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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.
Preprint
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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.