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ON EFFICIENT FRACTIONAL CAPUTO-TYPE SIMULTANEOUS SCHEME FOR FINDING ALL ROOTS OF POLYNOMIAL EQUATIONS WITH BIOMEDICAL ENGINEERING APPLICATIONS

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FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2023年第4期31卷 2340075-2340075页

作者： Shams, Mudassir Kausar, Nasreen Samaniego, Cuauhtemoc Agarwal, Praveen Ahmed, Shams Forruque Momani, Shaher Riphah Int Univ Dept Math & Stat Islamabad 44000 Pakistan Yildiz Tech Univ Fac Arts & Sci Dept Math Esenler TR-34220 Istanbul Turkiye Amer Univ Middle East Dept Math & Stat Egaila 54200 Kuwait Anand Int Coll Engn Jaipur Dept Math Jaipur Rajasthan India RUDN Univ Peoples Friendship Univ Russia 6 Miklukho Maklaya St Moscow Russia Ajman Univ Nonlinear Dynam Res Ctr NDRC Ajman U Arab Emirates Asian Univ Women Sci & Math Program Chattogram 4000 Bangladesh Univ Jordan Dept Math Amman 11942 Jordan

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.

关键词： Optimal Order Simultaneous Methods Caputo-Type Derivative Error Graph Computational Efficiency computer algorithm

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NOISE-CONTROL CHARACTERISTICS OF SYNCHROPHASING .2. EXPERIMENTAL INVESTIGATION

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AIAA JOURNAL 1986年第8期24卷 1271-1276页

作者： JONES, JD FULLER, CR Virginia Polytechnic Institute and State University Blacksburg Virginia

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 to define the characteristics of synchrophasing. The optimum synchrophasing angle for maximum noise reduction is found for several interior microphone positions with pure tone source conditions. Noise reductions of up to 30 dB are shown for some microphone positions;however, overall reductions are less. A computer algorithm is developed to decompose the modal composition of the cylinder vibration over a wide range of synchrophase angles. The circumferential modal response of the shell vibration is shown to govern the transmission of sound into the cylinder rather than localized transmission. © 1986 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Aircraft Fuselages Propeller Noise Aircraft Cabin Accelerometer Flight Testing Anechoic Chambers Data Acquisition System Oscilloscope computer algorithm Condenser

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Iterative Missing Value Estimation

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Journal of the Royal Statistical Society: Series C (Applied Statistics) 1000年第2期38卷 293-300页

作者： D. N. Hunt C. M. Triggs Coventry Polytechnic UK DSIR Auckland New Zealand

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.

关键词： computer algorithm Designed experiment Iterative methods Missing values Relaxation parameters Successive overrelaxation

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Renormalization-group approach to an Abelian sandpile model on planar lattices

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Physical Review E 2002年第2期66卷 021307-021307页

作者： Chai-Yu Lin Chin-Kun Hu []Institute of Physics Academia Sinica Nankang Taipei 11529 Taiwan

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.

关键词： .Abelian sandpile Chin-Kun renormalization-group RG equations Exact enumeration RG transformations RG approach computer algorithm PVZ real-height SQ lattice

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FluShuffle and FluResort: new algorithms to identify reassorted strains of the influenza virus by mass spectrometry

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BMC BIOINFORMATICS 2012年第1期13卷 1-13页

作者： Lun, Aaron T. L. Wong, Jason W. H. Downard, Kevin M. Univ Sydney Sch Mol Biosci G08 Sydney NSW 2006 Australia Univ Sydney Prince Wales Clin Sch Sydney NSW 2006 Australia Univ Sydney Lowy Canc Res Ctr Sydney NSW 2006 Australia

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.

关键词： Influenza virus Reassortment Proteotyping computer algorithm Phylogenetics Mass spectrometry

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TIME-DOMAIN PANEL METHOD FOR WINGS

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JOURNAL OF AIRCRAFT 1993年第4期30卷 439-445页

作者： BLAIR, M WILLIAMS, MH Wright Research and Development Center Wright-Patterson Air Force Base Ohio 45433 Purdue University West Lafayette Indiana 47907

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

关键词： Aerodynamic Simulation Rectangular Wing Frequency Domain Adaptive Control computer Programs computer algorithm High Aspect Ratio Low Aspect Ratio Wings Numerical Integration Random Access Memory

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Application of Vasileva's Singular Perturbation Method to Problems in Large Scale Power Systems

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IFAC Proceedings Volumes 1979年第5期12卷 41-49页

作者： P.K. Rajagopalan D.S. Naidu Department of Electrical Engineering Indian Institute of Technology Kharagpur 721302 India

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.

关键词： Singular perturbation method optimal control system order reduction computer algorithm large scale systems power system control voltage stabilizers

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SHAPE TRANSFORMATION MODELS AND THEIR APPLICATIONS IN PATTERN RECOGNITION

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International Journal of Pattern Recognition and Artificial Intelligence 1990年第1期4卷 65-94页

作者： Z.C. LI Y.Y. TANG T.D. BUI C.Y. SUEN Centre de recherche informatique de Montréal Inc. 1550 Maisonneuve Blvd. West Bureau 901 Montreal Quebec H3G 1N2 Canada Department of Computer Science Concordia University and Centre for Pattern Recognition and Machine Intelligence 1455 de Maisonneuve Blvd. West Montreal Quebec H3G 1M8 Canada

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.

关键词： Shape transformation Geometric transformation Linear transformation Bilinear transformation Angle distortion Distortion computer algorithm Geometric property Error analysis Character recognition Shape recognition One-to-one transformation Finite element method Numerical analysis

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Exchange and Interchange Procedures to Search for Optimal Designs

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Journal of the Royal Statistical Society: Series B (Statistical Methodology) 1980年第2期42卷 238-243页

作者： Byron Jones John A. Eccleston University of Kent at Canterbury University of New South Wales

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.

关键词： computer algorithm efficiency exchange procedure interchange procedure optimal block design trace minimization weighted covariance matrix of treatment contrasts

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Exchange and Interchange Procedures to Search for Optimal Row-And-Column Designs

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Journal of the Royal Statistical Society: Series B (Statistical Methodology) 1980年第3期42卷 372-376页

作者： John A. Eccleston Byron Jones University of New South Wales University of Kent at Canterbury

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.

关键词： computer algorithm exchange procedure interchange procedure optimal row-and-column design trace minimization weighted covariance matrix of treatment contrasts

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