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Mathematics & Computer Science, Applied Mathematics; probabilistic systems analysis; nonlinear systems; public management; pattern formation; resources distribution; information entropy
Online: 13 August 2018 (07:44:51 CEST)
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The article analyzes Bernoulli 's binary sequences in representation of empirical events about the distribution of natural resources and population sizes. Considering the event as a nonlinear system, and consisting of two dependent random variables, with memory and probabilities in maximum finite or infinite lengths, constant and equal to ½ for both variables (stationary process). The expressions of the possible trajectories remain constant in sequences that are repeated alternating the presence or absence of one of the variables at each iteration (asymmetric). There are constant oscillations in the event except if the variables X1 and X2 are regulated as a function of time Y. It is observed that the variables X1 and X2 assume in time Tk → ∞ specific behaviors (geometric variable) that can be used as management tools for random systems. In this way, the article seeks to know from this analyzes, the maximum entropy of information in the system by a theoretical view and how to model resources distribution or containment in the given problem.
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Mathematics & Computer Science, Applied Mathematics; Colebrook equation; Colebrook-White; iterative methods; three-point methods; turbulent flow; hydraulic resistances; pipes; explicit approximations;
Online: 11 August 2018 (18:56:29 CEST)
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Mathematics & Computer Science, Applied Mathematics; nonlinear wave-like equations; Elzaki transform; projected differential transform method
Online: 5 August 2018 (10:04:54 CEST)
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In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.
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Mathematics & Computer Science, Applied Mathematics; Pentagon; fivefold morphology; body plan; spatial organization; morphospace.
Online: 2 August 2018 (09:00:56 CEST)
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A basic pattern in the body plan architecture of many animals, plants and some molecular and cellular systems is five-part units. This pattern has been understood as a result of genetic blueprints in development and as a widely conserved evolutionary character. Despite some efforts, a definitive explanation of the abundance of pentagonal symmetry at so many levels of complexity is still missing. Based on both, a computational platform and a statistical spatial organization argument, we show that five-fold morphology is substantially different from other abundant symmetries like three-fold, four-fold and six-fold symmetries in terms of spatial interacting elements. We develop a measuring system to determine levels of spatial organization in 2D polygons (homogeneous or heterogeneous partition of defined areas) based in principles of regularity in a morphospace. We found that spatial organization of five-fold symmetry is statistically higher than all other symmetries studied here (three to ten-fold symmetries) in terms of spatial homogeneity. The significance of our findings is based on the statistical constancy of geometrical constraints derived from spatial organization of shapes, beyond the material or complexity level of the many different systems where pentagonal symmetry occurs.
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Mathematics & Computer Science, Applied Mathematics; complex networks; deterministic models; Farey-type graphs; vertex labeling; shortest path routing
Online: 1 August 2018 (08:36:16 CEST)
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The generalization of Farey graphs and extended Farey graphs are all originated from Farey graph and scale-free and small-world simultaneously. We propose a labeling of the vertices for it that allows determining all the shortest paths routing between any two vertices only based on their labels. The maximum number of shortest paths between any two vertices is huge as the product of two Fibonacci numbers, however, the label-based routing algorithm runs in linear time O(n). The existence of an efficient routing protocol for Farey-type models should help the understanding of several physical dynamic processes on it.
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Mathematics & Computer Science, Applied Mathematics; experimental economy; mathematical game theory; experimental game theory; behavioral experiment; business game; shopping centers; property management
Online: 1 August 2018 (06:27:55 CEST)
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The managers’ strategic behavior of commercial real estate in a competitive environment is discussed. The means of this research are methods of mathematical and experimental game theory. Illustrates an example of a decision-theoretic game problem with two players engaged in the management of competing shopping centers. The strategies of these players are determined by the costs of the development. Since the number of visitors is constantly and changing the quality of shopping centers, managers actually pull visitors from each other, the game-theoretical formulation of the problem of management of shopping centers corresponds to the zero-sum game. The model example shows that with the help of mathematical modeling it is possible to determine the theoretical expected behavior of agents. The model of the software module created specifically for experimental research is described. The experiments are designed to compare the theoretically predicted behavior with the real actions of people. The novelty is that at significant costs of the Manager for the development and promotion of shopping and entertainment centers, the strategies of managers are resistant to each other's actions, in contrast to changes in the external environment is shown.
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Mathematics & Computer Science, Applied Mathematics; differential games; non zero-sum games; cooperative games; resource extraction; random duration; IDP procedure
Online: 26 July 2018 (02:55:17 CEST)
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A nonrenewable resource extraction game model is analyzed in a differential game theory framework with random duration. If the c.d.f. of the final time is discontinuous, the related subgames are differentiated based on the position of the initial instant with respect to the jump. We investigate properties of optimal trajectories and of imputation distribution procedures if the game is played cooperatively.
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Mathematics & Computer Science, Applied Mathematics; Fractional Order derivative, Mood variation, Oscillator, Perturbation
Online: 23 July 2018 (12:06:00 CEST)
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Fractional – ordered oscillator is used to model the mood variation of bipolar II disorder patient and is investigated analytically. Based on multiple scale perturbation method, the approximate solution and the amplitude – frequency equation are obtained. The effect of fractional – order damping derivative on the mood variation is analyzed, and it is found that it does not only affect the damping mechanism but also the medication parameter. The stressors represented as the forcing function has adverse effects on the mood variation, succinctly leads to unbounded amplitude increase; which is checkmated by increasing the damping coefficient and the nonlinearity parameter or medication parameter.
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Mathematics & Computer Science, Applied Mathematics; nonstationary processes; spectral measure; differential geometry; shape manifold; square root velocity function; Lie group
Online: 23 July 2018 (06:02:32 CEST)
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We proposed in this work the introduction of a new vision of stochastic processes through geometry induced by dilation. The dilation matrices of a given process are obtained by a composition of rotation matrices built in with respect to partial correlation coefficients. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, only one dilation matrix is obtained and it corresponds therefore to Naimark dilation. When the process is nonstationary, a set of dilation matrices is obtained. They correspond to Kolmogorov decomposition. In this work, the nonstationary class of periodically correlated processes was of interest. The underlying periodicity of correlation coefficients is then transmitted to the set of dilation matrices. Because this set lives on the Lie group of rotation matrices, we can see them as points of a closed curve on the Lie group. Geometrical aspects can then be investigated through the shape of the obtained curves, and to give a complete insight into the space of curves, a metric and the derived geodesic equations are provided. The general results are adapted to the more specific case where the base manifold is the Lie group of rotation matrices, and because the metric in the space of curve naturally extends to the space of shapes, this enables a comparison between curves’ shapes and allows then the classification of processes’ measure.
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Mathematics & Computer Science, Applied Mathematics; double Roman domination; discharging approach; generalized Petersen graphs
Online: 20 July 2018 (11:59:01 CEST)
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A double Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2, 3} 2 with the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for 3 which f(v) = 3 or two vertices v1 and v2 for which f(v1) = f(v2) = 2, and every vertex u for which 4 f(u) = 1 is adjacent to at least one vertex v for which f(v) ≥ 2. The weight of a double Roman dominating function f is the value w(f) = ∑u∈V(G) 5 f(u). The minimum weight over all double 6 Roman dominating functions on a graph G is called the double Roman domination number γdR(G) 7 of G. In this paper we determine the exact value of the double Roman domination number of the 8 generalized Petersen graphs P(n, 2) by using a discharging approach.
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Mathematics & Computer Science, Applied Mathematics; stochastic processes; Langevin equation; Fokker-Planck equation; information length; Fisher information; relaxation; chaos; attractor
Online: 19 July 2018 (11:30:59 CEST)
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A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic processes and geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time and is called the information length. By using this concept, we investigate classical and quantum systems and demonstrate the utility of the information length as a unique Lagrangian diagnostic to quantify the information change as a system continuously evolves in time and to map out attractor structure. We further elucidate quantum effects (uncertainty relation) and the dual role of the width of PDF in quantum systems.
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Mathematics & Computer Science, Applied Mathematics; nonlinear ordinary differential operators; impulsive optimal control problems; evolution equations
Online: 16 July 2018 (10:55:36 CEST)
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This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.
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Mathematics & Computer Science, Applied Mathematics; Examination malpractice; stability analysis; basic malpractice number
Online: 11 July 2018 (11:43:03 CEST)
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While examination malpractice has been a recognized social problem among students, the control of the phenomenon remains a challenge. In this study, we formulate a mathematical model describing the population dynamics of examination malpractice among students. Initial insight into the dynamics of the model is gained by analyzing some important mathematical features of the model such as the basic malpractice number. The malpractice-free equilibrium and endemic equilibrium points of the model are shown to be locally asymptotically stable when the basic malpractice number is less than unity. This result implies that examination malpractice can be totally eradicated among students when the basic malpractice number is less than unity. To understand the impact of controlling this social problem, we extend the model to incorporate awareness campaign and disciplinary measure as control strategies in curtailing the act. Our analysis reveals that incorporating control strategies have some influence in reducing examination malpractice among students. Further analysis indicates that considering both control strategies simultaneously yields a better result in reducing examination malpractice and examination malpractice will grow faster when control strategies are not introduced.
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Mathematics & Computer Science, Applied Mathematics; verbal decision analysis; multi-objective optimization; software release planning; ZAPROS III-i
Online: 3 July 2018 (12:24:02 CEST)
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The activity of prioritizing software requirements should be done as efficiently as possible. Selecting the most stable requirements for the most important customers for the development company can be a positive factor when we consider that the available resource does not always encompass the implementation of all requirements. Quantitative methods for reaching software prioritization in releases are many in the field of Search-Based Software Engineering (SBSE). However, we show that it is possible to use qualitative Verbal Decision Analysis (VDA) methods to solve this same type of problem. Moreover, we will use the ZAPROS III-i methods to prioritize requirements considering the opinion of the decision-maker, who will participate in this process. Finally, the results obtained in the VDA structured methods were quite satisfactory when compared to the methods using SBSE. A comparison of results between quantitative and qualitative methods will be made and discussed later.
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Mathematics & Computer Science, Applied Mathematics; fractional differential equations; conformable derivative; Bernoulli equation; exact solution
Online: 3 July 2018 (06:04:53 CEST)
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In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.
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Mathematics & Computer Science, Applied Mathematics; Clustering; Forecasting; Hierarchical Time-Series; Individual Electrical Consumers; Scalable; Short Term; Smart Meters; Wavelets
Online: 2 July 2018 (17:43:29 CEST)
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Smart grids require flexible data driven forecasting methods. We propose clustering tools for bottom-up short-term load forecasting. We focus on individual consumption data analysis which plays a major role for energy management and electricity load forecasting. The two first sections are dedicated to the industrial context and a review of individual electrical data analysis. We are interested in hierarchical time-series for bottom-up forecasting. The idea is to disaggregate the signal in such a way that the sum of disaggregated forecasts improves the direct prediction. The 3-steps strategy defines numerous super-consumers by curve clustering, builds a hierarchy of partitions and selects the best one minimizing a forecast criterion. Using a nonparametric model to handle forecasting, and wavelets to define various notions of similarity between load curves, this disaggregation strategy applied to French individual consumers leads to a gain of 16\% in forecast accuracy. We then explore the upscaling capacity of this strategy facing massive data and implement proposals using R, the free software environment for statistical computing. The proposed solutions to make the algorithm scalable combines data storage, parallel computing and double clustering step to define the super-consumers.
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Mathematics & Computer Science, Applied Mathematics; computational neuroscience; spike train statistics; maximum entropy principle; large deviation theory; out-of-equilibrium statistical mechanics; thermodynamic formalism; entropy production
Online: 7 June 2018 (11:06:22 CEST)
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We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.
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Mathematics & Computer Science, Applied Mathematics; dixon elliptic functions; non-zero modulus; sumudu transform; hankel determinants; continued fractions; Quasi C fractions
Online: 6 June 2018 (13:05:28 CEST)
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Sumudu transform of the Dixon elliptic function with non zero modulus a ≠ 0 for arbitrary powers smN(x,a) ; N ≥ 1 ; smN(x,a)cm(x,a) ; N ≥ 0 and smN(x,a)cm2(x,a) ; N ≥ 0 is given by product of Quasi C fractions. Next by assuming denominators of Quasi C fraction to 1 and hence applying Heliermann correspondance relating formal power series (Maclaurin series of Dixon elliptic functions) and regular C fraction, Hankel determinants are calculated and showed by taking a = 0 gives the Hankel determinants of regular C fraction. The derived results were back tracked to the Laplace transform of sm(x,a) ; cm(x,a) and sm(x,a)cm(x,a).
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Mathematics & Computer Science, Applied Mathematics; domination, degree equal, independent degree equal, irredundance, degree equal complete graphs
Online: 5 June 2018 (16:51:15 CEST)
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A subset D of V is called dominating set if for any vertex u in V-D, there exist at least one vertex v in D such that u and v are adjacent. A subset D of a graph G is called a degree equal dominating set of G if for any u in V-D, there exists v in D such that u and v are adjacent and deg(u) = deg(v). In a social network, members who are neighbors and who have equal status can dominate each other. In the sense, the domination is symmetric. A graph model for this network leads to the concept of degree equal domination. In this paper we define and study the degree equal dominating set of a graph, degree equal irredundant sets in a graph, independent degree equal dominating set of a graph, degree equal complete graphs, 2-equal packing number of a graph.
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Mathematics & Computer Science, Applied Mathematics; multiobjective optimization; optimal control; model order reduction; model predictive control
Online: 31 May 2018 (08:02:29 CEST)
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Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto optimal solutions have led to a wide range of new applications related to optimal and feedback control which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview over recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.
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Mathematics & Computer Science, Applied Mathematics; reaction-diffusion equations; two dimensional Fisher Equation; Nagumo Equation; Kolmogorov-Petrovsky-Piskunov equation; traveling wave solution
Online: 7 May 2018 (08:35:54 CEST)
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We extended the usage of the expansion method based on Sine-Gordon equation to the two dimensional Fisher equation. The relation between the trigonometric and hyperbolic functions are derived from the Sine-Gordon equation de ned in two space dimension. The complex-valued traveling wave solutions to the two dimensional Fisher and Nagumo equations are set in forms a nite series of multiplications of powers of sech(.) and tanh(.) functions.
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Mathematics & Computer Science, Applied Mathematics; fluid dynamics; two phase flow; level set function; cylindrical coordinates; continuity equation
Online: 17 April 2018 (11:46:39 CEST)
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A new formulation for a proposed solution to the 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity and level set convection equation is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow and a connection between the level set function and composite velocity vector for the additive solution is shown. For the case of a vertical tube configuration with small inclination angle, results are obtained for the level set function defining the interface in both the radial and azimuthal directions. It is found that the curvature dependent part of the problem alone induces sinusoidal azimuthal interfacial waves wheras when the curvature together with the equation for the composite velocity is considered oscillating radial interfacial waves occur. The implications of two extremes indicate the importance of looking at the full equations including curvature.
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Mathematics & Computer Science, Applied Mathematics; neutrosophic set; interval bipolar neutrosophic set; multi-attribute decision making; distance measures; similarity measures
Online: 2 April 2018 (08:47:02 CEST)
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The paper investigates some similarity measures in interval bipolar neutrosophic environment for multi-attribute decision making problems. At first, we define Hamming and Euclidean distances measures between interval bipolar neutrosophic sets and establish their basic properties. We also propose two similarity measures based on the Hamming and Euclidean distance functions. Using maximum and minimum operators, we define new similarity measures and prove their basic properties. Using the proposed similarity measures, we propose a novel multi attribute decision making strategy in interval bipolar neutrosophic set environment. Lastly, we solve an illustrative example of multi attribute decision making and present comparison analysis to show the feasibility, applicability and effectiveness of the proposed strategy.
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Mathematics & Computer Science, Applied Mathematics; single valued neutrosophic set; logarithm similarity measure; logarithm entropy function; ideal solution; multi attribute group decision making
Online: 28 March 2018 (04:37:53 CEST)
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The objective of the paper is to introduce new similarity measure for single valued neutrosophic sets based on logarithm function. We define logarithm similarity measure and their weighted similarity measure for single valued neutrosophic sets. Then we define hybrid logarithm similarity measure and weighted hybrid logarithm similarity measure for single valued neutrosophic sets. We prove the basic properties of the proposed measures. We then define an entropy function using logarithm function to determine unknown attribute weights. We develop a novel multi attribute group decision making strategy for single valued neutrosophic sets based on the weighted hybrid logarithm similarity measure. We address an illustrative example to demonstrate the effectiveness and aptness of the proposed strategies. We conduct a sensitivity analysis of the developed strategy. We also make a comparison between the obtained results from proposed strategies and different existing strategies in the literature.
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Mathematics & Computer Science, Applied Mathematics; single valued neutrosophic set; interval neutrosophic set; neutrosophic cubic set; multi attribute decision making; NC-cross entropy
Online: 28 March 2018 (04:19:59 CEST)
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Neutrosophic cubic set (NCS) is one of the important family members of neutrosophic hybrid sets. Neutrosophic cubic set has more strength than other family members of neutrosophic hybrid sets to express incomplete information due to the presence of interval valued neutrosophic set (IVNS) and single valued neutrosophic set (SVNS) in its structure. Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. In this paper we first define a new cross entropy measure under NCSs environment which we call NC- cross entropy measure. We investigate the basic properties of NC-cross entropy. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision making (MADM) strategy based on weighted NC-cross entropy. To show the feasibility and applicability, we solve a MADM problem using the proposed strategy.
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Mathematics & Computer Science, Applied Mathematics; multi-objective multi-level programming; fuzzy parameters; TOPSIS; fuzzy goal programming; multi-objective decision making
Online: 15 February 2018 (20:29:20 CET)
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The paper proposes TOPSIS method for solving multi-objective multi-level programming problem (MO-MLPP) with fuzzy parameters via fuzzy goal programming (FGP). At first, - cut method is used to transform the fuzzily described MO-MLPP into deterministic MO-MLPP. Then, for specific , we construct the membership functions of distance functions from positive ideal solution (PIS) and negative ideal solution (NIS) of all level decision makers (DMs). Thereafter, FGP based multi-objective decision model is established for each level DM for obtaining individual optimal solution. A possible relaxation on decisions for all DMs is taken into account for satisfactory solution. Subsequently, two FGP models are developed and compromise optimal solutions are found by minimizing the sum of negative deviational variables. To recognize the better compromise optimal solution, the concept of distance functions is utilized. Finally, a novel algorithm for MO-MLPP involving fuzzy parameters is provided and an illustrative example is solved to verify the proposed procedure.
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Mathematics & Computer Science, Applied Mathematics; fuzzy bi-matrix game; equilibrium solution; non-linear optimization problem
Online: 5 February 2018 (15:44:19 CET)
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This article puts forward the bi-matrix games with crisp parametric payoffs based on interval value function approach. We conclude that the equilibrium solution of the game model can converted into optimal solutions of the pair of the non-linear optimization problem. Finally, experiment results show the efficiency of the model.
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Mathematics & Computer Science, Applied Mathematics; Sigmoid functions; dynamical systems; gene networks
Online: 5 February 2018 (10:54:21 CET)
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Predicting how a genetic change affects a given character is a major challenge in biology, and being able to tackle this problem relies on our ability to develop realistic models of gene networks. However, such models are rarely tractable mathematically. In this paper, we propose a mathematical analysis of the sigmoid variant of the Wagner gene-network model. By considering the simplest case, that is, one unique self-regulating gene, we show that numerical simulations are not the only tool available to study such models: theoretical studies can be done too, by mathematical analysis of discrete dynamical systems. It is first shown that the particular sigmoid function can be theoretically investigated. Secondly, we provide an illustration on how to apply such investigations in the case of the dynamical system representing the one self-regulating gene.
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Mathematics & Computer Science, Applied Mathematics; Chaotic itineracy; random dynamics; computer aided proof; neural networks
Online: 1 February 2018 (10:04:20 CET)
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We consider a random dynamical system arising in a 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 relatively long time visiting attractor's ruins.
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Mathematics & Computer Science, Applied Mathematics; breast cancer; optimal control; ketogenic diet; chemotherapy
Online: 1 February 2018 (04:45:40 CET)
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In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analysis was carried out using varieties of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure cancer persistence in the absence of anti-cancer drugs ketogenic diet and cancer emission when anti-cancer drugs, immune-booster, ketogenic diet are included were established. Furthermore, optimal control theory is applied to find out the optimal drug adjustment as an input control of the system therapies to minimize the number of cancerous cells by considering different controlled combinations of administering the chemotherapy agent and ketogenic diet using the popular Pontryagin’s Maximum Principle. Numerical simulations were presented to validate our theoretical results.
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Mathematics & Computer Science, Applied Mathematics; inflation-indexed bond; DC pension plan; stochastic optimal control; dynamic programming approach; HJB equation.
Online: 25 January 2018 (09:17:12 CET)
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In this paper we investigate the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phrase which is risk-averse and pays close attention to inflation risk. The plan aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal wealth by investing the wealth in a financial market consisting of an inflation-indexed bond, an ordinary zero coupon bond and a risk-free asset. We derive the optimal investment strategy in closed-form using the dynamic programming approach by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Our theoretical and numerical results reveal that under some rational assumptions, an inflation-indexed bond do has significant advantage to hedge inflation risk.
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Mathematics & Computer Science, Applied Mathematics; initial boundary value problem; Gross-Sobolev inequality; logarithmic wave equation; global existence of solution
Online: 19 January 2018 (10:34:59 CET)
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We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.
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Mathematics & Computer Science, Applied Mathematics; fourth-order diffusion; Allen-Cahn equation; Cahn-Hilliard equation; phase field; nonlinear reaction-diffusion
Online: 18 January 2018 (06:44:57 CET)
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Using a nonclassical symmetry of nonlinear reaction-diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen-Cahn-Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near the critical temperature. Solutions are given for the changing phase of a cylindrical or spherical inclusion, allowing for a 'mushy zone' with mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture, depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.
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Mathematics & Computer Science, Applied Mathematics; neutrosophic set; bipolar neutrosophic set; interval bipolar neutrosophic set; multi-attribute decision making; cross entropy measure
Online: 8 January 2018 (11:04:02 CET)
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Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods based on the proposed cross entropy measures. In the decision making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision making problems and compare the obtained result with the results of other existing methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.
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Mathematics & Computer Science, Applied Mathematics; neutrosophic set; single valued neutrosophic set; SN-cross entropy function; multi-attribute group decision making
Online: 2 January 2018 (09:11:21 CET)
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Single valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single valued neutrosophic cross entropy bears an asymmetrical behavior and produce an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under single valued neutrosophic set (SVNS) environment namely SN- cross entropy and prove its basic properties. Also we define weighted SN-cross entropy measure and investigate its basic properties. We develop a new multi attribute group decision making (MAGDM) strategy for ranking of the alternatives based on the proposed weighted SN-cross entropy measure between each alternative and the ideal alternative. Finally, a numerical example of MAGDM problem of investment potential is solved to show the validity and efficiency of proposed decision making strategy. We also present comparative anslysis of the obtained result with the results obtained form the existing solution strategies in the solution.
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Mathematics & Computer Science, Applied Mathematics; global existence; damping; boundary source; logarithmic wave equation; initial boundary value problem; decay estimate
Online: 30 December 2017 (14:58:51 CET)
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In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.
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Mathematics & Computer Science, Applied Mathematics; stochastic control; optimal dividend payment; ruin probability constraint
Online: 8 December 2017 (06:55:06 CET)
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Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp C., 2003). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp C., 2003). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry (see Hipp C., 2016). Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in (see Hipp C., 2016), Section 2.2.2 does also yield optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. These gaps always exist in De Finetti models, see (see Hipp C., 2017).
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Mathematics & Computer Science, Applied Mathematics; neutrosophic number; neutrosophic number harmonic mean operator (NNHMO); neutrosophic number weighted harmonic mean operator (NNWHMO); cosine function, score function; multi criteria group decision making
Online: 20 November 2017 (09:53:31 CET)
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The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.
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Mathematics & Computer Science, Applied Mathematics; fuzzy number; normal fuzzy number; addition and subtraction; approximation.
Online: 17 October 2017 (14:24:15 CEST)
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In fuzzy group decision making problems and fuzzy shortest path problems, the addition and subtraction are the basic problems. For the mixed normal fuzzy numbers and trapezoidal fuzzy numbers, the addition and subtraction operations are approximated by the normal fuzzy numbers in this paper. The behaviors of approximated normal fuzzy numbers are the same as those of the normal distributions from the viewpoint of probability. An application of the addition and subtraction operations of mixed fuzzy numbers to the fuzzy sample mean is also proposed.
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Mathematics & Computer Science, Applied Mathematics; evolutionary dynamics; quantitative trait; Manhattan norm; Euclidean norm; Chebyshev norm; parasitism; exploitation; egalitarianism
Online: 16 October 2017 (07:35:46 CEST)
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Various distance metrics and their induced norms are employed in the quantitative modeling of evolutionary dynamics. Minimization of these distance metrics when applied to evolutionary optimization are hypothesized to result in different outcomes. Here, we apply the different distance metrics to the evolutionary trait dynamics brought about by the interaction between two competing species infected by parasites (exploiters). We present deterministic cases showing the distinctive selection outcomes under the Manhattan, Euclidean and Chebyshev norms. Specifically, we show how they differ in the time of convergence to the desired optima (e.g., no disease), and in the egalitarian sharing of carrying capacity between the competing species. However, when randomness is introduced to the population dynamics of parasites and to the trait dynamics of the competing species, the distinctive characteristics of the outcomes under the three norms become indistinguishable. Our results provide theoretical cases when evolutionary dynamics using different distance metrics exhibit similar outcomes.
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Mathematics & Computer Science, Applied Mathematics; vibrations
Online: 25 September 2017 (16:23:04 CEST)
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This paper attempts to address the phenomenon of normal vibrations, (referred to as dynamic vibrations) occurring on a surface which is already in vibrational motion due to other kinematic phenomena. Such a surface will have a metric tensor, normal, and ambient velocity which diverges from the surface’s original various dynamic tensorial descriptors. This paper formulates the wave equation defined in a coordinate space, and extends the equation to observe vibrations on a surface with the use of the Laplace-Beltrami operator in a tensorial fashion drawing on conventions from the newly established Calculus of Moving Surfaces (CMS). The Paper then identifies the way which these normal vibrations will manifest within ambient space. Finally, a counter-intuitive relation between the magnitude of such dynamic vibrations and dynamic surface’s time-dependent mean curvature presents itself, for which dynamic vibrations superimposed on original dynamic motion will eliminate the other, and the surface remains static under an arbitrary initial motion. From this condition, resubstitution within the wave equation yields a novel coupled PDE system which within contains the time-evolution of the surface’s mean curvature and its dynamic vibrations. This analysis can have application for algorithms designed for mechanical stabilization during seismic activity, as well as analyzing stabilization algorithms for other various applications and can also have application with respect to biotechnological innovations for analyzing properties defined on the surface of cell-Like biological entities such as metabolism, lipid content, and actin dynamics.
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Mathematics & Computer Science, Applied Mathematics; significance level; sample size; bayes ratio; likelihood function; optimal decision; significance test
Online: 25 September 2017 (08:33:18 CEST)
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The main objective of this paper is to find a close link between the adaptive level of significance, presented here, and the sample size. We, statisticians, know of the inconsistency, or paradox, in the current classical tests of significance that are based on p-value statistics that is compared to the canonical significance levels (10%, 5% and 1%): "Raise the sample to reject the null hypothesis" is the recommendation of some ill-advised scientists! This paper will show that it is possible to eliminate this problem of significance tests. The Bayesian Lindley's paradox – "increase the sample to accept the hypothesis" – also disappears. Obviously, we present here only the beginning of a possible prominent research. The intention is to extend its use to more complex applications such as survival analysis, reliability tests and other areas. The main tools used here are the Bayes Factor and the extended Neyman-Pearson Lemma.
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Mathematics & Computer Science, Applied Mathematics; laminated beam; exponential stability; Cattaneo’s law; semigroup theory
Online: 25 September 2017 (07:10:35 CEST)
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In previous work (Z. Angew. Math. Phys. 68(2), 2017), Apalara considered a one dimensional thermoelastic laminated beam under Cattaneo’s law of heat conduction and proved the exponential and polynomial decay results depend on the stability number χT . In this paper, we continue to study the same system and show that the solution of the concerned system lacks of exponential decay result in the case χT ≠ 0 which solves the open problem proposed by Apalara (Z. Angew. Math. Phys. 68(2), 2017).
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Mathematics & Computer Science, Applied Mathematics; fuzzy number; ranking; preference relation
Online: 11 September 2017 (16:44:07 CEST)
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In fuzzy decision problems, the ordering of fuzzy numbers is the basic problem. Among which, the fuzzy preference relation is the reasonable one to represent preference relation by a fuzzy membership function. This paper studies the Nakamura’s and Kołodziejczyk’s preference relations. Eight cases of representing different level of overlapping between two triangular fuzzy numbers are considered. We analyze the ranking behaviors of all possible combinations of decomposition and intersection of two fuzzy numbers for the Nakamura’s and Kołodziejczyk’s preference relations of these test cases. The results indicate that the decomposition and intersection can affect the fuzzy preference relations, thereby the final total order relation of fuzzy numbers.
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Mathematics & Computer Science, Applied Mathematics; non-equlibrium; stochastic systems; langevin equation; fokker-planck equation; time-dependent PDFs; gamma distribution
Online: 21 August 2017 (12:11:18 CEST)
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Many systems in nature and laboratories are far from equilibrium and exhibit significant fluc- tuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time- dependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem, and show that as the strength of the stochastic noise increases the time-dependent PDFs increasingly deviate from gamma distributions. For sufficiently strong noise a transition occurs whereby the PDF never reaches a stationary state, but instead forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions, and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analyzed in terms of entropy and information length, the total number of statistically distinguishable states that a system passes through in time.
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Mathematics & Computer Science, Applied Mathematics; air- or iron-cored coil; polar coordinates; fourier analysis; two-dimensional; subdomain technique
Online: 14 August 2017 (06:07:40 CEST)
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This paper presents a new scientific contribution on the two-dimensional (2-D) subdomain technique in polar coordinates taking into account the finite relative permeability of the ferromagnetic material. The constant relative permeability corresponds to linear part of the nonlinear B(H) curve. As in conventional technique, the method of separation of variables and the Fourier’s series are used for the resolution of magnetostatic Maxwell’s equations in each region. Although, the general solutions of magnetic field in the subdomains and boundary conditions (BCs) between regions are different in the conventional and proposed method. In this later, the magnetic field solution in each subdomain is a superposition of two magnetic quantities in the two directions (i.e., r- and Q-axis) and the BCs between two regions are also in both directions. For example, the scientific contribution has been applied to an air- or iron-cored coil supplied by a constant current. The distribution of local quantities (i.e., the magnetic vector potential and flux density) has been validated by a corresponding 2-D finite-element analysis (FEA). The obtained semi-analytical results are in very good agreement with those of numerical method.
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Mathematics & Computer Science, Applied Mathematics; portfolio optimization; Kelly criterion; differential evolution; mean-variance
Online: 31 July 2017 (11:22:09 CEST)
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Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to verify the accuracy of the results obtained from differential evolution. The results show that evolutionary algorithms can be successfully applied to solve a portfolio optimization problem where returns are calculated by applying Kelly's Criterion to each of the assets in the portfolio.
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Mathematics & Computer Science, Applied Mathematics; S degree; S indices; topological indices; QSAR; QSPR
Online: 25 July 2017 (04:31:48 CEST)
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Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: S degree. And also we define S indices of a simple connected graph by using the S degree concept. We compute the S indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.
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Mathematics & Computer Science, Applied Mathematics; Gauss-exponential distribution; Gauss-Laplace distribution; stochastic vector representation; geometric measure representation; (p,q)-generalized polar coordinates; (p,q)-arc length; dynamic intersection proportion function; (p,q)-generalized Box-Muller simulation method; (p,q)-spherical uniform distribution; dynamic geometric disintegration
Online: 19 July 2017 (04:35:06 CEST)
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For evaluating probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based upon the Gauss-Laplace law. The latter will be considered here as an element of the newly introduced family of (p,q)-spherical distributions. Based upon a suitably defined non-Euclidean arc-length measure on (p,q)-circles we prove geometric and stochastic representations of these distributions and correspondingly distributed random vectors, respectively. These representations allow dealing with the new probability measures similarly like with elliptically contoured distributions and more general homogeneous star-shaped ones. This is demonstrated at hand of a generalization of the Box-Muller simulation method. En passant, we prove an extension of the sector and circle number functions.
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Mathematics & Computer Science, Applied Mathematics; generalized triangular intuitionistic fuzzy geometric aggregation operator; triangular intuitionistic fuzzy number; intuitionistic fuzzy set; multi-criteria decision-making; attitudinal character; flexibility
Online: 14 June 2017 (05:55:52 CEST)
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Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.
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Mathematics & Computer Science, Applied Mathematics; Boiling Water Reactors; density wave oscillations; stability monitor; Shannon Entropy; noise-assisted Empirical Mode Decomposition variants; mode-mixing; Hilbert-Huang transform; instantaneous frequency
Online: 29 May 2017 (10:28:28 CEST)
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There are currently around 78 Nuclear Power Plants (NPP) in the world based on Boiling Water Reactors (BWR). The current parameter to assess BWR instability issues is the linear Decay Ratio (DR). However, it is well known that BWRs are complex non-linear dynamical systems that may even exhibit chaotic dynamics that normally preclude the use of the DR when the BWR is working at a specific operating point during instability. In this work a novel methodology based on an adaptive Shannon Entropy estimator and on Noise Assisted Empirical Mode Decomposition variants is presented. This methodology was developed for real-time implementation of a stability monitor. This methodology was applied to a set of signals stemming from several NPPs reactors (Ringhals-Sweden, Forsmark-Sweden and Laguna Verde-Mexico) under commercial operating conditions, that experienced instabilities events, each one of a different nature
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Mathematics & Computer Science, Applied Mathematics; evolutionary stable strategies (ESS); Markov decision evolutionary games (MDEG); Hawk-Dove game; evolutionary dynamics; evolutionary game theory
Online: 18 May 2017 (03:34:39 CEST)
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A new evolutionary game is introduced which incorporates states and actions into the strategies of the organisms of the evolving populations. The game centrally features actions that result in demographic flow between states that may not conserve organism numbers. It is by this feature that the game encapsulate a range of other evolutionary games, and can encode almost very complex interactions between organisms, species and populations. The game's formalism is expounded and the nature of the game's equilibrium is discussed. This discussion leads to an algorithm for numerically determining the stable equilibrium points which is exemplified in the context of a modified Hawk-Dove game. The game's flexibility for modeling population dynamics is evaluated and compared with other evolutionary games.
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Mathematics & Computer Science, Applied Mathematics; Unsteady 3-D axisymmetric nanofluid; Entropy generation; Spectral quasi-linearization method.
Online: 17 March 2017 (15:10:32 CET)
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We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasilinearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account when the nanofluid particle volume fraction on the boundary in passively controlled. The results show that as the Hartman number increases, both the Nusselt number and the Sherwood number decrease whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with the physical parameters.
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Mathematics & Computer Science, Applied Mathematics; Solvency II; Standard Formula; Risk Measure; Diversification; Aggregation; Monotony; Homogeneity; Subadditivity; Euler's Principle; Capital Allocation
Online: 1 March 2017 (08:53:59 CET)
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The core of risk aggregation in the Solvency II Standard Formula is the so-called square root formula. We argue that it should be seen as a means for the aggregation of different risks to an overall risk rather than being associated with variance-covariance based risk analysis. Considering the Solvency II Standard Formula from the viewpoint of linear geometry, we immediately find that it defines a norm and therefore provides a homogeneous and sub-additive tool for risk aggregation. Hence Euler's Principle for the reallocation of risk capital applies and yields explicit formulas for capital allocation in the framework given by the Solvency II Standard Formula. This gives rise to the definition of diversification functions, which we define as monotone, subadditive, and homogeneous functions on a convex cone. Diversification functions constitute a class of models for the study of the aggregation of risk, and diversification. The aggregation of risk measures using a diversification function preserves the respective properties of these risk measures. Examples of diversification functions are given by seminorms, which are monotone on the convex cone of non-negative vectors. Each Lp norm has this property, and any scalar product given by a non-negative positive semidefinite matrix does as well. In particular, the Standard Formula is a diversification function and hence a risk measure that preserves homogeneity, subadditivity, and convexity.
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Mathematics & Computer Science, Applied Mathematics; general stability;laminated beam;infinite memory;multiplier technique;energy method
Online: 22 February 2017 (16:56:19 CET)
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In this work, we consider a one-dimensional laminated beam in the case of non-equal wave speeds with only one infinite memory on the effective rotation angle. In this case, we establish the general decay result for the energy of solution without any kind of internal or boundary control. The main result is obtained by applying the method used in Guesmia et al. (Electron. J. Differential Equations 193: 1-45, 2012) and the second-order energy.
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Mathematics & Computer Science, Applied Mathematics; laminated beam; Fourier's law; exponential stability; lack of exponential stability; polynomial stability
Online: 16 February 2017 (08:52:57 CET)
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In this paper, we study the well-posedness and the asymptotic behavior of a one-dimensional laminated beam system, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using the Hille-Yosida theorem and prove that the system is exponentially stable if and only if the wave speeds are equal. Furthermore, we show that the system is polynomially stable provided that the wave speeds are not equal.
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Mathematics & Computer Science, Applied Mathematics; stochastic differential equation; numerical simulation; real option; renewable energy; Egypt
Online: 30 January 2017 (12:04:34 CET)
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Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES). The RES investment is characterized by uncertainty, which is long-term, costly, depend on feed-in-tariff and support schemes. In this paper, we address the real option valuation (ROV) of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price, furthermore the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assess the value of deferred option are discussed. The new three stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM) methods. The numerical methods are integrated with concept of Black-Scholes option pricing theory, and applied in option valuation for solar energy investment with uncertainty. The numerical results of L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our data set refers to the Arab Republic of Egypt.
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Mathematics & Computer Science, Applied Mathematics; systems of nonlinear equations; nonlinear preconditioners; multi-step iterative methods; Frozen Jacobian
Online: 25 January 2017 (04:13:19 CET)
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The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.
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Mathematics & Computer Science, Applied Mathematics; ev-degree Zagreb index; octane isomers; QSPR; QSAR; ve-degree Randić index; ve-degree Zagreb indices
Online: 23 January 2017 (16:14:37 CET)
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Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph. Recently novel two degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study we define ev-degree Zagreb index, ve-degree Zagreb indices and ve-degree Randić index by using these new graph invariants as parallel to their corresponding classical degree versions. We compare these new group ev-degree and ve-degree indices with the other well-known and most used topological indices in literature such as; Wiener, Zagreb and Randić indices by modelling some physicochemical properties of octane isomers. We show that the ev-degree Zagreb index, the ve-degree Zagreb and the ve-degree Randić indices give better correlation than Wiener, Zagreb and Randić indices to predict the some specific physicochemical properties of octanes. We investigate the relations between the second Zagreb index and ev-degree and ve-degree Zagreb indices and some mathematical properties of ev-degree and ve-degree Zagreb indices.
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Mathematics & Computer Science, Applied Mathematics; well-posedness; asymptotic stability; infinite memory; Cattaneo's law; time-varying delay
Online: 19 January 2017 (10:53:04 CET)
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In this paper, we study a one-dimensional Bresse-Cattaneo system with infinite memories and time-dependent delay term (the coefficient of which is not necessarily positive) in the internal feedbacks. First, it is proved that the system is well-posed by means of the Hille-Yosida theorem under suitable assumptions on the relaxation functions. Then, without any restriction on the speeds of wave propagations, we establish the exponential or general decay result by introducing suitable energy and Lyapunov functionals.
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Mathematics & Computer Science, Applied Mathematics; air- or iron-cored coil; Cartesian coordinates; Fourier analysis; two-dimensional; saturation effect; subdomain technique
Online: 16 January 2017 (04:38:11 CET)
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The most significant assumptions in the subdomain technique (i.e., based on the formal resolution of Maxwell's equations applied in subdomain) is defined by: “The iron parts (i.e., the teeth and the back-iron) are considered to be infinitely permeable so that the saturation effect is neglected”. In this paper, the author presents a new scientific contribution on improving of this method in two-dimensional (2-D) and in Cartesian coordinates by focusing on the consideration of iron. The subdomains connection is carried out in the two directions (i.e., x- and y-edges). For example, the improvement was performed by solving magnetostatic Maxwell's equations for an air- or iron-cored coil supplied by a direct current. To evaluate the efficacy of the proposed technique, the magnetic flux density distributions have been compared with those obtained by the 2-D finite-element analysis (FEA). The semi-analytical results are in quite satisfying agreement with those obtained by the 2-D FEA, considering both amplitude and waveform.
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Mathematics & Computer Science, Applied Mathematics; ev-degree;ve-degree; ev-degree topological indices; ve-degree topological indices
Online: 10 January 2017 (10:10:13 CET)
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Recently two new degree concepts have been defined in graph theory: ev-degree and ve-degree. Also the ev-degree and ve-degree Zagreb and Randić indices have been defined very recently as parallel of the classical definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be used as possible tools in QSPR researches . In this paper we define the ve-degree and ev-degree Narumi–Katayama indices, investigate the predicting power of these novel indices and extremal graphs with respect to these novel topological indices. Also we give some basic mathematical properties of ev-degree and ve-degree Narumi-Katayama and Zagreb indices.
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Mathematics & Computer Science, Applied Mathematics; the modified simple equation method; Cahn–Allen equation; soliton solution; kink type solutions
Online: 4 January 2017 (10:22:40 CET)
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By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.
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Mathematics & Computer Science, Applied Mathematics; time fractional KdV equation; time fractional Burgers equation; Kudryashov method; wave solution
Online: 23 December 2016 (10:55:45 CET)
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The exact solutions in the wave form are derived for the time fractional KdV and the time fractional Burgers' equations in conformable fractional derivative sense. The fractional variable change using the fundamental properties of the conformable derivative reduces both equations to some nonlinear ODEs. The predicted solution is assumed to be a finite series form of a function satisfying a particular first-order ODE whose solution contains an exponential function in the denominator. The solutions are represented in the explicit forms and illustrated by some choices of the parameters for various fractional orders of the equations.
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Mathematics & Computer Science, Applied Mathematics; modified Kudryashov method; conformable time fractional RLW-Burgers Equation; conformable time fractional potential KdV Equation; conformable time fractional CRWP equation; conformable derivative
Online: 16 December 2016 (08:01:56 CET)
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The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long Wave-Burgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker's parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational form of an exponential function is substituted to the ODE generated from the conformable time fractional PDE by using wave transformation. The coefficients used in the finite series are determined by solving the algebraic system derived from the coefficients of the powers of the predicted solution.
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Mathematics & Computer Science, Applied Mathematics; computational model; lymph node; multiscale structure; vascular network; fibroblastic reticular cells; conduit network; lymph flow; destruction of conduits
Online: 9 December 2016 (10:19:20 CET)
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In this study we discuss critical issues in modelling the structure and function of lymph nodes (LNs), with emphasis on how LN physiology is related to its multi-scale structural organization. In addition to macroscopic domains such as B-cell follicles and the T cell zone, there are vascular networks which play a key role in the delivery of information to the inner parts of the LN, i.e., the conduit and blood microvascular networks. We propose object-oriented computational algorithms to model the 3D geometry of the fibroblastic reticular cell (FRC) network and the microvasculature. Assuming that a conduit cylinder is densely packed with collagen fibers, the computational flow study predicted that the diffusion should be a dominating process in mass transport than convective flow. The geometry models are used to analyze the lymph flow properties through the conduit network in unperturbed- and damaged states of the LN. The analysis predicts that elimination of up to 60–90 % of edges is required to stop the lymph flux. This result suggests a high degree of functional robustness of the network.
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Mathematics & Computer Science, Applied Mathematics; change point; estimation; consistency; panel data; short panels; boundary issue; structural change; bootstrap; non-life insurance; change in claim amounts
Online: 1 December 2016 (10:02:03 CET)
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Panel data of our interest consist of a moderate number of panels, while the panels contain a small number of observations. An estimator of common breaks in panel means without a boundary issue for this kind of scenario is proposed. In particular, the novel estimator is able to detect a common break point even when the change happens immediately after the first time point or just before the last observation period. Another advantage of the elaborated change point estimator is that it results in the last observation in situations with no structural breaks. The consistency of the change point estimator in panel data is established. The results are illustrated through a simulation study. As a by-product of the developed estimation technique, a theoretical utilization for correlation structure estimation, hypothesis testing, and bootstrapping in panel data is demonstrated. A practical application to non-life insurance is presented as well.
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Mathematics & Computer Science, Applied Mathematics; planar Brownian motion; complex-valued Ornstein-Uhlenbeck processes; Lévy~processes; Stable processes; windings; skew-product representation; Spitzer's Theorem; Bougerol's identity; Asian options; pricing
Online: 24 October 2016 (04:57:32 CEST)
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Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, we present Spitzer's asymptotic Theorem for each case. We also relate this study to the pricing of Asian options.
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Mathematics & Computer Science, Applied Mathematics; left ventricle; myofibre; myocardium structure; rule-based model; mathematical anatomy
Online: 20 October 2016 (08:22:39 CEST)
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Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibres. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualisation such as sonography. Symmetrical models are shown to be too rigid, so an analytical non-symmetrical model with enough flexibility is necessary. Based on previously made anatomical models of the left ventricle, we propose a new, much more flexible spline-based analytical model. The model is fully described and verified against DT-MRI data. We show a way to construct it on the basis of sonography data. To use this model in further physiological simulations, we propose a numerical method to utilise finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation.
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Mathematics & Computer Science, Applied Mathematics; point information gain; Rényi entropy; data processing
Online: 17 October 2016 (11:35:13 CEST)
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We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data on the example of several images, and discuss further possible utilizations in other fields of data processing.
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Mathematics & Computer Science, Applied Mathematics; Vehicular Ad Hoc Network (VANET); Cloud Computing; privacy preservation; security and privacy
Online: 3 October 2016 (20:40:50 CEST)
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This project designed a set of network security mechanisms for cloud applications in VANETs. At present, cloud computing is one of the government’s development priorities in the industry. We divide cloud into public, private, and hybrid clouds in this project. Vehicles or passengers can access road conditions or public transport information through the public cloud; public transportation can access current driving records and users can access relevant enterprise information on the private cloud and hybrid cloud is a combination of public and private clouds. Both cloud computing or VANETs require network and information security. At present, many researches on VANETs security only focus on message communication, and neglect information storage. Researches on cloud computing security only focus on information protection, and neglect user privacy and anonymity. This project designed a set of network and information security mechanisms in line with the requirements of Confidentiality, Authentication, Non-repudiation, Conditional Anonymity, and Conditional Untraceability. This project primarily needs to achieve the following: 1.an authentication mechanism to verify the identity of each other between the passenger and the vehicle and to verify the identity with Single Sign-On; 2. vehicle or user privacy and anonymity, which need to be able to replace the anonymous ID and related parameters for the vehicle or the user; 3. a private communication mechanism, which enables any vehicle or user to communicate privately; and 4. an information security encryption method, which can encrypt the information on a cloud server to avoid unauthorized access by internal personnel or hackers.
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Mathematics & Computer Science, Applied Mathematics; integral inequalities; special functions; fractional calculus; conformable fractional integral
Online: 27 September 2016 (11:05:29 CEST)
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In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.
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Mathematics & Computer Science, Applied Mathematics; basic reproduction number; disease free equilibrium; endemic equilibrium; local asymptotic stability; global asymptotic stability; influenza
Online: 30 August 2016 (08:54:15 CEST)
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This article investigates a proposed new mathematical model that considers the infected individuals using various rate coefficients such as transmission, progression, recovery and vaccination. The fact that the dynamic analysis is completely determined by the basic reproduction number is established. More specifically, local and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved under certain parameter conditions when the basic reproduction number is below or above unity. A realistic computer simulation is performed for better understanding of the variations in trends of different compartments after the outbreak of the disease.
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Mathematics & Computer Science, Applied Mathematics; bivariate generalized power series distribution; ruin probability; aggregate claims distribution
Online: 26 August 2016 (09:43:14 CEST)
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In this paper we consider type II bivariate generalized power series Poisson distribution as a compound Poisson distribution with bivariate generalized power series compounding distribution. We obtain some properties, p.m.f. and conditional distributions. In addition we also give a brief discussion about the multivariate extension of this case. Then we introduce type II bivariate generalized power series Poisson process and consider a bivariate risk model with type II bivariate generalized power series Poisson model as the counting process. For this model we derive distribution of the time to ruin and bounds for the probability of ruin. We obtain partial integro-di fferential equation for the ruin probabilities and express its bivariate transform through two univariate boundary transforms,where one of the initial capitals is fi xed at zero.
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Mathematics & Computer Science, Applied Mathematics; average run length; double moving average control chart; Poisson count process
Online: 18 August 2016 (07:27:23 CEST)
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Count data are used in many fields of practice, especially Poisson distribution as a popular choice for the marginal process distribution. If these counts exhibit serial dependence, a popular approach is to use a Poisson INAR(1) model to describe the autocorrelation structure of process. In this paper, the explicit formulas are proposed to evaluate performance characteristics of Double Moving Average control chart (DMA) for Integer valued autoregressive of serial dependence Poisson process. The characteristics of the control chart are frequently measured as Average Run Length (ARL) which means that the average of observations are taken before a system is signaled to be out-of-control. These proposed explicit formulas of ARL are simple and easy to implement for practitioner. The numerical results show that the DMA chart performs better than others when the magnitudes of shift are moderate and large.
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Mathematics & Computer Science, Applied Mathematics; biomedical imaging; covariogram; design-based stereology; estimation of volume; systematic sampling
Online: 16 August 2016 (11:39:57 CEST)
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The systematic sampling is used as a method to get the quantitative results from the tissues and the radiological images. Systematic sampling on real line (R) is a very attractive method within which the biomedical imaging is consulted by the practitioners. For the systematic sampling on R, the measurement function (MF) is occurred by slicing the three dimensional object equidistant systematically. If the parameter q of MF is estimated to be small enough for mean square error, we can make the important remarks for the design-based stereology. This study is an extension of [17], and an exact calculation method is proposed to calculate the constant λ(q,N) of confidence interval in the systematic sampling. In the results, synthetic data can support the results of real data. The currently used covariogram model in variance approximation proposed by [28,29] is tested for the different measurement functions to see the performance on the variance estimation of systematically sampled R. The exact value of constant λ(q,N) is examined for the different measurement functions as well.
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Mathematics & Computer Science, Applied Mathematics; exponentially weighted moving average control chart (EWMA); autoregressive integrated moving average (ARIMA); average run length (ARL)
Online: 15 August 2016 (10:43:14 CEST)
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In this paper we propose the explicit formulas of Average Run Length (ARL) of Exponentially Weighted Moving Average (EWMA) control chart for Autoregressive Integrated Moving Average: ARIMA (p,d,q) (P, D, Q)L process with exponential white noise. To check the accuracy, the ARL results were compared with numerical integral equations based on the Gauss-Legendre rule. There was an excellent agreement between the explicit formulas and the numerical solutions. Additionally, we compared the computational time between our explicit formulas for the ARL with the one obtained via Gauss-Legendre numerical scheme. The computational time for the explicit formulas was approximately one second that is much less than the numerical approximations. The explicit analytical formulas for evaluating ARL0 and ARL1 can produce a set of optimal parameters which depend on the smoothing parameter (λ) and the width of control limit (H), for designing an EWMA chart with a minimum ARL1.
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Mathematics & Computer Science, Applied Mathematics; integral inequalities; fractional integrals; Hermite-Hadamard inequality; preinvex functions
Online: 15 August 2016 (10:34:33 CEST)
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In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.
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Mathematics & Computer Science, Applied Mathematics; Principal of prediction; random sequences; recurrence; Law of Large Numbers; exponential; normal; bivariate; distribution; Entropy; Information
Online: 23 July 2016 (09:25:13 CEST)
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The philosophy of testing statistical hypothesis is a natural consequence and functional
extension of mathematical analysis of Probability. Along with the concept of recurrence when
applied to random sequences and functions, it leads to the analysis of a priori and posterior which
implies testing statistical hypothesis. Testing statistical hypothesis also involves algebraic,
functional and dimensional considerations, which are found in the works of Laplace. Aspects of
mathematical analysis such as universality of solutions, Laws of Large Numbers, Entropy,
Information, and various functional dependencies are the main factors explained in the five
properties that lead to implication of testing statistical hypothesis. Various interesting examples
with modern scientific significance from genetics, astrophysics, and other areas give
methodological access to answers of different problems and phenomena which are involved in the
logic of testing statistical hypothesis.
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Mathematics & Computer Science, Applied Mathematics; Impulsive conditions, Controllability, Neutral evolution integrodi erential equa- tions, Resolvent operators, State dependent delay
Online: 21 July 2016 (03:48:42 CEST)
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In this paper, we study the problem of controllability of impulsive neutral evolution integrodifferential equations with state dependent delay in Banach spaces. The main results are completely new and are obtained by using Sadovskii's fixed point theorem, theory of resolvent operators, and an abstract phase space. An example is given to illustrate the theory.