The Relationship between the Boundary Behavior of and the Comparison Principles Satisfied by Approximate Solutions of Elliptic Dirichlet Problems

2020 ◽  
pp. 237-259
Author(s):  
Kirk E. Lancaster
Keyword(s):  
Boundary Behavior ◽  
Approximate Solutions ◽  
Dirichlet Problems ◽  
Comparison Principles ◽  
The Relationship

scholarly journals Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Roberto C. Raimondo
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Boundary Behavior ◽  
Berezin Transform ◽  
Planar Domain ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Planar Domains ◽  
Necessary And Sufficient ◽  
The Relationship

We study the problem of the boundedness and compactness of when and is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of

The Changing Views of a Philosopher of Chemistry on the Question of Reduction

2016 ◽  
Author(s):  
Eric R. Scerri
Keyword(s):  
Quantum Mechanics ◽  
Mathematical Theory ◽  
Approximate Solutions ◽  
Electron Systems ◽  
Atomic Systems ◽  
Quantum Mechanical Description ◽  
The Subject ◽  
The Moment ◽  
The Relationship

The question of the reduction of chemistry to quantum mechanics has been inextricably linked with the development of the philosophy of chemistry since the field began to develop in the early 1990s. In the present chapter I would like to describe how my own views on the subject have developed over a period of roughly 30 years. A good place to begin might be the frequently cited reductionist dictum that was penned in 1929 by Paul Dirac, one of the founders of quantum mechanics. . . . The underlying laws necessary for the mathematical theory of a larger part of physics and the whole of chemistry are thus completely known, and the difficulty is only that exact applications of these laws lead to equations, which are too complicated to be soluble. (Dirac 1929) . . . These days most chemists would probably comment that Dirac had things backward. It is clear that nothing like “the whole of chemistry” has been mathematically understood. At the same time most would argue that the approximate solutions that are afforded by modern computers are so good as to overcome the fact that one cannot obtain exact or analytical solutions to the Schrödinger equation for many-electron systems. Be that as it may, Dirac’s famous quotation, coming from one of the creators of quantum mechanics, has convinced many people that chemistry has been more or less completely reduced to quantum mechanics. Another quotation of this sort (and one using more metaphorical language) comes from Walter Heitler who together with Fritz London was the first to give a quantum mechanical description of the chemical bond. . . . Let us assume for the moment that the two atomic systems ↑↑↑↑ . . . and ↓↓↓↓ . . . are always attracted in a homopolar manner. We can, then, eat Chemistry with a spoon. (Heitler 1927) . . . Philosophers of science eventually caught up with this climate of reductionism and chose to illustrate their views with the relationship with chemistry and quantum mechanics.

Random Vibration of a Nonlinear System With a Set-up Spring

1962 ◽  
Vol 29 (3) ◽  
pp. 477-482 ◽  
Author(s):  
S. H. Crandall
Keyword(s):  
Probability Density ◽  
Random Vibration ◽  
Planck Equation ◽  
Approximate Solutions ◽  
Equivalent Linearization ◽  
Zero Crossings ◽  
Mean Square Response ◽  
Spring System ◽  
Set Up ◽  
The Relationship

Several aspects of the problem of random vibration in nonlinear systems are discussed in terms of a particular set-up spring system. Exact solutions for the mean square response and the expected frequency of zero-crossings are obtained by means of the Fokker-Planck equation. These are compared with approximate solutions obtained from equivalent linearization techniques. The distribution of response peaks is then studied and a probability density is derived for the peaks on a relative frequency basis. The probability density of the response envelope is also obtained and the relationship between the two distributions is discussed.

scholarly journals Criteria analysis for deciding the LTL and FTL modes of transport

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Diego Armando Soto De La Vega ◽  
Paula Horta Lemos ◽  
João Eduardo Azevedo Ramos da Silva ◽  
José Geraldo Vidal Vieira
Keyword(s):  
High Weight ◽  
Approximate Solutions ◽  
Decision Makers ◽  
The Other ◽  
Delivery Time ◽  
Qualitative And Quantitative ◽  
Optimal Approach ◽  
Operation Results ◽  
The Relationship ◽  
Multicriteria Methodology

Abstract: Choosing between Less Than Truckload (LTL) and Full Truckload (FTL) is based on a multicriteria decision because it takes into account aspects such as costs and operational efficiency in transportation, handling and stock of goods. The aim of this article is to provide a detailed analysis of the criteria that comprise the LTL and FTL transport decision using a multicriteria methodology that considers decision makers´ preferences. The SMARTS method was applied in a telecommunications company that outsources its logistics operation. Results show that the main criteria for choosing LTL shipment are related to the relationship with the customer and the efficiency in the delivery of the freight (reliability of the delivery time). On the other hand, choosing FTL transport requires a high weight given to the criteria regarding benefits and cost of transit inventory. The contribution of the research is to provide a structured and flexible analysis to choose the types of shipment (FTL and FLT) when taking into account the risk aversion of decision makers using a non-optimal approach, but with approximate solutions encompassing several qualitative and quantitative criteria in this choice.

Study on Searching the Best Rise of Truss String Structure by Using Fibonacci Method

2011 ◽  
Vol 250-253 ◽  
pp. 1556-1560
Author(s):  
Hai Bo Zhou ◽  
Ping Liu ◽  
Guan Ze Hou
Keyword(s):  
Exact Solutions ◽  
Structure Optimization ◽  
Approximate Solutions ◽  
Search Method ◽  
Search Efficiency ◽  
Dynamic Search ◽  
String Structure ◽  
The Relationship ◽  
Search Program ◽  
Search Interval

In order to discuss the relationship between truss string structure weight and the rise, so as to find out the optimal rise of different spans, Fibonacci search method is used to write truss string structure optimization program which takes the rise as variable. To effectively improve search efficiency and ensure the accuracy, the dynamic search interval is introduced when writing the Fibonacci search program. This paper use Fibonacci to search the optimal rise in span of 100m of truss string structure, meanwhile analysis the dynamic search interval, the analysis results show that the approximate solutions of this method is very approximate to exact solutions, and search efficiency is improved.

On a momentum-mass flux diagram for turbulent jets, plumes and wakes

1961 ◽  
Vol 10 (1) ◽  
pp. 101-112 ◽  
Author(s):  
B. R. Morton
Keyword(s):  
Differential Equation ◽  
Mass Flux ◽  
Momentum Flux ◽  
Turbulent Jets ◽  
Approximate Solutions ◽  
Main Stream ◽  
Mean Flow ◽  
Actual Distribution ◽  
The Relationship ◽  
Moving Fluid

Many salient features of fully developed turbulent jets, plumes and wakes with steady mean flow are shown clearly by the relationship between the momentum flux and the mass flux in the column of moving fluid. Using a simple model for the flows, this relationship can be found from the solution of a single ordinary differential equation and the character of many related flows can be represented immediately (except for actual distribution in space) on a single momentummass flux diagram.In this note some approximate solutions based on dimensional arguments are outlined briefly for cases of buoyant and non-buoyant wakes and jets directed along the axis of a uniform main stream, and momentum-mass flux curves are presented.

Analytical study of the vibrating double-sided quintic nonlinear nano-torsional actuator using higher-order Hamiltonian approach

2021 ◽  
pp. 146134842110320
Author(s):  
Gamal Mohamed Ismail ◽  
Mahmoud Abul-Ez ◽  
Hijaz Ahmad ◽  
Nadia Mohamed Farea
Keyword(s):  
Analytical Study ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Higher Order ◽  
Second Order ◽  
Hamiltonian Approach ◽  
Homotopy Perturbation ◽  
The Relationship ◽  
Better Than

In this work, we investigate and apply higher-order Hamiltonian approach (HA) as one of the novelty techniques to find out the approximate analytical solution for vibrating double-sided quintic nonlinear nano-torsional actuator. Periodic solutions are analytically verified, and consequently, the relationship between the initial amplitude and the natural frequency are obtained in a novel analytical way. The HA is then extended to the second-order to find more accurate results. To show the accuracy and applicability of the technique, the approximated results are compared with the homotopy perturbation method and numerical solution. According to the numerical results, it is highly remarkable that the second-order approximate solutions produce better than previously existing results and almost similar in comparing with the numerical solutions.

BIFURCATIONS IN NUMERICAL METHODS FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

2003 ◽  
Vol 13 (11) ◽  
pp. 3255-3271 ◽  
Author(s):  
JOHN T. EDWARDS ◽  
NEVILLE J. FORD ◽  
JASON A. ROBERTS
Keyword(s):  
Differential Equations ◽  
Approximate Solutions ◽  
Qualitative Behavior ◽  
Fading Memory ◽  
Convolution Kernel ◽  
Numerical Schemes ◽  
Long Time ◽  
Test Equation ◽  
Parameter Dependent ◽  
The Relationship

We are interested in finding approximate solutions to parameter-dependent Volterra integro-differential equations over long time intervals using numerical schemes. This paper concentrates on changes in qualitative behavior (bifurcations) in the solutions and extends the work of Brunner and Lambert and Matthys (who considered only changes in stability behavior) to consider other bifurcations. We begin by considering a one-parameter equation with fading memory separable convolution kernel: we give an analytical discussion of bifurcations in this case and provide details of the behavior of numerical schemes. We extend our analysis to consider an equation with two-parameter fading memory convolution kernel and show the relationship to the classical test equation studied by the earlier authors. We draw attention to the fact that known stability results may not provide a reliable framework for choice of numerical scheme when other changes in qualitative behavior are also of interest. We give bifurcation plots for a variety of methods and show how, for known values of the parameters, stepsizes h>0 may be chosen to preserve the correct qualitative behavior in the numerical solution of the Volterra integro-differential equation.

scholarly journals Magnetic field diffusion in ferromagnetic materials: fractional calculus approaches

2021 ◽  
Vol 11 (3) ◽  
pp. 1-15
Author(s):  
Jordan Hristov
Keyword(s):  
Magnetic Field ◽  
Fractional Calculus ◽  
Approximate Solutions ◽  
Ferromagnetic Materials ◽  
Fading Memory ◽  
Dirichlet Problems ◽  
Integration Model ◽  
Parabolic Profile ◽  
Field Diffusion ◽  
Singular Memory

The paper addresses diffusion approximations of magnetic field penetration of ferromagnetic materials with emphasis on fractional calculus applications and relevant approximate solutions. Examples with applications of time-fractional semi-derivatives and singular kernel models (Caputo time fractional operator) in cases of field independent and field-dependent magnetic diffusivities have been developed: Dirichlet problems and time-dependent boundary condition (power-law ramp). Approximate solutions in all theses case have been developed by applications of the integral-balance method and assumed parabolic profile with unspecified exponents. Tow version of the integral method have been successfully implemented: SDIM (single integration applicable to time-fractional semi-derivative model) and DIM (double-integration model to fractionalized singular memory models). The fading memory approach in the sense of the causality concept and memory kernel effect on the model constructions have been discussed.

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