Showing papers in "Applied Mathematics and Computation in 1977"
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TL;DR: The analysis attempts to explain how the selection of a scheme influences the behavior of global error seen in high quality production codes.
34 citations
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TL;DR: In this paper, a theory of the scattering of electromagnetic waves by homogeneous spheres, the so-called Mie theory, is presented in a unique and coherent manner in which the transverse incident electric field is mapped in spherical coordinates and expanded in known mathematical functions satisfying the scalar wave equation.
27 citations
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TL;DR: The key importance of hypernumbers in enlarging and fruitfully generalizing (as distinct from abstraction of a sterile sort) algebra, function theory and computation is discussed, with specific examples and theorems.
27 citations
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TL;DR: In this article, the distributional properties of the statistic based on samples of size n for a homogeneous multinomial distribution were presented for [emailprotected][email protected]? 12 and [email protected][emailprotected]?12, respectively.
22 citations
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TL;DR: In this paper, location and scale parameters are estimated via window estimates, and the consistency and asymptotic normality of the estimates are established for the Cauchy distribution and the Pearson type-VII distribution.
13 citations
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TL;DR: In this paper, a method described previously by the authors is applied to certain smooth kernels of convolution type in order to obtain numerical solutions to certain Volterra integral equations, and the finite Tchebycheff expansion is found to be the most effective in terms of decreased computational effort.
13 citations
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TL;DR: In this paper, the authors discuss some properties of matrix polynomials and a computational procedure for finding the matrix roots of such polynomial coefficients and their relationship to spectral factorization.
13 citations
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12 citations
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TL;DR: In this paper, the authors consider the problem of the existence and iteration to a fixed point or a zero, of an operator on a closed subset of an abstract space, and generalize the construction mapping principle.
11 citations
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TL;DR: A modification of the sequential gradient-restoration algorithm, designed to improve the convergence characteristics, is presented, which consists of inserting a prerestorative step prior to any iteration of the algorithm to reduce the constraint violation.
10 citations
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TL;DR: In this paper, the authors give a positive answer to the question "if X"@a is @?-distributed of order @a, and X" @b of order@b, with X'@a and X''@b independent, is X" "@aX"@b infinitely divisible?'' This question, posed by Steutel in Ref.
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TL;DR: In this article, generalized product-interpolatory formulas for approximating the Fredholm integral equation were discussed, which model o as one mth-degree polynomial on each subinterval and model K as a (possibly large) sequence of nth degree polynomials.
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TL;DR: In this paper, a series of studies designed to develop and automate a method for quantification of type II pneumocyte populations of the lung and their changes in response to 2 ppm NO"2 exposure were discussed.
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TL;DR: In this article, a new method for computing the resolvent of a large class of Fredholm integral equations is presented, which is based on converting the integral equation satisfied by the resolver to a family of two point boundary value problems.
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TL;DR: In this paper, it was shown that the Nordsieck-gear method with maximum polynomial degree k+1 admits matched starting methods which are exact for all polynomials of degree = 1.
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TL;DR: A statistical analysis of brain waves from randomly connected neural nets shows that several neural networks have the ability to create periods of spontaneous rhythmic activity similar to those observed in animals and human thalamus, cerebral cortex and hippocampus.
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TL;DR: The quasilinearization method extends to the estimation of virgin arrest rates on the basis of data on total arrests, as well as to more general feedback models and other differential- and integral-equation models.
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TL;DR: The feedback neuron-pair model is applied to spike-train data from the hippocampus of a rabbit, and it is shown that even though each neuron generates a renewal process, the interaction of the spike trains produces a nonrenewal process.
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TL;DR: The sample size required for determination of a given degree of difference between two therapies or modalities A and B being compared with each other, assuming that the sample sizes are equal, is given by.
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TL;DR: Computational results show the feasibility of the quasilinearization method, but further investigation is needed to determine capabilities and limitations of this new approach.
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TL;DR: In this paper, a lower bound for the performance index is established by simple methods, and two important a posteriori error estimates are obtained, the first one measuring the deviation of the performance indices, while the other is for the deviations of the state and control variables from the optimal solution.
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TL;DR: In this article, Hermite interpolation in the form of Newton's divided difference expressions is employed to give a generating function for A-stable difference methods of order 2 n. These methods can be used to solve the initial value ordinary differential equation y'=g(y,t), y(a)=@h.
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TL;DR: In this paper, the Laplace transform expressions for the distribution functions and moments of residual waiting times in renewal theory are derived for the renewal theory and inverted numerically, and the results are contrasted with appropriate asymptotic expressions.
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TL;DR: A theoretical model based on the application of point process techniques is discussed in this paper, which proposes a new approach to ECG monitoring that is based on a comparison of the relative effectiveness of various systems.
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TL;DR: Procedures for diagonalization, rank calculation and computation of generalized inverses of singular matrices are developed and analyzed in this article, where the primary concern is with rational, multivariate entries, which may also be highly dimensional and highly singular.
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TL;DR: This paper considers the problem of designing a feedback controller for sampled-data systems by using a discrete observer and uses longitudinal control of an automated transit vehicle as an example to discuss the application of the discrete-observer design.
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TL;DR: In this article, the distribution of intervals between neighboring points or events on a line is derived for the case in which the events are independently and uniformly distributed, a situation motivating the derivation of the results in this paper.