This paper describes and illustrates a Windows-based, general-purpose, symbolically assisted numeric computation environment within power engineering education applications. The examples considered include fundamental...
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This paper describes and illustrates a Windows-based, general-purpose, symbolically assisted numeric computation environment within power engineering education applications. The examples considered include fundamental problems derived from three areas: power system analysis and optimization, electric machinery. and feedback control systems.
This paper illustrates how symbolically assisted numeric computation simulations can be effectively used in solving engineering problems. The examples considered are restricted to specific problems derived from electr...
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ISBN:
(纸本)9780889866874
This paper illustrates how symbolically assisted numeric computation simulations can be effectively used in solving engineering problems. The examples considered are restricted to specific problems derived from electric power, mechanical and electronics engineering and include: determination of a power system steady state operation conditions (so-called, power flow problem), so-called economic dispatch as one of the most important power system engineering optimization problems, dynamics of an elementary mechanical system with mass, damper, and spring, and finally a basic electronics engineering problem.
The spectrum of the Maxwell operator corresponding to propagation of electromagnetic waves in periodic dielectric media of square geometry is analyzed. In the 2-D case the Maxwell operator splits into two scalar opera...
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The spectrum of the Maxwell operator corresponding to propagation of electromagnetic waves in periodic dielectric media of square geometry is analyzed. In the 2-D case the Maxwell operator splits into two scalar operators corresponding to so-called TE and TM modes of propagating electromagnetic wave. In the present paper we show that both of these operators can be slightly modified in such a way that separation of variables can be used. The eigenfunctions and the spectra for the modified operators are then used to obtain Rayleigh-Ritz-type estimates of the spectrum of the Maxwell operator. ( See, for example, [Meade, Winn, and Joannopoulos, Photonic Crystals, Princeton University Press, 1995].).
We describe two algorithms of approximate GCD (greatest common divisor) for polynomials with coefficients of floating-point numbers. One is for univariate polynomials and the other for multivariate polynomials. The al...
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We describe two algorithms of approximate GCD (greatest common divisor) for polynomials with coefficients of floating-point numbers. One is for univariate polynomials and the other for multivariate polynomials. The algorithms are careful extensions of the conventional Euclidean algorithm, and they are applied to solving ill-conditioned algebraic equations. Ill-conditioned univariate algebraic equations have multiple or close roots, and we can separate both multiple and close roots by successive calculation of approximate GCDs. We also consider an ill-conditioned system of algebraic equations which have an approximate common divisor. Conventional numeric root-finding methods such as Newton's method give no satisfactory result for such ill-conditioned systems. By using an approximate GCD algorithm for multivariate polynomials, the system is transformed into a well-conditioned one to which numeric methods are applied safely. Thus, we solve some numerically ill-conditioned problems by a combination of algebraic and numeric methods;we call such algorithms hybrid algorithms. This paper shows the importance and possible fruitfulness of the hybrid algorithm.
This study proposes a mathematical model for stacked multicell (SM) converters (SMCs), to be exploited in the analytic determination of the natural voltage balancing dynamics of the SMCs, that is, investigation of the...
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This study proposes a mathematical model for stacked multicell (SM) converters (SMCs), to be exploited in the analytic determination of the natural voltage balancing dynamics of the SMCs, that is, investigation of the start-up behaviour, dynamic response and natural voltage balancing phenomenon. The crux of the proposed strategy is based on the closed-form analytic solution derivation for the switching functions used in the switching of the SMCs operated under phase disposition (PD) and phase-shifted carrier (PSC) pulse-width modulation (PD-PSC-PWM) technique. Hence, the suggested approach develops an analytic solution for the Fourier series and associated Fourier coefficients pertinent to the switching functions of the SMCs by obtaining the switching instants of the PD-PSC-PWM modulator in terms of 'Kapteyn series' when the frequency of the triangular carrier waveform (f(c)) and that of the sinusoidal reference waveform (f(r)) have an integer ratio, that is, f(c) f(r)(-1) = k, k is an element of N. This strategy results into a model ('first-order differential equation based model') which can be readily developed for the SMCs with any number of levels expediting the investigation of their performance. numeric computation results of the proposed analytic model for the SMCs and simulation results as well as measurements taken from an experimental set-up are presented in order to validate the suggested approach and derived model.
This paper describes the concept of symbolically-assisted numeric computation, with applications to power system simulation problems. The paper makes the case that symbolically-assisted computation can be a useful too...
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This paper describes the concept of symbolically-assisted numeric computation, with applications to power system simulation problems. The paper makes the case that symbolically-assisted computation can be a useful tool for prototyping and program design. The concept and features of a general purpose symbolically-assisted simulation environment ave described. Three case-studies ave presented: eigenvalue computations, solution of differential equation problems, and the study of interacting nonlinearities in electromagnetic transient studies. Copyright (C) 1996 Elsevier Science Ltd.
A hybrid integration algorithm obtaining an indefinite integral of a rational function (say q/r, q and r are polynomials) with floating-point but real coefficients is proposed. The algorithm consists of four steps and...
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A hybrid integration algorithm obtaining an indefinite integral of a rational function (say q/r, q and r are polynomials) with floating-point but real coefficients is proposed. The algorithm consists of four steps and is based on combinations of symbolic and numeric computations (hybrid computation). The first step is a hybrid preprocessing stage. An integrand is decomposed into rational and logarithmic parts by using an approximate Horowitz' method which allows floating-point coefficients. Here, we replace the Euclidean GCD algorithm with an approximate-GCD algorithm which was proposed by Sasaki and Noda recently. It is easy to integrate the rational part. The logarithmic part is integrated numerically in the second step. Zeros of a denominator of it are computed by the numerical Durand-Kerner method which computes all zeros of a polynomial equation simultaneously. The integrand is then decomposed into partial fractions in the third step. Coefficients of partial fractions are determined by residue theory. Finally, in the fourth step, partial fractions are transformed into the resulting indefinite integral by using well-known rules of integrals. The hybrid algorithm proposed here gives both indefinite integrals and accurate values of definite integrals. numerical errors in the hybrid algorithm depend only on errors in the second step. The algorithm evaluates some problems where numerical methods are inefficient or incapable, or a pure symbolic method is theoretically insufficient.
Simpson's paradox is a phenomenon arising from multivariate statistical analyses that often leads to paradoxical conclusions in the field of e-collaboration as well as many other fields where multivariate methods ...
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Simpson's paradox is a phenomenon arising from multivariate statistical analyses that often leads to paradoxical conclusions in the field of e-collaboration as well as many other fields where multivariate methods are employed. This work derives a general inequality for the occurrence of Simpson's paradox in path models with or without latent variables. The inequality is then used to estimate the probability that Simpson's paradox would occur at random in path models with two predictors and one criterion variable. This probability is found to be approximately 12.8 percent, slightly higher than 1 occurrence per 8 path models. This estimate suggests that Simpson's paradox is likely to occur in empirical studies, in the field of e-collaboration and other fields, frequently enough to be a source of concern.
In recent years, with the rapid development of symbolic computation, the integration of symbolic and numeric methods is increasingly applied in various applications. This paper proposed the use of symbolic computation...
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ISBN:
(纸本)9781424405886
In recent years, with the rapid development of symbolic computation, the integration of symbolic and numeric methods is increasingly applied in various applications. This paper proposed the use of symbolic computation for the evaluation of measurement uncertainty. The general method and procedure are discussed, and its great potential and powerful features for measurement uncertainty evaluation has been demonstrated through examples.
In this paper we present an experimental version of the Mizar proof checker equipped with new built-in routines for automating common numeric computations. This implementation has been directly motivated by recent for...
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ISBN:
(纸本)9783031427527;9783031427534
In this paper we present an experimental version of the Mizar proof checker equipped with new built-in routines for automating common numeric computations. This implementation has been directly motivated by recent formalizations of selected number theory topics that required extensive numeric calculations and proving numerical properties of specific numbers. The potential of automating parts of such proofs has been evaluated and, consequently, the Mizar checker has been extended with code that enabled refactoring the current contents of the Mizar Mathematical Library.
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