Search results for: differential invariant G-signature curves

Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

Abstract:

Newton-Lagrange Interpolations are widely used in numerical analysis. However, it requires a quadratic computational time for their constructions. In computer aided geometric design (CAGD), there are some polynomial curves: Wang-Ball, DP and Dejdumrong curves, which have linear time complexity algorithms. Thus, the computational time for Newton-Lagrange Interpolations can be reduced by applying the algorithms of Wang-Ball, DP and Dejdumrong curves. In order to use Wang-Ball, DP and Dejdumrong algorithms, first, it is necessary to convert Newton-Lagrange polynomials into Wang-Ball, DP or Dejdumrong polynomials. In this work, the algorithms for converting from both uniform and non-uniform Newton-Lagrange polynomials into Wang-Ball, DP and Dejdumrong polynomials are investigated. Thus, the computational time for representing Newton-Lagrange polynomials can be reduced into linear complexity. In addition, the other utilizations of using CAGD curves to modify the Newton-Lagrange curves can be taken.

Keywords: Lagrange interpolation, linear complexity, monomial matrix, Newton interpolation

Procedia PDF Downloads 211

Authors: Kankeyanathan Kannan

Abstract:

On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product.

Keywords: approximation property, weakly amenable, strong invariant approximation property, invariant approximation property

Procedia PDF Downloads 656

Authors: Mitat Uysal

Abstract:

A new met heuristic optimization algorithm called as Migrating Birds Optimization is used for curve fitting by rational cubic Bezier Curves. This requires solving a complicated multivariate optimization problem. In this study, the solution of this optimization problem is achieved by Migrating Birds Optimization algorithm that is a powerful met heuristic nature-inspired algorithm well appropriate for optimization. The results of this study show that the proposed method performs very well and being able to fit the data points to cubic Bezier Curves with a high degree of accuracy.

Keywords: algorithms, Bezier curves, heuristic optimization, migrating birds optimization

Procedia PDF Downloads 314

Authors: Yildiray Keskin, Omer Acan, Murat Akkus

Abstract:

In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

Procedia PDF Downloads 500

Authors: F. Maass, P. Martin, J. Olivares

Abstract:

The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

Procedia PDF Downloads 221

Authors: Lemonakis Panagiotis, Eliou Nikos, Karakasidis Theodoros, Botzoris George

Abstract:

It is well known that trajectory along with speed are two of the most important contributing factors in road accidents. Trajectory is meant as the "line“, usually different from the center-line that a driver traverses through horizontal curves which depends on the characteristics of the road environment (especially the curvature), the vehicle and the driver himself. Drivers and especially riders, tend to broaden their paths in order to succeed greater path radiuses and hence, reduce the applied centrifugal force enhancing safety. The objective of the present research is to investigate riders’ path on horizontal curves. Within the context of the research, field measurements were conducted on a rural two lane highway, with the participation of eight riders and the use of an instrumented motorcycle. The research has shown that the trajectory of the riders is correlated to the radius and the length of the horizontal curve as well.

Keywords: trajectory, path, riders, horizontal curves

Procedia PDF Downloads 324

Authors: Lan Du, Yan Wang, Hui Dai

Abstract:

Synthetic aperture radar (SAR) image change detection has recently become a challenging problem owing to the existence of speckle noises. In this paper, an unsupervised distribution-free change detection for SAR image based on scale-invariant feature transform (SIFT) keypoints and segmentation is proposed. Firstly, the noise-robust SIFT keypoints which reveal the blob-like structures in an image are extracted in the log-ratio image to reduce the detection range. Then, different from the traditional change detection which directly obtains the change-detection map from the difference image, segmentation is made around the extracted keypoints in the two original multitemporal SAR images to obtain accurate changed region. At last, the change-detection map is generated by comparing the two segmentations. Experimental results on the real SAR image dataset demonstrate the effectiveness of the proposed method.

Keywords: change detection, Synthetic Aperture Radar (SAR), Scale-Invariant Feature Transformation (SIFT), segmentation

Procedia PDF Downloads 360

Authors: V. V. Reddy, N. V. Sarma

Abstract:

A circularly polarized fractal boundary microstrip antenna is presented. The sides of a square patch along x-axis, y-axis are replaced with Minkowski and Koch curves correspondingly. By using the fractal curves as edges, asymmetry in the structure is created to excite two orthogonal modes for circular polarization (CP) operation. The indentation factors of the fractal curves are optimized for pure CP. The simulated results of the novel poly fractal antenna are demonstrated.

Keywords: fractal, circular polarization, Minkowski, Koch

Procedia PDF Downloads 339

Authors: G. Akgun, I. Algul, H. Kurtaran

Abstract:

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.

Keywords: generalized differential quadrature, geometric nonlinearity, laminated composite, super-elliptic cross-section

Procedia PDF Downloads 271

Authors: Lev Idels, Arcady Ponosov

Abstract:

Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

Procedia PDF Downloads 181

Authors: Abdullah A. AlShaher

Abstract:

In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2^nd order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We then proceed by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.

Keywords: character recognition, regression curves, handwritten Arabic letters, expectation maximization algorithm

Procedia PDF Downloads 123

Authors: S. Som-Am, B. Grechuk

Abstract:

Moser’s worm problem is the unsolved problem in geometry which asks for the minimal area of a convex region on the plane which can cover all curves of unit length, assuming that curves may be rotated and translated to fit inside the region. We study a version of this problem asking for a minimal convex cover for closed unit curves. By combining geometric methods with numerical box’s search algorithm, we show that any such cover should have an area at least 0.0975. This improves the best previous lower bound of 0.096694. In fact, we show that the minimal area of convex hull of circle, equilateral triangle, and rectangle of perimeter 1 is between 0.0975 and 0.09763.

Keywords: Moser’s worm problem, closed arcs, convex cover, minimal-area cover

Procedia PDF Downloads 194

Authors: J. Branstett, V. Gagneux, A. Leleu, B. Levadoux, J. Pascale

Abstract:

This paper presents the interface CONDUCTHOME which controls home automation systems with a Leap Motion using ‘invariant gesture protocols’. The function of this interface is to simplify the interaction of the user with its environment. A hardware part allows the Leap Motion to be carried around the house. A software part interacts with the home automation box and displays the useful information for the user. An objective of this work is the development a natural/invariant/simple gesture control interface to help elder people/people with disabilities.

Keywords: automation, ergonomics, gesture recognition, interoperability

Procedia PDF Downloads 405

Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

Abstract:

An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

Procedia PDF Downloads 581

Authors: Saeed Otarod

Abstract:

In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

Procedia PDF Downloads 23

Authors: Lina Wu, Ye Li

Abstract:

An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

Procedia PDF Downloads 431

Authors: Mustafa Bayram Gücen, Coşkun Yakar

Abstract:

In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

Procedia PDF Downloads 225

Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

Procedia PDF Downloads 182

Authors: Farid Nouioua, Abdelouaheb Ardjouni

Abstract:

In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

Procedia PDF Downloads 412

Authors: Haohao Wang

Abstract:

The purpose of this paper is to find elimination ideals via Grobner basis. We first introduce the concept of Grobner bases, and then, we provide computational algorithms to applications for curves and surfaces.

Keywords: curves, surfaces, Grobner basis, elimination

Procedia PDF Downloads 284

Authors: Mehtap Lafcı

Abstract:

In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

Procedia PDF Downloads 491

Authors: Abdelhakim Chillali, Abdelhamid Tadmori, Muhammed Ziane

Abstract:

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.

Keywords: elliptic curves, finite ring, cryptography, study

Procedia PDF Downloads 354

Authors: M. Fatmi, T. Chihi, M. A. Ghebouli, B. Ghebouli

Abstract:

This work presents the experimental results of the differential scanning calorimetry (DSC), hardness measurements (Hv) and XRD analysis, for order to investigate the kinetics of precipitation phenomena in Al-7%wt. Mg alloy. In the XRD and DSC curves indicates the formation of the intermediate precipitation of β-(Al3Mg2) phase respectively. The activation energies associated with the processes have been determined according to the three models proposed by Kissinger, Ozawa, and Boswell. Consequently, the nucleation mechanism of the precipitates can be explained. These phases are confirmed by XRD analysis.

Keywords: discontinuous precipitation, hardening, Al–Mg alloys, mechanical and mechatronics engineering

Procedia PDF Downloads 389

Authors: A. M. Sagir

Abstract:

Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

Procedia PDF Downloads 462

Authors: Gayatri Ghosh

Abstract:

In this work, a flavour theory of a neutrino mass model based on A_4 symmetry is considered to explain the phenomenology of neutrino mixing. The spontaneous symmetry breaking of A_4 symmetry in this model leads to tribimaximal mixing in the neutrino sector at a leading order. We consider the effect of Z_2 × Z_2 invariant perturbations in neutrino sector and find the allowed region of correction terms in the perturbation matrix that is consistent with 3σ ranges of the experimental values of the mixing angles. We study the entanglement of this formalism on the other phenomenological observables, such as δ_CP phase, the neutrino oscillation probability P(νµ → νe), the effective Majorana mass |mee| and |meff νe |. A Z_2 × Z_2 invariant perturbations in this model is introduced in the neutrino sector which leads to testable predictions of θ_13 and CP violation. By changing the magnitudes of perturbations in neutrino sector, one can generate viable values of δ_CP and neutrino oscillation parameters. Next we investigate the feasibility of charged lepton flavour violation in type-I seesaw models with leptonic flavour symmetries at high energy that leads to tribimaximal neutrino mixing. We consider an effective theory with an A_4 × Z_2 × Z_2 symmetry, which after spontaneous symmetry breaking at high scale which is much higher than the electroweak scale leads to charged lepton flavour violation processes once the heavy Majorana neutrino mass degeneracy is lifted either by renormalization group effects or by a soft breaking of the A_4 symmetry. In this context the implications for charged lepton flavour violation processes like µ → eγ, τ → eγ, τ → µγ are discussed.

Keywords: Z2 × Z2 invariant perturbations, CLFV, delta CP phase, tribimaximal neutrino mixing

Procedia PDF Downloads 61

Authors: Fakhreddin Abedi, Wah June Leong

Abstract:

Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

Procedia PDF Downloads 34

Authors: Elena Carcano, Mirzi Betasolo

Abstract:

This study helps Public Water Bureaus in giving reliable answers to water concession requests. Rapidly increasing water requests can be supported provided that further uses of a river course are not totally compromised, and environmental features are protected as well. Strictly speaking, a water concession can be considered a continuous drawing from the source and causes a mean annual streamflow reduction. Therefore, deciding if a water concession is appropriate or inappropriate seems to be easily solved by comparing the generic demand to the mean annual streamflow value at disposal. Still, the immediate shortcoming for such a comparison is that streamflow data are information available only for few catchments and, most often, limited to specific sites. Subsequently, comparing the generic water demand to mean daily discharge is indeed far from being completely satisfactory since the mean daily streamflow is greater than the water withdrawal for a long period of a year. Consequently, such a comparison appears to be of little significance in order to preserve the quality and the quantity of the river. In order to overcome such a limit, this study aims to complete the information provided by flow duration curves introducing a link between Flow Duration Curves (FDCs) and recession curves and aims to show the chronological sequence of flows with a particular focus on low flow data. The analysis is carried out on 25 catchments located in North-Eastern Italy for which daily data are provided. The results identify groups of catchments as hydrologically homogeneous, having the lower part of the FDCs (corresponding streamflow interval is streamflow Q between 300 and 335, namely: Q(300), Q(335)) smoothly reproduced by a common recession curve. In conclusion, the results are useful to provide more reliable answers to water request, especially for those catchments which show similar hydrological response and can be used for a focused regionalization approach on low flow data. A mathematical link between streamflow duration curves and recession curves is herein provided, thus furnishing streamflow duration curves information upon a temporal sequence of data. In such a way, by introducing assumptions on recession curves, the chronological sequence upon low flow data can also be attributed to FDCs, which are known to lack this information by nature.

Keywords: chronological sequence of discharges, recession curves, streamflow duration curves, water concession

Procedia PDF Downloads 158

Authors: Armin Ardekani, Mohammad Akbari

Abstract:

We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

Procedia PDF Downloads 317

Authors: Zhan Chen, Wenquan Bi

Abstract:

This paper focuses on examining the strength of Midori against impossible differential attack. The Midori family of light weight block cipher orienting to energy-efficiency is proposed in ASIACRYPT2015. Using a 6-round property, the authors implement an 11-round impossible differential attack on Midori64 by extending two rounds on the top and three rounds on the bottom. There is enough key space to consider pre-whitening keys in this attack. An impossible differential path that minimises the key bits involved is used to reduce computational complexity. Several additional observations such as partial abort technique are used to further reduce data and time complexities. This attack has data complexity of 2 ⁶⁹·² chosen plaintexts, requires 2 ¹⁴·⁵⁸ blocks of memory and 2 ⁹⁴·⁷ 11- round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

Procedia PDF Downloads 259

Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

Abstract:

In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

Procedia PDF Downloads 516