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problem</title> <meta name="description" content="Search results for: cauchy problem"> <meta name="keywords" content="cauchy problem"> <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 class="d-block d-lg-none navbar-toggler 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style="font-size:.9rem"><span class="badge badge-info">7181</span> Inverse Cauchy Problem of Doubly Connected Domains via Spectral Meshless Radial Point Interpolation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elyas%20Shivanian">Elyas Shivanian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the Cauchy problems of two-dimensional elliptic PDEs in doubly connected domains. It is obtained the unknown data on the inner boundary of the domain while overspecified boundary data are imposed on the outer boundary of the domain by using the SMRPI. Shape functions, which are constructed through point interpolation method using the radial basis functions, help us to treat problem locally with the aim of high order convergence rate. In this way, localization in SMRPI can reduce the ill-conditioning for Cauchy problem. Furthermore, we improve previous results and it is revealed the SMRPI is more accurate and stable by adding strong perturbations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cauchy%20problem" title="cauchy problem">cauchy problem</a>, <a href="https://publications.waset.org/abstracts/search?q=doubly%20connected%20domain" title=" doubly connected domain"> doubly connected domain</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20basis%20function" title=" radial basis function"> radial basis function</a>, <a href="https://publications.waset.org/abstracts/search?q=shape%20function" title=" shape function"> shape function</a> </p> <a href="https://publications.waset.org/abstracts/56408/inverse-cauchy-problem-of-doubly-connected-domains-via-spectral-meshless-radial-point-interpolation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56408.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">278</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">7180</span> Divergence Regularization Method for Solving Ill-Posed Cauchy Problem for the Helmholtz Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Benedict%20Barnes">Benedict Barnes</a>, <a href="https://publications.waset.org/abstracts/search?q=Anthony%20Y.%20Aidoo"> Anthony Y. Aidoo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=divergence%20regularization%20method" title="divergence regularization method">divergence regularization method</a>, <a href="https://publications.waset.org/abstracts/search?q=Helmholtz%20equation" title=" Helmholtz equation"> Helmholtz equation</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20inhomogeneous%20Cauchy%20boundary%20conditions" title=" ill-posed inhomogeneous Cauchy boundary conditions"> ill-posed inhomogeneous Cauchy boundary conditions</a> </p> <a href="https://publications.waset.org/abstracts/137727/divergence-regularization-method-for-solving-ill-posed-cauchy-problem-for-the-helmholtz-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/137727.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">189</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">7179</span> Large Time Asymptotic Behavior to Solutions of a Forced Burgers Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Satyanarayana%20Engu">Satyanarayana Engu</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Mohd"> Ahmed Mohd</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20Murugan"> V. Murugan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study the large time asymptotics of solutions to the Cauchy problem for a forced Burgers equation (FBE) with the initial data, which is continuous and summable on R. For which, we first derive explicit solutions of FBE assuming a different class of initial data in terms of Hermite polynomials. Later, by violating this assumption we prove the existence of a solution to the considered Cauchy problem. Finally, we give an asymptotic approximate solution and establish that the error will be of order O(t^(-1/2)) with respect to L^p -norm, where 1≤p≤∞, for large time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Burgers%20equation" title="Burgers equation">Burgers equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Cole-Hopf%20transformation" title=" Cole-Hopf transformation"> Cole-Hopf transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=Hermite%20polynomials" title=" Hermite polynomials"> Hermite polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=large%20time%20asymptotics" title=" large time asymptotics"> large time asymptotics</a> </p> <a href="https://publications.waset.org/abstracts/65872/large-time-asymptotic-behavior-to-solutions-of-a-forced-burgers-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65872.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">333</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">7178</span> Globally Attractive Mild Solutions for Non-Local in Time Subdiffusion Equations of Neutral Type</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Gonzalez%20Camus">Jorge Gonzalez Camus</a>, <a href="https://publications.waset.org/abstracts/search?q=Carlos%20Lizama"> Carlos Lizama</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=attractive%20mild%20solutions" title="attractive mild solutions">attractive mild solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20Volterra%20equations" title=" integral Volterra equations"> integral Volterra equations</a>, <a href="https://publications.waset.org/abstracts/search?q=neutral%20type%20equations" title=" neutral type equations"> neutral type equations</a>, <a href="https://publications.waset.org/abstracts/search?q=non-local%20in%20time%20equations" title=" non-local in time equations"> non-local in time equations</a> </p> <a href="https://publications.waset.org/abstracts/99925/globally-attractive-mild-solutions-for-non-local-in-time-subdiffusion-equations-of-neutral-type" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99925.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">158</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">7177</span> Existence of Minimal and Maximal Mild Solutions for Non-Local in Time Subdiffusion Equations of Neutral Type</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Gonzalez-Camus">Jorge Gonzalez-Camus</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20evolution%20equations" title="fractional evolution equations">fractional evolution equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Volterra%20integral%20equations" title=" Volterra integral equations"> Volterra integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=minimal%20and%20maximal%20mild%20solutions" title=" minimal and maximal mild solutions"> minimal and maximal mild solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=neutral%20type%20equations" title=" neutral type equations"> neutral type equations</a>, <a href="https://publications.waset.org/abstracts/search?q=non-local%20in%20time%20equations" title=" non-local in time equations"> non-local in time equations</a> </p> <a href="https://publications.waset.org/abstracts/105179/existence-of-minimal-and-maximal-mild-solutions-for-non-local-in-time-subdiffusion-equations-of-neutral-type" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/105179.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">176</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">7176</span> A Proof of the N. Davydov Theorem for Douglis Algebra Valued Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jean-Marie%20Vilaire">Jean-Marie Vilaire</a>, <a href="https://publications.waset.org/abstracts/search?q=Ricardo%20Abreu-Blaya"> Ricardo Abreu-Blaya</a>, <a href="https://publications.waset.org/abstracts/search?q=Juan%20Bory-Reyes"> Juan Bory-Reyes</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Beltrami%20equation" title="Beltrami equation">Beltrami equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Douglis%20algebra-valued%20function" title=" Douglis algebra-valued function"> Douglis algebra-valued function</a>, <a href="https://publications.waset.org/abstracts/search?q=Hypercomplex%20Cauchy%20type%20integral" title=" Hypercomplex Cauchy type integral"> Hypercomplex Cauchy type integral</a>, <a href="https://publications.waset.org/abstracts/search?q=Sokhotski-Plemelj%20formulae" title=" Sokhotski-Plemelj formulae"> Sokhotski-Plemelj formulae</a> </p> <a href="https://publications.waset.org/abstracts/92078/a-proof-of-the-n-davydov-theorem-for-douglis-algebra-valued-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/92078.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">250</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">7175</span> Optimization of Fourth Order Discrete-Approximation Inclusions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elimhan%20N.%20Mahmudov">Elimhan N. Mahmudov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper concerns the necessary and sufficient conditions of optimality for Cauchy problem of fourth order discrete (PD) and discrete-approximate (PDA) inclusions. The main problem is formulation of the fourth order adjoint discrete and discrete-approximate inclusions and transversality conditions, which are peculiar to problems including fourth order derivatives and approximate derivatives. Thus the necessary and sufficient conditions of optimality are obtained incorporating the Euler-Lagrange and Hamiltonian forms of inclusions. Derivation of optimality conditions are based on the apparatus of locally adjoint mapping (LAM). Moreover in the application of these results we consider the fourth order linear discrete and discrete-approximate inclusions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=difference" title="difference">difference</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=fourth" title=" fourth"> fourth</a>, <a href="https://publications.waset.org/abstracts/search?q=approximation" title=" approximation"> approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=transversality" title=" transversality"> transversality</a> </p> <a href="https://publications.waset.org/abstracts/25199/optimization-of-fourth-order-discrete-approximation-inclusions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25199.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">374</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">7174</span> Temperature Coefficients of the Refractive Index for Ge Film</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lingmao%20Xu">Lingmao Xu</a>, <a href="https://publications.waset.org/abstracts/search?q=Hui%20Zhou"> Hui Zhou</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Ge film is widely used in infrared optical systems. Because of the special requirements of space application, it is usually used in low temperature. The refractive index of Ge film is always changed with the temperature which has a great effect on the manufacture of high precision infrared optical film. Specimens of Ge single film were deposited at ZnSe substrates by EB-PVD method. During temperature range 80K ~ 300K, the transmittance of Ge single film within 2 ~ 15 μm were measured every 20K by PerkinElmer FTIR cryogenic testing system. By the full spectrum inversion method fitting, the relationship between refractive index and wavelength within 2 ~ 12μm at different temperatures was received. It can be seen the relationship consistent with the formula Cauchy, which can be fitted. Then the relationship between refractive index of the Ge film and temperature/wavelength was obtained by fitting method based on formula Cauchy. Finally, the designed value obtained by the formula and the measured spectrum were compared to verify the accuracy of the formula. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=infrared%20optical%20film" title="infrared optical film">infrared optical film</a>, <a href="https://publications.waset.org/abstracts/search?q=low%20temperature" title=" low temperature"> low temperature</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20refractive%20coefficient" title=" thermal refractive coefficient"> thermal refractive coefficient</a>, <a href="https://publications.waset.org/abstracts/search?q=Ge%20film" title=" Ge film"> Ge film</a> </p> <a href="https://publications.waset.org/abstracts/71052/temperature-coefficients-of-the-refractive-index-for-ge-film" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/71052.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">298</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">7173</span> [Keynote Talk]: Discovering Liouville-Type Problems for p-Energy Minimizing Maps in Closed Half-Ellipsoids by Calculus Variation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lina%20Wu">Lina Wu</a>, <a href="https://publications.waset.org/abstracts/search?q=Jia%20Liu"> Jia Liu</a>, <a href="https://publications.waset.org/abstracts/search?q=Ye%20Li"> Ye Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in this project is to construct a family of variation maps such that the images of variation maps must be guaranteed in a closed half-ellipsoid. The other challenging point is to find a contradiction between the lower bound and the upper bound in an analysis of p-Harmonic Stability Inequality when a p-energy minimizing map is not constant. Therefore, the possibility of a non-constant p-energy minimizing map has been ruled out and the constant property for a p-energy minimizing map has been obtained. Our research finding is to explore the constant property for a p-stable map from a Euclidean space into a closed half-ellipsoid in a certain range of p. The certain range of p is determined by the dimension values of a Euclidean space (the domain) and an ellipsoid (the target space). The certain range of p is also bounded by the curvature values on an ellipsoid (that is, the ratio of the longest axis to the shortest axis). Regarding Liouville-type results for a p-stable map, our research finding on an ellipsoid is a generalization of mathematicians’ results on a sphere. Our result is also an extension of mathematicians’ Liouville-type results from a special ellipsoid with only one parameter to any ellipsoid with (n+1) parameters in the general setting. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bochner%20formula" title="Bochner formula">Bochner formula</a>, <a href="https://publications.waset.org/abstracts/search?q=Calculus%20Stokes%27%20Theorem" title=" Calculus Stokes' Theorem"> Calculus Stokes' Theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=Cauchy-Schwarz%20Inequality" title=" Cauchy-Schwarz Inequality"> Cauchy-Schwarz Inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=first%20and%20second%20variation%20formulas" title=" first and second variation formulas"> first and second variation formulas</a>, <a href="https://publications.waset.org/abstracts/search?q=Liouville-type%20problem" title=" Liouville-type problem"> Liouville-type problem</a>, <a href="https://publications.waset.org/abstracts/search?q=p-harmonic%20map" title=" p-harmonic map"> p-harmonic map</a> </p> <a href="https://publications.waset.org/abstracts/54197/keynote-talk-discovering-liouville-type-problems-for-p-energy-minimizing-maps-in-closed-half-ellipsoids-by-calculus-variation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54197.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">274</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">7172</span> Hardy Type Inequalities of Two-Dimensional on Time Scales via Steklov Operator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wedad%20Albalawi">Wedad Albalawi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is defined as a closed subset contains real numbers. Then the inequalities of time scales version have received a lot of attention and has had a major field in both pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on double integrals to obtain new time-scale inequalities of Copson driven by Steklov operator. They will be applied in the solution of the Cauchy problem for the wave equation. The proof can be done by introducing restriction on the operator in several cases. In addition, the obtained inequalities done by using some concepts in time scale version such as time scales calculus, theorem of Fubini and the inequality of H¨older. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=time%20scales" title="time scales">time scales</a>, <a href="https://publications.waset.org/abstracts/search?q=inequality%20of%20Hardy" title=" inequality of Hardy"> inequality of Hardy</a>, <a href="https://publications.waset.org/abstracts/search?q=inequality%20of%20Coposon" title=" inequality of Coposon"> inequality of Coposon</a>, <a href="https://publications.waset.org/abstracts/search?q=Steklov%20operator" title=" Steklov operator"> Steklov operator</a> </p> <a href="https://publications.waset.org/abstracts/173546/hardy-type-inequalities-of-two-dimensional-on-time-scales-via-steklov-operator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/173546.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">7171</span> Study on Optimal Control Strategy of PM2.5 in Wuhan, China</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Qiuling%20Xie">Qiuling Xie</a>, <a href="https://publications.waset.org/abstracts/search?q=Shanliang%20Zhu"> Shanliang Zhu</a>, <a href="https://publications.waset.org/abstracts/search?q=Zongdi%20Sun"> Zongdi Sun</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=grey%20relational%20degree" title="grey relational degree">grey relational degree</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20linear%20regression" title=" multiple linear regression"> multiple linear regression</a>, <a href="https://publications.waset.org/abstracts/search?q=membership%20function" title=" membership function"> membership function</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20programming" title=" nonlinear programming"> nonlinear programming</a> </p> <a href="https://publications.waset.org/abstracts/54538/study-on-optimal-control-strategy-of-pm25-in-wuhan-china" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54538.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">299</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">7170</span> A Study of Evolutional Control Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ti-Jun%20Xiao">Ti-Jun Xiao</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhe%20Xu"> Zhe Xu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Controllability is one of the fundamental issues in control systems. In this paper, we study the controllability of second order evolutional control systems in Hilbert spaces with memory and boundary controls, which model dynamic behaviors of some viscoelastic materials. Transferring the control problem into a moment problem and showing the Riesz property of a family of functions related to Cauchy problems for some integrodifferential equations, we obtain a general boundary controllability theorem for these second order evolutional control systems. This controllability theorem is applicable to various concrete 1D viscoelastic systems and recovers some previous related results. It is worth noting that Riesz sequences can be used for numerical computations of the control functions and the identification of new Riesz sequence is of independent interest for the basis-function theory. Moreover, using the Riesz sequences, we obtain the existence and uniqueness of (weak) solutions to these second order evolutional control systems in Hilbert spaces. Finally, we derive the exact boundary controllability of a viscoelastic beam equation, as an application of our abstract theorem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=evolutional%20control%20system" title="evolutional control system">evolutional control system</a>, <a href="https://publications.waset.org/abstracts/search?q=controllability" title=" controllability"> controllability</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20control" title=" boundary control"> boundary control</a>, <a href="https://publications.waset.org/abstracts/search?q=existence%20and%20uniqueness" title=" existence and uniqueness"> existence and uniqueness</a> </p> <a href="https://publications.waset.org/abstracts/93935/a-study-of-evolutional-control-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/93935.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">222</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">7169</span> Inventory Policy Above Country Level for Cooperating Countries for Vaccines</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aysun%20P%C4%B1narba%C5%9F%C4%B1">Aysun Pınarbaşı</a>, <a href="https://publications.waset.org/abstracts/search?q=B%C3%A9la%20Vizv%C3%A1ri"> Béla Vizvári</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The countries are the units that procure the vaccines during the COVID-19 pandemic. The delivered quantities are huge. The countries must bear the inventory holding cost according to the variation of stock quantities. This cost depends on the speed of the vaccination in the country. This speed is time-dependent. The vaccinated portion of the population can be approximated by the cumulative distribution function of the Cauchy distribution. A model is provided for determining the minimal-cost inventory policy, and its optimality conditions are provided. The model is solved for 20 countries for different numbers of procurements. The results reveal the individual behavior of each country. We provide an inventory policy for the pandemic period for the countries. This paper presents a deterministic model for vaccines with a demand rate variable over time for the countries. It is aimed to provide an analytical model to deal with the minimization of holding cost and develop inventory policies regarding this aim to be used for a variety of perishable products such as vaccines. The saturation process is introduced, and an approximation of the vaccination curve of the countries has been discussed. According to this aspect, a deterministic model for inventory policy has been developed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=covid-19" title="covid-19">covid-19</a>, <a href="https://publications.waset.org/abstracts/search?q=vaccination" title=" vaccination"> vaccination</a>, <a href="https://publications.waset.org/abstracts/search?q=inventory%20policy" title=" inventory policy"> inventory policy</a>, <a href="https://publications.waset.org/abstracts/search?q=bounded%20total%20demand" title=" bounded total demand"> bounded total demand</a>, <a href="https://publications.waset.org/abstracts/search?q=inventory%20holding%20cost" title=" inventory holding cost"> inventory holding cost</a>, <a href="https://publications.waset.org/abstracts/search?q=cauchy%20distribution" title=" cauchy distribution"> cauchy distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=sigmoid%20function" title=" sigmoid function"> sigmoid function</a> </p> <a href="https://publications.waset.org/abstracts/162848/inventory-policy-above-country-level-for-cooperating-countries-for-vaccines" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/162848.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">75</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">7168</span> Dynamic Analysis of Differential Systems with Infinite Memory and Damping</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kun-Peng%20Jin">Kun-Peng Jin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jin%20Liang"> Jin Liang</a>, <a href="https://publications.waset.org/abstracts/search?q=Ti-Jun%20Xiao"> Ti-Jun Xiao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we are concerned with the dynamic behaviors of solutions to some coupled systems with infinite memory, which consist of two partial differential equations where only one partial differential equation has damping. Such coupled systems are good mathematical models to describe the deformation and stress characteristics of some viscoelastic materials affected by temperature change, external forces, and other factors. By using the theory of operator semigroups, we give wellposedness results for the Cauchy problem for these coupled systems. Then, with the help of some auxiliary functions and lemmas, which are specially designed for overcoming difficulties in the proof, we show that the solutions of the coupled systems decay to zero in a strong way under a few basic conditions. The results in this dynamic analysis of coupled systems are generalizations of many existing results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20analysis" title="dynamic analysis">dynamic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=coupled%20system" title=" coupled system"> coupled system</a>, <a href="https://publications.waset.org/abstracts/search?q=infinite%20memory" title=" infinite memory"> infinite memory</a>, <a href="https://publications.waset.org/abstracts/search?q=damping." title=" damping."> damping.</a> </p> <a href="https://publications.waset.org/abstracts/93937/dynamic-analysis-of-differential-systems-with-infinite-memory-and-damping" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/93937.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">220</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">7167</span> New Hardy Type Inequalities of Two-Dimensional on Time Scales via Steklov Operator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wedad%20Albalawi">Wedad Albalawi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques, and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then, dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is an arbitrary nonempty closed subset of the real numbers. Then, the dynamic inequalities on time scales have received a lot of attention in the literature and has become a major field in pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on Hardy and Coposon inequalities, using Steklov operator on time scale in double integrals to obtain special cases of time-scale inequalities of Hardy and Copson on high dimensions. The advantage of this study is that it uses the one-dimensional classical Hardy inequality to obtain higher dimensional on time scale versions that will be applied in the solution of the Cauchy problem for the wave equation. In addition, the obtained inequalities have various applications involving discontinuous domains such as bug populations, phytoremediation of metals, wound healing, maximization problems. The proof can be done by introducing restriction on the operator in several cases. The concepts in time scale version such as time scales calculus will be used that allows to unify and extend many problems from the theories of differential and of difference equations. In addition, using chain rule, and some properties of multiple integrals on time scales, some theorems of Fubini and the inequality of H¨older. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=time%20scales" title="time scales">time scales</a>, <a href="https://publications.waset.org/abstracts/search?q=inequality%20of%20hardy" title=" inequality of hardy"> inequality of hardy</a>, <a href="https://publications.waset.org/abstracts/search?q=inequality%20of%20coposon" title=" inequality of coposon"> inequality of coposon</a>, <a href="https://publications.waset.org/abstracts/search?q=steklov%20operator" title=" steklov operator"> steklov operator</a> </p> <a href="https://publications.waset.org/abstracts/173399/new-hardy-type-inequalities-of-two-dimensional-on-time-scales-via-steklov-operator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/173399.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">95</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">7166</span> 3D Codes for Unsteady Interaction Problems of Continuous Mechanics in Euler Variables</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Abuziarov">M. Abuziarov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The designed complex is intended for the numerical simulation of fast dynamic processes of interaction of heterogeneous environments susceptible to the significant formability. The main challenges in solving such problems are associated with the construction of the numerical meshes. Currently, there are two basic approaches to solve this problem. One is using of Lagrangian or Lagrangian Eulerian grid associated with the boundaries of media and the second is associated with the fixed Eulerian mesh, boundary cells of which cut boundaries of the environment medium and requires the calculation of these cut volumes. Both approaches require the complex grid generators and significant time for preparing the code’s data for simulation. In this codes these problems are solved using two grids, regular fixed and mobile local Euler Lagrange - Eulerian (ALE approach) accompanying the contact and free boundaries, the surfaces of shock waves and phase transitions, and other possible features of solutions, with mutual interpolation of integrated parameters. For modeling of both liquids and gases, and deformable solids the Godunov scheme of increased accuracy is used in Lagrangian - Eulerian variables, the same for the Euler equations and for the Euler- Cauchy, describing the deformation of the solid. The increased accuracy of the scheme is achieved by using 3D spatial time dependent solution of the discontinuity problem (3D space time dependent Riemann's Problem solver). The same solution is used to calculate the interaction at the liquid-solid surface (Fluid Structure Interaction problem). The codes does not require complex 3D mesh generators, only the surfaces of the calculating objects as the STL files created by means of engineering graphics are given by the user, which greatly simplifies the preparing the task and makes it convenient to use directly by the designer at the design stage. The results of the test solutions and applications related to the generation and extension of the detonation and shock waves, loading the constructions are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fluid%20structure%20interaction" title="fluid structure interaction">fluid structure interaction</a>, <a href="https://publications.waset.org/abstracts/search?q=Riemann%27s%20solver" title=" Riemann's solver"> Riemann's solver</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler%20variables" title=" Euler variables"> Euler variables</a>, <a href="https://publications.waset.org/abstracts/search?q=3D%20codes" title=" 3D codes"> 3D codes</a> </p> <a href="https://publications.waset.org/abstracts/17837/3d-codes-for-unsteady-interaction-problems-of-continuous-mechanics-in-euler-variables" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17837.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">439</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">7165</span> Solving the Transportation Problem for Warehouses and Dealers in Bangalore City</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Aditya">S. Aditya</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20T.%20Nideesh"> K. T. Nideesh</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Guruprasad"> N. Guruprasad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Being a subclass of linear programing problem, the Transportation Problem is a classic Operations Research problem where the objective is to determine the schedule for transporting goods from source to destination in a way that minimizes the shipping cost while satisfying supply and demand constraints. In this paper, we are representing the transportation problem for various warehouses along with various dealers situated in Bangalore city to reduce the transportation cost incurred by them as of now. The problem is solved by obtaining the Initial Basic feasible Solution through various methods and further proceeding to obtain optimal cost. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=NW%20method" title="NW method">NW method</a>, <a href="https://publications.waset.org/abstracts/search?q=optimum%20utilization" title=" optimum utilization"> optimum utilization</a>, <a href="https://publications.waset.org/abstracts/search?q=transportation%20problem" title=" transportation problem"> transportation problem</a>, <a href="https://publications.waset.org/abstracts/search?q=Vogel%E2%80%99s%20approximation%20method" title=" Vogel’s approximation method"> Vogel’s approximation method</a> </p> <a href="https://publications.waset.org/abstracts/19160/solving-the-transportation-problem-for-warehouses-and-dealers-in-bangalore-city" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19160.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">437</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">7164</span> Using Convergent and Divergent Thinking in Creative Problem Solving in Mathematics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Keng%20Keh%20Lim">Keng Keh Lim</a>, <a href="https://publications.waset.org/abstracts/search?q=Zaleha%20Ismail"> Zaleha Ismail</a>, <a href="https://publications.waset.org/abstracts/search?q=Yudariah%20Mohammad%20Yusof"> Yudariah Mohammad Yusof</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper aims to find out how students using convergent and divergent thinking in creative problem solving to solve mathematical problems creatively. Eight engineering undergraduates in a local university took part in this study. They were divided into two groups. They solved the mathematical problems with the use of creative problem solving skills. Their solutions were collected and analyzed to reveal all the processes of problem solving, namely: problem definition, ideas generation, ideas evaluation, ideas judgment, and solution implementation. The result showed that the students were able to solve the mathematical problem with the use of creative problem solving skills. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convergent%20thinking" title="convergent thinking">convergent thinking</a>, <a href="https://publications.waset.org/abstracts/search?q=divergent%20thinking" title=" divergent thinking"> divergent thinking</a>, <a href="https://publications.waset.org/abstracts/search?q=creative%20problem%20solving" title=" creative problem solving"> creative problem solving</a>, <a href="https://publications.waset.org/abstracts/search?q=creativity" title=" creativity"> creativity</a> </p> <a href="https://publications.waset.org/abstracts/77631/using-convergent-and-divergent-thinking-in-creative-problem-solving-in-mathematics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77631.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">349</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">7163</span> Fuzzy Vehicle Routing Problem for Extreme Environment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=G.%20Sirbiladze">G. Sirbiladze</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Ghvaberidze"> B. Ghvaberidze</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Matsaberidze"> B. Matsaberidze</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A fuzzy vehicle routing problem is considered in the possibilistic environment. A new criterion, maximization of expectation of reliability for movement on closed routes is constructed. The objective of the research is to implement a two-stage scheme for solution of this problem. Based on the algorithm of preferences on the first stage, the sample of so-called “promising” routes will be selected. On the second stage, for the selected promising routes new bi-criteria problem will be solved - minimization of total traveled distance and maximization of reliability of routes. The problem will be stated as a fuzzy-partitioning problem. Two possible solutions of this scheme are considered. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=vehicle%20routing%20problem" title="vehicle routing problem">vehicle routing problem</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20partitioning%20problem" title=" fuzzy partitioning problem"> fuzzy partitioning problem</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple-criteria%20optimization" title=" multiple-criteria optimization"> multiple-criteria optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=possibility%20theory" title=" possibility theory"> possibility theory</a> </p> <a href="https://publications.waset.org/abstracts/9460/fuzzy-vehicle-routing-problem-for-extreme-environment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9460.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">547</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">7162</span> Partial Knowledge Transfer Between the Source Problem and the Target Problem in Genetic Algorithms</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Terence%20Soule">Terence Soule</a>, <a href="https://publications.waset.org/abstracts/search?q=Tami%20Al%20Ghamdi"> Tami Al Ghamdi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> To study how the partial knowledge transfer may affect the Genetic Algorithm (GA) performance, we model the Transfer Learning (TL) process using GA as the model solver. The objective of the TL is to transfer the knowledge from one problem to another related problem. This process imitates how humans think in their daily life. In this paper, we proposed to study a case where the knowledge transferred from the S problem has less information than what the T problem needs. We sampled the transferred population using different strategies of TL. The results showed transfer part of the knowledge is helpful and speeds the GA process of finding a solution to the problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=transfer%20learning" title="transfer learning">transfer learning</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20transfer" title=" partial transfer"> partial transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=evolutionary%20computation" title=" evolutionary computation"> evolutionary computation</a>, <a href="https://publications.waset.org/abstracts/search?q=genetic%20algorithm" title=" genetic algorithm"> genetic algorithm</a> </p> <a href="https://publications.waset.org/abstracts/147924/partial-knowledge-transfer-between-the-source-problem-and-the-target-problem-in-genetic-algorithms" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/147924.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">132</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">7161</span> Bee Colony Optimization Applied to the Bin Packing Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kenza%20Aida%20Amara">Kenza Aida Amara</a>, <a href="https://publications.waset.org/abstracts/search?q=Bachir%20Djebbar"> Bachir Djebbar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bee%20colony%20optimization" title="bee colony optimization">bee colony optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=bin%20packing" title=" bin packing"> bin packing</a>, <a href="https://publications.waset.org/abstracts/search?q=heuristic%20algorithm" title=" heuristic algorithm"> heuristic algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=pretreatment" title=" pretreatment"> pretreatment</a> </p> <a href="https://publications.waset.org/abstracts/65005/bee-colony-optimization-applied-to-the-bin-packing-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65005.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">633</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">7160</span> A Method for Solving a Bi-Objective Transportation Problem under Fuzzy Environment </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sukhveer%20Singh">Sukhveer Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Sandeep%20Singh"> Sandeep Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=uncertain%20transportation%20problem" title="uncertain transportation problem">uncertain transportation problem</a>, <a href="https://publications.waset.org/abstracts/search?q=efficient%20solution" title=" efficient solution"> efficient solution</a>, <a href="https://publications.waset.org/abstracts/search?q=ranking%20function" title=" ranking function"> ranking function</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20transportation%20problem" title=" fuzzy transportation problem"> fuzzy transportation problem</a> </p> <a href="https://publications.waset.org/abstracts/73312/a-method-for-solving-a-bi-objective-transportation-problem-under-fuzzy-environment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73312.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">525</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">7159</span> Cooperative Coevolution for Neuro-Evolution of Feed Forward Networks for Time Series Prediction Using Hidden Neuron Connections</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ravneil%20Nand">Ravneil Nand</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Cooperative coevolution uses problem decomposition methods to solve a larger problem. The problem decomposition deals with breaking down the larger problem into a number of smaller sub-problems depending on their method. Different problem decomposition methods have their own strengths and limitations depending on the neural network used and application problem. In this paper we are introducing a new problem decomposition method known as Hidden-Neuron Level Decomposition (HNL). The HNL method is competing with established problem decomposition method in time series prediction. The results show that the proposed approach has improved the results in some benchmark data sets when compared to the standalone method and has competitive results when compared to methods from literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cooperative%20coevaluation" title="cooperative coevaluation">cooperative coevaluation</a>, <a href="https://publications.waset.org/abstracts/search?q=feed%20forward%20network" title=" feed forward network"> feed forward network</a>, <a href="https://publications.waset.org/abstracts/search?q=problem%20decomposition" title=" problem decomposition"> problem decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=neuron" title=" neuron"> neuron</a>, <a href="https://publications.waset.org/abstracts/search?q=synapse" title=" synapse"> synapse</a> </p> <a href="https://publications.waset.org/abstracts/29237/cooperative-coevolution-for-neuro-evolution-of-feed-forward-networks-for-time-series-prediction-using-hidden-neuron-connections" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29237.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">335</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">7158</span> Solution of Nonlinear Fractional Programming Problem with Bounded Parameters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mrinal%20Jana">Mrinal Jana</a>, <a href="https://publications.waset.org/abstracts/search?q=Geetanjali%20Panda"> Geetanjali Panda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20programming" title="fractional programming">fractional programming</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20valued%20function" title=" interval valued function"> interval valued function</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20inequalities" title=" interval inequalities"> interval inequalities</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20order%20relation" title=" partial order relation"> partial order relation</a> </p> <a href="https://publications.waset.org/abstracts/22261/solution-of-nonlinear-fractional-programming-problem-with-bounded-parameters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22261.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">519</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">7157</span> Exhaustive Study of Essential Constraint Satisfaction Problem Techniques Based on N-Queens Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Md.%20Ahsan%20Ayub">Md. Ahsan Ayub</a>, <a href="https://publications.waset.org/abstracts/search?q=Kazi%20A.%20Kalpoma"> Kazi A. Kalpoma</a>, <a href="https://publications.waset.org/abstracts/search?q=Humaira%20Tasnim%20Proma"> Humaira Tasnim Proma</a>, <a href="https://publications.waset.org/abstracts/search?q=Syed%20Mehrab%20Kabir"> Syed Mehrab Kabir</a>, <a href="https://publications.waset.org/abstracts/search?q=Rakib%20Ibna%20Hamid%20Chowdhury"> Rakib Ibna Hamid Chowdhury</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Constraint Satisfaction Problem (CSP) is observed in various applications, i.e., scheduling problems, timetabling problems, assignment problems, etc. Researchers adopt a CSP technique to tackle a certain problem; however, each technique follows different approaches and ways to solve a problem network. In our exhaustive study, it has been possible to visualize the processes of essential CSP algorithms from a very concrete constraint satisfaction example, NQueens Problem, in order to possess a deep understanding about how a particular constraint satisfaction problem will be dealt with by our studied and implemented techniques. Besides, benchmark results - time vs. value of N in N-Queens - have been generated from our implemented approaches, which help understand at what factor each algorithm produces solutions; especially, in N-Queens puzzle. Thus, extended decisions can be made to instantiate a real life problem within CSP’s framework. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=arc%20consistency%20%28AC%29" title="arc consistency (AC)">arc consistency (AC)</a>, <a href="https://publications.waset.org/abstracts/search?q=backjumping%20algorithm%20%28BJ%29" title=" backjumping algorithm (BJ)"> backjumping algorithm (BJ)</a>, <a href="https://publications.waset.org/abstracts/search?q=backtracking%20algorithm%20%28BT%29" title=" backtracking algorithm (BT)"> backtracking algorithm (BT)</a>, <a href="https://publications.waset.org/abstracts/search?q=constraint%20satisfaction%20problem%20%28CSP%29" title=" constraint satisfaction problem (CSP)"> constraint satisfaction problem (CSP)</a>, <a href="https://publications.waset.org/abstracts/search?q=forward%20checking%20%28FC%29" title=" forward checking (FC)"> forward checking (FC)</a>, <a href="https://publications.waset.org/abstracts/search?q=least%20constrained%20values%20%28LCV%29" title=" least constrained values (LCV)"> least constrained values (LCV)</a>, <a href="https://publications.waset.org/abstracts/search?q=maintaining%20arc%20consistency%20%28MAC%29" title=" maintaining arc consistency (MAC)"> maintaining arc consistency (MAC)</a>, <a href="https://publications.waset.org/abstracts/search?q=minimum%20remaining%20values%20%28MRV%29" title=" minimum remaining values (MRV)"> minimum remaining values (MRV)</a>, <a href="https://publications.waset.org/abstracts/search?q=N-Queens%20problem" title=" N-Queens problem"> N-Queens problem</a> </p> <a href="https://publications.waset.org/abstracts/69933/exhaustive-study-of-essential-constraint-satisfaction-problem-techniques-based-on-n-queens-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/69933.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">364</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">7156</span> Explicit Iterative Scheme for Approximating a Common Solution of Generalized Mixed Equilibrium Problem and Fixed Point Problem for a Nonexpansive Semigroup in Hilbert Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Farid">Mohammad Farid</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generalized%20mixed%20equilibrium%20problem" title="generalized mixed equilibrium problem">generalized mixed equilibrium problem</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed-point%20problem" title=" fixed-point problem"> fixed-point problem</a>, <a href="https://publications.waset.org/abstracts/search?q=nonexpansive%20semigroup" title=" nonexpansive semigroup"> nonexpansive semigroup</a>, <a href="https://publications.waset.org/abstracts/search?q=variational%20inequality%20problem" title=" variational inequality problem"> variational inequality problem</a>, <a href="https://publications.waset.org/abstracts/search?q=iterative%20algorithms" title=" iterative algorithms"> iterative algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20extragradient%20method" title=" hybrid extragradient method"> hybrid extragradient method</a> </p> <a href="https://publications.waset.org/abstracts/14070/explicit-iterative-scheme-for-approximating-a-common-solution-of-generalized-mixed-equilibrium-problem-and-fixed-point-problem-for-a-nonexpansive-semigroup-in-hilbert-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14070.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">7155</span> Regret-Regression for Multi-Armed Bandit Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Deyadeen%20Ali%20Alshibani">Deyadeen Ali Alshibani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the literature, the multi-armed bandit problem as a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. There are several different algorithms models and their applications on this problem. In this paper, we evaluate the Regret-regression through comparing with Q-learning method. A simulation on determination of optimal treatment regime is presented in detail. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimal" title="optimal">optimal</a>, <a href="https://publications.waset.org/abstracts/search?q=bandit%20problem" title=" bandit problem"> bandit problem</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20programming" title=" dynamic programming"> dynamic programming</a> </p> <a href="https://publications.waset.org/abstracts/18593/regret-regression-for-multi-armed-bandit-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/18593.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">453</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">7154</span> Analysis of Chatterjea Type F-Contraction in F-Metric Space and Application</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Awais%20Asif">Awais Asif</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This article investigates fixed point theorems of Chatterjea type F-contraction in the setting of F-metric space. We relax the conditions of F-contraction and define modified F-contraction for two mappings. The study provides fixed point results for both single-valued and multivalued mappings. The results are further extended to common fixed point theorems for two mappings. Moreover, to discuss the applicability of our results, an application is provided, which shows the role of our results in finding the solution to functional equations in dynamic programming. Our results generalize and extend the existing results in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chatterjea%20type%20F-contraction" title="Chatterjea type F-contraction">Chatterjea type F-contraction</a>, <a href="https://publications.waset.org/abstracts/search?q=F-cauchy%20sequence" title=" F-cauchy sequence"> F-cauchy sequence</a>, <a href="https://publications.waset.org/abstracts/search?q=F-convergent" title=" F-convergent"> F-convergent</a>, <a href="https://publications.waset.org/abstracts/search?q=multi%20valued%20mappings" title=" multi valued mappings"> multi valued mappings</a> </p> <a href="https://publications.waset.org/abstracts/108223/analysis-of-chatterjea-type-f-contraction-in-f-metric-space-and-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/108223.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">143</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">7153</span> A Fuzzy Programming Approach for Solving Intuitionistic Fuzzy Linear Fractional Programming Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sujeet%20Kumar%20Singh">Sujeet Kumar Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Shiv%20Prasad%20Yadav"> Shiv Prasad Yadav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=triangular%20intuitionistic%20fuzzy%20number" title="triangular intuitionistic fuzzy number">triangular intuitionistic fuzzy number</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming%20problem" title=" linear programming problem"> linear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=multi%20objective%20linear%20programming%20problem" title=" multi objective linear programming problem"> multi objective linear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20mathematical%20programming" title=" fuzzy mathematical programming"> fuzzy mathematical programming</a>, <a href="https://publications.waset.org/abstracts/search?q=membership%20function" title=" membership function"> membership function</a> </p> <a href="https://publications.waset.org/abstracts/16411/a-fuzzy-programming-approach-for-solving-intuitionistic-fuzzy-linear-fractional-programming-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16411.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">566</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">7152</span> Hybrid Equity Warrants Pricing Formulation under Stochastic Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Teh%20Raihana%20Nazirah%20Roslan">Teh Raihana Nazirah Roslan</a>, <a href="https://publications.waset.org/abstracts/search?q=Siti%20Zulaiha%20Ibrahim"> Siti Zulaiha Ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=Sharmila%20Karim"> Sharmila Karim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cox-Ingersoll-Ross%20model" title="Cox-Ingersoll-Ross model">Cox-Ingersoll-Ross model</a>, <a href="https://publications.waset.org/abstracts/search?q=equity%20warrants" title=" equity warrants"> equity warrants</a>, <a href="https://publications.waset.org/abstracts/search?q=Heston%20model" title=" Heston model"> Heston model</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20models" title=" hybrid models"> hybrid models</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic" title=" stochastic"> stochastic</a> </p> <a href="https://publications.waset.org/abstracts/124157/hybrid-equity-warrants-pricing-formulation-under-stochastic-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124157.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">129</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=cauchy%20problem&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=cauchy%20problem&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=cauchy%20problem&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=cauchy%20problem&page=5">5</a></li> <li class="page-item"><a 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