Diffraction of light by two parallel superposed supersonic waves, one being then-th harmonic of the other: A critical study of the methods leading to approximate solutions in finite form

1962 ◽  
Vol 55 (2) ◽  
pp. 63-98 ◽  
Author(s):  
Robert Mertens
Keyword(s):  
Approximate Solutions ◽  
The Other ◽  
Critical Study ◽  
Finite Form ◽  
Diffraction Of Light

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

Vibration of Rectangular Plates by the Ritz Method

1950 ◽  
Vol 17 (4) ◽  
pp. 448-453 ◽  
Author(s):  
Dana Young
Keyword(s):  
Ritz Method ◽  
Normal Modes ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Modes Of Vibration ◽  
Ritz’S Method ◽  
Square Plate ◽  
Set Up

Abstract Ritz’s method is one of several possible procedures for obtaining approximate solutions for the frequencies and modes of vibration of thin elastic plates. The accuracy of the results and the practicability of the computations depend to a great extent upon the set of functions that is chosen to represent the plate deflection. In this investigation, use is made of the functions which define the normal modes of vibration of a uniform beam. Tables of values of these functions have been computed as well as values of different integrals of the functions and their derivatives. With the aid of these data, the necessary equations can be set up and solved with reasonable effort. Solutions are obtained for three specific plate problems, namely, (a) square plate clamped at all four edges, (b) square plate clamped along two adjacent edges and free along the other two edges, and (c) square plate clamped along one edge and free along the other three edges.

scholarly journals A Stochastic Differential Equation Driven by Poisson Random Measure and Its Application in a Duopoly Market

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Tong Wang ◽  
Hao Liang
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Finite Number ◽  
Random Measure ◽  
Approximate Solutions ◽  
The Other ◽  
Poisson Random Measure ◽  
Verification Theorem ◽  
Hamilton Jacobi Bellman ◽  
Duopoly Market

We investigate a stochastic differential equation driven by Poisson random measure and its application in a duopoly market for a finite number of consumers with two unknown preferences. The scopes of pricing for two monopolistic vendors are illustrated when the prices of items are determined by the number of buyers in the market. The quantity of buyers is proved to obey a stochastic differential equation (SDE) driven by Poisson random measure which exists a unique solution. We derive the Hamilton-Jacobi-Bellman (HJB) about vendors’ profits and provide a verification theorem about the problem. When all consumers believe a vendor’s guidance about their preferences, the conditions that the other vendor’s profit is zero are obtained. We give an example of this problem and acquire approximate solutions about the profits of the two vendors.

scholarly journals Pushdown flow analysis with abstract garbage collection

2014 ◽  
Vol 24 (2-3) ◽  
pp. 218-283 ◽  
Author(s):  
J. IAN JOHNSON ◽  
ILYA SERGEY ◽  
CHRISTOPHER EARL ◽  
MATTHEW MIGHT ◽  
DAVID VAN HORN
Keyword(s):  
Garbage Collection ◽  
Flow Analysis ◽  
Approximate Solutions ◽  
Higher Order ◽  
Control Flow ◽  
The Other ◽  
Return Flow ◽  
Dynamic Nature ◽  
Pushdown Analysis ◽  
Better Than

AbstractIn the static analysis of functional programs, pushdown flow analysis and abstract garbage collection push the boundaries of what we can learn about programs statically. This work illuminates and poses solutions to theoretical and practical challenges that stand in the way of combining the power of these techniques. Pushdown flow analysis grants unbounded yet computable polyvariance to the analysis of return-flow in higher-order programs. Abstract garbage collection grants unbounded polyvariance to abstract addresses which become unreachable between invocations of the abstract contexts in which they were created. Pushdown analysis solves the problem of precisely analyzing recursion in higher-order languages; abstract garbage collection is essential in solving the “stickiness” problem. Alone, our benchmarks demonstrate that each method can reduce analysis times and boost precision by orders of magnitude. We combine these methods. The challenge in marrying these techniques is not subtle: computing the reachable control states of a pushdown system relies on limiting access during transition to the top of the stack; abstract garbage collection, on the other hand, needs full access to the entire stack to compute a root set, just as concrete collection does.Conditionalpushdown systems were developed for just such a conundrum, but existing methods are ill-suited for the dynamic nature of garbage collection. We show fully precise and approximate solutions to the feasible paths problem for pushdown garbage-collecting control-flow analysis. Experiments reveal synergistic interplay between garbage collection and pushdown techniques, and the fusion demonstrates “better-than-both-worlds” precision.

scholarly journals Solving Nonstiff Higher-Order Ordinary Differential Equations Using 2-Point Block Method Directly

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Hazizah Mohd Ijam ◽  
Mohamed Suleiman ◽  
Ahmad Fadly Nurullah Rasedee ◽  
Norazak Senu ◽  
Ali Ahmadian ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Difference Method ◽  
Divided Difference ◽  
Approximate Solutions ◽  
Higher Order ◽  
Numerical Results ◽  
The Other ◽  
Block Method ◽  
Better Than

We describe the development of a 2-point block backward difference method (2PBBD) for solving system of nonstiff higher-order ordinary differential equations (ODEs) directly. The method computes the approximate solutions at two points simultaneously within an equidistant block. The integration coefficients that are used in the method are obtained only once at the start of the integration. Numerical results are presented to compare the performances of the method developed with 1-point backward difference method (1PBD) and 2-point block divided difference method (2PBDD). The result indicated that, for finer step sizes, this method performs better than the other two methods, that is, 1PBD and 2PBDD.

scholarly journals A combined methodology for the approximate estimation of the roots of the general sextic polynomial equation

2021 ◽  
Author(s):  
Giorgos P. Kouropoulos
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Polynomial Equation ◽  
Approximate Solutions ◽  
The Other ◽  
Polynomial Equations ◽  
Polynomial Coefficients ◽  
Approximate Estimation ◽  
Predetermined Interval

Abstract In this article we present the methodology, according to which it is possible to derive approximate solutions for the roots of the general sextic polynomial equation as well as some other forms of sextic polynomial equations that normally cannot be solved by radicals; the approximate roots can be expressed in terms of polynomial coefficients. This methodology is a combination of two methods. The first part of the procedure pertains to the reduction of a general sextic equation H(x) to a depressed equation G(y), followed by the determination of solutions by radicals of G(y) which does not include a quintic term, provided that the fixed term of the equation depends on its other coefficients. The second method is a continuation of the first and pertains to the numerical correlation of the roots and the fixed term of a given sextic polynomial P(x) with the radicals and the fixed term of the sextic polynomial Q(x), where the two polynomials P(x) and Q(x) have the same coefficients except for the fixed term which might be different. From the application of the methodology presented above, the following formulation is derived; For any given general sextic polynomial equation P with coefficients within the interval [a, b], a defined polynomial equation Q corresponds which has equal coefficients to P except for its fixed term which might be different and dependent on the other coefficients so that Q has radical solutions. If we assume a pair of equations P, Q with coefficients within a predetermined interval [a, b], the numerical correlation through regression analysis of the radicals of Q, the roots of P and the fixed terms of P, Q, leads to the derivation of a mathematical model for the approximate estimation of the roots of sextic equations whose coefficients belong to the interval [a, b].

scholarly journals Lexical Choices and Ideology in Translation: A Case Study of 'The old Man and the Sea

2011 ◽  
Vol 2 (6) ◽  
pp. 258-265
Author(s):  
Maryam Najafian
Keyword(s):  
Ernest Hemingway ◽  
Real Life ◽  
The Other ◽  
Critical Study ◽  
Original Novel ◽  
Original Text ◽  
The Novel ◽  
Original Sample ◽  
Significant Difference

The present research aims at conducting a critical study of the novel 'The Old Man and the Sea' written by Ernest Hemingway (1976) and its two translated versions in Persian; one rendered by Faramarzi (2006) the other by Shahin (1979). The researchers apply a comparative lexical analysis proposed by Newmark (1988) and Venuti (1995). An attempt has been made to reveal the ideology behind the original sample words and to show how translators and the effect thereof handle it. The data of this research consists of 10 ideological laden terms selected randomly among 45 words from the original text and the corresponding Persian translations. The results of this study suggest a significant difference between the two Persian translations and the original novel. It revealed that one of the translators has attempted to 'domesticate' his translation while another has been attentive to 'foreignize' it. As for implication, it seems necessary to note that translational decisions made by actual translators under different socio-cultural and ideological settings in real life and real situations should be considered. The perlocutionary consequences resulted from adoption of such decisions are of importance.

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