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Showing 1 to 20 of 103 for “"Chebyshev"”.
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Chebyshev spectral methods for potential field computation
We investigate Chebyshev spectral methods for solving Poisson's equation and the generalized Poisson's equations and apply them to 3-D gravity and DC resistivity modeling. When we approximate a function by a finite sum of Chebyshev polynomials, there are two kinds of errors: truncation and …
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Regularized weighted Chebyshev approximations for support estimation
… analysis relies on introducing a new weighted Chebyshev polynomial approximation method, jointly optimizing the bias and variance components of the risk, and combining the weighted minmax polynomial approximation method with discretized semi-infinite programming solvers. Such a setting allows …
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Chebyshev Approximation of Discrete polynomials and Splines
… an integer processor. In many applications, Chebyshev approximation with polynomials and splines is useful in representing a stream of data or a function. Because the impulse/summation approach is developed for discrete systems, some aspects of traditional continuous approximation are not …
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Chebyshev-like polynomials, conic distribution of roots, and continued fractions
… of the properties of the roots of translated Chebyshev polynomials of the first kind (call these complex numbers Chebyshev points), are illuminated by the study of geometric properties of the ellipse and conversely. This includes the following; Chebyshev points lie on certain ellipses centered …
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Key-Based Authentication Scheme for eVTOL Drones Using Chebyshev Chaotic Maps
… a key-based authentication scheme that utilizes Chebyshev polynomials as chaotic maps, hash functions, and the AES-256 encryption technique. The network members can securely generate all encryption keys without sharing secret data, which solves one of the main problems of the symmetric encryption …
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Solution of non-linear partial differential equations with the Chebyshev Spectral method
… modeled, but multiple sub-domains may be used. A Chebyshev-Collocation Spectral method is used to solve a variety of ordinary and partial differential equations. The Chebyshev Polynomial series follows a well established recursion relation for calculation of the polynomials and their derivatives. …
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Modeling spider webs as multilinked structures using a Chebyshev pseudospectral collocation method
… solve the associated eigenvalue problem using a Chebyshev pseudospectral collocation method to discretize the system. This thesis first examines the vibrations of webs with uniform material properties throughout, then investigates the effects of using biologically realistic material parameters …
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Chebyshev Series Expansion of the Solution of Kepler's Equation and Its Numerical Computation
Made available in DSpace on 2014-12-11T18:24:11Z (GMT). No. of bitstreams: 1 7500355.pdf: 1711155 bytes, checksum: 69982c5b61ac73d3a5edaa082c70b175 (MD5) Previous issue date: 1974
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El método de Chebyshev para el cálculo de las raíces de ecuaciones no lineales
… we enter the initial ideas that resulted in the Chebyshev method. Also sheds light on the controversy surrounding the different allocation enclose the authorship of that method. In the following two approaches, we delve into the study of real and complex dynamics of the method emphasizing …
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Application of Chebyshev Formalism to Identify Nonlinear Magnetic Field Components in Beam Transport System
… that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was …
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Chebyshev spectral method for incompressible viscous flow with boundary layer control via suction or blowing
… this method from being implemented. Second, a Chebyshev spectral method using the wall function technique was applied to the defect form of the incompressible viscous momentum equation. A turbulent jet profile was computed with N = 40 modes, a number low enough to allow the method's …
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An application of Chebyshev polynomials to the solution of a two-dimensional elliptic boundary-value problem
… investigate the feasibility of using a bivariate Chebyshev polynomial to approximate solutions to the two-dimensional neutron diffusion equation. The two-dimensional two-group neutron diffusion equations are solved by expanding neutron fluxes in a finite series of Chebyshev polynomials over large …
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Three-Dimensional Fluid Simulations of Mid-Latitude Ionospheric Processes with Hybrid Chebyshev/Fourier Pseudo-Spectral Methods
Ionospheric irregularities are small-scale plasma density structures driven by instabilities arising from combinations of plasma drifts, density gradients, and electric fields. These irregularities can cause mid-latitude GPS scintillations, characterized by amplitude and phase fluctuations that …
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The Role of The Kolmogoroff Condition in The Characterization of Best Chebyshev Approximation of R('n)-Valued Continuous-Functions
Made available in DSpace on 2014-12-11T18:23:54Z (GMT). No. of bitstreams: 1 7310043.pdf: 2259609 bytes, checksum: f8f285bc98fdbc7497b6d0e58a2346ca (MD5) Previous issue date: 1972
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The Use of Chebyshev Matrix Polynomials in The Iterative Solution of Linear Equations Compared to The Method of Successive Overrelaxation
Made available in DSpace on 2014-12-05T21:50:13Z (GMT). No. of bitstreams: 1 5904512.pdf: 3744616 bytes, checksum: 36f7058b6a22a150846a4adc2a8f8360 (MD5) Previous issue date: 1959
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Pulse Design for Two-Qubit Gates in Superconducting Circuits
… design problem. Our research indicates that the Chebyshev trajectories – the trajectories based on the Chebyshev pulse and weighted Chebyshev approximation – have the potential to outperform the Slepian trajectories based on the Slepian pulse, which are currently widely used in quantum …
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Efficient Solution of Large Sparse Eigenvalue Problems in Microelectronic Simulation
We present a new Chebyshev-Arnoldi algorithm for finding the lowest energy eigen-functions of an elliptic operator. The algorithm, which is essentially the same for symmetric, nonsymmetric, and complex nonhermitian matrices, is adapted to a specific problem by two subroutines which encapsulate the …
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Computation of interlaminar stresses from finite element solutions to plate theories
… w(,y) over the subdomain is expanded in a Chebyshev series. Then collocation is used to determine the unknown Chebyshev coefficients such that the Chebyshev series matches displacement w and its normal derivative from the finite element solution at discrete points on the boundary of the …
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Combined analytical and numerical solutions in liquid metal flows in a rectangular duct with uniform or non-uniform, strong magnetic fields
… magnetic fields. Spectral methods with the Chebyshev collocation method or Chebyshev-Fourier collocation method have been used successfully for the numerical solutions.
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Synthesis of coupled resonator circuits with multiple outputs using coupling matrix optimization
… with novel topologies that can achieve Chebyshev and Quasi-elliptic filtering responses. To verify the design methodology, some components with Chebyshev filtering response have been designed, fabricated and tested. X-band coupled resonator devices have been realized using waveguide …
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