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Thesis (M.S. in A.E.)--Naval Postgraduate School, Sept. 1977

Square root calculation is a widely used task in real-time control systems especially in those, which control power electronics: motors drives, power converters, power factor correctors, etc. At the same time calculation of square roots is a bottle-neck in the optimization of code execution time. Taking into account that for many applications approximate calculation of a square root is enough, calculation time can be decreased with the price of precision of calculation. This paper analyses existing methods for fast square root calculation, which can be implemented for fixed point microcontrollers. It discusses algorithms’ pros and cons, analyses calculation errors and gives some recommendations on their use. The paper also proposes an original method for fast square root calculation, which does not use hardware acceleration and therefore, is suitable for implementation at a variety of modern Digital Signal Processors, which have high-speed hardware multipliers, but do not have effective dividers. The maximum relative error of the proposed method is 3.36% for calculation without division, and can be decreased to 0.055% using one division operation. Finally, the most promising methods are compared and results of their performance comparisons are depicted in tables.

Five main classes of nth rooting methods are discussed. An nth rooting method derivable from the binomial series expansion is developed, and both restoring and nonrestoring versions are treated. For the special case of the binary square root, a nonrestoring version of this method using normalized remainders is simulated and a statistical timing distribution obtained. Other nth rooting methods discussed are a truncated series method, Euler iteration formulae, extensions of a square root method given by M. Nadler, Pade approximations and the log exponential method. A particular mechanization of the log and exponential functions developed by Cantor, Estrin, and Turn is compared timewise with the other nth rooting methods. Hardware and storage requirements are considered in all cases.

Real world phenomena commonly exhibit nonlinear relationships, complex geometry, and intricate processes. Analytic or exact solution methods only address a minor class of such phenomena. Consequently, numerical approximation methods, such as root-finding methods, can be used. The goal is, by making use of a variety of root-finding methods (Newton-Rhapson, Chebyshev, Halley and Laguerre), to gain a qualitative appreciation on how various root- finding methods address many prevailing real-world concerns, to include, how are suitable approximation methods determined; when do root finding methods converge; and how long for convergence? Answers to the questions were gained through examining the basins of attraction of the root-finding methods. Different methods generate different basins of attraction. In the end, each method appears to have its own advantages and disadvantages.

Post-genomic research deals with challenging problems in screening genomes of organisms for particular functions or potential for being the targets of genetic engineering for desirable biological features. 'Phenotyping' of wild type and mutants is a time-consuming and costly effort by many individuals. This article is a preliminary progress report in research on large-scale automation of phenotyping steps (imaging, informatics and data analysis) needed to study plant gene-proteins networks that influence growth and development of plants. Our results undermine the significance of phenotypic traits that are implicit in patterns of dynamics in plant root response to sudden changes of its environmental conditions, such as sudden re-orientation of the root tip against the gravity vector. Including dynamic features besides the common morphological ones has paid off in design of robust and accurate machine learning methods to automate a typical phenotyping scenario, i.e. to distinguish the wild type from the mutants.

A square root approach is considered for the problem of accounting for model noise in the forecast step of the ensemble Kalman filter (EnKF) and related algorithms. The primary aim is to replace the method of simulated, pseudo-random, additive noise so as to eliminate the associated sampling errors. The core method is based on the analysis step of ensemble square root filters, and consists in the deterministic computation of a transform matrix. The theoretical advantages regarding dynamical consistency are surveyed, applying equally well to the square root method in the analysis step. A fundamental problem due to the limited size of the ensemble subspace is discussed, and novel solutions that complement the core method are suggested and studied. Benchmarks from twin experiments with simple, low-order dynamics indicate improved performance over standard approaches such as additive, simulated noise and multiplicative inflation.

Kyurkchiev and Andreev (1985) constructed an infinite sequence of Weierstrass-type iterative methods for approximating all zeros of a polynomial simultaneously. The first member of this sequence of iterative methods is the famous method of Weierstrass (1891) and the second one is the method of Nourein (1977). For a given integer $N \ge 1$, the $N$th method of this family has the order of convergence ${N+1}$. Currently in the literature, there are only local convergence results for these methods. The main purpose of this paper is to present semilocal convergence results for the Weierstrass-type methods under computationally verifiable initial conditions and with computationally verifiable a posteriori error estimates.

Notched flat plate specimens have been tested to examine Neuber's equation and other relations with respect to their application in the determination of stresses in the plastic range at the notch root when the far field strain is known. A nonlinear finite element solution has also been obtained for notched flat plates in plane stress to facilitate an evaluation of it as an analytical method for calculating the behavior of stresses at the notch root. Experimental results indicate that Neuber's equation is ten to twenty-five percent in error for the notch geometry, strain level and material behavior encountered in the present study. Finite element analysis results were in close agreement with experimental results. (Author)

The research project is a systematic review that aims to synthesize and describe the different clinical protocols used for collecting root canal samples in studies that investigate the endodontic microbiota using molecular techniques. The motivation for this work is the lack of a universally standardized method for root canal sampling, which leads to methodological heterogeneity and potentially affects the comparability of research findings. To address this, the review will identify and analyze the sampling strategies reported in studies published since 2012 that involve human subjects and employ molecular microbiological methods. The literature search will be conducted in five major databases and the grey literature, and data extraction will focus on details such as sample size, tooth type, molecular technique, and specific sampling procedures. Two reviewers will independently select studies and extract data, with a third reviewer resolving any disagreements. The expected outcome is a comprehensive qualitative synthesis of root canal sampling protocols, highlighting methodological trends, similarities, and differences, which may inform future research and promote greater standardization in the field.

This article is from International Journal of Oral Science , volume 4 . Abstract The aims of the study were to investigate the incidence of C-shaped root canal systems in mandibular second molars in a native Chinese population using radiography and clinical examination under microscope and to compare the relative efficacies of these methods. For the recognition of C-shaped root canal system, 1 146 mandibular second molars were selected and examined. Teeth with C-shaped canal systems were categorized by using the radiographic classification criteria and the modified Melton's method. C-shaped canals were identified in 397 (34.64%) mandibular second molars by radiography (type I, 31.23% type II, 38.29% type III, 30.48%). Clinical examination showed that 449 (39.18%) cases exhibited C-shaped canal systems (C1, 22.94% C2, 48.11% C3a, 15.59% C3b, 13.36%). As for the result of the radiographic and clinical combined examination, C-shaped root canals were found in 473 (41.27%) mandibular second molars (C1, 21.78% C2, 45.67% C3a, 16.70% C3b, 15.86%). The incidence of C-shaped root canal diagnosed by radiographic method was statistically different from that by clinical examination and the combined examination (P

This article is from International Journal of Oral Science , volume 4 . Abstract The aims of the study were to investigate the incidence of C-shaped root canal systems in mandibular second molars in a native Chinese population using radiography and clinical examination under microscope and to compare the relative efficacies of these methods. For the recognition of C-shaped root canal system, 1 146 mandibular second molars were selected and examined. Teeth with C-shaped canal systems were categorized by using the radiographic classification criteria and the modified Melton's method. C-shaped canals were identified in 397 (34.64%) mandibular second molars by radiography (type I, 31.23% type II, 38.29% type III, 30.48%). Clinical examination showed that 449 (39.18%) cases exhibited C-shaped canal systems (C1, 22.94% C2, 48.11% C3a, 15.59% C3b, 13.36%). As for the result of the radiographic and clinical combined examination, C-shaped root canals were found in 473 (41.27%) mandibular second molars (C1, 21.78% C2, 45.67% C3a, 16.70% C3b, 15.86%). The incidence of C-shaped root canal diagnosed by radiographic method was statistically different from that by clinical examination and the combined examination (P

This article is from International Journal of Oral Science , volume 4 . Abstract The aims of the study were to investigate the incidence of C-shaped root canal systems in mandibular second molars in a native Chinese population using radiography and clinical examination under microscope and to compare the relative efficacies of these methods. For the recognition of C-shaped root canal system, 1 146 mandibular second molars were selected and examined. Teeth with C-shaped canal systems were categorized by using the radiographic classification criteria and the modified Melton's method. C-shaped canals were identified in 397 (34.64%) mandibular second molars by radiography (type I, 31.23% type II, 38.29% type III, 30.48%). Clinical examination showed that 449 (39.18%) cases exhibited C-shaped canal systems (C1, 22.94% C2, 48.11% C3a, 15.59% C3b, 13.36%). As for the result of the radiographic and clinical combined examination, C-shaped root canals were found in 473 (41.27%) mandibular second molars (C1, 21.78% C2, 45.67% C3a, 16.70% C3b, 15.86%). The incidence of C-shaped root canal diagnosed by radiographic method was statistically different from that by clinical examination and the combined examination (P

The construction of initial conditions of an iterative method is one of the most important problems in solving nonlinear equations. In this paper, we obtain relationships between different types of initial conditions that guarantee the convergence of iterative methods for simultaneous finding all zeros of a polynomial. In particular, we show that any local convergence theorem for a simultaneous method can be converted into a convergence theorem with computationally verifiable initial conditions which is of practical importance. Thus, we propose a new approach for obtaining semilocal convergence results for simultaneous methods via local convergence results.

Frequency domain methods are used to study the angles of arrival and departure for multivariable root loci. Explicit equations are obtained. For a special class of poles and zeros, some simpler equations that are generalizations of the single input/single output equations are presented.

Mathematical analysis technique generalizes a root squaring and root cubing method into a general root powering method. The introduction of partitioned polynomials into this general root powering method simplifies the coding of the polynomial transformations into input data suitable for processing by computer. The method includes analytic functions.

Notched flat plate specimens have been tested to examine Neuber's equation and other relations with respect to their application in the determination of stresses in the plastic range at the notch root when the far field strain is known. A nonlinear finite element solution has also been obtained for notched flat plates in plane stress to facilitate an evaluation of it as an analytical method for calculating the behavior of stresses at the notch root. Experimental results indicate that Neuber's equation is ten to twenty- five percent in error for the notch geometry, strain level and material behavior encountered in the present study. Finite element analysis results were in close agreement with experimental results.

A comprehensive understanding of mitigation measures for space radiation protection necessarily involves the relevant fields of nuclear physics and particle transport modeling. One method of modeling the interaction of radiation traversing matter is Monte Carlo analysis, a subject that has been evolving since the very advent of nuclear reactors and particle accelerators in experimental physics. Countermeasures for radiation protection from neutrons near nuclear reactors, for example, were an early application and Monte Carlo methods were quickly adapted to this general field of investigation. The project discussed here is concerned with taking the latest tools and technology in Monte Carlo analysis and adapting them to space applications such as radiation shielding design for spacecraft, as well as investigating how next-generation Monte Carlos can complement the existing analytical methods currently used by NASA. We have chosen to employ the Monte Carlo program known as FLUKA (A legacy acronym based on the German for FLUctuating KAscade) used to simulate all of the particle transport, and the CERN developed graphical-interface object-oriented analysis software called ROOT. One aspect of space radiation analysis for which the Monte Carlo s are particularly suited is the study of secondary radiation produced as albedoes in the vicinity of the structural geometry involved. This broad goal of simulating space radiation transport through the relevant materials employing the FLUKA code necessarily requires the addition of the capability to simulate all heavy-ion interactions from 10 MeV/A up to the highest conceivable energies. For all energies above 3 GeV/A the Dual Parton Model (DPM) is currently used, although the possible improvement of the DPMJET event generator for energies 3-30 GeV/A is being considered. One of the major tasks still facing us is the provision for heavy ion interactions below 3 GeV/A. The ROOT interface is being developed in conjunction with the CERN ALICE (A Large Ion Collisions Experiment) software team through an adaptation of their existing AliROOT (ALICE Using ROOT) architecture. In order to check our progress against actual data, we have chosen to simulate the ATIC14 (Advanced Thin Ionization Calorimeter) cosmic-ray astrophysics balloon payload as well as neutron fluences in the Mir spacecraft. This paper contains a summary of status of this project, and a roadmap to its successful completion.

A comprehensive understanding of mitigation measures for space radiation protection necessarily involves the relevant fields of nuclear physics and particle transport modeling. One method of modeling the interaction of radiation traversing matter is Monte Carlo analysis, a subject that has been evolving since the very advent of nuclear reactors and particle accelerators in experimental physics. Countermeasures for radiation protection from neutrons near nuclear reactors, for example, were an early application and Monte Carlo methods were quickly adapted to this general field of investigation. The project discussed here is concerned with taking the latest tools and technology in Monte Carlo analysis and adapting them to space applications such as radiation shielding design for spacecraft, as well as investigating how next-generation Monte Carlos can complement the existing analytical methods currently used by NASA. We have chosen to employ the Monte Carlo program known as FLUKA (A legacy acronym based on the German for FLUctuating KAscade) used to simulate all of the particle transport, and the CERN developed graphical-interface object-oriented analysis software called ROOT. One aspect of space radiation analysis for which the Monte Carlo s are particularly suited is the study of secondary radiation produced as albedoes in the vicinity of the structural geometry involved. This broad goal of simulating space radiation transport through the relevant materials employing the FLUKA code necessarily requires the addition of the capability to simulate all heavy-ion interactions from 10 MeV/A up to the highest conceivable energies. For all energies above 3 GeV/A the Dual Parton Model (DPM) is currently used, although the possible improvement of the DPMJET event generator for energies 3-30 GeV/A is being considered. One of the major tasks still facing us is the provision for heavy ion interactions below 3 GeV/A. The ROOT interface is being developed in conjunction with the CERN ALICE (A Large Ion Collisions Experiment) software team through an adaptation of their existing AliROOT (ALICE Using ROOT) architecture. In order to check our progress against actual data, we have chosen to simulate the ATIC14 (Advanced Thin Ionization Calorimeter) cosmic-ray astrophysics balloon payload as well as neutron fluences in the Mir spacecraft. This paper contains a summary of status of this project, and a roadmap to its successful completion.

A comprehensive understanding of mitigation measures for space radiation protection necessarily involves the relevant fields of nuclear physics and particle transport modeling. One method of modeling the interaction of radiation traversing matter is Monte Carlo analysis, a subject that has been evolving since the very advent of nuclear reactors and particle accelerators in experimental physics. Countermeasures for radiation protection from neutrons near nuclear reactors, for example, were an early application and Monte Carlo methods were quickly adapted to this general field of investigation. The project discussed here is concerned with taking the latest tools and technology in Monte Carlo analysis and adapting them to space applications such as radiation shielding design for spacecraft, as well as investigating how next-generation Monte Carlos can complement the existing analytical methods currently used by NASA. We have chosen to employ the Monte Carlo program known as FLUKA (A legacy acronym based on the German for FLUctuating KAscade) used to simulate all of the particle transport, and the CERN developed graphical-interface object-oriented analysis software called ROOT. One aspect of space radiation analysis for which the Monte Carlo s are particularly suited is the study of secondary radiation produced as albedoes in the vicinity of the structural geometry involved. This broad goal of simulating space radiation transport through the relevant materials employing the FLUKA code necessarily requires the addition of the capability to simulate all heavy-ion interactions from 10 MeV/A up to the highest conceivable energies. For all energies above 3 GeV/A the Dual Parton Model (DPM) is currently used, although the possible improvement of the DPMJET event generator for energies 3-30 GeV/A is being considered. One of the major tasks still facing us is the provision for heavy ion interactions below 3 GeV/A. The ROOT interface is being developed in conjunction with the CERN ALICE (A Large Ion Collisions Experiment) software team through an adaptation of their existing AliROOT (ALICE Using ROOT) architecture. In order to check our progress against actual data, we have chosen to simulate the ATIC14 (Advanced Thin Ionization Calorimeter) cosmic-ray astrophysics balloon payload as well as neutron fluences in the Mir spacecraft. This paper contains a summary of status of this project, and a roadmap to its successful completion.

This paper addresses the numerical aspects of the maximum likelihood estimation of linear discrete-time dynamic stochastic systems. The gradient-search optimization methods require the computation of the likelihood function, its gradient (known as a "score") and the Fisher information matrix (FIM). This leads to implementation of the Kalman filter (and its derivatives with respect to unknown system parameters), which is known to be numerically unstable. The array square-root (ASR) algorithms are the most preferable now for practical implementation of the Kalman filter. In this paper, we develop an elegant and simple method for computation of the derivatives of the filter variables to unknown system parameters required in a variety of applications. The new technique easily extends functionality of any ASR filter and leads to a stable score and FIM evaluation. Furthermore, the method is ideal for simultaneous state estimation and parameter identification since all values are computed in parallel. Finally, the new approach replaces the standard technique based on direct differentiation of the Kalman filtering equations (with their inherent numerical instability) and, hence, improves the robustness of computations against roundoff errors.

We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with $n+1$ nodes is used the resulting iterative method has convergence order at least $n+2$, starting with the case $n=0$ (which corresponds to the Newton's method).

We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with $n+1$ nodes is used the resulting iterative method has convergence order at least $n+2$, starting with the case $n=0$ (which corresponds to the Newton's method).

This article is from International Journal of Oral Science , volume 4 . Abstract The tooth root cementum is a thin, mineralized tissue covering the root dentin that is present primarily as acellular cementum on the cervical root and cellular cementum covering the apical root. While cementum shares many properties in common with bone and dentin, it is a unique mineralized tissue and acellular cementum is critical for attachment of the tooth to the surrounding periodontal ligament (PDL). Resources for methodologies for hard tissues often overlook cementum and approaches that may be of value for studying this tissue. To address this issue, this report offers detailed methodology, as well as comparisons of several histological and immunohistochemical stains available for imaging the cementum–PDL complex by light microscopy. Notably, the infrequently used Alcian blue stain with nuclear fast red counterstain provided utility in imaging cementum in mouse, porcine and human teeth. While no truly unique extracellular matrix markers have been identified to differentiate cementum from the other hard tissues, immunohistochemistry for detection of bone sialoprotein (BSP), osteopontin (OPN), and dentin matrix protein 1 (DMP1) is a reliable approach for studying both acellular and cellular cementum and providing insight into developmental biology of these tissues. Histological and immunohistochemical approaches provide insight on developmental biology of cementum.

For certain Lie algebras g, we can use a Z/5Z-grading and define a quartic form and a skew-symmetric bilinear form on the degree 1 component, g_1, thereby constructing a Freudenthal triple system. The structure of the Freudenthal triple system is examined using root system methods available in the Lie algebra context. In the cases g = E_8 (where g_1 is the minuscule representation of E_7) and g = D_4, we determine the groups stabilizing the quartic form and both the quartic and bilinear forms.

xiii,188p. : 25 cm

xiii,188p. : 25 cm

xiii,188p. : 25 cm

xiii,188p. : 25 cm

Plant propagation from cuttings, adventitious root formation, is the most important use of rooting hormones. There are several other ways that these substances can be effectively used including grafting & stenting, layering, and improved transplanting using Hortus and Rhizopon plant rooting hormones. Article includes a case study of rose propagation.

"Two Hydraulic Methods to Extract the nth Root of any Number" is an article from The American Mathematical Monthly, Volume 8 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2970154

Thesis advisor, George J. Thaler

This article is from Plant Methods , volume 7 . Abstract Pea has lagged behind other model legumes in the molecular study of nodulation and mycorrhizae-formation because of the difficulty to transform its roots and its poor growth on agar plates. Here we describe for pea 1) a transformation technique which permits the complementation of two known non-nodulating pea mutants, 2) a rhizobial inoculation method which allows the study of early cellular events giving rise to nodule primordia, and 3) a targeted fungal inoculation method which allows us to study short segments of mycorrhizal roots assured to be infected. These tools are certain to advance our knowledge of pea root symbioses.

This instructional unit is intended for use in training operations personnel and others involved in scram analysis at nuclear power plants in the techniques of root cause analysis. Four lessons are included. The first lesson provides an overview of the goals and benefits of the root cause analysis method. Root cause analysis techniques are covered next. Section 3 presents a scenario exercise, and section 4 provides an overview and summary of the root cause analysis technique. The unit includes a terminal objective, enabling objectives, a list of study questions, and instructional text. Abstracts of 10 documents for root cause analysis are appended. (MN)

Includes references

Real world phenomena commonly exhibit nonlinear relationships, complex geometry, and intricate processes. Analytic or exact solution methods only address a minor class of such phenomena. Consequently, numerical approximation methods, such as root-finding methods, can be used. The goal is, by making use of a variety of root-finding methods (Newton-Rhapson, Chebyshev, Halley and Laguerre), to gain a qualitative appreciation on how various root-finding methods address many prevailing real-world concerns, to include, how are suitable approximation methods determined; when do root finding methods converge; and how long for convergence? Answers to the questions were gained through examining the basins of attraction of the root-finding methods. Different methods generate different basins of attraction. In the end, each method appears to have its own advantages and disadvantages.

Adam's luxury, and Eve's cookery; or, the kitchen-garden display'd. In two parts. I. Shewing the best and most approved methods of raising ... all the products of the kitchen-garden; ... II. Containing a large collection of receipts ... To which is added, The physical virtues of every herb and root. ... 1744.. Digitized from IA40316217-54 . Previous issue: bim_eighteenth-century_the-young-builders-rudi_langley-batty_1730 . Next issue: bim_eighteenth-century_the-second-part-of-a-nar_wills-william-surgeon-_1751 .

A design technique for root placement with full state feedback using transfer functions for all-pole plant is presented in this thesis. A number of examples are presented to demonstrate the procedure with this design technique when all the system states are available to be measured and fedback. The design procedure presented is applicable for linear, time invariant (LTI) systems in the s-domain for continuous time. In order to get the roots at desired locations by transfer function methods very high gains are required. Therefore, the design procedure should place the zeros in offset locations. To obtain some guidelines for offsetting the zeros, the root movement as a function of gain, offset zero locations chosen by matrix methods to put the roots at the desired locations, and arbitrarily chosen offset zero locations are observed on numerous system examples. The obtained guidelines are applied to the all-pole plants.

Monroe Form 769-S, how to compute square roots on a Monroe mechanical calculator.

Monroe Form 769-S, how to compute square roots on a Monroe mechanical calculator.

A design technique for root placement with full state feedback using transfer functions for all-pole plant is presented in this thesis. A number of examples are presented to demonstrate the procedure with this design technique when all the system states are available to be measured and fedback. The design procedure presented is applicable for linear, time invariant (LTI) systems in the s-domain for continuous time. In order to get the roots at desired locations by transfer function methods very high gains are required. Therefore, the design procedure should place the zeros in offset locations. To obtain some guidelines for offsetting the zeros, the root movement as a function of gain, offset zero locations chosen by matrix methods to put the roots at the desired locations, and arbitrarily chosen offset zero locations are observed on numerous system examples. The obtained guidelines are applied to the all-pole plants.

This article is from Iranian Endodontic Journal , volume 5 . Abstract INTRODUCTION: The purpose of this study was to evaluate the efficacy of three methods in removal of Resilon/new Epiphany self-etch (SE) soft resin endodontic obturation system. MATERIALS AND METHODS: Thirty extracted single rooted human teeth were prepared for endodontic treatment and obturated with Resilon/Epiphany SE. The roots were randomly divided into three groups; group 1 roots were retreated using Mtwo R/Mtwo files; group 2 were retreated using Mtwo R/Mtwo accompanied with chloroform; and group 3 were retreated using Mtwo R/Mtwo accompanied with Endosolv R. The cleanliness of canal walls was determined using scanning electron microscopy. Data were analyzed using ANOVA and LSD tests. RESULTS: Endosolv R combined with rotary files was more efficient in material removal compared to chloroform combined with rotary files and rotary files alone (P

Monroe Machine Methods For the Extraction of Square Root Monroe Calculating Machine Company, Inc. 1933 11 page stapled booklet 150mm x; 229mm Form 769-S This booklet explains how to take square roots when using the Monroe calculator.

Thesis advisor, George J. Thaler

Thesis advisor, George J. Thaler