filippov’s- type results for this problem. Full article

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

10 pages, 538 KiB

Open AccessArticle

Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models

by Ricardo Bioni Liberalquino, Maurizio Monge, Stefano Galatolo and Luigi Marangio

Mathematics 2018, 6(3), 39; https://doi.org/10.3390/math6030039 - 7 Mar 2018

Cited by 2 | Viewed by 3847

Abstract

We consider a random dynamical system arising as a model of the behavior of a macrovariable related to a more complicated model of associative memory. This system can be seen as a small (stochastic and deterministic) perturbation of a determinstic system having two [...] Read more.

We consider a random dynamical system arising as a model of the behavior of a macrovariable related to a more complicated model of associative memory. This system can be seen as a small (stochastic and deterministic) perturbation of a determinstic system having two weak attractors which are destroyed after the perturbation. We show, with a computer aided proof, that the system has a kind of chaotic itineracy. Typical orbits are globally chaotic, while they spend a relatively long time visiting the attractor’s ruins. 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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19 pages, 1095 KiB

Open AccessArticle

Advanced Expected Tail Loss Measurement and Quantification for the Moroccan All Shares Index Portfolio

by Marouane Airouss, Mohamed Tahiri, Amale Lahlou and Abdelhak Hassouni

Mathematics 2018, 6(3), 38; https://doi.org/10.3390/math6030038 - 7 Mar 2018

Cited by 4 | Viewed by 4181

Abstract

In this paper, we have analyzed and tested the Expected Tail Loss (ETL) approach for the Value at Risk (VaR) on the Moroccan stock market portfolio. We have compared the results with the general approaches for the standard VaR, which has been the [...] Read more.

In this paper, we have analyzed and tested the Expected Tail Loss (ETL) approach for the Value at Risk (VaR) on the Moroccan stock market portfolio. We have compared the results with the general approaches for the standard VaR, which has been the most suitable method for Moroccan stock investors up to now. These methods calculate the maximum loss that a portfolio is likely to experience over a given time span. Our work advances those modeling methods with supplementation by inputs from the ETL approach for application to the Moroccan stock market portfolio—the Moroccan All Shares Index (MASI). We calculate these indicators using several methods, according to an easy and fast implementation with a high-level probability and with accommodation for extreme risks; this is in order to numerically simulate and study their behavior to better understand investment opportunities and, thus, form a clear view of the Moroccan financial landscape. Full article

(This article belongs to the Special Issue Financial Mathematics)

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8 pages, 236 KiB

Open AccessArticle

Fixed Point Theorems for Almost Z-Contractions with an Application

by Huseyin Isik, Nurcan Bilgili Gungor, Choonkil Park and Sun Young Jang

Mathematics 2018, 6(3), 37; https://doi.org/10.3390/math6030037 - 7 Mar 2018

Cited by 16 | Viewed by 4262

Abstract

In this paper, we investigate the existence and uniqueness of a fixed point of almost contractions via simulation functions in metric spaces. Moreover, some examples and an application to integral equations are given to support availability of the obtained results. Full article

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

16 pages, 3154 KiB

Open AccessArticle

Role of Bi-Directional Migration in Two Similar Types of Ecosystems

by Nikhil Pal, Sudip Samanta, Maia Martcheva and Joydev Chattopadhyay

Mathematics 2018, 6(3), 36; https://doi.org/10.3390/math6030036 - 2 Mar 2018

Cited by 7 | Viewed by 3976

Abstract

Migration is a key ecological process that enables connections between spatially separated populations. Previous studies have indicated that migration can stabilize chaotic ecosystems. However, the role of migration for two similar types of ecosystems, one chaotic and the other stable, has not yet [...] Read more.

Migration is a key ecological process that enables connections between spatially separated populations. Previous studies have indicated that migration can stabilize chaotic ecosystems. However, the role of migration for two similar types of ecosystems, one chaotic and the other stable, has not yet been studied properly. In the present paper, we investigate the stability of ecological systems that are spatially separated but connected through migration. We consider two similar types of ecosystems that are coupled through migration, where one system shows chaotic dynamics, and other shows stable dynamics. We also note that the direction of the migration is bi-directional and is regulated by the population densities. We propose and analyze the coupled system. We also apply our proposed scheme to three different models. Our results suggest that bi-directional migration makes the coupled system more regular. We have performed numerical simulations to illustrate the dynamics of the coupled systems. Full article

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

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5 pages, 204 KiB

Open AccessFeature PaperArticle

A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone

by Stéphane Chrétien and Juan-Pablo Ortega

Mathematics 2018, 6(3), 35; https://doi.org/10.3390/math6030035 - 2 Mar 2018

Viewed by 2989

Abstract

The Hilbert metric is a widely used tool for analysing the convergence of Markov processes and the ergodic properties of deterministic dynamical systems. A useful representation formula for the Hilbert metric was given by Liverani. The goal of the present paper is to [...] Read more.

The Hilbert metric is a widely used tool for analysing the convergence of Markov processes and the ergodic properties of deterministic dynamical systems. A useful representation formula for the Hilbert metric was given by Liverani. The goal of the present paper is to extend this formula to the non-compact and multidimensional setting with a different cone, taylored for sub-Gaussian tails. Full article

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

19 pages, 446 KiB

Open AccessFeature PaperArticle

Forecast Combinations in the Presence of Structural Breaks: Evidence from U.S. Equity Markets

by Davide De Gaetano

Mathematics 2018, 6(3), 34; https://doi.org/10.3390/math6030034 - 1 Mar 2018

Cited by 8 | Viewed by 3478

Abstract

Realized volatility, building on the theory of a simple continuous time process, has recently received attention as a nonparametric ex-post estimate of the return variation. This paper addresses the problem of parameter instability due to the presence of structural breaks in realized volatility [...] Read more.

Realized volatility, building on the theory of a simple continuous time process, has recently received attention as a nonparametric ex-post estimate of the return variation. This paper addresses the problem of parameter instability due to the presence of structural breaks in realized volatility in the context of three HAR-type models. The analysis is conducted on four major U.S. equity indices. More specifically, a recursive testing methodology is performed to evaluate the null hypothesis of constant parameters, and then, the performance of several forecast combinations based on different weighting schemes is compared in an out-of-sample variance forecasting exercise. The main findings are the following: (i) the hypothesis of constant model parameters is rejected for all markets under consideration; (ii) in all cases, the recursive forecasting approach, which is appropriate in the absence of structural changes, is outperformed by forecast combination schemes; and (iii) weighting schemes that assign more weight in most recent observations are superior in the majority of cases. Full article

(This article belongs to the Special Issue Stochastic Processes with Applications)

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15 pages, 335 KiB

Open AccessArticle

Computation of Topological Indices of Some Special Graphs

by Mohammed Salaheldeen Abdelgader, Chunxiang Wang and Sarra Abdalrhman Mohammed

Mathematics 2018, 6(3), 33; https://doi.org/10.3390/math6030033 - 1 Mar 2018

Cited by 14 | Viewed by 5866

Abstract

There are several chemical indices that have been introduced in theoretical chemistry to measure the properties of molecular topology, such as distance-based topological indices, degree-based topological indices and counting-related topological indices. Among the degree-based topological indices, the atom-bond connectivity ( [...] Read more.

There are several chemical indices that have been introduced in theoretical chemistry to measure the properties of molecular topology, such as distance-based topological indices, degree-based topological indices and counting-related topological indices. Among the degree-based topological indices, the atom-bond connectivity (

A B C

) index and geometric–arithmetic (

G A

) index are the most important, because of their chemical significance. Certain physicochemical properties, such as the boiling point, stability and strain energy, of chemical compounds are correlated by these topological indices. In this paper, we study the molecular topological properties of some special graphs. The indices

(A B C)

,

(A B C_{4})

,

(G A)

and

(G A_{5})

of these special graphs are computed. Full article

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15 pages, 239 KiB

Open AccessArticle

Babenko’s Approach to Abel’s Integral Equations

by Chenkuan Li and Kyle Clarkson

Mathematics 2018, 6(3), 32; https://doi.org/10.3390/math6030032 - 1 Mar 2018

Cited by 20 | Viewed by 4003

Abstract

The goal of this paper is to investigate the following Abel’s integral equation of the second kind: [...] Read more.

The goal of this paper is to investigate the following Abel’s integral equation of the second kind:

y (t) + \frac{λ}{Γ (α)} \int_{0}^{t} {(t - τ)}^{α - 1} y (τ) d τ = f (t), (t > 0)

and its variants by fractional calculus. Applying Babenko’s approach and fractional integrals, we provide a general method for solving Abel’s integral equation and others with a demonstration of different types of examples by showing convergence of series. In particular, we extend this equation to a distributional space for any arbitrary

α \in R

by fractional operations of generalized functions for the first time and obtain several new and interesting results that cannot be realized in the classical sense or by the Laplace transform. Full article

(This article belongs to the Special Issue Operators of Fractional Calculus and Their Applications)

15 pages, 274 KiB

Open AccessFeature PaperArticle

Bi-Additive s-Functional Inequalities and Quasi-∗-Multipliers on Banach Algebras

by Choonkil Park

Mathematics 2018, 6(3), 31; https://doi.org/10.3390/math6030031 - 26 Feb 2018

Cited by 7 | Viewed by 3488

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of quasi-∗-multipliers on Banach ∗-algebras and unital C*-algebras, associated to bi-additive s-functional inequalities. Full article

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

13 pages, 258 KiB

Open AccessFeature PaperArticle

C*-Ternary Biderivations and C*-Ternary Bihomomorphisms

by Choonkil Park

Mathematics 2018, 6(3), 30; https://doi.org/10.3390/math6030030 - 26 Feb 2018

Cited by 6 | Viewed by 2585

Abstract

In this paper, we investigate

C^{*}

-ternary biderivations and

C^{*}

-ternary bihomomorphism in

C^{*}

-ternary algebras, associated with bi-additive s-functional inequalities. [...] Read more.

In this paper, we investigate

C^{*}

-ternary biderivations and

C^{*}

-ternary bihomomorphism in

C^{*}

-ternary algebras, associated with bi-additive s-functional inequalities. Full article

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Mathematics, Volume 6, Issue 3 (March 2018) – 15 articles

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