scholarly journals Mandelbrot, Fama and the emergence of econophysics

2016 ◽  
Vol 35 (69) ◽  
pp. 637-662
Author(s):  
Boris Salazar Trujillo
Keyword(s):  
Analytical Solutions ◽  
Financial Economics ◽  
Analytical Techniques ◽  
Infinite Variance ◽  
Pareto Distributions

It is argued that Mandelbrot's stable Lévy-Pareto distributions were not accepted into the emerging field of financial economics due to their incompatibility with the analytical techniques and properties of equilibrium economics, and to the absence -both in physics and in economics- of analytical solutions to the infinite variance associated with those distributions. Whilst physicists made stable Lévy distributions plausible, creating Econophysics in the meantime, economists just forgot about them, suggesting their strong bias towards desirable properties and against established facts.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

Identification of Nonlinear Systems Parameters Using Polyspectral Measurements and Analysis

1995 ◽  
Author(s):  
Muhammad R. Hajj ◽  
Ali H. Nayfeh ◽  
Pavol Popovic
Keyword(s):  
Experimental Study ◽  
Nonlinear Systems ◽  
Analytical Solutions ◽  
Analytical Techniques ◽  
Modal Interactions ◽  
Unknown Parameters ◽  
Nonlinear Parameters ◽  
The Subject ◽  
Beam Frame ◽  
Subharmonic Resonances

Abstract Experimental and analytical techniques that characterize nonlinear modal interactions in structures are used to quantify parameters in representative nonlinear systems. The subject of the experimental study is a three-beam frame. Subharmonic resonances and interaction between widely spaced modes are exploited to determine nonlinear parameters in models that represent these interactions. The phases of the auto-bispectra of the response of this structure appear in the analytical solutions of the representative models. Values of these phases could thus aid in determining other unknown parameters of nonlinear systems.

scholarly journals The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 987 ◽  
Author(s):  
A. A. Alderremy ◽  
Hassan Khan ◽  
Rasool Shah ◽  
Shaban Aly ◽  
Dumitru Baleanu
Keyword(s):  
Mathematical Modeling ◽  
Analytical Solution ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Analytical Techniques ◽  
Whitham Equations ◽  
Suggested Technique ◽  
Approximate Analytical Solutions ◽  
Physical Phenomena

This article is dealing with the analytical solution of Fornberg–Whitham equations in fractional view of Caputo operator. The effective method among the analytical techniques, natural transform decomposition method, is implemented to handle the solutions of the proposed problems. The approximate analytical solutions of nonlinear numerical problems are determined to confirm the validity of the suggested technique. The solution of the fractional-order problems are investigated for the suggested mathematical models. The solutions-graphs are then plotted to understand the effectiveness of fractional-order mathematical modeling over integer-order modeling. It is observed that the derived solutions have a closed resemblance with the actual solutions. Moreover, using fractional-order modeling various dynamics can be analyzed which can provide sophisticated information about physical phenomena. The simple and straight-forward procedure of the suggested technique is the preferable point and thus can be used to solve other nonlinear fractional problems.

scholarly journals Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 597 ◽  
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Wave Equation ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Wave Equations ◽  
Analytical Techniques ◽  
Nonlinear Problems ◽  
High Rate ◽  
Numerical Examples ◽  
Linear And Nonlinear

In the present article, fractional-order heat and wave equations are solved by using the natural transform decomposition method. The series form solutions are obtained for fractional-order heat and wave equations, using the proposed method. Some numerical examples are presented to understand the procedure of natural transform decomposition method. The natural transform decomposition method procedure has shown that less volume of calculations and a high rate of convergence can be easily applied to other nonlinear problems. Therefore, the natural transform decomposition method is considered to be one of the best analytical techniques, in order to solve fractional-order linear and nonlinear Partial deferential equations, particularly fractional-order heat and wave equation.

Bounded dam-break flows with tailwaters

2011 ◽  
Vol 686 ◽  
pp. 160-186 ◽  
Author(s):  
Alexander J. N. Goater ◽  
Andrew J. Hogg
Keyword(s):  
Analytical Solutions ◽  
Shallow Water Equations ◽  
Analytical Techniques ◽  
Rear Wall ◽  
Continuous Solutions ◽  
Nonlinear Shallow Water Equations ◽  
Stationary Layer ◽  
Hodograph Transformation ◽  
Finite Extent ◽  
Quiescent Fluid

AbstractThe gravitationally driven collapse of a reservoir into an initially stationary layer of fluid, termed the tailwater, is studied using the nonlinear shallow water equations. The motion is tackled using the hodograph transformation of the governing equation which allows the solutions for velocity and depth of the shallow flowing layer to be constructed by analytical techniques. The front of the flow emerges as a bore across which the depth of the fluid jumps discontinuously to the tailwater depth. The speed of the front is initially constant, but progressively slows once the finite extent of the reservoir begins to influence the motion. There then emerges a variety of phenomena depending upon the depth of the tailwater relative to the initial depth of the reservoir. Provided that the tailwater is sufficiently deep, a region of quiescent fluid emerges adjacent to the rear wall of the reservoir, followed by a region within which the velocity is negative. Also it is shown that for non-vanishing tailwater depths, continuous solutions for the velocity and height of the flowing layer breakdown after a sufficient period and develop an interior bore, the location and time of inception of which are calculated directly from quasi-analytical solutions.

scholarly journals Analytical Solutions of Some Strong Nonlinear Oscillators

2021 ◽  
Author(s):  
Alvaro Humberto Salas ◽  
Samir Abd El-Hakim El-Tantawy
Keyword(s):  
Analytical Solutions ◽  
Initial Conditions ◽  
Exact Analytical Solution ◽  
Main Idea ◽  
Analytical Techniques ◽  
Elliptic Functions ◽  
Nonlinear Oscillators ◽  
Continuous Functions ◽  
Soliton Theory ◽  
Quintic Polynomial

Oscillators are omnipresent; most of them are inherently nonlinear. Though a nonlinear equation mostly does not yield an exact analytic solution for itself, plethora of elementary yet practical techniques exist for extracting important information about the solution of equation. The purpose of this chapter is to introduce some new techniques for the readers which are carefully illustrated using mainly the examples of Duffing’s oscillator. Using the exact analytical solution to cubic Duffing and cubic-quinbic Duffing oscillators, we describe the way other conservative and some non conservative damped nonlinear oscillators may be studied using analytical techniques described here. We do not make use of perturbation techniques. However, some comparison with such methods are performed. We consider oscillators having the form x¨+fx=0 as well as x¨+2εẋ+fx=Ft, where x=xt and f=fx and Ft are continuous functions. In the present chapter, sometimes we will use f−x=−fx and take the approximation fx≈∑j=1Npjxj, where j=1,3,5,⋯N only odd integer values and x∈−AA. Moreover, we will take the approximation fx≈∑j=0Npjxj, where j=1,2,3,⋯N, and x∈−AA. Arbitrary initial conditions are considered. The main idea is to approximate the function f=fx by means of some suitable cubic or quintic polynomial. The analytical solutions are expressed in terms of the Jacobian and Weierstrass elliptic functions. Applications to plasma physics, electronic circuits, soliton theory, and engineering are provided.

The Use of Advanced Analytical Techniques for Characterization of the Chemical, Physical, and Crystallographic Nature of a Surface

1973 ◽  
Vol 31 ◽  
pp. 132-133 ◽  
Author(s):  
R. E. Herfert
Keyword(s):  
Surface Characterization ◽  
Analytical Techniques ◽  
X Ray Diffraction ◽  
Depth Of Penetration ◽  
X Ray ◽  
The Past ◽  
Transmission Electron ◽  
Scanning Electron

Studies of the nature of a surface, either metallic or nonmetallic, in the past, have been limited to the instrumentation available for these measurements. In the past, optical microscopy, replica transmission electron microscopy, electron or X-ray diffraction and optical or X-ray spectroscopy have provided the means of surface characterization. Actually, some of these techniques are not purely surface; the depth of penetration may be a few thousands of an inch. Within the last five years, instrumentation has been made available which now makes it practical for use to study the outer few 100A of layers and characterize it completely from a chemical, physical, and crystallographic standpoint. The scanning electron microscope (SEM) provides a means of viewing the surface of a material in situ to magnifications as high as 250,000X.

Recent Applications of High Resolution Electron Microscopy to Crystalline Arrays of Virus Particles

1978 ◽  
Vol 36 (3) ◽  
pp. 470-482 ◽  
Author(s):  
R.W. Horne
Keyword(s):  
Electron Microscopy ◽  
Image Processing ◽  
Analytical Techniques ◽  
Staining Technique ◽  
High Resolution Electron Microscopy ◽  
Optical Diffraction ◽  
Full Potential ◽  
Virus Particles ◽  
Resolution Electron ◽  
Wide Range

The technique of surrounding virus particles with a neutralised electron dense stain was described at the Fourth International Congress on Electron Microscopy, Berlin 1958 (see Home & Brenner, 1960, p. 625). For many years the negative staining technique in one form or another, has been applied to a wide range of biological materials. However, the full potential of the method has only recently been explored following the development and applications of optical diffraction and computer image analytical techniques to electron micrographs (cf. De Hosier & Klug, 1968; Markham 1968; Crowther et al., 1970; Home & Markham, 1973; Klug & Berger, 1974; Crowther & Klug, 1975). These image processing procedures have allowed a more precise and quantitative approach to be made concerning the interpretation, measurement and reconstruction of repeating features in certain biological systems.

Some applications of electron beam microanalysis techniques in VLSI process evaluation

1983 ◽  
Vol 41 ◽  
pp. 160-161
Author(s):  
Simon Thomas
Keyword(s):  
Integrated Circuits ◽  
Process Evaluation ◽  
Large Scale ◽  
Technology Development ◽  
Analytical Techniques ◽  
Successful Implementation ◽  
Analysis Of Failures ◽  
Characterization Of Materials ◽  
Circuits Vlsi

Trends in the technology development of very large scale integrated circuits (VLSI) have been in the direction of higher density of components with smaller dimensions. The scaling down of device dimensions has been not only laterally but also in depth. Such efforts in miniaturization bring with them new developments in materials and processing. Successful implementation of these efforts is, to a large extent, dependent on the proper understanding of the material properties, process technologies and reliability issues, through adequate analytical studies. The analytical instrumentation technology has, fortunately, kept pace with the basic requirements of devices with lateral dimensions in the micron/ submicron range and depths of the order of nonometers. Often, newer analytical techniques have emerged or the more conventional techniques have been adapted to meet the more stringent requirements. As such, a variety of analytical techniques are available today to aid an analyst in the efforts of VLSI process evaluation. Generally such analytical efforts are divided into the characterization of materials, evaluation of processing steps and the analysis of failures.

Preferential Sputtering of Ni3Al Single Crystals Studied Using Atom-Probe Field-Ion Microscopy and XPS

1981 ◽  
Vol 39 ◽  
pp. 16-17
Author(s):  
M.P. Thomas ◽  
A.R. Waugh ◽  
M.J. Southon ◽  
Brian Ralph
Keyword(s):  
Single Crystals ◽  
Photoelectron Spectroscopy ◽  
Surface Composition ◽  
Depth Profiling ◽  
Analytical Techniques ◽  
Atom Probe ◽  
Probe Field ◽  
Preferential Sputtering ◽  
Argon Ion Bombardment ◽  
Argon Ion

It is well known that ion-induced sputtering from numerous multicomponent targets results in marked changes in surface composition (1). Preferential removal of one component results in surface enrichment in the less easily removed species. In this investigation, a time-of-flight atom-probe field-ion microscope A.P. together with X-ray photoelectron spectroscopy XPS have been used to monitor alterations in surface composition of Ni3Al single crystals under argon ion bombardment. The A.P. has been chosen for this investigation because of its ability using field evaporation to depth profile through a sputtered surface without the need for further ion sputtering. Incident ion energy and ion dose have been selected to reflect conditions widely used in surface analytical techniques for cleaning and depth-profiling of samples, typically 3keV and 1018 - 1020 ion m-2.

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