1,721,009 research outputs found
Dimiter Prodanov and Sumit Vohra introduce their Active Segmentation tool for plant image analysis.
No full textDimiter Prodanov (IMEC, Belgium) and Sumit Vohra (Zuse Institute, Germany) introduce Active Segmentation as a tool for plant cell image analysis
Cole Hopf Transformations in Maxima
No full text<p>Cole Hopf transformations in Maxima.</p>
<p>The code accompaines a paper in Entropy. </p>
Conditions for continuity of fractional velocity and existence of fractional Taylor expansions
No full textFractional Velocity as a Tool for the Study of Non-Linear Problems
No full textSingular functions and, in general, Hölder functions represent conceptual models of nonlinear physical phenomena. The purpose of this survey is to demonstrate the applicability of fractional velocities as tools to characterize Hölder and singular functions, in particular. Fractional velocities are defined as limits of the difference quotients of a fractional power and they generalize the local notion of a derivative. On the other hand, their properties contrast some of the usual properties of derivatives. One of the most peculiar properties of these operators is that the set of their non trivial values is disconnected. This can be used for example to model instantaneous interactions, for example Langevin dynamics. Examples are given by the De Rham and Neidinger’s singular functions, represented by limits of iterative function systems. Finally, the conditions for equivalence with the Kolwankar-Gangal local fractional derivative are investigated
Analytical and Numerical Treatments of Conservative Diffusions and the Burgers Equation
No full textThe present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.</jats:p
Computation of the Wright function from its integral representation
No full textThe Wright function arises in the theory of fractional differential equations.
It is a very general mathematical object having diverse connections with other special and elementary functions.
The Wright function provides a unified treatment of several classes of special functions, such as the Gaussian, Airy, Bessel, error functions, etc. The manuscript presents a novel numerical technique for approximation of the Wright function using quadratures.
The algorithm is implemented as a standalone library using the double-exponential quadrature integration technique using the method of stationary phase. Function plots for a variety of parameter values are demonstrated
Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras
No full textClifford algebras are an active area of mathematical research having numerous applications in mathematical physics and computer graphics, among many others. This paper demonstrates algorithms for the computation of characteristic polynomials, inverses, and minimal polynomials of general multivectors residing in a non-degenerate Clifford algebra of an arbitrary dimension. The characteristic polynomial and inverse computation are achieved by a translation of the classical Faddeev–LeVerrier–Souriau (FVS) algorithm in the language of Clifford algebra. The demonstrated algorithms are implemented in the Clifford package of the open source computer algebra system Maxima. Symbolic and numerical examples residing in different Clifford algebras are presented
Clifford Maxima package v 2.5.4
No full text<p><strong>Clifford</strong></p>
<p>is a lightweight package for performing Geometric and Clifford Algebra calculations in Maxima.</p>
<p>The release includes new versions of <strong>climatrep.mac</strong> v. 2.5.7 (matrix representations and FVS algorithm) and <strong>cliffordlin.mac</strong> v. 1.2 (linear algebra calculations).</p>
dprodanov/clifford: version 2.4
No full text<p>Maintenance release</p>
<p><code>2.4.1 Date 17 Jun 20177 </code></p>
<p><code>- simplification of Clifford exponents </code></p>
<p><code>- trigsimp inncorporated in cliffsimpall </code></p>
<p><code>- solving</code></p>
<p><code>2.4 Date 27 Nov 2016 - new implementation clicoeff </code></p>
<p><code>- new implementation clidual </code></p>
<p><code>- convenience matrix functions </code></p>
<p><code>- added algebraical dual functionality </code></p>
<p><code>- fixed regressive product </code></p>
<p><code>- added Hestenes product </code></p>
<p><code>- added xor function </code></p>
Examples for CGI2023
No full textExamples for CGI2023. Calculations are described in the paper "Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras"
- …
