scholarly journals Numerical Calculation of Area of Elliptical Segments

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1411
Author(s):  
Dusan Vallo ◽  
Jozef Fulier ◽  
Lucia Rumanova
Keyword(s):  
Numerical Calculation ◽  
Analytical Method ◽  
Numerical Approximation ◽  
Circular Segment ◽  
The Given

In this paper, we introduce the notion of an elliptical segment as some analogy of the circular segment and we focus on the problem of calculation of its area. Based on the analytical method, we derive the formulas, which can be used for the numerical approximation of the area of the given segment.

scholarly journals Numerical Evaluation of Structural Safety of Linear Actuator for Flap Control of Aircraft Based on Airworthiness Standard

Aerospace ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 104
Author(s):  
Dong-Hyeop Kim ◽  
Young-Cheol Kim ◽  
Sang-Woo Kim
Keyword(s):  
Numerical Analysis ◽  
Analytical Method ◽  
Safety Evaluation ◽  
Experimental Tests ◽  
Structural Safety ◽  
Linear Actuator ◽  
The Finite Element Method ◽  
Margin Of Safety ◽  
Verification Methodology ◽  
The Given

Airworthiness standards of Korea recommend verifying structural safety by experimental tests and analytical methods, owing to the development of analysis technology. In this study, we propose a methodology to verify the structural safety of aircraft components based on airworthiness requirements using an analytical method. The structural safety and fatigue integrity of a linear actuator for flap control of aircraft was evaluated through numerical analysis. The static and fatigue analyses for the given loads obtained from the multibody dynamics analysis were performed using the finite element method. Subsequently, the margin of safety and vulnerable area were acquired and the feasibility of the structural safety evaluation using the analytical method was confirmed. The proposed numerical analysis method in this study can be adopted as an analytical verification methodology for the airworthiness standards of civilian aircraft in Korea.

Approximating the stationary distribution of an infinite stochastic matrix

1991 ◽  
Vol 28 (1) ◽  
pp. 96-103 ◽  
Author(s):  
Daniel P. Heyman
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Stationary Distribution ◽  
Numerical Approximation ◽  
Stochastic Matrix ◽  
Sufficient Conditions ◽  
Finite System ◽  
Balance Equations ◽  
The Given ◽  
Steady State Balance

We are given a Markov chain with states 0, 1, 2, ···. We want to get a numerical approximation of the steady-state balance equations. To do this, we truncate the chain, keeping the first n states, make the resulting matrix stochastic in some convenient way, and solve the finite system. The purpose of this paper is to provide some sufficient conditions that imply that as n tends to infinity, the stationary distributions of the truncated chains converge to the stationary distribution of the given chain. Our approach is completely probabilistic, and our conditions are given in probabilistic terms. We illustrate how to verify these conditions with five examples.

Numerical simulation of charged wire interferometer for atoms

2016 ◽  
Vol 30 (30) ◽  
pp. 1650369
Author(s):  
Hai-Feng Yang ◽  
Yong-Gang Tan ◽  
Yao-Hua Hu
Keyword(s):  
Numerical Simulation ◽  
Numerical Calculation ◽  
Path Integral ◽  
Analytical Method ◽  
Classical Method ◽  
Fringe Visibility ◽  
Analytical Expression

In recent paper, Nowak et al. report a charged wire interferometer for atoms, and employ analytical method to explain the interference patterns [Phys. Rev. Lett. 81 (1998) 5792]. In this paper, a numerical calculation with semi-classical method is carried out and the experimental patterns are rebuilt very well. The interference patterns are interpreted by path integral. We also calculate the fringe period for different voltages and the agreement with experiment is more rigorous than the analytical expression. Besides, the fringe visibility of the interference patterns at different applied voltages and degrees is also discussed.

scholarly journals Existence of solution to transpiration control problem

1992 ◽  
Vol 5 (4) ◽  
pp. 339-361 ◽  
Author(s):  
Guanstian Zhu ◽  
Jingang Wu ◽  
Benzhong Liang ◽  
Xinhua Ji ◽  
Xueshi Yang
Keyword(s):  
Numerical Calculation ◽  
Control Problem ◽  
High Speed ◽  
Practical Importance ◽  
Existence Of Solution ◽  
Dynamic Responses ◽  
Control Parameters ◽  
Mathematical Equations ◽  
The Given ◽  
High Speed Vehicle

Transpiration control can avoid change of the shape of a high-speed vehicle resulting from ablation of the nose, therefore also can avoid the change of the performance of Aerodynamics. Hence it is of practical importance. A set of mathematical equations and their boundary conditions are founded and justified by an example of non-ablation calculation in reference [1]. In [2], the ablation model is studied by the method of finite differences, the applicable margin of the equations is estimated through numerical calculation, and the dynamic responses of control parameters are analyzed numerically. In this paper we prove that the solution to transpiration control problem given in [1] exists uniquely under the assumption that the given conditions (i.e. given functions) are continuous.

Motion Analyses of D-Type Driving Mechanism

2013 ◽  
Vol 816-817 ◽  
pp. 786-789
Author(s):  
Shi Yi Li ◽  
Wen Pu Shi
Keyword(s):  
Numerical Method ◽  
Analytical Method ◽  
Linear Velocity ◽  
Driving Mechanism ◽  
Connecting Rod ◽  
Numerical Example ◽  
Angular Velocities ◽  
The Given

Geometric analyses and mechanical analytical method are used to study a kind of D-type driving mechanism. The theoretical formulae of computing angular velocities of the connecting rod and the rocker are given, and the linear velocity of the driving point C is obtained, and the finite differential numerical method for computing the angular velocities of the connecting rod and the rocker is also introduced. The results of the given numerical example show the feasibility of the theoretical conclusions here.

scholarly journals An analytical method of estimating Value-at-Risk on the Belgrade Stock Exchange

2009 ◽  
Vol 54 (183) ◽  
pp. 119-138 ◽  
Author(s):  
Milica Obadovic ◽  
Mirjana Obadovic
Keyword(s):  
At Risk ◽  
Failure Rate ◽  
Confidence Level ◽  
Analytical Method ◽  
Value At Risk ◽  
Risk Evaluation ◽  
Risk Model ◽  
Stock Exchange ◽  
Confidence Levels ◽  
The Given

This paper presents market risk evaluation for a portfolio consisting of shares that are continuously traded on the Belgrade Stock Exchange, by applying the Value-at-Risk model - the analytical method. It describes the manner of analytical method application and compares the results obtained by implementing this method at different confidence levels. Method verification was carried out on the basis of the failure rate that demonstrated the confidence level for which this method was acceptable in view of the given conditions.

scholarly journals PRODUCTIVE SUFFXES - [ets], - [nik] and - [ik] OF NOUNS WITH THE MEANING OF A PERSON INDICATING PERSONAL AND ETHICAL CHARACTERISTICS OF A PERSON IN RUSSIAN, AND WAYS OF EXPRESSING THEM IN PERSIAN

2021 ◽  
Vol 31 (6) ◽  
pp. 1358-1361
Author(s):  
Seyed Reza Hosseininejad ◽  
Ali Madaeni Avval ◽  
Seyed Hasan Zahraei
Keyword(s):  
Analytical Method ◽  
Similarities And Differences ◽  
The Given

This article discusses the productive suffixes - ец [ets], - ник [nik] и - ик [ik], when joined to nouns with the meaning of a person, indicating the personal and ethical characteristics of a person in Russian, and further discusses their equivalents in Persian. After examining several authoritative sources, we came to the conclusion that these three suffixes are highly productive. Then, using the comparative-analytical method, based on the given examples, we discovered similarities and differences between such nouns in Russian and Persian.

scholarly journals A Jacobi collocation approximation for nonlinear coupled viscous Burgers’ equation

Open Physics ◽  
2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Eid Doha ◽  
Ali Bhrawy ◽  
Mohamed Abdelkawy ◽  
Ramy Hafez
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Methods ◽  
Spectral Methods ◽  
Numerical Approximation ◽  
Burgers Equation ◽  
Jacobi Polynomials ◽  
Initial Boundary ◽  
Nonlinear Ordinary Differential Equation ◽  
The Given

AbstractThis article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers’ equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers’ equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

scholarly journals CONTEMPORARY PSYCHOANALYSIS - PERSPECTIVES AND THE SCIENTIFIC STATUS

TEME ◽  
2020 ◽  
pp. 121
Author(s):  
Jana Milić
Keyword(s):  
20Th Century ◽  
Analytical Method ◽  
Third Century ◽  
Contemporary Society ◽  
Relational Psychoanalysis ◽  
The Third ◽  
Scientific Status ◽  
The Status ◽  
The Given

This paper is actually a review of the status of psychoanalysis versus science. The lack of articles in contemporary discussions, and the absence of the topic of psychoanalysis suggests that there is less interest in the given topic. The impression is that the therapist who has the function of a patient does not have the time for other means of research and work. This supports the contemporary views that a therapist is, figuratively speaking, married to therapy and, therefore, cannot do anything for its sake. Strong criticism persisting even today is that addressed to Freud (in reference to relational psychoanalysis), arguing that he could not even bear to be seen as a warm and gentle figure by his patients. He is even known to have sat in a chair behind the headrest of the sofa used by the patient, in order to avoid looking the patients in the eyes, claiming it to be bothersome. The third century of the existence of psychoanalysis seems to be the time of questioning of whether the interest in this topic is disappearing. The corpus of psychoanalysis has been implemented throughout the 20th century. The general attitudes are that the analytical method has to change. Contemporary society wants quick results because the contemporary individual has little time. Psychoanalysis has always preferred the quiet, which now is a bad strategy, because very little has been done about its visibility and promotion.

scholarly journals Stress-Strain State Of Elastic Plate With An Arbitrary Smooth Notch

2015 ◽  
Vol 9 (4) ◽  
pp. 241-244 ◽  
Author(s):  
Ihor Kuz ◽  
Olga Kuz ◽  
Heorgij Sulym
Keyword(s):  
Numerical Calculation ◽  
Analytical Solution ◽  
Elastic Plate ◽  
Strain State ◽  
Stress Fields ◽  
Analytic Method ◽  
Relative Depth ◽  
Numerical Implementation ◽  
Numerical Variation ◽  
The Given

Abstract The paper contains comparing calculations of the stress fields in an elastic plate with notch along the arc of a circle, ellipse or parabola obtained by analytic method based on complex Kolosov-Muskhelishvili potentials and by numerical variation-difference method. These fields differ by no more than 2%, which, in particular, indicates the reliability of such numerical implementation. This discrepancy can be explained by the fact that in the analytical solution domain is unbounded, while the numerical calculation was carried out, obviously, for a finite field. The given stresses at the top of the notch along the arc of an ellipse or a parabola significantly increase with increasing of the relative depth of the notch (while increasing its depth or decreasing width).

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