To Numerical Solution of Synthesis Problem of Flat Aperture According to the Given Requirements to Amplitude Directivity Pattern

2007 ◽  
Author(s):  
P. O. Savenko ◽  
M. D. Tkach
Keyword(s):  
Numerical Solution ◽  
Directivity Pattern ◽  
Synthesis Problem ◽  
The Given

scholarly journals Synthesizing Argumentation Frameworks from Examples

2019 ◽  
Vol 66 ◽  
pp. 503-554 ◽  
Author(s):  
Andreas Niskanen ◽  
Johannes Wallner ◽  
Matti Järvisalo
Keyword(s):  
Natural Extension ◽  
Research Abstract ◽  
Expressive Power ◽  
Synthesis Problem ◽  
Constraint Optimization ◽  
Abstract Argumentation ◽  
Central Notion ◽  
Definition Of ◽  
The Given ◽  
Representation Formalism

Argumentation is today a topical area of artificial intelligence (AI) research. Abstract argumentation, with argumentation frameworks (AFs) as the underlying knowledge representation formalism, is a central viewpoint to argumentation in AI. Indeed, from the perspective of AI and computer science, understanding computational and representational aspects of AFs is key in the study of argumentation. Realizability of AFs has been recently proposed as a central notion for analyzing the expressive power of AFs under different semantics. In this work, we propose and study the AF synthesis problem as a natural extension of realizability, addressing some of the shortcomings arising from the relatively stringent definition of realizability. In particular, realizability gives means of establishing exact conditions on when a given collection of subsets of arguments has an AF with exactly the given collection as its set of extensions under a specific argumentation semantics. However, in various settings within the study of dynamics of argumentation---including revision and aggregation of AFs---non-realizability can naturally occur. To accommodate such settings, our notion of AF synthesis seeks to construct, or synthesize, AFs that are semantically closest to the knowledge at hand even when no AFs exactly representing the knowledge exist. Going beyond defining the AF synthesis problem, we study both theoretical and practical aspects of the problem. In particular, we (i) prove NP-completeness of AF synthesis under several semantics, (ii) study basic properties of the problem in relation to realizability, (iii) develop algorithmic solutions to NP-hard AF synthesis using the constraint optimization paradigms of maximum satisfiability and answer set programming, (iv) empirically evaluate our algorithms on different forms of AF synthesis instances, as well as (v) discuss variants and generalizations of AF synthesis.

scholarly journals Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
R. C. Mittal ◽  
Rachna Bhatia
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Gordon Equation ◽  
Spline Collocation ◽  
Sine Gordon Equation ◽  
B Spline ◽  
Spline Collocation Method ◽  
B Splines ◽  
Spline Basis ◽  
The Given

Modified cubic B-spline collocation method is discussed for the numerical solution of one-dimensional nonlinear sine-Gordon equation. The method is based on collocation of modified cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. The given equation is decomposed into a system of equations and modified cubic B-spline basis functions have been used for spatial variable and its derivatives, which gives results in amenable system of ordinary differential equations. The resulting system of equation has subsequently been solved by SSP-RK54 scheme. The efficacy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and are in good agreement with earlier studies.

scholarly journals Numerical Solution for the Extrapolation Problem of Analytic Functions

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Nikolaos P. Bakas
Keyword(s):  
Numerical Solution ◽  
Basis Functions ◽  
Test Cases ◽  
Multiple Dimensions ◽  
Error Magnitude ◽  
Approximation Errors ◽  
Rapid Calculation ◽  
Extrapolation Problem ◽  
The Given ◽  
Domain Length

In this work, a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed. The proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives, exhibiting high accuracy, with error magnitude of O(10−100) or less. A variety of integrated radial basis functions are utilized for the solution, as well as variable precision arithmetic for the calculations. Multiple alterations in the function’s direction, with no curvature or periodicity information specified, are efficiently foreseen. Interestingly, the proposed procedure can be extended in multiple dimensions. The attained extrapolation spans are greater than two times the given domain length. The significance of the approximation errors is comprehensively analyzed and reported, for 5832 test cases.

scholarly journals Visualization Analysis of Numerical Solution With 32x32 and 64x64 Mesh Grid Lid-Driven Square Cavity Flow

2020 ◽  
Vol 5 (9) ◽  
pp. 652-656
Author(s):  
Santhana Krishnan Narayanan ◽  
Antony Alphonnse Ligor ◽  
Jagan Raj
Keyword(s):  
Reynolds Number ◽  
Numerical Solution ◽  
Constant Velocity ◽  
Flow Problem ◽  
Cavity Flow ◽  
Square Cavity ◽  
Visualization Analysis ◽  
Finite Volume Discretization ◽  
Mesh Grid ◽  
The Given

In this paper, the flow problem of constant velocity of a square cavity whose lid is solved and obtained a numerical solution on 2 grid levels, having 32x32 and 64x64 cells. Reynolds number of 1x102 , 1x103 was selected for laminar flow and 8x103 was selected for turbulent flow. The problem is identified in NavierStokes equations. The finite volume discretization is based on the numerical model. The simulated results are in valid agreement with those that are available in the given report. The numerical solution of these works are accurately obtained for this problem.

A Study on the Combined Effect of Axle Friction and Rolling Resistance

2003 ◽  
Vol 31 (2) ◽  
pp. 101-107 ◽  
Author(s):  
Murat Sönmez
Keyword(s):  
Dry Friction ◽  
Engineering Students ◽  
Rolling Resistance ◽  
Combined Effect ◽  
Synthesis Problem ◽  
Free Body Diagram ◽  
Free Body ◽  
The Given ◽  
Diagram Analysis

Many textbooks on mechanics for engineering students and engineers consider the concepts of rolling resistance and axle friction separately, expecting readers to combine the given analysis for each of them in determining, for instance, the magnitude of the force needed to move a railroad car. However, this requires a thorough free-body diagram analysis and, since examples are not typically included in the textbooks, students may have difficulty solving such problems. This study represents the solution of the problem in terms of both the dry axle friction and the rolling resistance. It is also suggested as a good synthesis problem that may be considered in teaching the effect of dry friction to engineering students.

scholarly journals Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis

2019 ◽  
Vol 9 (2) ◽  
pp. 471-480 ◽  
Author(s):  
Y. H. Youssri ◽  
R. M. Hafez
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Chebyshev Polynomials ◽  
Matrix Equation ◽  
Chebyshev Collocation ◽  
Chebyshev Nodes ◽  
Potential Applicability ◽  
The Given

Abstract This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss–Chebyshev nodes were then used to reduce the Volterra–Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.

scholarly journals A NEW NUMERICAL TREATMENT FOR FRACTIONAL DIFFERENTIAL EQUATIONS BASED ON NON-DISCRETIZATION OF DATA USING LAGUERRE POLYNOMIALS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040046
Author(s):  
ADNAN KHAN ◽  
KAMAL SHAH ◽  
MUHAMMAD ARFAN ◽  
THABET ABDELJAWAD ◽  
FAHD JARAD
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Differential Equations ◽  
Laguerre Polynomials ◽  
Research Work ◽  
Operational Matrices ◽  
Numerical Treatment ◽  
Approximation Techniques ◽  
Fractional Differential ◽  
The Given

In this research work, we discuss an approximation techniques for boundary value problems (BVPs) of differential equations having fractional order (FODE). We avoid the method from discretization of data by applying polynomials of Laguerre and developed some matrices of operational types for the obtained numerical solution. By applying the operational matrices, the given problem is converted to some algebraic equation which on evaluation gives the required numerical results. These equations are of Sylvester types and can be solved by using matlab. We present some testing examples to ensure the correctness of the considered techniques.

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