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A novel design scheme for acoustic cloaking of complex shape based on region partitioning and multi-origin coordinate transformation
Acoustic cloaking is an important application of acoustic metamaterials. This article proposes a novel design scheme for acoustic cloaking based on...
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Coordinate-Adaptive Integration of PDEs on Tensor Manifolds
We introduce a new tensor integration method for time-dependent partial differential equations (PDEs) that controls the tensor rank of the PDE...
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Coordinate Transformations
We have learned in \({\mathbb {C}}={\mathbb {R}}^{2}\) two ways to...
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Coordinate-wise transformation of probability distributions to achieve a Stein-type identity
It is shown that for any given multi-dimensional probability distribution with regularity conditions, there exists a unique coordinate-wise...
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Convergence of Gibbs Sampling: Coordinate Hit-and-Run Mixes Fast
Gibbs sampling, also known as Coordinate Hit-and-Run (CHAR), is a Markov chain Monte Carlo algorithm for sampling from high-dimensional...
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On Viscous Fluid Flow in Curvilinear Coordinate Systems
In the present contribution, we discuss the incompressible Navier–Stokes and Poisson equations for a curvilinear coordinate system constructed from...
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Alternate coordinate systems
UpSquircular coordinates until now we have generally worked in Cartesian coordinates to locate points in the plane. Our past experience with calculus...
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LIE SYMMETRY ANALYSIS AND CONSERVATION LAWS FOR A TIME FRACTIONAL PERTURBED STANDARD KDV EQUATION IN THE STATIONARY COORDINATE
In this paper, we apply the Lie symmetry analysis method for a time fractional perturbed standard KdV equation in the stationary coordinate (FPSKdV)....
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Transformation Model of the Dynamic Deformation of an Elongated Cantilever Plate Mounted on an Elastic Support Element
AbstractA transformation model of the dynamic deformation of an elongated orthotropic composite rod-type plate, consisting of two sections (fastened...
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Bäcklund Transformation for the Nonlinear Schrödinger Equation
In this note we present a new derivation of Bäcklund transformations for the nonlinear Schroedinger equation. We discuss the conserved quantities...
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An Accelerated Coordinate Gradient Descent Algorithm for Non-separable Composite Optimization
Coordinate descent algorithms are popular in machine learning and large-scale data analysis problems due to their low computational cost iterative...
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Linear Map**s and Transformation Matrices
A linear map** is a map** f : V → W between \({\mathbb {K}}\)...
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Operator Spectrum Transformation in Hartree–Fock and Kohn–Sham Equations
AbstractThe paper proposes a method for preliminary transformation of the spectrum of the equation operator both in the Hartree–Fock method and in...
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Base Transformation
Every linear map** f between finite-dimensional \({\mathbb {K}}\)...
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New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation
We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214,...
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Integral Equations of Coordinate Diffraction Problems of Elastic Waves in Stratified Media
AbstractIntegral equations of a number of problems of diffraction of elastic waves on defects, located on the layers interface in plane-parallel...
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A Linear System Output Transformation for Sparse Approximation*
We propose an approach that provides a stable transformation of the output of a linear system into the output of a system with the desired basis. The...
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A Special Coordinate Basis (SCB) of Linear Multivariable Systems
What is called the special coordinate basis (SCB) of a multivariable linear time-invariant system plays a dominant role throughout this book; hence,...