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integral</title> <meta name="description" content="Search results for: elliptic integral"> <meta name="keywords" content="elliptic integral"> <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 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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="elliptic integral"> <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> 887</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: elliptic integral</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">887</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">886</span> Remarks on the Lattice Green's Function for the Anisotropic Face Cantered Cubic Lattice</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jihad%20H.%20Asad">Jihad H. Asad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An expression for the Green’s function (GF) of anisotropic face cantered cubic (IFCC) lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kind. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=lattice%20Green%27s%20function" title="lattice Green's function">lattice Green's function</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20integral" title=" elliptic integral"> elliptic integral</a>, <a href="https://publications.waset.org/abstracts/search?q=physics" title=" physics"> physics</a>, <a href="https://publications.waset.org/abstracts/search?q=cubic%20lattice" title=" cubic lattice"> cubic lattice</a> </p> <a href="https://publications.waset.org/abstracts/5976/remarks-on-the-lattice-greens-function-for-the-anisotropic-face-cantered-cubic-lattice" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5976.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">466</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">885</span> Improved of Elliptic Curves Cryptography over a Ring</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdelhakim%20Chillali">Abdelhakim Chillali</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdelhamid%20Tadmori"> Abdelhamid Tadmori</a>, <a href="https://publications.waset.org/abstracts/search?q=Muhammed%20Ziane"> Muhammed Ziane</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article we will study the elliptic curve defined over the ring An and we define the mathematical operations of ECC, which provides a high security and advantage for wireless applications compared to other asymmetric key cryptosystem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=elliptic%20curves" title="elliptic curves">elliptic curves</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20ring" title=" finite ring"> finite ring</a>, <a href="https://publications.waset.org/abstracts/search?q=cryptography" title=" cryptography"> cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=study" title=" study"> study</a> </p> <a href="https://publications.waset.org/abstracts/24042/improved-of-elliptic-curves-cryptography-over-a-ring" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24042.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">372</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">884</span> A Study of General Attacks on Elliptic Curve Discrete Logarithm Problem over Prime Field and Binary Field</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tun%20Myat%20Aung">Tun Myat Aung</a>, <a href="https://publications.waset.org/abstracts/search?q=Ni%20Ni%20Hla"> Ni Ni Hla</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper begins by describing basic properties of finite field and elliptic curve cryptography over prime field and binary field. Then we discuss the discrete logarithm problem for elliptic curves and its properties. We study the general common attacks on elliptic curve discrete logarithm problem such as the Baby Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman method, and describe in detail experiments of these attacks over prime field and binary field. The paper finishes by describing expected running time of the attacks and suggesting strong elliptic curves that are not susceptible to these attacks.c <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete%20logarithm%20problem" title="discrete logarithm problem">discrete logarithm problem</a>, <a href="https://publications.waset.org/abstracts/search?q=general%20attacks" title=" general attacks"> general attacks</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20curve" title=" elliptic curve"> elliptic curve</a>, <a href="https://publications.waset.org/abstracts/search?q=prime%20field" title=" prime field"> prime field</a>, <a href="https://publications.waset.org/abstracts/search?q=binary%20field" title=" binary field"> binary field</a> </p> <a href="https://publications.waset.org/abstracts/82212/a-study-of-general-attacks-on-elliptic-curve-discrete-logarithm-problem-over-prime-field-and-binary-field" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/82212.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">233</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">883</span> Exact Solutions of K(N,N)-Type Equations Using Jacobi Elliptic Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Edamana%20Krishnan">Edamana Krishnan</a>, <a href="https://publications.waset.org/abstracts/search?q=Khalil%20Al-Ghafri"> Khalil Al-Ghafri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=travelling%20wave%20solutions" title="travelling wave solutions">travelling wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20wave%20solutions" title=" solitary wave solutions"> solitary wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=compactons" title=" compactons"> compactons</a>, <a href="https://publications.waset.org/abstracts/search?q=Jacobi%20elliptic%20functions" title=" Jacobi elliptic functions"> Jacobi elliptic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=mapping%20methods" title=" mapping methods"> mapping methods</a> </p> <a href="https://publications.waset.org/abstracts/59011/exact-solutions-of-knn-type-equations-using-jacobi-elliptic-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59011.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">305</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">882</span> Nonlinear Static Analysis of Laminated Composite Hollow Beams with Super-Elliptic Cross-Sections</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=G.%20Akgun">G. Akgun</a>, <a href="https://publications.waset.org/abstracts/search?q=I.%20Algul"> I. Algul</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Kurtaran"> H. Kurtaran</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generalized%20differential%20quadrature" title="generalized differential quadrature">generalized differential quadrature</a>, <a href="https://publications.waset.org/abstracts/search?q=geometric%20nonlinearity" title=" geometric nonlinearity"> geometric nonlinearity</a>, <a href="https://publications.waset.org/abstracts/search?q=laminated%20composite" title=" laminated composite"> laminated composite</a>, <a href="https://publications.waset.org/abstracts/search?q=super-elliptic%20cross-section" title=" super-elliptic cross-section"> super-elliptic cross-section</a> </p> <a href="https://publications.waset.org/abstracts/74966/nonlinear-static-analysis-of-laminated-composite-hollow-beams-with-super-elliptic-cross-sections" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/74966.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">295</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">881</span> Passive Control of Elliptic Jet by Using Triangular and Truncated Tabs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saif%20Akram">Saif Akram</a>, <a href="https://publications.waset.org/abstracts/search?q=E.%20Rathakrishnan"> E. Rathakrishnan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The mixing promoting efficiency of two identical sharp and truncated vertex triangular tabs offering geometrical blockage of 2.5% each, placed at the exit of a Mach 1.5 elliptic nozzle was studied experimentally. The effectiveness of both the tabs in enhancing the mixing of jets with the ambient air are determined by measuring the Pitot pressure along the jet axis and the jet spread in both the minor and major axes of the elliptic nozzle, covering marginally overexpanded to moderately underexpanded levels at the nozzle exit. The results reveal that both the tabs enhance mixing characteristics of the uncontrolled elliptic jet when placed at minor axis. A core length reduction of 67% is achieved at NPR 3 which is the overexpanded state. Similarly, the core length is reduced by about 67%, 50% and 57% at NPRs of 4, 5 and 6 (underexpanded states) respectively. However, unlike the considerable increment in mixing promoting efficiency by the use of truncated vertex tabs for axisymmetric jets, the effect is not much pronounced for the case of supersonic elliptic jets. The CPD plots for both the cases almost overlap, especially when tabs are placed at minor axis, at all the pressure conditions. While, when the tabs are used at major axis, in the case of overexpanded condition, the sharp vertex triangular tabs act as a better mixing enhancer for the supersonic elliptic jets. For the jet controlled with truncated vertex triangular tabs, the core length reductions are of the same order as those for the sharp vertex triangular tabs. The jet mixing is hardly influenced by the tip effect in case of supersonic elliptic jet. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=elliptic%20jet" title="elliptic jet">elliptic jet</a>, <a href="https://publications.waset.org/abstracts/search?q=tabs" title=" tabs"> tabs</a>, <a href="https://publications.waset.org/abstracts/search?q=truncated" title=" truncated"> truncated</a>, <a href="https://publications.waset.org/abstracts/search?q=triangular" title=" triangular"> triangular</a> </p> <a href="https://publications.waset.org/abstracts/38593/passive-control-of-elliptic-jet-by-using-triangular-and-truncated-tabs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/38593.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">383</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">880</span> An Attack on the Lucas Based El-Gamal Cryptosystem in the Elliptic Curve Group Over Finite Field Using Greater Common Divisor</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lee%20Feng%20Koo">Lee Feng Koo</a>, <a href="https://publications.waset.org/abstracts/search?q=Tze%20Jin%20Wong"> Tze Jin Wong</a>, <a href="https://publications.waset.org/abstracts/search?q=Pang%20Hung%20Yiu"> Pang Hung Yiu</a>, <a href="https://publications.waset.org/abstracts/search?q=Nik%20Mohd%20Asri%20Nik%20Long"> Nik Mohd Asri Nik Long</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=decryption" title="decryption">decryption</a>, <a href="https://publications.waset.org/abstracts/search?q=encryption" title=" encryption"> encryption</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20curve" title=" elliptic curve"> elliptic curve</a>, <a href="https://publications.waset.org/abstracts/search?q=greater%20common%20divisor" title=" greater common divisor"> greater common divisor</a> </p> <a href="https://publications.waset.org/abstracts/97382/an-attack-on-the-lucas-based-el-gamal-cryptosystem-in-the-elliptic-curve-group-over-finite-field-using-greater-common-divisor" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/97382.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">256</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">879</span> Implementation of Integer Sub-Decomposition Method on Elliptic Curves with J-Invariant 1728</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Siti%20Noor%20Farwina%20Anwar">Siti Noor Farwina Anwar</a>, <a href="https://publications.waset.org/abstracts/search?q=Hailiza%20Kamarulhaili"> Hailiza Kamarulhaili</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present the idea of implementing the Integer Sub-Decomposition (ISD) method on elliptic curves with j-invariant 1728. The ISD method was proposed in 2013 to compute scalar multiplication in elliptic curves, which remains to be the most expensive operation in Elliptic Curve Cryptography (ECC). However, the original ISD method only works on integer number field and solve integer scalar multiplication. By extending the method into the complex quadratic field, we are able to solve complex multiplication and implement the ISD method on elliptic curves with j-invariant 1728. The curve with j-invariant 1728 has a unique discriminant of the imaginary quadratic field. This unique discriminant of quadratic field yields a unique efficiently computable endomorphism, which later able to speed up the computations on this curve. However, the ISD method needs three endomorphisms to be accomplished. Hence, we choose all three endomorphisms to be from the same imaginary quadratic field as the curve itself, where the first endomorphism is the unique endomorphism yield from the discriminant of the imaginary quadratic field. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=efficiently%20computable%20endomorphism" title="efficiently computable endomorphism">efficiently computable endomorphism</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20scalar%20multiplication" title=" elliptic scalar multiplication"> elliptic scalar multiplication</a>, <a href="https://publications.waset.org/abstracts/search?q=j-invariant%201728" title=" j-invariant 1728"> j-invariant 1728</a>, <a href="https://publications.waset.org/abstracts/search?q=quadratic%20field" title=" quadratic field"> quadratic field</a> </p> <a href="https://publications.waset.org/abstracts/89234/implementation-of-integer-sub-decomposition-method-on-elliptic-curves-with-j-invariant-1728" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/89234.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">199</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">878</span> The Application of Variable Coefficient Jacobian elliptic Function Method to Differential-Difference Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chao-Qing%20Dai">Chao-Qing Dai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete%20sine-Gordon%20equation" title="discrete sine-Gordon equation">discrete sine-Gordon equation</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20coefficient%20Jacobian%20elliptic%20function%20method" title=" variable coefficient Jacobian elliptic function method"> variable coefficient Jacobian elliptic function method</a>, <a href="https://publications.waset.org/abstracts/search?q=exact%20solutions" title=" exact solutions"> exact solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=equation" title=" equation"> equation</a> </p> <a href="https://publications.waset.org/abstracts/12987/the-application-of-variable-coefficient-jacobian-elliptic-function-method-to-differential-difference-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12987.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">668</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">877</span> On Fourier Type Integral Transform for a Class of Generalized Quotients</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20S.%20Issa">A. S. Issa</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20K.%20Q.%20AL-Omari"> S. K. Q. AL-Omari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Boehmian" title="Boehmian">Boehmian</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20integral" title=" Fourier integral"> Fourier integral</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20type%20integral" title=" Fourier type integral"> Fourier type integral</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20quotient" title=" generalized quotient"> generalized quotient</a> </p> <a href="https://publications.waset.org/abstracts/45947/on-fourier-type-integral-transform-for-a-class-of-generalized-quotients" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45947.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">365</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">876</span> Investigating Smoothness: An In-Depth Study of Extremely Degenerate Elliptic Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zahid%20Ullah">Zahid Ullah</a>, <a href="https://publications.waset.org/abstracts/search?q=Atlas%20Khan"> Atlas Khan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=investigating%20smoothness" title="investigating smoothness">investigating smoothness</a>, <a href="https://publications.waset.org/abstracts/search?q=extremely%20degenerate%20elliptic%20equations" title=" extremely degenerate elliptic equations"> extremely degenerate elliptic equations</a>, <a href="https://publications.waset.org/abstracts/search?q=regularity%20properties" title=" regularity properties"> regularity properties</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical%20analysis" title=" mathematical analysis"> mathematical analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=complexity%20solutions" title=" complexity solutions"> complexity solutions</a> </p> <a href="https://publications.waset.org/abstracts/181742/investigating-smoothness-an-in-depth-study-of-extremely-degenerate-elliptic-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/181742.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">59</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">875</span> Arithmetic Operations Based on Double Base Number Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20Sanjayani">K. Sanjayani</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20Saraswathy"> C. Saraswathy</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Sreenivasan"> S. Sreenivasan</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Sudhahar"> S. Sudhahar</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20Suganya"> D. Suganya</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20S.%20Neelukumari"> K. S. Neelukumari</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Vijayarangan"> N. Vijayarangan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Double Base Number System (DBNS) is an imminent system of representing a number using two bases namely 2 and 3, which has its application in Elliptic Curve Cryptography (ECC) and Digital Signature Algorithm (DSA).The previous binary method representation included only base 2. DBNS uses an approximation algorithm namely, Greedy Algorithm. By using this algorithm, the number of digits required to represent a larger number is less when compared to the standard binary method that uses base 2 algorithms. Hence, the computational speed is increased and time being reduced. The standard binary method uses binary digits 0 and 1 to represent a number whereas the DBNS method uses binary digit 1 alone to represent any number (canonical form). The greedy algorithm uses two ways to represent the number, one is by using only the positive summands and the other is by using both positive and negative summands. In this paper, arithmetic operations are used for elliptic curve cryptography. Elliptic curve discrete logarithm problem is the foundation for most of the day to day elliptic curve cryptography. This appears to be a momentous hard slog compared to digital logarithm problem. In elliptic curve digital signature algorithm, the key generation requires 160 bit of data by usage of standard binary representation. Whereas, the number of bits required generating the key can be reduced with the help of double base number representation. In this paper, a new technique is proposed to generate key during encryption and extraction of key in decryption. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cryptography" title="cryptography">cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=double%20base%20number%20system" title=" double base number system"> double base number system</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20curve%20cryptography" title=" elliptic curve cryptography"> elliptic curve cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20curve%20digital%20signature%20algorithm" title=" elliptic curve digital signature algorithm"> elliptic curve digital signature algorithm</a> </p> <a href="https://publications.waset.org/abstracts/1760/arithmetic-operations-based-on-double-base-number-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/1760.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">396</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">874</span> Alternative Key Exchange Algorithm Based on Elliptic Curve Digital Signature Algorithm Certificate and Usage in Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Andreasyan">A. Andreasyan</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20Connors"> C. Connors</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Elliptic Curve Digital Signature algorithm-based X509v3 certificates are becoming more popular due to their short public and private key sizes. Moreover, these certificates can be stored in Internet of Things (IoT) devices, with limited resources, using less memory and transmitted in network security protocols, such as Internet Key Exchange (IKE), Transport Layer Security (TLS) and Secure Shell (SSH) with less bandwidth. The proposed method gives another advantage, in that it increases the performance of the above-mentioned protocols in terms of key exchange by saving one scalar multiplication operation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cryptography" title="cryptography">cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20curve%20digital%20signature%20algorithm" title=" elliptic curve digital signature algorithm"> elliptic curve digital signature algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=key%20exchange" title=" key exchange"> key exchange</a>, <a href="https://publications.waset.org/abstracts/search?q=network%20security%20protocol" title=" network security protocol"> network security protocol</a> </p> <a href="https://publications.waset.org/abstracts/120384/alternative-key-exchange-algorithm-based-on-elliptic-curve-digital-signature-algorithm-certificate-and-usage-in-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/120384.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">873</span> Hohmann Transfer and Bi-Elliptic Hohmann Transfer in TRAPPIST-1 System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20L.%20Nisperuza">Jorge L. Nisperuza</a>, <a href="https://publications.waset.org/abstracts/search?q=Wilson%20Sandoval"> Wilson Sandoval</a>, <a href="https://publications.waset.org/abstracts/search?q=Edward.%20A.%20Gil"> Edward. A. Gil</a>, <a href="https://publications.waset.org/abstracts/search?q=Johan%20A.%20Jimenez"> Johan A. Jimenez</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In orbital mechanics, an active research topic is the calculation of interplanetary trajectories efficient in terms of energy and time. In this sense, this work concerns the calculation of the orbital elements for sending interplanetary probes in the extrasolar system TRAPPIST-1. Specifically, using the mathematical expressions of the circular and elliptical trajectory parameters, expressions for the flight time and the orbital transfer rate increase between orbits, the orbital parameters and the graphs of the trajectories of Hohmann and Hohmann bi-elliptic for sending a probe from the innermost planet to all the other planets of the studied system, are obtained. The relationship between the orbital transfer rate increments and the relationship between the flight times for the two transfer types is found. The results show that, for all cases under consideration, the Hohmann transfer results to be the least energy and temporary cost, a result according to the theory associated with Hohmann and Hohmann bi-elliptic transfers. Saving in the increase of the speed reaches up to 87% was found, and it happens for the transference between the two innermost planets, whereas the time of flight increases by a factor of up to 6.6 if one makes use of the bi-elliptic transfer, this for the case of sending a probe from the innermost planet to the outermost. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bi-elliptic%20Hohmann%20transfer" title="bi-elliptic Hohmann transfer">bi-elliptic Hohmann transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=exoplanet" title=" exoplanet"> exoplanet</a>, <a href="https://publications.waset.org/abstracts/search?q=extrasolar%20system" title=" extrasolar system"> extrasolar system</a>, <a href="https://publications.waset.org/abstracts/search?q=Hohmann%20transfer" title=" Hohmann transfer"> Hohmann transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=TRAPPIST-1" title=" TRAPPIST-1"> TRAPPIST-1</a> </p> <a href="https://publications.waset.org/abstracts/98728/hohmann-transfer-and-bi-elliptic-hohmann-transfer-in-trappist-1-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/98728.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">192</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">872</span> Implementation of Elliptic Curve Cryptography Encryption Engine on a FPGA</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamad%20Khairi%20Ishak">Mohamad Khairi Ishak</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Conventional public key crypto systems such as RSA (Ron Rivest, Adi Shamir and Leonard Adleman), DSA (Digital Signature Algorithm), and Elgamal are no longer efficient to be implemented in the small, memory constrained devices. Elliptic Curve Cryptography (ECC), which allows smaller key length as compared to conventional public key crypto systems, has thus become a very attractive choice for many applications. This paper describes implementation of an elliptic curve cryptography (ECC) encryption engine on a FPGA. The system has been implemented in 2 different key sizes, which are 131 bits and 163 bits. Area and timing analysis are provided for both key sizes for comparison. The crypto system, which has been implemented on Altera’s EPF10K200SBC600-1, has a hardware size of 5945/9984 and 6913/9984 of logic cells for 131 bits implementation and 163 bits implementation respectively. The crypto system operates up to 43 MHz, and performs point multiplication operation in 11.3 ms for 131 bits implementation and 14.9 ms for 163 bits implementation. In terms of speed, our crypto system is about 8 times faster than the software implementation of the same system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=elliptic%20curve%20cryptography" title="elliptic curve cryptography">elliptic curve cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=FPGA" title=" FPGA"> FPGA</a>, <a href="https://publications.waset.org/abstracts/search?q=key%20sizes" title=" key sizes"> key sizes</a>, <a href="https://publications.waset.org/abstracts/search?q=memory" title=" memory "> memory </a> </p> <a href="https://publications.waset.org/abstracts/13762/implementation-of-elliptic-curve-cryptography-encryption-engine-on-a-fpga" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13762.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">319</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">871</span> Exact Solutions of Discrete Sine-Gordon Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chao-Qing%20Dai">Chao-Qing Dai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=exact%20solutions" title="exact solutions">exact solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=variable-coefficient%20Jacobian%20elliptic%20function%20method" title=" variable-coefficient Jacobian elliptic function method"> variable-coefficient Jacobian elliptic function method</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20sine-Gordon%20equation" title=" discrete sine-Gordon equation"> discrete sine-Gordon equation</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamical%20behaviors" title=" dynamical behaviors"> dynamical behaviors</a> </p> <a href="https://publications.waset.org/abstracts/48966/exact-solutions-of-discrete-sine-gordon-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48966.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">420</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">870</span> Three-Dimensional Numerical Analysis of the Harmfulness of Defects in Oil Pipes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=B.%20Medjadji">B. Medjadji</a>, <a href="https://publications.waset.org/abstracts/search?q=L.%20Aminallah"> L. Aminallah</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Serier"> B. Serier</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Benlebna"> M. Benlebna</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, the finite element method in 3-D is used to calculate the integral J in the semi-elliptical crack in a pipe subjected to internal pressure. The stress-strain curve of the pipe has been determined experimentally. The J-integral was calculated in two fronts crack (Ф = 0 and Ф = π/2). The effect of the configuration of the crack on the J integral is analysed. The results show that an external longitudinal crack in a pipe is the most dangerous. It also shows that the increase in the applied pressure causes a remarkable increase of the integral J. The effect of the depth of the crack becomes important when the ratio between the depth of the crack and the thickness of the pipe (a / t) tends to 1. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=J%20integral" title="J integral">J integral</a>, <a href="https://publications.waset.org/abstracts/search?q=pipeline" title=" pipeline"> pipeline</a>, <a href="https://publications.waset.org/abstracts/search?q=crack" title=" crack"> crack</a>, <a href="https://publications.waset.org/abstracts/search?q=MEF" title=" MEF"> MEF</a> </p> <a href="https://publications.waset.org/abstracts/4115/three-dimensional-numerical-analysis-of-the-harmfulness-of-defects-in-oil-pipes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4115.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">409</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">869</span> A Lightweight Authentication and Key Exchange Protocol Design for Smart Homes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zhifu%20Li">Zhifu Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Lei%20Li"> Lei Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Wanting%20Zhou"> Wanting Zhou</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuanhang%20He"> Yuanhang He</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper proposed a lightweight certificate-less authentication and key exchange protocol (Light-CL-PKC) based on elliptic curve cryptography and the Chinese Remainder Theorem for smart home scenarios. Light-CL-PKC can efficiently reduce the computational cost of both sides of authentication by forgoing time-consuming bilinear pair operations and making full use of point-addition and point-multiplication operations on elliptic curves. The authentication and key exchange processes in this system are also completed in a a single round of communication between the two parties. The analysis result demonstrates that it can significantly minimize the communication overhead of more than 32.14% compared with the referenced protocols, while the runtime for both authentication and key exchange have also been significantly reduced. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=authentication" title="authentication">authentication</a>, <a href="https://publications.waset.org/abstracts/search?q=key%20exchange" title=" key exchange"> key exchange</a>, <a href="https://publications.waset.org/abstracts/search?q=certificateless%20public%20key%20cryptography" title=" certificateless public key cryptography"> certificateless public key cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20curve%20cryptography" title=" elliptic curve cryptography"> elliptic curve cryptography</a> </p> <a href="https://publications.waset.org/abstracts/164480/a-lightweight-authentication-and-key-exchange-protocol-design-for-smart-homes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/164480.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">98</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">868</span> A Comparative Study on a Tilt-Integral-Derivative Controller with Proportional-Integral-Derivative Controller for a Pacemaker</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aysan%20Esgandanian">Aysan Esgandanian</a>, <a href="https://publications.waset.org/abstracts/search?q=Sabalan%20Daneshvar"> Sabalan Daneshvar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study is done to determine the comparison between proportional-integral-derivative controller (PID controller) and tilt-integral-derivative (TID controller) for cardiac pacemaker systems, which can automatically control the heart rate to accurately track a desired preset profile. The controller offers good adaption of heart to the physiological needs of the patient. The parameters of the both controllers are tuned by particle swarm optimization (PSO) algorithm which uses the integral of time square error as a fitness function to be minimized. Simulation results are performed on the developed cardiovascular system of humans and results demonstrate that the TID controller produces superior control performance than PID controllers. In this paper, all simulations were performed in Matlab. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=integral%20of%20time%20square%20error" title="integral of time square error">integral of time square error</a>, <a href="https://publications.waset.org/abstracts/search?q=pacemaker%20systems" title=" pacemaker systems"> pacemaker systems</a>, <a href="https://publications.waset.org/abstracts/search?q=proportional-integral-derivative%20controller" title=" proportional-integral-derivative controller"> proportional-integral-derivative controller</a>, <a href="https://publications.waset.org/abstracts/search?q=PSO%20algorithm" title=" PSO algorithm"> PSO algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=tilt-integral-derivative%20controller" title=" tilt-integral-derivative controller"> tilt-integral-derivative controller</a> </p> <a href="https://publications.waset.org/abstracts/43351/a-comparative-study-on-a-tilt-integral-derivative-controller-with-proportional-integral-derivative-controller-for-a-pacemaker" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/43351.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">462</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">867</span> Exploring Regularity Results in the Context of Extremely Degenerate Elliptic Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zahid%20Ullah">Zahid Ullah</a>, <a href="https://publications.waset.org/abstracts/search?q=Atlas%20Khan"> Atlas Khan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=elliptic%20equations" title="elliptic equations">elliptic equations</a>, <a href="https://publications.waset.org/abstracts/search?q=extremely%20degenerate" title=" extremely degenerate"> extremely degenerate</a>, <a href="https://publications.waset.org/abstracts/search?q=regularity%20results" title=" regularity results"> regularity results</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations" title=" partial differential equations"> partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical%20modeling" title=" mathematical modeling"> mathematical modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=porous%20media%20flow" title=" porous media flow"> porous media flow</a> </p> <a href="https://publications.waset.org/abstracts/181735/exploring-regularity-results-in-the-context-of-extremely-degenerate-elliptic-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/181735.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">72</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">866</span> Integral Image-Based Differential Filters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kohei%20Inoue">Kohei Inoue</a>, <a href="https://publications.waset.org/abstracts/search?q=Kenji%20Hara"> Kenji Hara</a>, <a href="https://publications.waset.org/abstracts/search?q=Kiichi%20Urahama"> Kiichi Urahama</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=integral%20images" title="integral images">integral images</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20images" title=" differential images"> differential images</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20filters" title=" differential filters"> differential filters</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20fusion" title=" image fusion"> image fusion</a> </p> <a href="https://publications.waset.org/abstracts/8531/integral-image-based-differential-filters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8531.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">506</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">865</span> Cryptanalysis of ID-Based Deniable Authentication Protocol Based On Diffie-Hellman Problem on Elliptic Curve</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eun-Jun%20Yoon">Eun-Jun Yoon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Deniable authentication protocol is a new security authentication mechanism which can enable a receiver to identify the true source of a given message, but not to prove the identity of the sender to a third party. In 2013, Kar proposed a secure ID-based deniable authentication protocol whose security is based on computational infeasibility of solving Elliptic Curve Diffie-Hellman Problem (ECDHP). Kar claimed that the proposed protocol achieves properties of deniable authentication, mutual authentication, and message confidentiality. However, this paper points out that Kar's protocol still suffers from sender spoofing attack and message modification attack unlike its claims. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=deniable%20authentication" title="deniable authentication">deniable authentication</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20curve%20cryptography" title=" elliptic curve cryptography"> elliptic curve cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=Diffie-Hellman%20problem" title=" Diffie-Hellman problem"> Diffie-Hellman problem</a>, <a href="https://publications.waset.org/abstracts/search?q=cryptanalysis" title=" cryptanalysis"> cryptanalysis</a> </p> <a href="https://publications.waset.org/abstracts/33884/cryptanalysis-of-id-based-deniable-authentication-protocol-based-on-diffie-hellman-problem-on-elliptic-curve" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33884.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">331</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">864</span> Differentiation of the Functional in an Optimization Problem for Coefficients of Elliptic Equations with Unbounded Nonlinearity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aigul%20Manapova">Aigul Manapova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cost%20functional" title="cost functional">cost functional</a>, <a href="https://publications.waset.org/abstracts/search?q=differentiability" title=" differentiability"> differentiability</a>, <a href="https://publications.waset.org/abstracts/search?q=divergent%20elliptic%20operator" title=" divergent elliptic operator"> divergent elliptic operator</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title=" optimal control"> optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=unbounded%20nonlinearity" title=" unbounded nonlinearity"> unbounded nonlinearity</a> </p> <a href="https://publications.waset.org/abstracts/86468/differentiation-of-the-functional-in-an-optimization-problem-for-coefficients-of-elliptic-equations-with-unbounded-nonlinearity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86468.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">172</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">863</span> Stability of Out-Of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem with Oblateness up to Zonal Harmonic J₄ of Both Primaries</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kanshio%20Richard%20Tyokyaa">Kanshio Richard Tyokyaa</a>, <a href="https://publications.waset.org/abstracts/search?q=Jagadish%20Singh"> Jagadish Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we examined the location and stability of Out-Of-Plane Equilibrium points in the elliptic restricted three-body problem of an infinitesimal body when both primaries are taken as oblate spheroids with oblateness up to zonal harmonic J₄. The positions of the Equilibrium points L₆,₇ and their stability depend on the oblateness of the primaries and the eccentricity of their orbits. We explored the problem numerically to show the effects of parameters involved in the position and stability of the Out-Of-Plane Equilibrium points for the systems: HD188753 and Gliese 667. It is found that their positions are affected by the oblateness of the primaries, eccentricity and the semi-major axis of the orbits, but its stability behavior remains unchanged and is unstable. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=out-of-plane" title="out-of-plane">out-of-plane</a>, <a href="https://publications.waset.org/abstracts/search?q=equilibrium%20points" title=" equilibrium points"> equilibrium points</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20restricted%20three-body%20problem" title=" elliptic restricted three-body problem"> elliptic restricted three-body problem</a>, <a href="https://publications.waset.org/abstracts/search?q=oblateness" title=" oblateness"> oblateness</a>, <a href="https://publications.waset.org/abstracts/search?q=zonal%20harmonic" title=" zonal harmonic"> zonal harmonic</a> </p> <a href="https://publications.waset.org/abstracts/91381/stability-of-out-of-plane-equilibrium-points-in-the-elliptic-restricted-three-body-problem-with-oblateness-up-to-zonal-harmonic-j4-of-both-primaries" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91381.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">193</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">862</span> The Finite Element Method for Nonlinear Fredholm Integral Equation of the Second Kind</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Melusi%20Khumalo">Melusi Khumalo</a>, <a href="https://publications.waset.org/abstracts/search?q=Anastacia%20Dlamini"> Anastacia Dlamini</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title="finite element method">finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=Galerkin%20approach" title=" Galerkin approach"> Galerkin approach</a>, <a href="https://publications.waset.org/abstracts/search?q=Fredholm%20integral%20equations" title=" Fredholm integral equations"> Fredholm integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20integral%20equations" title=" nonlinear integral equations"> nonlinear integral equations</a> </p> <a href="https://publications.waset.org/abstracts/140832/the-finite-element-method-for-nonlinear-fredholm-integral-equation-of-the-second-kind" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/140832.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">375</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">861</span> Fingerprint Image Encryption Using a 2D Chaotic Map and Elliptic Curve Cryptography</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=D.%20M.%20S.%20Bandara">D. M. S. Bandara</a>, <a href="https://publications.waset.org/abstracts/search?q=Yunqi%20Lei"> Yunqi Lei</a>, <a href="https://publications.waset.org/abstracts/search?q=Ye%20Luo"> Ye Luo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fingerprints are suitable as long-term markers of human identity since they provide detailed and unique individual features which are difficult to alter and durable over life time. In this paper, we propose an algorithm to encrypt and decrypt fingerprint images by using a specially designed Elliptic Curve Cryptography (ECC) procedure based on block ciphers. In addition, to increase the confusing effect of fingerprint encryption, we also utilize a chaotic-behaved method called Arnold Cat Map (ACM) for a 2D scrambling of pixel locations in our method. Experimental results are carried out with various types of efficiency and security analyses. As a result, we demonstrate that the proposed fingerprint encryption/decryption algorithm is advantageous in several different aspects including efficiency, security and flexibility. In particular, using this algorithm, we achieve a margin of about 0.1% in the test of Number of Pixel Changing Rate (NPCR) values comparing to the-state-of-the-art performances. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=arnold%20cat%20map" title="arnold cat map">arnold cat map</a>, <a href="https://publications.waset.org/abstracts/search?q=biometric%20encryption" title=" biometric encryption"> biometric encryption</a>, <a href="https://publications.waset.org/abstracts/search?q=block%20cipher" title=" block cipher"> block cipher</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20curve%20cryptography" title=" elliptic curve cryptography"> elliptic curve cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=fingerprint%20encryption" title=" fingerprint encryption"> fingerprint encryption</a>, <a href="https://publications.waset.org/abstracts/search?q=Koblitz%E2%80%99s%20%20encoding" title=" Koblitz’s encoding"> Koblitz’s encoding</a> </p> <a href="https://publications.waset.org/abstracts/96251/fingerprint-image-encryption-using-a-2d-chaotic-map-and-elliptic-curve-cryptography" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/96251.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">204</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">860</span> On a Univalent Function and the Integral Means of Its Derivative</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shatha%20S.%20Alhily">Shatha S. Alhily</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of this research paper is to show all the possible values of the pth power of the integrable function which make the integral means of the derivative of univalent function existing and ﬁnite. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=derivative" title="derivative">derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20means" title=" integral means"> integral means</a>, <a href="https://publications.waset.org/abstracts/search?q=self%20conformal%20maps" title=" self conformal maps"> self conformal maps</a>, <a href="https://publications.waset.org/abstracts/search?q=univalent%20function" title=" univalent function"> univalent function</a> </p> <a href="https://publications.waset.org/abstracts/34053/on-a-univalent-function-and-the-integral-means-of-its-derivative" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34053.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">629</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">859</span> Image Transform Based on Integral Equation-Wavelet Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Yan%20Tang">Yuan Yan Tang</a>, <a href="https://publications.waset.org/abstracts/search?q=Lina%20Yang"> Lina Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Hong%20Li"> Hong Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonic%20model" title="harmonic model">harmonic model</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation%20%28PDE%29" title=" partial differential equation (PDE)"> partial differential equation (PDE)</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equation" title=" integral equation"> integral equation</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20representation" title=" integral representation"> integral representation</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20measure%20formula" title=" boundary measure formula"> boundary measure formula</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet%20collocation" title=" wavelet collocation"> wavelet collocation</a> </p> <a href="https://publications.waset.org/abstracts/3920/image-transform-based-on-integral-equation-wavelet-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3920.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">558</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">858</span> Cellular Automata Using Fractional Integral Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yasser%20F.%20Hassan">Yasser F. Hassan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a proposed model of cellular automata is studied by means of fractional integral function. A cellular automaton is a decentralized computing model providing an excellent platform for performing complex computation with the help of only local information. The paper discusses how using fractional integral function for representing cellular automata memory or state. The architecture of computing and learning model will be given and the results of calibrating of approach are also given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20integral" title="fractional integral">fractional integral</a>, <a href="https://publications.waset.org/abstracts/search?q=cellular%20automata" title=" cellular automata"> cellular automata</a>, <a href="https://publications.waset.org/abstracts/search?q=memory" title=" memory"> memory</a>, <a href="https://publications.waset.org/abstracts/search?q=learning" title=" learning"> learning</a> </p> <a href="https://publications.waset.org/abstracts/55312/cellular-automata-using-fractional-integral-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55312.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 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