Two types of multivariate M-estimators of the parameter matrix in the standard growth curve model are obtained via the Potthoff-Roy transformation. Their asymptotic distributions are derived through an extension of th...
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Two types of multivariate M-estimators of the parameter matrix in the standard growth curve model are obtained via the Potthoff-Roy transformation. Their asymptotic distributions are derived through an extension of the methods considered in Singer and Sen (1985) and computational algorithms are suggested. The problem of optimality in the choice of the transformation matrix is discussed and a numerical example is used to compare Huber-type M-estimates to the Normal maximum likelihood estimates.
In this paper of the series, elliptic expansions in terms of the sectorial variablesθ (i) j introduced recently in Paper IV (Sharaf, 1982) to regularize highly oscillating perturbations force of some orbital systems ...
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In this paper of the series, elliptic expansions in terms of the sectorial variablesθ (i) j introduced recently in Paper IV (Sharaf, 1982) to regularize highly oscillating perturbations force of some orbital systems will be established analytically and computationally for the fifth and sixth categories. For each of the elliptic expansions belonging to a category, literal analytical expressions for the coefficients of its trigonometric series representation are established. Moreover, some recurrence formulae satisfied by these coefficients are also established to facilitate their computations; numerical results are included to provide test examples for constructing computational algorithms.
In this paper of the series, elliptic expansions in terms of the sectorial variables θ (i) j introduced in Paper IV (Sharaf, 1982) to regularise highly oscillating perturbation force of some orbital systems will be e...
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In this paper of the series, elliptic expansions in terms of the sectorial variables θ (i) j introduced in Paper IV (Sharaf, 1982) to regularise highly oscillating perturbation force of some orbital systems will be explored for the first four categories. For each of the elliptic expansions belonging to a category, literal analytical expressions for the coefficients of its trigonometric series representation are established. Moreover, some recurrence formulae satisfied by these coefficients are also established to facilitate their computations, numerical results are included to provide test examples for constructing computational algorithms.
A newly developed, semi-elliptic computational algorithm is employed to predict the transonic flow inside an axisymmetric, convergent-divergent nozzle featuring small wall radius of curvature at the throat. The predic...
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A newly developed, semi-elliptic computational algorithm is employed to predict the transonic flow inside an axisymmetric, convergent-divergent nozzle featuring small wall radius of curvature at the throat. The predictions obtained are compared against flow measurements for this nozzle, which have been reported elsewhere. Good agreement between the corresponding measurements and predictions is revealed, thus validating the computational algorithm and demonstrating its value as a design tool.
A computational algorithm is discussed, which is based on the modified recursive quadratic-programming method and is suitable for the solution of the optimal load flow problem. Efficiency of the algorithm is verified ...
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A computational algorithm is discussed, which is based on the modified recursive quadratic-programming method and is suitable for the solution of the optimal load flow problem. Efficiency of the algorithm is verified by solving several test problems including optimal load flow test problems associated with the 5-, 14-, 23-, and 57-bus power systems
In this paper of the series, literal analytical expressions for the coefficients of the Fourier series representation ofG will be established for anyxi; withn, N positive integers and |ξi|<1 fori=1, 2, ... n. More...
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In this paper of the series, literal analytical expressions for the coefficients of the Fourier series representation ofG will be established for anyxi; withn, N positive integers and |ξi|<1 fori=1, 2, ... n. Moreover, the recurrence formulae satisfied by these coefficients will also be established. Illustrative analytical examples and a full recursive computational algorithm, with its numerical results, are included. The applications of the recurrence formulae are also illustrated by their stencils. As by-products of the analyses are two important periodic integrals developed analytically and computationally.
In this paper of the series, literal analytical expressions for the coefficients of the Fourier series representation ofF will be established for anyx i ; withn, N positive integers ≥1 and |ξ i | fori=1, 2,...n. Mor...
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In this paper of the series, literal analytical expressions for the coefficients of the Fourier series representation ofF will be established for anyx i ; withn, N positive integers ≥1 and |ξ i | fori=1, 2,...n. Moreover, the recurrence formulae satisfied by these coefficients will also be established. Illustrative analytical examples and a full recursive computational algorithm, with its numerical results, are included. The applications of the recurrence formulae are also illustrated by their stencils. As a by-product of the analyses is an integral which we may call a complete elliptic integral of thenth kind, in which the known complete elliptic integrals (1st, 2nd and 3rd kinds) are special cases of it.
In this paper, general model analysis of the form ∑c i φ i (θ) for the fractional loss of lightf(ϑ) exhibited by a close binary system will be considered in the sense of the least-squares criterion. A general recur...
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In this paper, general model analysis of the form ∑c i φ i (θ) for the fractional loss of lightf(ϑ) exhibited by a close binary system will be considered in the sense of the least-squares criterion. A general recursive method will be established for constructing the normal equations for the most useful functionsφ i (θ), and an economical storage of the method on a digital computer, with its computational steps, will also be given. Moreover, a full recursive computational algorithm for the least-squares approximation will also be established. By means of this algorithm, all the solution vectors, the variance for different orders of fit and the corresponding variance-covariance matrix could be computed once and for all and, moreover, recursively. The economical storage of the algorithm and its computational steps will be given. Finally, some of the practical difficulties encountered in the application of the least-squares criterion will be analysed, and some techniques for detecting and controlling these difficulties are also given. Numerical examples on the Algol system using a Fourier cosine series of the form ∑c i cos [(j - 1) π θ/η] will be given for illustration.
In this paper a computational algorithm is derived for the determination of the moments of the time between failures for a class of repairable systems whose components have prescribed failure distributions. Such syste...
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In this paper a computational algorithm is derived for the determination of the moments of the time between failures for a class of repairable systems whose components have prescribed failure distributions. Such systems are generally non-Markovian and the approach adopted here approximates system behaviour by application of the method of stages. Computation of the first moment (the mean time between failures), for the class of systems considered, was posed as an unsolved problem in an earlier issue of this journal.
General integral transform of the exponential integralsE n is considered and will be denoted asB n (k) (τ). Different expressions and the equations satisfied byB n (k) are developed. Two-term recurrence formula forB ...
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General integral transform of the exponential integralsE n is considered and will be denoted asB n (k) (τ). Different expressions and the equations satisfied byB n (k) are developed. Two-term recurrence formula forB n (k) (0) and three-term recurrence formula forB n (k) (τ); τ≠0 will be established for a givenk≥1 andn=2,3, ...,N. The computational algorithms based on these formulae are also constructed for the casesk=1,2,3, andn≥2. Finally the numerical results fork=2,3 andn=2(1)25 are presented to 15-digit accuracy
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