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ON GAUSS TYPE FUNCTIONAL EQUATIONS AND MEAN VALUES BY H. HARUKI AND TH. M. RASSIAS
"... Abstract. In this paper we give a concise summary of some recent results on Gauss type functional equations and mean values by H. Haruki and Th. M. Rassias. ..."
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Abstract. In this paper we give a concise summary of some recent results on Gauss type functional equations and mean values by H. Haruki and Th. M. Rassias.
© Hindawi Publishing Corp. A GAUSS TYPE FUNCTIONAL EQUATION
, 2000
"... Abstract. Gauss ’ functional equation (used in the study of the arithmeticgeometricmean) is generalized by replacing the arithmetic mean and the geometric mean by two arbitrary means. 2000 Mathematics Subject Classification. Primary 39B22; Secondary 26E60. 1. Introduction. By ..."
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Abstract. Gauss ’ functional equation (used in the study of the arithmeticgeometricmean) is generalized by replacing the arithmetic mean and the geometric mean by two arbitrary means. 2000 Mathematics Subject Classification. Primary 39B22; Secondary 26E60. 1. Introduction. By
Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations
, 1988
"... We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front also can be passively advected by an underlying flow. These algorithms approximate the equations of motion, w ..."
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Cited by 1183 (60 self)
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We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front also can be passively advected by an underlying flow. These algorithms approximate the equations of motion
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a qanalogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order differenti ..."
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Cited by 578 (6 self)
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differential or difference equation, the forward and backward shift operator, the Rodriguestype formula and generating functions of all classes of orthogonal polynomials in this scheme. In chapter 2 we give the limit relations between different classes of orthogonal polynomials listed in the Askey
Excitatory and inhibitory interactions in localized populations of model
 Biophysics
, 1972
"... ABSMAcr Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The res ..."
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Cited by 495 (11 self)
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ABSMAcr Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli
A Signal Processing Approach To Fair Surface Design
, 1995
"... In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fai ..."
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Cited by 654 (15 self)
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, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities
Shape modeling with front propagation: A level set approach
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1995
"... Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods and over ..."
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Cited by 808 (20 self)
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along its gradient field with constant speed or a speed that depends on the curvature. It is moved by solving a “HamiltonJacob? ’ type equation written for a function in which the interface is a particular level set. A speed term synthesizpd from the image is used to stop the interface in the vicinity
HOMOGENIZATION AND TWOSCALE CONVERGENCE
, 1992
"... Following an idea of G. Nguetseng, the author defines a notion of "twoscale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector ..."
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Cited by 451 (14 self)
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Following an idea of G. Nguetseng, the author defines a notion of "twoscale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A correctortype
Sparse Reconstruction by Separable Approximation
, 2007
"... Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), waveletbased deconvolution and reconstruction, and compressed sensing ..."
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Cited by 373 (38 self)
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(CS) are a few wellknown areas in which problems of this type appear. One standard approach is to minimize an objective function that includes a quadratic (ℓ2) error term added to a sparsityinducing (usually ℓ1) regularizer. We present an algorithmic framework for the more general problem
Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1992
"... Consider the problem of finding a root of the multivariate gradient equation that arises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general KieferWolfowitz type is appropriate for estimating the root. This p ..."
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Cited by 318 (14 self)
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Consider the problem of finding a root of the multivariate gradient equation that arises in function minimization. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm of the general KieferWolfowitz type is appropriate for estimating the root
Results 1  10
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