Search results for "Abstract algebra"
showing 10 items of 452 documents
Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics
2006
We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero-Sutherland type.
Decision Suport System for Manufacturing Processes Reengineering based upon Fuzzy Logic Techniques
2012
Abstract This work presents a method for taking the decision of reengineering a production system, based upon fuzzy techniques. The main advantage of this method is, after authors' opinion, is the ease of its implementation together with the reduced time for gathering data and processing it. Multi-variable decision systems are usually based upon complicated mathematical methods and involved a large amount of data to be processed. The fuzzy approach presented here is based only on five input variables and one output variable. The data for the model are gathered by simple queries and quizzes. Human perception, the main point of fuzzy logic, is widely used here for gathering input data for the…
THE GOLDMAN CONSTANT FIELD ASSUMPTION - SIGNIFICANCE AND APPLICABILITY CONDITIONS
1986
Ionic transport phenomena in simple, porous membranes can be approximately represented by the Nernst-Planck flux equations and Poisson's equation. In order to solve this set of equations for each particular case, the Goldman constant field assumption is one of the most widely used. In the present paper the significance and the applicability conditions of the above hypothesis is critically examined. and the particular situations where it is exact are shown. These conditions are later verified by solving numerically the electrodiffusion equations. The analysis carried out shows that some of the earlier studies based on asymptotic expansions and numerical solutions should be partially revised.
PRACTICAL ASPECTS OF THE ANALYSIS OF THE PROGRESSION CURVES OF FIRST AND PSEUDO-FIRST ORDER REACTIONS
2020
The paper presents a simple method of determining iteratively the progression curve asymptote for first and pseudo-first order reactions. For selected student exercises, thus obtained results were compared (see Supplementary Material) with those found by means of the method of determining asymptotes experimentally. A nonlinear fitting method was additionally employed to assess the accuracy.
On the analysis of the cat's pattern recognition system
1983
The objective of the paper is to determine in abstract terms the algorithms used by the cat detecting simple patterns and to quantify the contributions of the visual areas 17, 18, 19 for this task. The data incorporated in the algorithm are collected from behavioral experiments where the animals had to distinguish between two patterns. The patterns were superimposed with gaussian noise and the detection probability was measured. The resulting model describes pattern recognition in two steps: first extraction of features and second classification. The test of the validity of the model system was to predict the outcome of similar experiments but with different patterns. With the help of the m…
Chaotic behavior in deformable models: the double-well doubly periodic oscillators
2001
Abstract The motion of a particle in a one-dimensional perturbed double-well doubly periodic potential is investigated analytically and numerically. A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. The parameter regions of chaotic behavior predicted by the theoretical analysis agree very well with numerical simulations.
Chaotic behaviour in deformable models: the asymmetric doubly periodic oscillators
2002
Abstract The motion of a particle in a one-dimensional perturbed asymmetric doubly periodic (ASDP) potential is investigated analytically and numerically. A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. Theory predicts the regions of chaotic behaviour of orbits in a good agreement with computer calculations.
Adaptive interpolation with maximum order close to discontinuities
2022
Abstract Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to this method giving explicit expressions for all the weights for any order of the algorithm. It has a similar behavior to weighted essentially non oscillatory (WENO) technique but the design of the weights in this case is more simple. Also, we propose a new way to construct them obtaining the maximum order near the discontinuities. Some experiments are performed to demonstrate our results and to compare them with standard methods.
Eight Simple Guidelines for Improved Understanding of Transformations and Nonlinear Effects
2021
Jyväskylästä kirjoitettiin: Käyn läpi Extra-Vipusessa ristiriitaisiksi luokitettuja yhteisjulkaisuja. Julkaisu " Eight Simple Guidelines for Improved Understanding of Transformations and Nonlinear Effects" on meillä laitettu A2 ja teillä A1. Meillä varmaan päädytty tuohon A2:een kun tiivistelmässä sanotaan "Building on a systematic review of six leading management journals..". Mutta mitä mieltä olette, kumpi olisi parempi? Transforming variables before analysis or applying a transformation as a part of a generalized linear model are common practices in organizational research. Several methodological articles addressing the topic, either directly or indirectly, have been published in the rec…
Discrete Structure Shakedown Design Ices ’95, Hawai, July 30 – August 3, 1995
1995
The minimum volume shakedown design problem was already approached by several authors with studies devoted to discrete structures (see e.g. [1]–[5]) and to continuous structures (see e.g. [6]). Except some very simple structural typologies, also the optimal shakedown design problem formulations for continuous structures need to be discretized in the application stage. In any case, the relevant optimal shakedown design problem for discrete (or discretized) structures is formulated in terms of design variables as well as behavioural variables, and consists in the search for the/a minimum volume design among all feasible designs (i.e. able to shakedown). Due to its strong non-linearity, the la…