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Results 1 - 10
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59,706
Spaces of functions satisfying simple differential equations
, 1994
"... In [6]–[9] the first author published an algorithm for the conversion of analytic functions for which derivative rules are given into their representing power series ∞∑ akzk at the origin and vice versa, implementations of which exist in Mathematica [19], (s. [9]), Maple [12] (s. [4]) and Reduce [5] ..."
Abstract
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Cited by 10 (8 self)
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] (s. [13]). One main part of this procedure is an algorithm to derive a homogeneous linear differential equation with polynomial coefficients for the given function. We call this type of ordinary differential equations simple. Whereas the opposite question to find functions satisfying given
Addendum to ”A Simple Differential Equation System for the Description of Competition among Religions”
"... We propose a linear differential equation system for the description of competitions among populations (e.g. religions) for followers. The interaction among the populations is modeled by the use of constant coefficients and, as the new feature, by additional damping factors. ..."
Abstract
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Cited by 2 (2 self)
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We propose a linear differential equation system for the description of competitions among populations (e.g. religions) for followers. The interaction among the populations is modeled by the use of constant coefficients and, as the new feature, by additional damping factors.
Radial cluster lensing -- A simple differential equation describing arclet fields
, 1994
"... Clusters of galaxies acting as gravitational lenses deform the images of background galaxies. For small galaxies the deformation is determined by the local properties of the lens (shear, convergence). Small circular shaped galaxies are seen as small ellipses. The orientation and axial ratio of the ..."
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of the ellipses could then be used to trace the properties of the lens. We introduce and solve an ordinary homogeneous linear first order differential equation which describes completely the radial cluster lens. It can be used to reconstruct the lens mapping from the measured axial ratios of lensed background
USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
Abstract
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Cited by 1399 (16 self)
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The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking
Strongly Elliptic Systems and Boundary Integral Equations
, 2000
"... Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition of the mathematic ..."
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Cited by 501 (0 self)
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Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition
An iterative method for the solution of the eigenvalue problem of linear differential and integral
, 1950
"... The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the ..."
Abstract
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Cited by 537 (0 self)
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the process of "minimized iterations". Moreover, the method leads to a well convergent successive approximation procedure by which the solution of integral equations of the Fredholm type and the solution of the eigenvalue problem of linear differential and integral operators may be accomplished. I.
Linear models and empirical bayes methods for assessing differential expression in microarray experiments.
- Stat. Appl. Genet. Mol. Biol.
, 2004
"... Abstract The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a simple hierarchical parametric model. ..."
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Cited by 1321 (24 self)
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Abstract The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a simple hierarchical parametric model
Numerical integration of the Cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes
- J. Comput. Phys
, 1977
"... A numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method ..."
Abstract
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Cited by 704 (6 self)
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A numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method
Nonlinear total variation based noise removal algorithms
, 1992
"... A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the g ..."
Abstract
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Cited by 2271 (51 self)
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the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t--- ~ 0o the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear
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59,706
