This research paper introduces a novel fractional Caputo-type simultaneous method for finding all simple and multiple roots of polynomial equations. Without any additional polynomial and derivative evaluations using s...
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This research paper introduces a novel fractional Caputo-type simultaneous method for finding all simple and multiple roots of polynomial equations. Without any additional polynomial and derivative evaluations using suitable correction, the order of convergence of the basic Aberth-Ehrlich simultaneous method has been increased from three to a + 3. In terms of accuracy, residual graph, computational efficiency and computation CPU time, the newly proposed families of simultaneous methods outperforms existing methods in numerical applications.
A simplified cylindrical model of an aircraft fuselage is used to investigate the mechanisms of interior noise suppression of the synchrophasing technique. This investigation allows isolation of important parameters t...
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This paper examines iterative methods for estimating missing values in a general designed experiment having a single error term in the analysis of variance. Both the method of Healy and Westmacott and the improved Hea...
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This paper examines iterative methods for estimating missing values in a general designed experiment having a single error term in the analysis of variance. Both the method of Healy and Westmacott and the improved Healy-Westmacott method of Pearce and others are identified as special cases of successive overrelaxation techniques used in the numerical solution of linear equations. The improved Healy-Westmacott method is shown to diverge under certain specified conditions. Optimal relaxation parameters are given which guarantee, and in some cases accelerate, convergence. Rates of convergence are compared for selected Latin square designs with missing data. A known disadvantage of iterative methods is their failure to give warning of the confounding which can arise from degenerative configurations of missing values. An extension of the iteration is suggested which enables such confounding to be detected.
One important step in the renormalization-group (RG) approach to a lattice sandpile model is the exact enumeration of all possible toppling processes of sandpile dynamics inside a cell for RG transformations. Here we ...
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One important step in the renormalization-group (RG) approach to a lattice sandpile model is the exact enumeration of all possible toppling processes of sandpile dynamics inside a cell for RG transformations. Here we propose a computer algorithm to carry out such exact enumeration for cells of planar lattices in the RG approach to the Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett. 59, 381 (1987)] and consider both the reduced-high RG equations proposed by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. 72, 1690 (1994)], and the real-height RG equations proposed by Ivashkevich [Phys. Rev. Lett. 76, 3368 (1996)]. Using this algorithm, we are able to carry out RG transformations more quickly with large cell size, e.g., 3×3 cell for the square (SQ) lattice in PVZ RG equations, which is the largest cell size at the present, and find some mistakes in a previous paper [Phys. Rev. E 51, 1711 (1995)]. For SQ and plane triangular (PT) lattices, we obtain the only attractive fixed point for each lattice and calculate the avalanche exponent τ and the dynamical exponent z. Our results suggest that the increase of the cell size in the PVZ RG transformation does not lead to more accurate results. The implication of such result is discussed.
Background: Influenza is one of the oldest and deadliest infectious diseases known to man. Reassorted strains of the virus pose the greatest risk to both human and animal health and have been associated with all pande...
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Background: Influenza is one of the oldest and deadliest infectious diseases known to man. Reassorted strains of the virus pose the greatest risk to both human and animal health and have been associated with all pandemics of the past century, with the possible exception of the 1918 pandemic, resulting in tens of millions of deaths. We have developed and tested new computer algorithms, FluShuffle and FluResort, which enable reassorted viruses to be identified by the most rapid and direct means possible. These algorithms enable reassorted influenza, and other, viruses to be rapidly identified to allow prevention strategies and treatments to be more efficiently implemented. Results: The FluShuffle and FluResort algorithms were tested with both experimental and simulated mass spectra of whole virus digests. FluShuffle considers different combinations of viral protein identities that match the mass spectral data using a Gibbs sampling algorithm employing a mixed protein Markov chain Monte Carlo (MCMC) method. FluResort utilizes those identities to calculate the weighted distance of each across two or more different phylogenetic trees constructed through viral protein sequence alignments. Each weighted mean distance value is normalized by conversion to a Z-score to establish a reassorted strain. Conclusions: The new FluShuffle and FluResort algorithms can correctly identify the origins of influenza viral proteins and the number of reassortment events required to produce the strains from the high resolution mass spectral data of whole virus proteolytic digestions. This has been demonstrated in the case of constructed vaccine strains as well as common human seasonal strains of the virus. The algorithms significantly improve the capability of the proteotyping approach to identify reassorted viruses that pose the greatest pandemic risk.
A computer algorithm and Fortran code have been developed to simulate a time history of aerodynamic loads on planar lifting surfaces using the subsonic linearized potential integral formulation of Guderley.1,2 This wo...
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A computer algorithm and Fortran code have been developed to simulate a time history of aerodynamic loads on planar lifting surfaces using the subsonic linearized potential integral formulation of Guderley.1,2 This work is intended for application to the simulation of flexible wing motion with active controls. In this article the method is validated by examining the indicial responses of wings. The results are transformed to the frequency domain and compared to the results of a frequency domain doublet-lattice code H7WC.3
The two-point boundary value problem arising in the optimal control of a singularly perturbed system is considered. Using the Vasileva’s method, the asymptotic series solution is obtained in terms of the outer series...
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The two-point boundary value problem arising in the optimal control of a singularly perturbed system is considered. Using the Vasileva’s method, the asymptotic series solution is obtained in terms of the outer series expansion of the original system and the inner and intermediate series expansions of the initial and terminal boundary layer systems. The method is presented to obtain the zeroth, first and second order approximations. Due to the complex interleaving of the various steps involved in solving the equations, an algorithm indicating the sequence of the steps is developed for implementation on a digital computer. A fifth order voltage regulator problem is given as an illustrative example.
This paper presents linear and bilinear shape transformations including basic transformations, analyzes their geometric properties, and provides computer algorithms. The shape transformations can be used to simplify t...
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This paper presents linear and bilinear shape transformations including basic transformations, analyzes their geometric properties, and provides computer algorithms. The shape transformations can be used to simplify the recognition of Roman letters, Chinese characters and other pictorial patterns by normalizing their shapes to the standard forms. Important theoretical analyses have been performed to illustrate that the linear and bilinear transformations are applicable to computer recognition of digitized patterns. A number of pictorial examples have been computed to confirm the analyses and conclusions made.
An algorithm to search for optimal block designs is described. This algorithm consists of an exchange procedure and an interchange procedure. During the exchange procedure the “correct” treatment replications are de...
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An algorithm to search for optimal block designs is described. This algorithm consists of an exchange procedure and an interchange procedure. During the exchange procedure the “correct” treatment replications are determined and during the interchange procedure an optimal set of treatment concurrences is searched for. The optimality criterion is the sum of the weighted variances of a set of treatment contrasts of interest. Examples which illustrate how the algorithm can be used to obtain designs which have a variance structure that reflects the interest expressed in a set of treatment contrasts are given and the performance of the algorithm is discussed.
An algorithm to search for optimal row-and-column designs is described. It is similar to the one for block designs described by Jones and Eccleston (1980). The algorithm determines the treatment replications and searc...
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An algorithm to search for optimal row-and-column designs is described. It is similar to the one for block designs described by Jones and Eccleston (1980). The algorithm determines the treatment replications and searches for an optimal set of treatment concurrences. The optimality criterion is the sum of the weighted variances of a set of treatment contrasts of interest. Examples which illustrate the use of the algorithm are given and discussed.
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