Search results for: Chebyshev polynomials

Authors: M. W. Sun, Y. Zhang, L. M. Zhang, Z. H. Wang, Z. Q. Chen

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In the realm of flight control, the Proportional- Derivative (PD) control is still widely used for the attitude control in practice, particularly for the pitch control, and the attitude dynamics using PD controller should be investigated deeply. According to the empirical knowledge about the unstable flight dynamics, the control parameter combination conditions to generate sole or finite number of closed-loop oscillations, which is a quite smooth response and is more preferred by practitioners, are presented in analytical or numerical manners. To analyze the effects of the combination conditions of the control parameters, the roots of several polynomials are sought to obtain feasible solutions. These conditions can also be plotted in a 2-D plane which makes the conditions be more explicit by using multiple interval operations. Finally, numerical examples are used to validate the proposed methods and some comparisons are also performed.

Keywords: attitude control, dynamic performance, numerical solving method, interval, unstable flight dynamics

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Authors: Mohammed S. Al-Rawi, J. Bastos, J. Rodriguez

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Object detection and object recognition are essential components of every computer vision system. Despite the high computational complexity and other problems related to numerical stability and accuracy, Zernike moments of 2D images (ZMs) have shown resilience when used in object recognition and have been used in various image analysis applications. In this work, we propose a novel method for computing ZMs via Fast Fourier Transform (FFT). Notably, this is the first algorithm that can generate ZMs up to extremely high orders accurately, e.g., it can be used to generate ZMs for orders up to 1000 or even higher. Furthermore, the proposed method is also simpler and faster than the other methods due to the availability of FFT software and/or hardware. The accuracies and numerical stability of ZMs computed via FFT have been confirmed using the orthogonality property. We also introduce normalizing ZMs with Neumann factor when the image is embedded in a larger grid, and color image reconstruction based on RGB normalization of the reconstructed images. Astonishingly, higher-order image reconstruction experiments show that the proposed methods are superior, both quantitatively and subjectively, compared to the q-recursive method.

Keywords: Chebyshev polynomial, fourier transform, fast algorithms, image recognition, pseudo Zernike moments, Zernike moments

Procedia PDF Downloads 235

Authors: Malika Yaici, Kamel Hariche, Tim Clarke

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The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

Keywords: eigenvalues/eigenvectors, latent values/vectors, matrix fraction description, state space description

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Authors: Srinivasacharya Darbhasayanam, Jagadeeshwar Pashikanti

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This paper analyzes the Soret and Dufour effects on mixed convection flow, heat and mass transfer from an exponentially stretching surface in a viscous fluid with Hall Effect. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations. The nonlinear coupled ordinary differential equations are reduced to a system of linear differential equations using the successive linearization method and then solved the resulting linear system using the Chebyshev pseudo spectral method. The numerical results for the velocity components, temperature and concentration are presented graphically. The obtained results are compared with the previously published results, and are found to be in excellent agreement. It is observed from the present analysis that the primary and secondary velocities and concentration are found to be increasing, and temperature is decreasing with the increase in the values of the Soret parameter. An increase in the Dufour parameter increases both the primary and secondary velocities and temperature and decreases the concentration.

Keywords: Exponentially stretching sheet, Hall current, Heat and Mass transfer, Soret and Dufour Effects

Procedia PDF Downloads 183

Authors: Ruchi, A. M. Acu, Purshottam N. Agrawal

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The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, Peetre’s K-functional, Lipschitz class, mixed modulus of smoothness

Procedia PDF Downloads 166

Authors: Areej M. Abduldaim, Nadia M. G. Al-Saidi

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Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.

Keywords: cryptosystem, identification, skew π-Armendariz rings, skew polynomial rings, zero knowledge protocol

Procedia PDF Downloads 180

Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

Procedia PDF Downloads 139

Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Gubhinder Kundhi, Paul Rilstone

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Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: edgeworth expansions, higher order asymptotics, saddlepoint expansions, weak instruments

Procedia PDF Downloads 249

Authors: B. Touati, A. Saad, B. Lips, A. Abdenbi, M. Mokhtari.

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The purpose of this study is an application of experiment design method for dimensioning of a solar drying system. NIMROD software was used to build up the matrix of experiments and to analyze the results. The software has the advantages of being easy to use and consists of a forced way, with some choices about the number and range of variation of the parameters, and the desired polynomial shape. The first design of experiments performed concern the drying with constant input characteristics of the hot air in the dryer and a second design of experiments in which the drying chamber is coupled with a solar collector. The first design of experiments allows us to study the influence of various parameters and get the studied answers in a polynomial form. The correspondence between the polynomial thus determined, and the model results were good. The results of the polynomials of the second design of experiments and those of the model are worse than the results in the case of drying with constant input conditions. This is due to the strong link between all the input parameters, especially, the surface of the sensor and the drying chamber, and the mass of the product.

Keywords: solar drying, experiment design method, NIMROD, mint leaves

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Authors: Tareq Hamadneh, Jochen Merker, Hassan Al-Zoubi

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Bernstein's expansion for exponentials in Taylor functions provides lower and upper optimization values for the range of its original function. these values converge to the original functions if the degree is elevated or the domain subdivided. Taylor polynomial can be applied so that the exponential is a polynomial of finite degree over a given domain. Bernstein's basis has two main properties: its sum equals 1, and positive for all x 2 (0; 1). In this work, we prove the existence of fixed points for exponential functions in a given domain using the optimization values of Bernstein. The Bernstein basis of finite degree T over a domain D is defined non-negatively. Any polynomial p of degree t can be expanded into the Bernstein form of maximum degree t ≤ T, where we only need to compute the coefficients of Bernstein in order to optimize the original polynomial. The main property is that p(x) is approximated by the minimum and maximum Bernstein coefficients (Bernstein bound). If the bound is contained in the given domain, then we say that p(x) has fixed points in the same domain.

Keywords: Bernstein polynomials, Stability of control functions, numerical optimization, Taylor function

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Authors: Prawal Sinha, Peeyush Singh, Pravir Dutt

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Problems in elastohydrodynamic lubrication have attracted a lot of attention in the last few decades. Solving a two-dimensional problem has always been a big challenge. In this paper, a new discontinuous finite volume method (DVM) for two-dimensional point contact Elastohydrodynamic Lubrication (EHL) problem has been developed and analyzed. A complete algorithm has been presented for solving such a problem. The method presented is robust and easily parallelized in MPI architecture. GMRES technique is implemented to solve the matrix obtained after the formulation. A new approach is followed in which discontinuous piecewise polynomials are used for the trail functions. It is natural to assume that the advantages of using discontinuous functions in finite element methods should also apply to finite volume methods. The nature of the discontinuity of the trail function is such that the elements in the corresponding dual partition have the smallest support as compared with the Classical finite volume methods. Film thickness calculation is done using singular quadrature approach. Results obtained have been presented graphically and discussed. This method is well suited for solving EHL point contact problem and can probably be used as commercial software.

Keywords: elastohydrodynamic, lubrication, discontinuous finite volume method, GMRES technique

Procedia PDF Downloads 229

Authors: B. Makhlouf, O. Bouchhida, M. Nibouche, K. Laidi

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A variety of methods for selective harmonics elimination pulse width modulation have been developed, the most frequently used for real-time implementation based on look-up tables method. To address real-time requirements based in modified carrier signal is proposed in the presented work, with a general formulation to real-time harmonics control/elimination in switched inverters. Firstly, the proposed method has been demonstrated for a single value of the modulation index. However, in reality, this parameter is variable as a consequence of the voltage (amplitude) variability. In this context, a simple interpolation method for calculating the modified sine carrier signal is proposed. The method allows a continuous adjustment in both amplitude and frequency of the fundamental. To assess the performance of the proposed method, software simulations and hardware experiments have been carried out in the case of a single-phase inverter. Obtained results are very satisfactory.

Keywords: harmonic elimination, Particle Swarm Optimisation (PSO), polynomial interpolation, pulse width modulation, real-time harmonics control, voltage inverter

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Authors: Jalal Karam

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The methods of Fourier, Laplace, and Wavelet Transforms provide transfer functions and relationships between the input and the output signals in linear time invariant systems. This paper shows the equivalence among these three methods and in each case presenting an application of the appropriate (Fourier, Laplace or Wavelet) to the convolution theorem. In addition, it is shown that the same holds for a direct integration method. The Biorthogonal wavelets Bior3.5 and Bior3.9 are examined and the zeros distribution of their polynomials associated filters are located. This paper also presents the significance of utilizing wavelets as effective tools in processing speech signals for common multimedia applications in general, and for recognition and compression in particular. Theoretically and practically, wavelets have proved to be effective and competitive. The practical use of the Continuous Wavelet Transform (CWT) in processing and analysis of speech is then presented along with explanations of how the human ear can be thought of as a natural wavelet transformer of speech. This generates a variety of approaches for applying the (CWT) to many paradigms analysing speech, sound and music. For perception, the flexibility of implementation of this transform allows the construction of numerous scales and we include two of them. Results for speech recognition and speech compression are then included.

Keywords: continuous wavelet transform, biorthogonal wavelets, speech perception, recognition and compression

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Authors: Dmitry Dikarev, Ajit Nimbalker, Alexei Davydov

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Polar coding is a novel example of error correcting codes, which can achieve Shannon limit at block length N→∞ with log-linear complexity. Active research is being carried to adopt this theoretical concept for using in practical applications such as 5th generation wireless communication systems. Cyclic redundancy check (CRC) error detection code is broadly used in conjunction with successive cancellation list (SCL) decoding algorithm to improve finite-length polar code performance. However, there are two issues: increase of code block payload overhead by CRC bits and decrease of CRC error-detection capability. This paper proposes a method to control CRC overhead and false alarm rate of polar decoding. As shown in the computer simulations results, the proposed method provides the ability to use any set of CRC polynomials with any list size while maintaining the desired level of false alarm rate. This level of flexibility allows using polar codes in 5G New Radio standard.

Keywords: 5G New Radio, channel coding, cyclic redundancy check, list decoding, polar codes

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Authors: Soroush Hooshyar, Mohamadali Masoudian, Natalie Germann

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Many soft materials such as polymer solutions can develop localized bands with different shear rates, which are known as shear bands. Using the generalized bracket approach of nonequilibrium thermodynamics, we recently developed a new two-fluid model to study shear banding for semi-dilute polymer solutions. The two-fluid approach is an appropriate means for describing diffusion processes such as Fickian diffusion and stress-induced migration. In this approach, it is assumed that the local gradients in concentration and, if accounted for, also stress generate a nontrivial velocity difference between the components. Since the differential velocity is treated as a state variable in our model, the implementation of the boundary conditions arising from the derivative diffusive terms is straightforward. Our model is a good candidate for benchmark simulations because of its simplicity. We analyzed its behavior in cylindrical Couette flow, a rectilinear channel flow, and a 4:1 planar contraction flow. The latter problem was solved using the OpenFOAM finite volume package and the impact of shear banding on the lip and salient vortices was investigated. For the other smooth geometries, we employed a standard Chebyshev pseudospectral collocation method. The results showed that the steady-state solution is unique with respect to initial conditions, deformation history, and the value of the diffusivity constant. However, smaller the value of the diffusivity constant is, the more time it takes to reach the steady state.

Keywords: nonequilibrium thermodynamics, planar contraction, polymer solutions, shear banding, two-fluid approach

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Authors: Zhenming Wang, Jun Zhu, Yuchen Yang, Ning Zhao

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In the present paper, an alternative framework is proposed to construct a class of finite difference multi-resolution nested weighted essentially non-oscillatory (WENO) schemes with an increasingly higher order of accuracy for solving inviscid Euler equations. These WENO schemes firstly obtain a set of reconstruction polynomials by a hierarchy of nested central spatial stencils, and then recursively achieve a higher order approximation through the lower-order precision WENO schemes. The linear weights of such WENO schemes can be set as any positive numbers with a requirement that their sum equals one and they will not pollute the optimal order of accuracy in smooth regions and could simultaneously suppress spurious oscillations near discontinuities. Numerical results obtained indicate that these alternative finite-difference multi-resolution nested WENO schemes with different accuracies are very robust with low dissipation and use as few reconstruction stencils as possible while maintaining the same efficiency, achieving the high-resolution property without any equivalent multi-resolution representation. Besides, its finite volume form is easier to implement in unstructured grids.

Keywords: finite-difference, WENO schemes, high order, inviscid Euler equations, multi-resolution

Procedia PDF Downloads 115

Authors: Chirine Aouichaoui, Mohamed Tounsi, Ines Mrizak, Zouhair Tabka, Yassine Trabelsi

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The aim of this study was to provide percentile values for vertical jumping performances and anthropometric characteristics for athletic Tunisian children. One thousand and fifty-five athletic Tunisian children and adolescents (643 boys and 412 girls) aged 7-18 years were randomly selected to participate in our study. They were asked to perform squat jumps and countermovement jumps. For each measurement, a least square regression model with high order polynomials was fitted to predict mean and standard deviation of vertical jumping parameters and anthropometric variables. Smoothed percentile curves and percentile values for the 5th, 10th, 25th, 50th, 75th, 90th, and 95th percentiles are presented for boys and girls. In conclusion, percentiles values of vertical jumping performances and anthropometric characteristics are provided. The new Tunisian reference charts obtained can be used as a screening tool to determine growth disorders and to estimate the proportion of adolescents with high or low muscular strength levels. This study may help in verifying the effectiveness of a specific training program and detecting highly talented athletes.

Keywords: percentile values, jump height, leg muscle power, athletes, anthropometry

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Nidhal Jamia, Sami El-Borgi

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In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: functionally graded piezoelectric material (FGPM), mixed-mode crack, non-local theory, Schmidt method

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Authors: Alina Fedossova, Jose Jorge Sierra Molina

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SIP problems are part of non-classical optimization. There are problems in which the number of variables is finite, and the number of constraints is infinite. These are semi-infinite programming problems. Most algorithms for semi-infinite programming problems reduce the semi-infinite problem to a finite one and solve it by classical methods of linear or nonlinear programming. Typically, any of the constraints or the objective function is nonlinear, so the problem often involves nonlinear programming. An investment portfolio is a set of instruments used to reach the specific purposes of investors. The risk of the entire portfolio may be less than the risks of individual investment of portfolio. For example, we could make an investment of M euros in N shares for a specified period. Let yi> 0, the return on money invested in stock i for each dollar since the end of the period (i = 1, ..., N). The logical goal here is to determine the amount xi to be invested in stock i, i = 1, ..., N, such that we maximize the period at the end of ytx value, where x = (x1, ..., xn) and y = (y1, ..., yn). For us the optimal portfolio means the best portfolio in the ratio "risk-return" to the investor portfolio that meets your goals and risk ways. Therefore, investment goals and risk appetite are the factors that influence the choice of appropriate portfolio of assets. The investment returns are uncertain. Thus we have a semi-infinite programming problem. We solve a semi-infinite optimization problem of portfolio selection using the outer approximations methods. This approach can be considered as a developed Eaves-Zangwill method applying the multi-start technique in all of the iterations for the search of relevant constraints' parameters. The stochastic outer approximations method, successfully applied previously for robotics problems, Chebyshev approximation problems, air pollution and others, is based on the optimal criteria of quasi-optimal functions. As a result we obtain mathematical model and the optimal investment portfolio when yields are not clear from the beginning. Finally, we apply this algorithm to a specific case of a Colombian bank.

Keywords: outer approximation methods, portfolio problem, semi-infinite programming, numerial solution

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Authors: Jihad Daba, Jean-Pierre Dubois

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Multi path fading noise degrades the performance of cellular communication, most notably in femto- and pico-cells in 3G and 4G systems. When the wireless channel consists of a small number of scattering paths, the statistics of fading noise is not analytically tractable and poses a serious challenge to developing closed canonical forms that can be analysed and used in the design of efficient and optimal receivers. In this context, noise is multiplicative and is referred to as stochastically local fading. In many analytical investigation of multiplicative noise, the exponential or Gamma statistics are invoked. More recent advances by the author of this paper have utilized a Poisson modulated and weighted generalized Laguerre polynomials with controlling parameters and uncorrelated noise assumptions. In this paper, we investigate the statistics of multi-diversity stochastically local area fading channel when the channel consists of randomly distributed Rayleigh and Rician scattering centers with a coherent specular Nakagami-distributed line of sight component and an underlying doubly stochastic Poisson process driven by a lognormal intensity. These combined statistics form a unifying triply stochastic filtered marked Poisson point process model.

Keywords: cellular communication, femto and pico-cells, stochastically local area fading channel, triply stochastic filtered marked Poisson point process

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Authors: Luiz G. Véras, Felipe L. Medeiros, Lamartine F. Guimarães

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This work approaches the automatic planning of paths for Unmanned Aerial Vehicles (UAVs) through the application of the Rapidly Exploring Random Tree Star-Smart (RRT*-Smart) algorithm. RRT*-Smart is a sampling process of positions of a navigation environment through a tree-type graph. The algorithm consists of randomly expanding a tree from an initial position (root node) until one of its branches reaches the final position of the path to be planned. The algorithm ensures the planning of the shortest path, considering the number of iterations tending to infinity. When a new node is inserted into the tree, each neighbor node of the new node is connected to it, if and only if the extension of the path between the root node and that neighbor node, with this new connection, is less than the current extension of the path between those two nodes. RRT*-smart uses an intelligent sampling strategy to plan less extensive routes by spending a smaller number of iterations. This strategy is based on the creation of samples/nodes near to the convex vertices of the navigation environment obstacles. The planned paths are smoothed through the application of the method called quintic pythagorean hodograph curves. The smoothing process converts a route into a dynamically-viable one based on the kinematic constraints of the vehicle. This smoothing method models the hodograph components of a curve with polynomials that obey the Pythagorean Theorem. Its advantage is that the obtained structure allows computation of the curve length in an exact way, without the need for quadratural techniques for the resolution of integrals.

Keywords: path planning, path smoothing, Pythagorean hodograph curve, RRT*-Smart

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Authors: Tugba Bayoglu

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Aerodynamic parameter estimation is very crucial in missile design phase, since accurate high fidelity aerodynamic model is required for designing high performance and robust control system, developing high fidelity flight simulations and verification of computational and wind tunnel test results. However, in literature, there is not enough missile aerodynamic parameter identification study for three main reasons: (1) most air to air missiles cannot fly with constant speed, (2) missile flight test number and flight duration are much less than that of fixed wing aircraft, (3) variation of the missile aerodynamic parameters with respect to Mach number is higher than that of fixed wing aircraft. In addition to these challenges, identification of aerodynamic parameters for high wind angles by using classical estimation techniques brings another difficulty in the estimation process. The reason for this, most of the estimation techniques require employing polynomials or splines to model the behavior of the aerodynamics. However, for the missiles with a large variation of aerodynamic parameters with respect to flight variables, the order of the proposed model increases, which brings computational burden and complexity. Therefore, in this study, it is aimed to solve nonlinear aerodynamic parameter identification problem for a supersonic air to air missile by using Artificial Neural Networks. The method proposed will be tested by using simulated data which will be generated with a six degree of freedom missile model, involving a nonlinear aerodynamic database. The data will be corrupted by adding noise to the measurement model. Then, by using the flight variables and measurements, the parameters will be estimated. Finally, the prediction accuracy will be investigated.

Keywords: air to air missile, artificial neural networks, open loop simulation, parameter identification

Procedia PDF Downloads 245

Authors: Nessa-Amie T. Peñaflor, Antonio Cinto

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This is a descriptive research on the level of math anxiety and mathematics misconceptions in algebra. This research is composed of four parts: (1) analysis of the level of anxiety of the respondents; (2) analysis of the common mathematical misconceptions in algebra; (3) relationship of socio-demographic profile in math anxiety and mathematical misconceptions and (4) analysis of the relationship of math anxiety and misconceptions in algebra. Through the demographic profile questionnaire it was found out that most of the respondents were female. Majority had ages that ranged from 13-15. Most of them had parents who finished secondary education. The biggest portion of Grade Seven students where from families with annual family income ranging from PhP 100, 000 to PhP 299, 999. Most of them came from public school. Mathematics Anxiety Scale for Secondary and Senior Secondary School Students (MAS) and set of 10 open-ended algebraic expressions and polynomials were also administered to determine the anxiety level and the common misconceptions in algebra. Data analysis revealed that respondents had high anxiety in mathematics. Likewise, the common mathematical misconceptions of the Grade Seven students were: combining unlike terms; multiplying the base and exponents; regarding the variable x as 0; squaring the first and second terms only in product of two binomials; wrong meaning attached to brackets; writing the terms next to each other but not simplifying in using the FOIL Method; writing the literal coefficient even if the numerical coefficient is 0; and dividing the denominator by the numerator when the numerical coefficient in the numerator is smaller than the numerical coefficient of the denominator. Results of the study show that the socio-demographic characteristics were not related to mathematics anxiety and misconceptions. Furthermore, students from higher section had high anxiety than those students on the lower section. Thus, belonging to higher or lower section may affect the mathematical misconceptions of the respondents.

Keywords: algebra, grade 7 math, math anxiety, math misconceptions

Procedia PDF Downloads 381

Authors: Marwa A. A. Ragab, Hadir M. Maher, Eman I. El-Kimary

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Co-administration of methotrexate (MTX) and aspirin (ASP) can cause a pharmacokinetic interaction and a subsequent increase in blood MTX concentrations which may increase the risk of MTX toxicity. Therefore, it is important to develop a sensitive, selective, accurate and precise method for their simultaneous determination in urine. A new hybrid chemometric method has been applied to the emission response data of the two drugs. Spectrofluorimetric method for determination of MTX through measurement of its acid-degradation product, 4-amino-4-deoxy-10-methylpteroic acid (4-AMP), was developed. Moreover, the acid-catalyzed degradation reaction enables the spectrofluorimetric determination of ASP through the formation of its active metabolite salicylic acid (SA). The proposed chemometric method deals with convolution of emission data using 8-points sin xi polynomials (discrete Fourier functions) after the derivative treatment of these emission data. The first and second derivative curves (D1 & D2) were obtained first then convolution of these curves was done to obtain first and second derivative under Fourier functions curves (D1/FF) and (D2/FF). This new application was used for the resolution of the overlapped emission bands of the degradation products of both drugs to allow their simultaneous indirect determination in human urine. Not only this chemometric approach was applied to the emission data but also the obtained data were subjected to non-parametric linear regression analysis (Theil’s method). The proposed method was fully validated according to the ICH guidelines and it yielded linearity ranges as follows: 0.05-0.75 and 0.5-2.5 µg mL-1 for MTX and ASP respectively. It was found that the non-parametric method was superior over the parametric one in the simultaneous determination of MTX and ASP after the chemometric treatment of the emission spectra of their degradation products. The work combines the advantages of derivative and convolution using discrete Fourier function together with the reliability and efficacy of the non-parametric analysis of data. The achieved sensitivity along with the low values of LOD (0.01 and 0.06 µg mL-1) and LOQ (0.04 and 0.2 µg mL-1) for MTX and ASP respectively, by the second derivative under Fourier functions (D2/FF) were promising and guarantee its application for monitoring the two drugs in patients’ urine samples.

Keywords: chemometrics, emission curves, derivative, convolution, Fourier transform, human urine, non-parametric regression, Theil’s method

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Authors: Erick Pruchnicki, Nikhil Padhye

Abstract:

Plates are important engineering structures which have attracted extensive research since the 19th century. The subject of this work is statical analysis of a linearly elastic homogenous plate under small deformations. A 'thin plate' is a three-dimensional structure comprising of a small transverse dimension with respect to a flat mid-surface. The general aim of any plate theory is to deduce a two-dimensional model, in terms of mid-surface quantities, to approximately and accurately describe the plate's deformation in terms of mid-surface quantities. In recent decades, a common starting point for this purpose is to utilize series expansion of a displacement field across the thickness dimension in terms of the thickness parameter (h). These attempts are mathematically consistent in deriving leading-order plate theories based on certain a priori scaling between the thickness and the applied loads; for example, asymptotic methods which are aimed at generating leading-order two-dimensional variational problems by postulating formal asymptotic expansion of the displacement fields. Such methods rigorously generate a hierarchy of two-dimensional models depending on the order of magnitude of the applied load with respect to the plate-thickness. However, in practice, applied loads are external and thus not directly linked or dependent on the geometry/thickness of the plate; thus, rendering any such model (based on a priori scaling) of limited practical utility. In other words, the main limitation of these approaches is that they do not furnish a single plate model for all orders of applied loads. Following analogy of recent efforts of deploying Fourier-series expansion to study convergence of reduced models, we propose two-dimensional model(s) resulting from truncation of the potential energy and rigorously prove the convergence of these two-dimensional plate models to the parent three-dimensional linear elasticity with increasing truncation order of the potential energy.

Keywords: plate theory, Fourier-series expansion, convergence result, Legendre polynomials

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Authors: Ning Chang, Zelong Yuan, Yunpeng Wang, Jianchun Wang

Abstract:

The utilization of Large Eddy Simulation (LES) has been extensive in turbulence research. LES concentrates on resolving the significant grid-scale motions while representing smaller scales through subfilter-scale (SFS) models. The deconvolution model, among the available SFS models, has proven successful in LES of engineering and geophysical flows. Nevertheless, the thorough investigation of how sub-filter scale dynamics and filter anisotropy affect SFS modeling accuracy remains lacking. The outcomes of LES are significantly influenced by filter selection and grid anisotropy, factors that have not been adequately addressed in earlier studies. This study examines two crucial aspects of LES: Firstly, the accuracy of direct deconvolution models (DDM) is evaluated concerning sub-filter scale (SFS) dynamics across varying filter-to-grid ratios (FGR) in isotropic turbulence. Various invertible filters are employed, including Gaussian, Helmholtz I and II, Butterworth, Chebyshev I and II, Cauchy, Pao, and rapidly decaying filters. The importance of FGR becomes evident as it plays a critical role in controlling errors for precise SFS stress prediction. When FGR is set to 1, the DDM models struggle to faithfully reconstruct SFS stress due to inadequate resolution of SFS dynamics. Notably, prediction accuracy improves when FGR is set to 2, leading to accurate reconstruction of SFS stress, except for cases involving Helmholtz I and II filters. Remarkably high precision, nearly 100%, is achieved at an FGR of 4 for all DDM models. Furthermore, the study extends to filter anisotropy and its impact on SFS dynamics and LES accuracy. By utilizing the dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and direct deconvolution model (DDM) with anisotropic filters, aspect ratios (AR) ranging from 1 to 16 are examined in LES filters. The results emphasize the DDM’s proficiency in accurately predicting SFS stresses under highly anisotropic filtering conditions. Notably high correlation coefficients exceeding 90% are observed in the a priori study for the DDM’s reconstructed SFS stresses, surpassing those of the DSM and DMM models. However, these correlations tend to decrease as filter anisotropy increases. In the a posteriori analysis, the DDM model consistently outperforms the DSM and DMM models across various turbulence statistics, including velocity spectra, probability density functions related to vorticity, SFS energy flux, velocity increments, strainrate tensors, and SFS stress. It is evident that as filter anisotropy intensifies, the results of DSM and DMM deteriorate, while the DDM consistently delivers satisfactory outcomes across all filter-anisotropy scenarios. These findings underscore the potential of the DDM framework as a valuable tool for advancing the development of sophisticated SFS models for LES in turbulence research.

Keywords: deconvolution model, large eddy simulation, subfilter scale modeling, turbulence

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Authors: Ning Chang, Zelong Yuan, Yunpeng Wang, Jianchun Wang

Abstract:

Large eddy simulation (LES) has been extensively used in the investigation of turbulence. LES calculates the grid-resolved large-scale motions and leaves small scales modeled by sublfilterscale (SFS) models. Among the existing SFS models, the deconvolution model has been used successfully in the LES of the engineering flows and geophysical flows. Despite the wide application of deconvolution models, the effects of subfilter scale dynamics and filter anisotropy on the accuracy of SFS modeling have not been investigated in depth. The results of LES are highly sensitive to the selection of filters and the anisotropy of the grid, which has been overlooked in previous research. In the current study, two critical aspects of LES are investigated. Firstly, we analyze the influence of sub-filter scale (SFS) dynamics on the accuracy of direct deconvolution models (DDM) at varying filter-to-grid ratios (FGR) in isotropic turbulence. An array of invertible filters are employed, encompassing Gaussian, Helmholtz I and II, Butterworth, Chebyshev I and II, Cauchy, Pao, and rapidly decaying filters. The significance of FGR becomes evident, as it acts as a pivotal factor in error control for precise SFS stress prediction. When FGR is set to 1, the DDM models cannot accurately reconstruct the SFS stress due to the insufficient resolution of SFS dynamics. Notably, prediction capabilities are enhanced at an FGR of 2, resulting in accurate SFS stress reconstruction, except for cases involving Helmholtz I and II filters. A remarkable precision close to 100% is achieved at an FGR of 4 for all DDM models. Additionally, the further exploration extends to the filter anisotropy to address its impact on the SFS dynamics and LES accuracy. By employing dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and direct deconvolution model (DDM) with the anisotropic filter, aspect ratios (AR) ranging from 1 to 16 in LES filters are evaluated. The findings highlight the DDM's proficiency in accurately predicting SFS stresses under highly anisotropic filtering conditions. High correlation coefficients exceeding 90% are observed in the a priori study for the DDM's reconstructed SFS stresses, surpassing those of the DSM and DMM models. However, these correlations tend to decrease as lter anisotropy increases. In the a posteriori studies, the DDM model consistently outperforms the DSM and DMM models across various turbulence statistics, encompassing velocity spectra, probability density functions related to vorticity, SFS energy flux, velocity increments, strain-rate tensors, and SFS stress. It is observed that as filter anisotropy intensify, the results of DSM and DMM become worse, while the DDM continues to deliver satisfactory results across all filter-anisotropy scenarios. The findings emphasize the DDM framework's potential as a valuable tool for advancing the development of sophisticated SFS models for LES of turbulence.

Keywords: deconvolution model, large eddy simulation, subfilter scale modeling, turbulence

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Authors: Stephen McCarthy, Joanne Gray, Esther Carr, Gerard Danjoux, Paul Baker, Rhiannon Hackett

Abstract:

Background: The Go Well Health (GWH) platform is a web-based programme that allows patients to access personalised care plans and resources, aimed at prehabilitation prior to surgery. The online digital platform delivers essential patient education and support for patients prior to undergoing total hip replacements (THR) and total knee replacements (TKR). This study evaluated the impact of an online digital platform (ODP) in terms of functional health outcomes, health related quality of life and hospital length of stay following surgery. Methods: A retrospective cohort study comparing a cohort of patients who used the online digital platform (ODP) to deliver patient education and support (PES) prior to undergoing THR and TKR surgery relative to a cohort of patients who did not access the ODP and received usual care. Routinely collected Patient Reported Outcome Measures (PROMs) data was obtained on 2,406 patients who underwent a knee replacement (n=1,160) or a hip replacement (n=1,246) between 2018 and 2019 in a single surgical centre in the United Kingdom. The Oxford Hip and Knee Score and the European Quality of Life Five-Dimensional tool (EQ5D-5L) was obtained both pre-and post-surgery (at 6 months) along with hospital LOS. Linear regression was used to compare the estimate the impact of GWH on both health outcomes and negative binomial regressions were used to impact on LOS. All analyses adjusted for age, sex, Charlson Comorbidity Score and either pre-operative Oxford Hip/Knee scores or pre-operative EQ-5D scores. Fractional polynomials were used to represent potential non-linear relationships between the factors included in the regression model. Findings: For patients who underwent a knee replacement, GWH had a statistically significant impact on Oxford Knee Scores and EQ5D-5L utility post-surgery (p=0.039 and p=0.002 respectively). GWH did not have a statistically significant impact on the hospital length of stay. For those patients who underwent a hip replacement, GWH had a statistically significant impact on Oxford Hip Scores and EQ5D-5L utility post (p=0.000 and p=0.009 respectively). GWH also had a statistically significant reduction in the hospital length of stay (p=0.000). Conclusion: Health Outcomes were higher for patients who used the GWH platform and underwent THR and TKR relative to those who received usual care prior to surgery. Patients who underwent a hip replacement and used GWH also had a reduced hospital LOS. These findings are important for health policy and or decision makers as they suggest that prehabilitation via an ODP can maximise health outcomes for patients following surgery whilst potentially making efficiency savings with reductions in LOS.

Keywords: digital prehabilitation, online digital platform, orthopaedics, surgery

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