Numerical Methods I

2021 ◽  
Author(s):  
Boris Obsieger
Keyword(s):  
Numerical Methods ◽  
Direct Methods ◽  
Historical Background ◽  
Random Errors ◽  
Practical Application ◽  
Fourth Degree ◽  
Numerical Errors ◽  
The Third ◽  
Numeral Systems ◽  
The Given

Textbook, established at several universities. Second edition. *** Written primarily for students at technical studies. Valuable handbook for engineers, PhD students and scientists. *** Published in several variants. *** Seven chapters. In the first chapter, a historical background and basic properties of various numeral systems, as well as conversion of numbers from one system to another are briefly explained. In the second chapter, numbers in digital computers, namely integers and floating point numbers are described. This helps the reader to choose precision and range limits of stored numbers. The third chapter explains constant variables and related numerical errors, including error propagation and algorithm instability. The fourth and fifth chapters explain random variables and related random errors, uncertainty, confidence level, as well as propagation of random errors. Various types of regression analyses of experimental data are described in the sixth chapter. Direct methods for finding roots of the third and fourth degree polynomials are described in the seventh chapter, followed by general iterative methods for polynomials of any degree. *** Why the presented topics are so important? Simply, they are common to all numerical methods. *** Practical application is supported by 84 examples and 17 algorithms. For reasons of simplicity, algorithms are written in pseudo-code, so they can easily be implemented in any computer program. Finally, the given text with 98 figures and 52 tables represents a valuable background for understanding, applying and developing various numerical analyses.

Numerical Methods I

2021 ◽  
Author(s):  
Boris Obsieger
Keyword(s):  
Numerical Methods ◽  
Computer Program ◽  
Iterative Methods ◽  
Error Propagation ◽  
Random Variables ◽  
Regression Analyses ◽  
Practical Application ◽  
Numeral Systems ◽  
Roots Of Polynomials ◽  
Digital Computers

Textbook of several universities. 2nd edition. The color edition is also available at Glasstree Bookstore. It is recommended for students. The series of books Numerical Methods is written primarily for students at technical universities, but also as a useful handbook for engineers, PhD students and scientists. This volume introduces the reader into numeral systems and representation of numbers in digital computers. Possibly the most important part of this book are descriptions of differences between constant and random variables, related types of errors and error propagation. These topics are supplemented with various types of regression analyses. Finally, direct and iterative methods for finding roots of polynomials are explained. Practical application is supported by 77 examples and 13 algorithms. For reasons of simplicity, algorithms are written in pseudo-code, so they can easily be included in any computer program.

scholarly journals Application of quasiconformal mapping methods to the investigation of the explosive processes impact on the environment

2019 ◽  
pp. 17-18
Author(s):  
Kateryna Mykolaiivna Malash ◽  
Andrii Yaroslavovych Bomba
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Quasiconformal Mapping ◽  
Quasiconformal Mappings ◽  
Practical Application

The mathematical models used to study explosive processes are given. A class of problems investigating the influence of explosive processes on the environment by the quasiconformal mappings numerical methods are outlined and their practical application are described

scholarly journals Fattening indicators of young rabbits when feeding Prebiolact-Kr

2021 ◽  
Vol 23 (95) ◽  
pp. 96-100
Author(s):  
O. B. Tsyhanchuk
Keyword(s):  
Control Group ◽  
Meat Production ◽  
Practical Application ◽  
State Certification ◽  
Low Level ◽  
Fattening Performance ◽  
The Third ◽  
Rabbit Population ◽  
Rabbit Meat ◽  
Holding Back

Measures to increase production are used to address the issue of providing the population with food. During the peak of the industry (1975–1985), Ukraine annually produced 120–165 thousand tons of rabbit meat, 30–45 million skins, and its share in world rabbit production reached 8 %. In the national volume of meat production, the share of highly dietary rabbit accounted for 8–10 %. Rabbit breeding in Ukraine was a very lucrative industry, which employed more than 600 thousand rabbit breeders. However, in recent years, rabbit breeding has declined due to the lack of modern scientific developments on the issues of complete feeding, rabbit keeping technology, low level of breeding and veterinary support. The development of the industry and the lack of coordinating bodies, both in the center and on the ground, are holding back. At present, the rabbit population of Ukraine is 97–98 % concentrated in individual farms and is 1.2–1.3 million breeding and repair livestock, and the rest in farms and breeding entities of various forms of ownership and management. According to the results of state certification, the breeding base of the industry in Ukraine today consists of 1 breeding plant and 7 breeding breeders of rabbit breeds. For feeding young rabbits used complete ration granular feed, the structure of which had different prebiotic content: I control group – the drug was not received, 2 experimental – 1.5, 3 – 2.0, 4 – 2.5 g/goal. per day. The studies were conducted on four groups of young rabbits, selected on the principle of groups of analogues, 25 heads in each. Thus, the total amount of feed increased from 80 g/goal. per day (35–41 days), up to 100 g (42–48 days), 120 g (49–55 days), up to 140 g (56–62 days), up to 160 g (63–69 days) up to 180 g (70–76 days). Feeding of young rabbits when reared for meat Prebiolact-Kr in animals of the second group at 43.1 g, the third 44.6 g and 45.0 g. The use of Prebiolact-Kr in the feeding of young rabbits when fed meat contributes to an increase in fattening performance, which may be the basis for the practical application of this supplement. Perebiolakt-KR showed the best results in feeding fattening and repair young animals at a dose of 2.0 g/goal per day.

Concept-less Schemata: The Reciprocity of Imagination and Understanding in Kant’s Aesthetics

2021 ◽  
Vol 26 (4) ◽  
pp. 511-529
Author(s):  
Luigi Filieri
Keyword(s):  
Empirical Concept ◽  
The Third ◽  
The Aesthetic ◽  
The Given

AbstractIn this paper, I discuss Kant’s concept-less schematism (KU, 5: 287) in the third Critique1 and make three claims: 1) concept-less schematism is entirely consistent with the schematism in the first Critique; 2) concept-less schematism is schematism with no empirical concept as an outcome; and 3) in accordance with 1) and 2), the imagination is free to synthesize the given manifold and leads to judgements of taste without this meaning either that the categories play no role at all or that these judgements are full-fledged cognitive determining judgements. While most commentators read the freedom of the imagination as its independence from the understanding, I argue that the freedom of the imagination is based on a non-determining employment of the pure concepts of the understanding. The freedom of the aesthetic imagination consists in the temporal schematization of the categories without any complementary determination of the empirical concept.

Forward Displacement Analysis of Three New Classes of Analytic Spherical Parallel Manipulators

1998 ◽  
Author(s):  
Xian-Wen Kong
Keyword(s):  
Characteristic Polynomial ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Dual Solutions ◽  
Fourth Degree ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
The Third ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

Abstract The analytic manipulator is a manipulator the characteristic polynomial of which is of fourth degree or lower. Three new classes of analytic spherical parallel manipulators with prismatic actuators are proposed. The first is the spherical parallel manipulator with non-similar planar platforms, the second is the spherical parallel manipulator with similar planar platforms, and the third is the spherical parallel manipulator with orthogonal platforms. The forward displacement analysis of these new classes of spherical parallel manipulators is investigated in sequence. Polynomials of degree 4, 2 and 2 in one unknown respectively can be obtained to inscribe this problem. Due to dual solutions of other unknowns, a maximum of eight solutions might be possible for each of the new analytic spherical parallel manipulators.

Automatic Creation of Virtual Artefacts from Video Sequences

2005 ◽  
Author(s):  
Andrew W. Fitzgibbon ◽  
Geoff Cross ◽  
Andrew Zisserman
Keyword(s):  
Focal Length ◽  
3D Models ◽  
Video Sequences ◽  
Digital Representation ◽  
The Third ◽  
3D Presentation ◽  
Object Features ◽  
The Given ◽  
System Geometry ◽  
2D Images

Digital representation of an artefact is necessary in order to measure, admire and analyse such ancient pieces. For the purpose of storing, recoding and transmitting information, digital photographs may be enough. However, in the examination purposes of an artefact, a 3D presentation is invaluable as it allows the object viewpoint to be modified freely and 3D measurements to be taken on object features. This chapter describes the system by which 3D models from photographs can be acquired, without the need for the calibration of system geometry such as the camera focal length, relative motion of the camera and object, and the relative positions of the camera and object. This system instead computes the representation of all possible objects and camera configurations which are consistent with the given image. The first section discusses how tracking points observed in 2D images allows for the computation of the relative camera and object geometry. The second section discusses the construction of a triangulated 3D model from the object projections. The third section discusses the refinement of the model based on surface texture.

Bajla Gelblung und Johannes Bobrowskis Gedicht BERICHT

2019 ◽  
Vol 60 (1) ◽  
pp. 373-383
Author(s):  
Eduard R. Müller
Keyword(s):  
Jewish Woman ◽  
Historical Background ◽  
Warsaw Ghetto ◽  
The Third ◽  
Over Time ◽  
German Wehrmacht

Johannes Bobrowski’s iconic poem BERICHT (REPORT) refers to an historical photograph showing the interrogation of a young Polish Jewish woman by officers of the German Wehrmacht in Brest-Litovsk. It has long been assumed that the woman referred to as Bajla Belblung was a resistance fighter who escaped from the Warsaw ghetto in 1943. But further research has shown that the interrogation took place in September 1939 after the end of the third week of the war. This work examines the historical background of the photos of Bajla Gelblung taken at that time as well how the photograph captions have changed over time. It also raises questions about the development of a legend, to which Bobrowski’s poem has made a decisive contribution.

scholarly journals Optimal Coordination of Last Trains for Maximum Transfer Accessibility with Heterogeneous Walking Time

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yao Chen ◽  
Baohua Mao ◽  
Yun Bai ◽  
Tin Kin Ho ◽  
Zhujun Li
Keyword(s):  
Dwell Time ◽  
Random Variable ◽  
Minimal Extension ◽  
The Third ◽  
Train Timetable ◽  
Urban Rail ◽  
Optimal Coordination ◽  
Transfer Stations ◽  
The Given ◽  
Walking Time

Last train coordination aims to synchronize the arrival and departure times of the last feeder trains and the last connecting trains at transfer stations to improve the transfer accessibility of urban rail networks. This study focuses on the transfer accessibility between last trains with considering heterogeneous transfer walking time. Three mathematical models are developed on the last train timetable optimization. The first model fine-tunes the last train timetable under the given bound of the dwell time. The second one aims to allow the mutual transfers with the prolonged dwell time to maximize the transfer accessibility. A biobjective function is proposed to seek the trade-off between the maximal transfer accessibility and the minimal extension of dwell time. The third model considers the heterogeneity of transfer walking time that is represented as a random variable following a probability distribution. A discrete approximation method is proposed to reformulate the nonlinear model. The embedded Branch & Cut algorithm of CPLEX is applied to solve the models. A real case on the Shenzhen metro network is conducted to demonstrate the performance of the models. The three models all provide better last train timetable than the current timetable in practice. The sensitivity analysis manifests that the third model are always advantageous in the optimization of successful transfer passengers.

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