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chaos expansion</title> <meta name="description" content="Search results for: polynomial chaos expansion"> <meta name="keywords" content="polynomial chaos expansion"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="polynomial chaos expansion"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1632</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: polynomial chaos expansion</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1632</span> Polynomial Chaos Expansion Combined with Exponential Spline for Singularly Perturbed Boundary Value Problems with Random Parameter</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=W.%20K.%20Zahra">W. K. Zahra</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20El-Beltagy"> M. A. El-Beltagy</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20R.%20Elkhadrawy"> R. R. Elkhadrawy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20problem" title="singular perturbation problem">singular perturbation problem</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20chaos%20expansion" title=" polynomial chaos expansion"> polynomial chaos expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=Shishkin%20mesh" title=" Shishkin mesh"> Shishkin mesh</a>, <a href="https://publications.waset.org/abstracts/search?q=two%20small%20parameters" title=" two small parameters"> two small parameters</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20spline" title=" exponential spline"> exponential spline</a> </p> <a href="https://publications.waset.org/abstracts/100441/polynomial-chaos-expansion-combined-with-exponential-spline-for-singularly-perturbed-boundary-value-problems-with-random-parameter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/100441.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">160</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1631</span> A Generalization of Planar Pascal’s Triangle to Polynomial Expansion and Connection with Sierpinski Patterns</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wajdi%20Mohamed%20Ratemi">Wajdi Mohamed Ratemi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The very well-known stacked sets of numbers referred to as Pascal’s triangle present the coefficients of the binomial expansion of the form (x+y)n. This paper presents an approach (the Staircase Horizontal Vertical, SHV-method) to the generalization of planar Pascal’s triangle for polynomial expansion of the form (x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle is different from other generalizations of Pascal’s triangles given in the literature. The coefficients of the generalized Pascal’s triangles, presented in this work, are generated by inspection, using embedded Pascal’s triangles. The coefficients of I-variables expansion are generated by horizontally laying out the Pascal’s elements of (I-1) variables expansion, in a staircase manner, and multiplying them with the relevant columns of vertically laid out classical Pascal’s elements, hence avoiding factorial calculations for generating the coefficients of the polynomial expansion. Furthermore, the classical Pascal’s triangle has some pattern built into it regarding its odd and even numbers. Such pattern is known as the Sierpinski’s triangle. In this study, a presentation of Sierpinski-like patterns of the generalized Pascal’s triangles is given. Applications related to those coefficients of the binomial expansion (Pascal’s triangle), or polynomial expansion (generalized Pascal’s triangles) can be in areas of combinatorics, and probabilities. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pascal%E2%80%99s%20triangle" title="pascal’s triangle">pascal’s triangle</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20pascal%E2%80%99s%20triangle" title=" generalized pascal’s triangle"> generalized pascal’s triangle</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20expansion" title=" polynomial expansion"> polynomial expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=sierpinski%E2%80%99s%20triangle" title=" sierpinski’s triangle"> sierpinski’s triangle</a>, <a href="https://publications.waset.org/abstracts/search?q=combinatorics" title=" combinatorics"> combinatorics</a>, <a href="https://publications.waset.org/abstracts/search?q=probabilities" title=" probabilities"> probabilities</a> </p> <a href="https://publications.waset.org/abstracts/37988/a-generalization-of-planar-pascals-triangle-to-polynomial-expansion-and-connection-with-sierpinski-patterns" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37988.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">367</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1630</span> Probabilistic Slope Stability Analysis of Excavation Induced Landslides Using Hermite Polynomial Chaos</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Schadrack%20Mwizerwa">Schadrack Mwizerwa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The characterization and prediction of landslides are crucial for assessing geological hazards and mitigating risks to infrastructure and communities. This research aims to develop a probabilistic framework for analyzing excavation-induced landslides, which is fundamental for assessing geological hazards and mitigating risks to infrastructure and communities. The study uses Hermite polynomial chaos, a non-stationary random process, to analyze the stability of a slope and characterize the failure probability of a real landslide induced by highway construction excavation. The correlation within the data is captured using the Karhunen-Loève (KL) expansion theory, and the finite element method is used to analyze the slope's stability. The research contributes to the field of landslide characterization by employing advanced random field approaches, providing valuable insights into the complex nature of landslide behavior and the effectiveness of advanced probabilistic models for risk assessment and management. The data collected from the Baiyuzui landslide, induced by highway construction, is used as an illustrative example. The findings highlight the importance of considering the probabilistic nature of landslides and provide valuable insights into the complex behavior of such hazards. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hermite%20polynomial%20chaos" title="Hermite polynomial chaos">Hermite polynomial chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=Karhunen-Loeve" title=" Karhunen-Loeve"> Karhunen-Loeve</a>, <a href="https://publications.waset.org/abstracts/search?q=slope%20stability" title=" slope stability"> slope stability</a>, <a href="https://publications.waset.org/abstracts/search?q=probabilistic%20analysis" title=" probabilistic analysis"> probabilistic analysis</a> </p> <a href="https://publications.waset.org/abstracts/176089/probabilistic-slope-stability-analysis-of-excavation-induced-landslides-using-hermite-polynomial-chaos" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/176089.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">76</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1629</span> A Robust Optimization of Chassis Durability/Comfort Compromise Using Chebyshev Polynomial Chaos Expansion Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hanwei%20Gao">Hanwei Gao</a>, <a href="https://publications.waset.org/abstracts/search?q=Louis%20Jezequel"> Louis Jezequel</a>, <a href="https://publications.waset.org/abstracts/search?q=Eric%20Cabrol"> Eric Cabrol</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernard%20Vitry"> Bernard Vitry</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The chassis system is composed of complex elements that take up all the loads from the tire-ground contact area and thus it plays an important role in numerous specifications such as durability, comfort, crash, etc. During the development of new vehicle projects in Renault, durability validation is always the main focus while deployment of comfort comes later in the project. Therefore, sometimes design choices have to be reconsidered because of the natural incompatibility between these two specifications. Besides, robustness is also an important point of concern as it is related to manufacturing costs as well as the performance after the ageing of components like shock absorbers. In this paper an approach is proposed aiming to realize a multi-objective optimization between chassis endurance and comfort while taking the random factors into consideration. The adaptive-sparse polynomial chaos expansion method (PCE) with Chebyshev polynomial series has been applied to predict responses’ uncertainty intervals of a system according to its uncertain-but-bounded parameters. The approach can be divided into three steps. First an initial design of experiments is realized to build the response surfaces which represent statistically a black-box system. Secondly within several iterations an optimum set is proposed and validated which will form a Pareto front. At the same time the robustness of each response, served as additional objectives, is calculated from the pre-defined parameter intervals and the response surfaces obtained in the first step. Finally an inverse strategy is carried out to determine the parameters’ tolerance combination with a maximally acceptable degradation of the responses in terms of manufacturing costs. A quarter car model has been tested as an example by applying the road excitations from the actual road measurements for both endurance and comfort calculations. One indicator based on the Basquin’s law is defined to compare the global chassis durability of different parameter settings. Another indicator related to comfort is obtained from the vertical acceleration of the sprung mass. An optimum set with best robustness has been finally obtained and the reference tests prove a good robustness prediction of Chebyshev PCE method. This example demonstrates the effectiveness and reliability of the approach, in particular its ability to save computational costs for a complex system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chassis%20durability" title="chassis durability">chassis durability</a>, <a href="https://publications.waset.org/abstracts/search?q=Chebyshev%20polynomials" title=" Chebyshev polynomials"> Chebyshev polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-objective%20optimization" title=" multi-objective optimization"> multi-objective optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20chaos%20expansion" title=" polynomial chaos expansion"> polynomial chaos expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=ride%20comfort" title=" ride comfort"> ride comfort</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20design" title=" robust design"> robust design</a> </p> <a href="https://publications.waset.org/abstracts/102912/a-robust-optimization-of-chassis-durabilitycomfort-compromise-using-chebyshev-polynomial-chaos-expansion-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/102912.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">152</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1628</span> Solving SPDEs by Least Squares Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Manouzi">Hassan Manouzi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=least%20squares" title="least squares">least squares</a>, <a href="https://publications.waset.org/abstracts/search?q=wick%20product" title=" wick product"> wick product</a>, <a href="https://publications.waset.org/abstracts/search?q=SPDEs" title=" SPDEs"> SPDEs</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element" title=" finite element"> finite element</a>, <a href="https://publications.waset.org/abstracts/search?q=wiener%20chaos%20expansion" title=" wiener chaos expansion"> wiener chaos expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=gradient%20method" title=" gradient method"> gradient method</a> </p> <a href="https://publications.waset.org/abstracts/4074/solving-spdes-by-least-squares-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4074.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">419</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1627</span> Chebyshev Polynomials Relad with Fibonacci and Lucas Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vandana%20N.%20Purav">Vandana N. Purav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fibonacci and Lucas polynomials are special cases of Chebyshev polynomial. There are two types of Chebyshev polynomials, a Chebyshev polynomial of first kind and a Chebyshev polynomial of second kind. Chebyshev polynomial of second kind can be derived from the Chebyshev polynomial of first kind. Chebyshev polynomial is a polynomial of degree n and satisfies a second order homogenous differential equation. We consider the difference equations which are related with Chebyshev, Fibonacci and Lucas polynomias. Thus Chebyshev polynomial of second kind play an important role in finding the recurrence relations with Fibonacci and Lucas polynomials. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=" title=""></a> </p> <a href="https://publications.waset.org/abstracts/24133/chebyshev-polynomials-relad-with-fibonacci-and-lucas-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24133.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">368</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1626</span> Transformations between Bivariate Polynomial Bases</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dimitris%20Varsamis">Dimitris Varsamis</a>, <a href="https://publications.waset.org/abstracts/search?q=Nicholas%20Karampetakis"> Nicholas Karampetakis</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is well known that any interpolating polynomial P(x,y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis etc. The aim of this paper is twofold: a) to present transformations between the coordinates of the polynomial P(x,y) in the aforementioned basis and b) to present transformations between these bases. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bivariate%20interpolation%20polynomial" title="bivariate interpolation polynomial">bivariate interpolation polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20basis" title=" polynomial basis"> polynomial basis</a>, <a href="https://publications.waset.org/abstracts/search?q=transformations" title=" transformations"> transformations</a>, <a href="https://publications.waset.org/abstracts/search?q=interpolating%20polynomial" title=" interpolating polynomial"> interpolating polynomial</a> </p> <a href="https://publications.waset.org/abstracts/14542/transformations-between-bivariate-polynomial-bases" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14542.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">405</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1625</span> From Convexity in Graphs to Polynomial Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ladznar%20S.%20Laja">Ladznar S. Laja</a>, <a href="https://publications.waset.org/abstracts/search?q=Rosalio%20G.%20Artes"> Rosalio G. Artes</a>, <a href="https://publications.waset.org/abstracts/search?q=Jr."> Jr.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20subgraph" title="convex subgraph">convex subgraph</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20index" title=" convex index"> convex index</a>, <a href="https://publications.waset.org/abstracts/search?q=generating%20function" title=" generating function"> generating function</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20ring" title=" polynomial ring"> polynomial ring</a> </p> <a href="https://publications.waset.org/abstracts/9019/from-convexity-in-graphs-to-polynomial-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9019.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">215</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1624</span> Introduction to Paired Domination Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Puttaswamy">Puttaswamy</a>, <a href="https://publications.waset.org/abstracts/search?q=Anwar%20Alwardi"> Anwar Alwardi</a>, <a href="https://publications.waset.org/abstracts/search?q=Nayaka%20S.%20R."> Nayaka S. R.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=domination%20polynomial" title="domination polynomial">domination polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20dominating%20set" title=" paired dominating set"> paired dominating set</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20domination%20number" title=" paired domination number"> paired domination number</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20domination%20polynomial" title=" paired domination polynomial"> paired domination polynomial</a> </p> <a href="https://publications.waset.org/abstracts/52964/introduction-to-paired-domination-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52964.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">232</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1623</span> Solving Stochastic Eigenvalue Problem of Wick Type</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Manouzi">Hassan Manouzi</a>, <a href="https://publications.waset.org/abstracts/search?q=Taous-Meriem%20Laleg-Kirati"> Taous-Meriem Laleg-Kirati</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=eigenvalue%20problem" title="eigenvalue problem">eigenvalue problem</a>, <a href="https://publications.waset.org/abstracts/search?q=Wick%20product" title=" Wick product"> Wick product</a>, <a href="https://publications.waset.org/abstracts/search?q=SPDEs" title=" SPDEs"> SPDEs</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element" title=" finite element"> finite element</a>, <a href="https://publications.waset.org/abstracts/search?q=Wiener-Ito%20chaos%20expansion" title=" Wiener-Ito chaos expansion"> Wiener-Ito chaos expansion</a> </p> <a href="https://publications.waset.org/abstracts/7652/solving-stochastic-eigenvalue-problem-of-wick-type" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7652.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">359</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1622</span> The Bernstein Expansion for Exponentials in Taylor Functions: Approximation of Fixed Points</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tareq%20Hamadneh">Tareq Hamadneh</a>, <a href="https://publications.waset.org/abstracts/search?q=Jochen%20Merker"> Jochen Merker</a>, <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Al-Zoubi"> Hassan Al-Zoubi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Bernstein's expansion for exponentials in Taylor functions provides lower and upper optimization values for the range of its original function. these values converge to the original functions if the degree is elevated or the domain subdivided. Taylor polynomial can be applied so that the exponential is a polynomial of finite degree over a given domain. Bernstein's basis has two main properties: its sum equals 1, and positive for all x 2 (0; 1). In this work, we prove the existence of fixed points for exponential functions in a given domain using the optimization values of Bernstein. The Bernstein basis of finite degree T over a domain D is defined non-negatively. Any polynomial p of degree t can be expanded into the Bernstein form of maximum degree t ≤ T, where we only need to compute the coefficients of Bernstein in order to optimize the original polynomial. The main property is that p(x) is approximated by the minimum and maximum Bernstein coefficients (Bernstein bound). If the bound is contained in the given domain, then we say that p(x) has fixed points in the same domain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bernstein%20polynomials" title="Bernstein polynomials">Bernstein polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=Stability%20of%20control%20functions" title="Stability of control functions">Stability of control functions</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20optimization" title="numerical optimization">numerical optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%20function" title="Taylor function">Taylor function</a> </p> <a href="https://publications.waset.org/abstracts/149910/the-bernstein-expansion-for-exponentials-in-taylor-functions-approximation-of-fixed-points" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/149910.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">135</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1621</span> On the Zeros of the Degree Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20R.%20Nayaka">S. R. Nayaka</a>, <a href="https://publications.waset.org/abstracts/search?q=Putta%20Swamy"> Putta Swamy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=degree%20polynomial" title="degree polynomial">degree polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=regular%20graph" title=" regular graph"> regular graph</a>, <a href="https://publications.waset.org/abstracts/search?q=minimum%20and%20maximum%20degree" title=" minimum and maximum degree"> minimum and maximum degree</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20operations" title=" graph operations"> graph operations</a> </p> <a href="https://publications.waset.org/abstracts/56602/on-the-zeros-of-the-degree-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56602.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">249</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1620</span> Modeling and Simulation of a CMOS-Based Analog Function Generator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Madina%20Hamiane">Madina Hamiane</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Modelling and simulation of an analogy function generator is presented based on a polynomial expansion model. The proposed function generator model is based on a 10th order polynomial approximation of any of the required functions. The polynomial approximations of these functions can then be implemented using basic CMOS circuit blocks. In this paper, a circuit model is proposed that can simultaneously generate many different mathematical functions. The circuit model is designed and simulated with HSPICE and its performance is demonstrated through the simulation of a number of non-linear functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=modelling%20and%20simulation" title="modelling and simulation">modelling and simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=analog%20function%20generator" title=" analog function generator"> analog function generator</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20approximation" title=" polynomial approximation"> polynomial approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=CMOS%20transistors" title=" CMOS transistors"> CMOS transistors</a> </p> <a href="https://publications.waset.org/abstracts/7108/modeling-and-simulation-of-a-cmos-based-analog-function-generator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7108.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">459</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1619</span> On Deterministic Chaos: Disclosing the Missing Mathematics from the Lorenz-Haken Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Meziane%20Belkacem">Meziane Belkacem</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Physics" title="Physics">Physics</a>, <a href="https://publications.waset.org/abstracts/search?q=optics" title=" optics"> optics</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20dynamics" title=" nonlinear dynamics"> nonlinear dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=chaos" title=" chaos"> chaos</a> </p> <a href="https://publications.waset.org/abstracts/140512/on-deterministic-chaos-disclosing-the-missing-mathematics-from-the-lorenz-haken-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/140512.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">156</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1618</span> Main Chaos-Based Image Encryption Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ibtissem%20Talbi">Ibtissem Talbi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> During the last decade, a variety of chaos-based cryptosystems have been investigated. Most of them are based on the structure of Fridrich, which is based on the traditional confusion-diffusion architecture proposed by Shannon. Compared with traditional cryptosystems (DES, 3DES, AES, etc.), the chaos-based cryptosystems are more flexible, more modular and easier to be implemented, which make them suitable for large scale-data encyption, such as images and videos. The heart of any chaos-based cryptosystem is the chaotic generator and so, a part of the efficiency (robustness, speed) of the system depends greatly on it. In this talk, we give an overview of the state of the art of chaos-based block ciphers and we describe some of our schemes already proposed. Also we will focus on the essential characteristics of the digital chaotic generator, The needed performance of a chaos-based block cipher in terms of security level and speed of calculus depends on the considered application. There is a compromise between the security and the speed of the calculation. The security of these block block ciphers will be analyzed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaos-based%20cryptosystems" title="chaos-based cryptosystems">chaos-based cryptosystems</a>, <a href="https://publications.waset.org/abstracts/search?q=chaotic%20generator" title=" chaotic generator"> chaotic generator</a>, <a href="https://publications.waset.org/abstracts/search?q=security%20analysis" title=" security analysis"> security analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=structure%20of%20Fridrich" title=" structure of Fridrich"> structure of Fridrich</a> </p> <a href="https://publications.waset.org/abstracts/13064/main-chaos-based-image-encryption-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13064.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">684</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1617</span> Generic Polynomial of Integers and Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nidal%20Ali">Nidal Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Consider an algebraic number field K of degree n, A0 K is its ring of integers and a prime number p inert in K. Let F(u1, . . . , un, x) be the generic polynomial of integers of K. We will study in advance the stability of this polynomial and then, we will apply it in order to obtain all the monic irreducible polynomials in Fp[x] of degree d dividing n. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generic%20polynomial" title="generic polynomial">generic polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=irreducibility" title=" irreducibility"> irreducibility</a>, <a href="https://publications.waset.org/abstracts/search?q=iteration" title=" iteration"> iteration</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=inert%20prime" title=" inert prime"> inert prime</a>, <a href="https://publications.waset.org/abstracts/search?q=totally%20ramified" title=" totally ramified"> totally ramified</a> </p> <a href="https://publications.waset.org/abstracts/16820/generic-polynomial-of-integers-and-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16820.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">346</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1616</span> A Novel Parametric Chaos-Based Switching System PCSS for Image Encryption</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Salah%20Azzaz">Mohamed Salah Azzaz</a>, <a href="https://publications.waset.org/abstracts/search?q=Camel%20Tanougast"> Camel Tanougast</a>, <a href="https://publications.waset.org/abstracts/search?q=Tarek%20Hadjem"> Tarek Hadjem</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a new low-cost image encryption technique is proposed and analyzed. The developed chaos-based key generator provides complex behavior and can change it automatically via a random-like switching rule. The designed encryption scheme is called PCSS (Parametric Chaos-based Switching System). The performances of this technique were evaluated in terms of data security and privacy. Simulation results have shown the effectiveness of this technique, and it can thereafter, ready for a hardware implementation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaos" title="chaos">chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=encryption" title=" encryption"> encryption</a>, <a href="https://publications.waset.org/abstracts/search?q=security" title=" security"> security</a>, <a href="https://publications.waset.org/abstracts/search?q=image" title=" image "> image </a> </p> <a href="https://publications.waset.org/abstracts/23606/a-novel-parametric-chaos-based-switching-system-pcss-for-image-encryption" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23606.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">475</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1615</span> The K-Distance Neighborhood Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Soner%20Nandappa%20D.">Soner Nandappa D.</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Mohammed%20Naji"> Ahmed Mohammed Naji</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=vertex%20degrees" title="vertex degrees">vertex degrees</a>, <a href="https://publications.waset.org/abstracts/search?q=distance%20in%20graphs" title=" distance in graphs"> distance in graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20operation" title=" graph operation"> graph operation</a>, <a href="https://publications.waset.org/abstracts/search?q=Nk-polynomials" title=" Nk-polynomials"> Nk-polynomials</a> </p> <a href="https://publications.waset.org/abstracts/52946/the-k-distance-neighborhood-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52946.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">549</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1614</span> An Efficient Discrete Chaos in Generalized Logistic Maps with Applications in Image Encryption </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ashish%20Ashish">Ashish Ashish</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the last few decades, the discrete chaos of difference equations has gained a massive attention of academicians and scholars due to its tremendous applications in each and every branch of science, such as cryptography, traffic control models, secure communications, weather forecasting, and engineering. In this article, a generalized logistic discrete map is established and discrete chaos is reported through period doubling bifurcation, period three orbit and Lyapunov exponent. It is interesting to see that the generalized logistic map exhibits superior chaos due to the presence of an extra degree of freedom of an ordered parameter. The period doubling bifurcation and Lyapunov exponent are demonstrated for some particular values of parameter and the discrete chaos is determined in the sense of Devaney's definition of chaos theoretically as well as numerically. Moreover, the study discusses an extended chaos based image encryption and decryption scheme in cryptography using this novel system. Surprisingly, a larger key space for coding and more sensitive dependence on initial conditions are examined for encryption and decryption of text messages, images and videos which secure the system strongly from external cyber attacks, coding attacks, statistic attacks and differential attacks. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaos" title="chaos">chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=period-doubling" title=" period-doubling"> period-doubling</a>, <a href="https://publications.waset.org/abstracts/search?q=logistic%20map" title=" logistic map"> logistic map</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20exponent" title=" Lyapunov exponent"> Lyapunov exponent</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20encryption" title=" image encryption"> image encryption</a> </p> <a href="https://publications.waset.org/abstracts/112408/an-efficient-discrete-chaos-in-generalized-logistic-maps-with-applications-in-image-encryption" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/112408.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">152</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1613</span> Hosoya Polynomials of Zero-Divisor Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdul%20Jalil%20M.%20Khalaf">Abdul Jalil M. Khalaf</a>, <a href="https://publications.waset.org/abstracts/search?q=Esraa%20M.%20Kadhim"> Esraa M. Kadhim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x= 1 is equal to the Wiener index and second derivative at x=1 is equal to the Hyper-Wiener index. In this paper we study the Hosoya polynomial of zero-divisor graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hosoya%20polynomial" title="Hosoya polynomial">Hosoya polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=wiener%20index" title=" wiener index"> wiener index</a>, <a href="https://publications.waset.org/abstracts/search?q=Hyper-Wiener%20index" title=" Hyper-Wiener index"> Hyper-Wiener index</a>, <a href="https://publications.waset.org/abstracts/search?q=zero-divisor%20graphs" title=" zero-divisor graphs"> zero-divisor graphs</a> </p> <a href="https://publications.waset.org/abstracts/27159/hosoya-polynomials-of-zero-divisor-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27159.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">531</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1612</span> Segmentation of Piecewise Polynomial Regression Model by Using Reversible Jump MCMC Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Suparman">Suparman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=piecewise%20regression" title="piecewise regression">piecewise regression</a>, <a href="https://publications.waset.org/abstracts/search?q=bayesian" title=" bayesian"> bayesian</a>, <a href="https://publications.waset.org/abstracts/search?q=reversible%20jump%20MCMC" title=" reversible jump MCMC"> reversible jump MCMC</a>, <a href="https://publications.waset.org/abstracts/search?q=segmentation" title=" segmentation"> segmentation</a> </p> <a href="https://publications.waset.org/abstracts/46201/segmentation-of-piecewise-polynomial-regression-model-by-using-reversible-jump-mcmc-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46201.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">373</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1611</span> Whether Chaos Theory Could Reconstruct the Ancient Societies</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zahra%20Kouzehgari">Zahra Kouzehgari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Since the early emergence of chaos theory in the 1970s in mathematics and physical science, it has increasingly been developed and adapted in social sciences as well. The non-linear and dynamic characteristics of the theory make it a useful conceptual framework to interpret the complex social systems behavior. Regarding chaotic approach principals, sensitivity to initial conditions, dynamic adoption, strange attractors and unpredictability this paper aims to examine whether chaos approach could interpret the ancient social changes. To do this, at first, a brief history of the chaos theory, its development and application in social science as well as the principals making the theory, then its application in archaeological since has been reviewed. The study demonstrates that although based on existing archaeological records reconstruct the whole social system of the human past, the non-linear approaches in studying social complex systems would be of a great help in finding general order of the ancient societies and would enable us to shed light on some of the social phenomena in the human history or to make sense of them. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=archaeology" title="archaeology">archaeology</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20approach" title=" non-linear approach"> non-linear approach</a>, <a href="https://publications.waset.org/abstracts/search?q=chaos%20theory" title=" chaos theory"> chaos theory</a>, <a href="https://publications.waset.org/abstracts/search?q=ancient%20social%20systems" title=" ancient social systems"> ancient social systems</a> </p> <a href="https://publications.waset.org/abstracts/15685/whether-chaos-theory-could-reconstruct-the-ancient-societies" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15685.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">283</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1610</span> Chaotic Dynamics of Cost Overruns in Oil and Gas Megaprojects: A Review</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=O.%20J.%20Olaniran">O. J. Olaniran</a>, <a href="https://publications.waset.org/abstracts/search?q=P.%20E.%20D.%20Love"> P. E. D. Love</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20J.%20Edwards"> D. J. Edwards</a>, <a href="https://publications.waset.org/abstracts/search?q=O.%20Olatunji"> O. Olatunji</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Matthews"> J. Matthews</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Cost overruns are a persistent problem in oil and gas megaprojects. Whilst the extant literature is filled with studies on incidents and causes of cost overruns, underlying theories to explain their emergence in oil and gas megaprojects are few. Yet, a way to contain the syndrome of cost overruns is to understand the bases of ‘how and why’ they occur. Such knowledge will also help to develop pragmatic techniques for better overall management of oil and gas megaprojects. The aim of this paper is to explain the development of cost overruns in hydrocarbon megaprojects through the perspective of chaos theory. The underlying principles of chaos theory and its implications for cost overruns are examined and practical recommendations proposed. In addition, directions for future research in this fertile area provided. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaos%20theory" title="chaos theory">chaos theory</a>, <a href="https://publications.waset.org/abstracts/search?q=oil%20and%20gas" title=" oil and gas"> oil and gas</a>, <a href="https://publications.waset.org/abstracts/search?q=cost%20overruns" title=" cost overruns"> cost overruns</a>, <a href="https://publications.waset.org/abstracts/search?q=megaprojects" title=" megaprojects "> megaprojects </a> </p> <a href="https://publications.waset.org/abstracts/25395/chaotic-dynamics-of-cost-overruns-in-oil-and-gas-megaprojects-a-review" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25395.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">559</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1609</span> Small Entrepreneurs as Creators of Chaos: Increasing Returns Requires Scaling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20B.%20Neace">M. B. Neace</a>, <a href="https://publications.waset.org/abstracts/search?q=Xin%20GAo"> Xin GAo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Small entrepreneurs are ubiquitous. Regardless of location their success depends on several behavioral characteristics and several market conditions. In this concept paper, we extend this paradigm to include elements from the science of chaos. Our observations, research findings, literature search and intuition lead us to the proposition that all entrepreneurs seek increasing returns, as did the many small entrepreneurs we have interviewed over the years. There will be a few whose initial perturbations may create tsunami-like waves of increasing returns over time resulting in very large market consequences–the butterfly impact. When small entrepreneurs perturb the market-place and their initial efforts take root a series of phase-space transitions begin to occur. They sustain the stream of increasing returns by scaling up. Chaos theory contributes to our understanding of this phenomenon. Sustaining and nourishing increasing returns of small entrepreneurs as complex adaptive systems requires scaling. In this paper we focus on the most critical element of the small entrepreneur scaling process–the mindset of the owner-operator. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=entrepreneur" title="entrepreneur">entrepreneur</a>, <a href="https://publications.waset.org/abstracts/search?q=increasing%20returns" title=" increasing returns"> increasing returns</a>, <a href="https://publications.waset.org/abstracts/search?q=scaling" title=" scaling"> scaling</a>, <a href="https://publications.waset.org/abstracts/search?q=chaos" title=" chaos"> chaos</a> </p> <a href="https://publications.waset.org/abstracts/5166/small-entrepreneurs-as-creators-of-chaos-increasing-returns-requires-scaling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5166.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">456</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1608</span> Durability and Early-Age Behavior of Sprayed Concrete with an Expansion Admixture </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kyong-Ku%20Yun">Kyong-Ku Yun</a>, <a href="https://publications.waset.org/abstracts/search?q=Kyeo-Re%20Lee"> Kyeo-Re Lee</a>, <a href="https://publications.waset.org/abstracts/search?q=Kyong%20Namkung"> Kyong Namkung</a>, <a href="https://publications.waset.org/abstracts/search?q=Seung-Yeon%20Han"> Seung-Yeon Han</a>, <a href="https://publications.waset.org/abstracts/search?q=Pan-Gil%20Choi"> Pan-Gil Choi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Sprayed concrete is a way to spray a concrete using a machinery with high air pressure. There are insufficient studies on the durability and early-age behavior of sprayed concrete using high quality expansion agent. A series of an experiment were executed with 5 varying expansion agent replacement rates, while all the other conditions were kept constant, including cement binder content and water-cement ratio. The tests includes early-age shrinkage test, rapid chloride permeability test, and image analysis of air void structure. The early-age expansion test with the variation of expansion agent show that the expansion strain increases as the ratio of expansion agent increases. The rapid chloride permeability test shows that it decrease as the expansion agent increase. Therefore, expansion agent affects into the rapid chloride permeability in a better way. As expansion agent content increased, spacing factor slightly decreased while specific surface kept relatively stable. As a results, the optimum ratio of expansion agent would be selected between 7 % and 11%. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=sprayed%20concrete" title="sprayed concrete">sprayed concrete</a>, <a href="https://publications.waset.org/abstracts/search?q=durability" title=" durability"> durability</a>, <a href="https://publications.waset.org/abstracts/search?q=early-age%20behavior" title=" early-age behavior"> early-age behavior</a>, <a href="https://publications.waset.org/abstracts/search?q=expansion%20admixture" title=" expansion admixture "> expansion admixture </a> </p> <a href="https://publications.waset.org/abstracts/30715/durability-and-early-age-behavior-of-sprayed-concrete-with-an-expansion-admixture" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30715.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">507</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1607</span> Stabilization Control of the Nonlinear AIDS Model Based on the Theory of Polynomial Fuzzy Control Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shahrokh%20Barati">Shahrokh Barati</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we introduced AIDS disease at first, then proposed dynamic model illustrate its progress, after expression of a short history of nonlinear modeling by polynomial phasing systems, we considered the stability conditions of the systems, which contained a huge amount of researches in order to modeling and control of AIDS in dynamic nonlinear form, in this approach using a frame work of control any polynomial phasing modeling system which have been generalized by part of phasing model of T-S, in order to control the system in better way, the stability conditions were achieved based on polynomial functions, then we focused to design the appropriate controller, firstly we considered the equilibrium points of system and their conditions and in order to examine changes in the parameters, we presented polynomial phase model that was the generalized approach rather than previous Takagi Sugeno models, then with using case we evaluated the equations in both open loop and close loop and with helping the controlling feedback, the close loop equations of system were calculated, to simulate nonlinear model of AIDS disease, we used polynomial phasing controller output that was capable to make the parameters of a nonlinear system to follow a sustainable reference model properly. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=polynomial%20fuzzy" title="polynomial fuzzy">polynomial fuzzy</a>, <a href="https://publications.waset.org/abstracts/search?q=AIDS" title=" AIDS"> AIDS</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20AIDS%20model" title=" nonlinear AIDS model"> nonlinear AIDS model</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20control%20systems" title=" fuzzy control systems"> fuzzy control systems</a> </p> <a href="https://publications.waset.org/abstracts/36231/stabilization-control-of-the-nonlinear-aids-model-based-on-the-theory-of-polynomial-fuzzy-control-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36231.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">468</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1606</span> Melnikov Analysis for the Chaos of the Nonlocal Nanobeam Resting on Fractional-Order Softening Nonlinear Viscoelastic Foundations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Guy%20Joseph%20Eyebe">Guy Joseph Eyebe</a>, <a href="https://publications.waset.org/abstracts/search?q=Gambo%20Betchewe"> Gambo Betchewe</a>, <a href="https://publications.waset.org/abstracts/search?q=Alidou%20Mohamadou"> Alidou Mohamadou</a>, <a href="https://publications.waset.org/abstracts/search?q=Timoleon%20Crepin%20Kofane"> Timoleon Crepin Kofane</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaos" title="chaos">chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional-order" title=" fractional-order"> fractional-order</a>, <a href="https://publications.waset.org/abstracts/search?q=Melnikov%20method" title=" Melnikov method"> Melnikov method</a>, <a href="https://publications.waset.org/abstracts/search?q=nanobeam" title=" nanobeam"> nanobeam</a> </p> <a href="https://publications.waset.org/abstracts/102726/melnikov-analysis-for-the-chaos-of-the-nonlocal-nanobeam-resting-on-fractional-order-softening-nonlinear-viscoelastic-foundations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/102726.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">159</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1605</span> Chaotic Analysis of Acid Rains with Times Series of pH Degree, Nitrate and Sulphate Concentration on Wet Samples</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aysegul%20Sener">Aysegul Sener</a>, <a href="https://publications.waset.org/abstracts/search?q=Gonca%20Tuncel%20Memis"> Gonca Tuncel Memis</a>, <a href="https://publications.waset.org/abstracts/search?q=Mirac%20Kamislioglu"> Mirac Kamislioglu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Chaos theory is one of the new paradigms of science since the last century. After determining chaos in the weather systems by Edward Lorenz the popularity of the theory was increased. Chaos is observed in many natural systems and studies continue to defect chaos to other natural systems. Acid rain is one of the environmental problems that have negative effects on environment and acid rains values are monitored continuously. In this study, we aim that analyze the chaotic behavior of acid rains in Turkey with the chaotic defecting approaches. The data of pH degree of rain waters, concentration of sulfate and nitrate data of wet rain water samples in the rain collecting stations which are located in different regions of Turkey are provided by Turkish State Meteorology Service. Lyapunov exponents, reconstruction of the phase space, power spectrums are used in this study to determine and predict the chaotic behaviors of acid rains. As a result of the analysis it is found that acid rain time series have positive Lyapunov exponents and wide power spectrums and chaotic behavior is observed in the acid rain time series. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=acid%20rains" title="acid rains">acid rains</a>, <a href="https://publications.waset.org/abstracts/search?q=chaos" title=" chaos"> chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=chaotic%20analysis" title=" chaotic analysis"> chaotic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=Lypapunov%20exponents" title=" Lypapunov exponents"> Lypapunov exponents</a> </p> <a href="https://publications.waset.org/abstracts/105814/chaotic-analysis-of-acid-rains-with-times-series-of-ph-degree-nitrate-and-sulphate-concentration-on-wet-samples" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/105814.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">146</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1604</span> On CR-Structure and F-Structure Satisfying Polynomial Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manisha%20Kankarej">Manisha Kankarej</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CR-submainfolds" title="CR-submainfolds">CR-submainfolds</a>, <a href="https://publications.waset.org/abstracts/search?q=CR-structure" title=" CR-structure"> CR-structure</a>, <a href="https://publications.waset.org/abstracts/search?q=integrability%20condition" title=" integrability condition"> integrability condition</a>, <a href="https://publications.waset.org/abstracts/search?q=Nijenhuis%20tensor" title=" Nijenhuis tensor"> Nijenhuis tensor</a> </p> <a href="https://publications.waset.org/abstracts/63709/on-cr-structure-and-f-structure-satisfying-polynomial-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63709.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">526</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1603</span> Design of Chaos Algorithm Based Optimal PID Controller for SVC </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saeid%20Jalilzadeh">Saeid Jalilzadeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> SVC is one of the most significant devices in FACTS technology which is used in parallel compensation, enhancing the transient stability, limiting the low frequency oscillations and etc. designing a proper controller is effective in operation of svc. In this paper the equations that describe the proposed system have been linearized and then the optimum PID controller has been designed for svc which its optimal coefficients have been earned by chaos algorithm. Quick damping of oscillations of generator is the aim of designing of optimum PID controller for svc whether the input power of generator has been changed suddenly. The system with proposed controller has been simulated for a special disturbance and the dynamic responses of generator have been presented. The simulation results showed that a system composed with proposed controller has suitable operation in fast damping of oscillations of generator. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaos" title="chaos">chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=PID%20controller" title=" PID controller"> PID controller</a>, <a href="https://publications.waset.org/abstracts/search?q=SVC" title=" SVC"> SVC</a>, <a href="https://publications.waset.org/abstracts/search?q=frequency%20oscillation" title=" frequency oscillation"> frequency oscillation</a> </p> <a href="https://publications.waset.org/abstracts/15527/design-of-chaos-algorithm-based-optimal-pid-controller-for-svc" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15527.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads 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