Mathematical Analysis on Helicoids Architectural Form

2013 ◽  
Vol 790 ◽  
pp. 273-277
Author(s):  
Zhong Yi ◽  
Cheng Zhi Yuan
Keyword(s):  
Mathematical Analysis ◽  
Mathematical Theory ◽  
Architecture Design ◽  
Curved Surfaces ◽  
Mathematical Transformation ◽  
Geometric Figure ◽  
Topological Transformation ◽  
Architectural Form ◽  
Geometric Figures ◽  
Architecture Modeling

In a sense, architecture may be called as a geometric figure. Although architectural forms are very different, the form from one kind of architecture to another kind of architecture is equivalent to one kind of mathematical transformation in view of mathematics; for example, the transformation between a cube architecture and a spherical architecture belongs to a topological transformation. Currently, many sculptural features appear in the architecture design, which may be called as the nonlinear architecture. Curves and curved surfaces are widely used in the architecture modeling. Moreover, functional spaces are divided inside the architecture shell according to requirements. Architects are inclined to use a mathematical theory especially the geometrical knowledge in an architecture design. However, architects can not imagine many artistic geometric figures in geometry. Besides, such wonderful geometric figures always include some miraculous mathematical and physical properties.

Reviews - A. E. Heath. Preface. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 7–8. - R. Rhees. Note in editing. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 9–43. - George Boole. The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning. A reprint of 191. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 45–119. - George Boole. Later notes (to the foregoing). Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 119–124. (Taken from manuscript in the Library of the Royal Society.) - George Boole. The calculus of logic. A reprint of 192. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 125–140. - George Boole. Sketch of a theory and method of probabilities founded upon the calculus of logic. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 141–166. (From manuscripts in the Royal Society Library, probably before 1851.) - George Boole. Of propositions numerically definite. A reprint of 194. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 167–186. - George Boole. The claims of science, especially as founded in its relation to human nature. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 187–210. (Lecture published in London, 1851.) - George Boole. Logic and reasoning. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 211–229. (From Royal Society manuscripts, after 1855.) - George Boole. Extracts from a paper entitled “On the mathematical theory of logic and on the philosophical interpretation of its methods and processes.”Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 230–246. (From Royal Society manuscripts, later than 1855.)

1959 ◽  
Vol 24 (3) ◽  
pp. 203-209 ◽  
Author(s):  
Michael Dummett
Keyword(s):  
Mathematical Analysis ◽  
Royal Society ◽  
Mathematical Theory ◽  
Deductive Reasoning ◽  
Publishing Company ◽  
Philosophical Interpretation ◽  
Open Court ◽  
Court Publishing ◽  
George Boole ◽  
Nature Studies

The Mathematical Theory of the Snaking of Two-wheeled Trailers, with Practical Rules and Devices for Preventing Snaking

1951 ◽  
Vol 5 (1) ◽  
pp. 175-190 ◽  
Author(s):  
D. Williams
Keyword(s):  
General Solution ◽  
Detailed Analysis ◽  
Mathematical Analysis ◽  
Mathematical Theory ◽  
Degrees Of Freedom ◽  
Critical Speed ◽  
Elastic System ◽  
Practical Experience ◽  
Dynamical Equations ◽  
All Speeds

It is well known that a prime essential in bringing about unstable motion in any elastic system is the presence of at least two degrees of freedom. A trailer and its towing vehicle constitute a mechanical system with a number of degrees of freedom, and a main feature of the present problem is the necessity for deciding which are essential factors in the unstable motion and which are trivial or merely incidental. The idea of including all the possible degrees of freedom in the dynamical equations, thereby obtaining a general solution in which the part played by the several parameters can be seen, is quite impracticable. In Part I of the paper the results obtained from the mathematical analysis of the problem are given and discussed. There is a general agreement with practical experience. Part II contains the detailed analysis on which the conclusions in Part I are based. It is emphasized that the main purpose of the analysis is not to enable calculations to be made of the precise critical speed at which snaking begins for any particular combination of tractor and trailer, but to discover what factors make for stability and for instability, and how to design for immunity from snaking at all speeds.

How to Develop Multiform Geometric Vision in Schoolchildren

10.12737/3075 ◽  
2014 ◽  
Vol 2 (1) ◽  
pp. 13-21
Author(s):  
Виситаева ◽  
Maret Visitaeva
Keyword(s):  
Geometric Figure ◽  
Geometric Figures

Different interpretations for the notion of «section» are presented followed by classification of tasks, aimed at developing ability to operate with different configurations of geometric sections by types thereof (propaedeutical tasks on geometric sections; tasks on recognizing geometric figures by their geometric sections configurations; tasks on recognizing geometric sections by configurations of a given geometric figure; tasks on constructing geometric figure by a set of its geometric sections; tasks on constructing geometric sections by configuration of a given geometric figure, mixed tasks).

Reactivity and Event-Related Potentials in Attentional Tests: Effect of Training

2002 ◽  
Vol 94 (3) ◽  
pp. 817-833 ◽  
Author(s):  
Giuliano Fontani ◽  
Leda Lodi
Keyword(s):  
Reaction Time ◽  
Selective Attention ◽  
Event Related Potentials ◽  
Stimulus Onset ◽  
Negative Wave ◽  
Geometric Figure ◽  
Trained Subjects ◽  
Geometric Figures ◽  
Close Relationship ◽  
Related Potentials

To study the effects of training on reactivity and event-related potentials a complex attentional shifting test involving reaction time was administered (Test 1) to 24 healthy, young students. After five days, 12 subjects were tested with the same procedure (Test 2) without training (Untrained Subjects) while 12 repeated the test at the fifth day after four days of training (Trained Subjects). During Tests 1 and 2, event-related potentials were recorded by electroencephalogram. The task consisted of each subject responding to a stimulus of a letter appearing in the centre of a geometric figure on the screen of a computer monitor. In the prestimulus period black points were drawn and crowded randomly into a zone of the screen. The geometric figure and the letter were shown in the centre of the crowding. There were two letters and four geometric figures randomly combined in different ways. The subject had to press different keys of the computer keyboard when specific combinations appeared. The averaged event-related potentials were characterized by a negative wave with a close relationship to selective attention before the onset of the stimulus of a geometric figure followed by letters. After the stimulus onset, a P3 complex was recorded. Trained subjects were no different from untrained subjects in Test 1, while in Test 2 they had a shorter reaction time, an earlier peak of the selective attention related wave and P3, and a higher amplitude for the P3 complex. These measures and the correlations between them can be considered an index of the training effect. Thus, these tests could be used for evaluation of the attentional style and its modification with training.

Completion of Simple Geometric Forms as a Function of Varied Degrees of Incomplete Presentation

1966 ◽  
Vol 23 (3_suppl) ◽  
pp. 1303-1309 ◽  
Author(s):  
Amedeo P. Giorgi ◽  
Paul F. Colaizzi
Keyword(s):  
Functional Significance ◽  
Stimulus Figure ◽  
Task Demand ◽  
Good Continuation ◽  
Geometric Figure ◽  
Geometric Figures ◽  
Data Support ◽  
Complete Figure ◽  
Generic Sense ◽  
And Task

26 Ss were shown 9 partial presentations of 3 simple geometric figures. The figures were a circle, a square, and a diamond, and they were presented in stages of ¼, ½, and ¾ completion. Ss were told that the stimuli were parts of a more complete figure which they were to draw. They were also required to explain why they drew the figure they did. The following conclusions seem most significant. (1) All Ss complete partial figures according to a generic sense of good continuation in the sense that all completions conform to the incomplete stimulus figure. (2) In order to account for all of the data a distinction between situation demand and task demand was introduced. All Ss who experienced task demand did experience the partial figures as in need of completion. (3) A ¾ presentation of a familiar geometric figure can lead to the experience of demand to complete the figure in a univocal way for most Ss. (4) The partial squares, circles, and diamonds, conceived as incipient systems, constitute 3 different systems with respect to their functional significance. Also, in the sense that all Ss who experienced the parts as parts did so on the basis of functional significance, the data support Gurwitsch's functionalistic conception of a whole.

scholarly journals Rearrangement, convection, convexity and entropy

2013 ◽  
Vol 371 (2005) ◽  
pp. 20120343 ◽  
Author(s):  
Yann Brenier
Keyword(s):  
Conservation Laws ◽  
Mathematical Analysis ◽  
Crucial Role ◽  
Mathematical Theory ◽  
Hyperbolic Systems ◽  
Mathematical Concept ◽  
Systems Of Conservation Laws

The concepts of convexity and entropy play a crucial role in the mathematical theory of hyperbolic systems of conservation laws. We show that they also play an important role in the mathematical analysis of convection theory, through the mathematical concept of rearrangement.

scholarly journals Seed Morphology in Key Spanish Grapevine Cultivars

Agronomy ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 734
Author(s):  
Emilio Cervantes ◽  
José Javier Martín-Gómez ◽  
Francisco Emmanuel Espinosa-Roldán ◽  
Gregorio Muñoz-Organero ◽  
Ángel Tocino ◽  
...  
Keyword(s):  
Image Analysis ◽  
Morphological Characters ◽  
Seed Morphology ◽  
Dna Polymorphisms ◽  
Seed Shape ◽  
Geometric Figure ◽  
Geometric Figures ◽  
New Methods ◽  
New Models

Ampelography, the botanical discipline dedicated to the identification and classification of grapevine cultivars, was grounded on the description of morphological characters and more recently is based on the application of DNA polymorphisms. New methods of image analysis may help to optimize morphological approaches in ampelography. The objective of this study was the classification of representative cultivars of Vitis vinifera conserved in the Spanish collection of IMIDRA according to seed shape. Thirty eight cultivars representing the diversity of this collection were analyzed. A consensus seed silhouette was defined for each cultivar representing the geometric figure that better adjusted to their seed shape. All the cultivars tested were classified in ten morphological groups, each corresponding to a new model. The models are geometric figures defined by equations and similarity to each model is evaluated by quantification of percent of the area shared by the two figures, the seed and the model (J index). The comparison of seed images with geometric models is a rapid and convenient method to classify cultivars. A large proportion of the collection may be classified according to the new models described and the method permits to find new models according to seed shape in other cultivars.

Improvement of Documentation Workflow in FMCG Chain Retailing Companies Based on Data Architecture Design

2019 ◽  
pp. 87-96
Author(s):  
A. D. Borremans ◽  
O. V. Voronova ◽  
I. V. Il’in
Keyword(s):  
Conceptual Model ◽  
Data Storage ◽  
Business Processes ◽  
Third Party ◽  
Architecture Design ◽  
Workflow Model ◽  
Workflow System ◽  
Data Architecture ◽  
Architecture Modeling ◽  
Active Implementation

The presented study improves the model of top-level documentation workflow in FMCG chain retailing companies by building a special data architecture.Aim. The study aims to develop a model of top-level documentation workflow for building architectural solutions of FMCG chain retailing companies based on data architecture modeling.Tasks. First, it is necessary to examine the general documentation workflow system of FMCG chain retailing companies, identifying the major interested parties — participants of external, internal, and supporting workflow. It is also advisable to analyze certain types of internal workflow and to determine the relationships between them. Based on the conducted analysis, it is necessary to develop a conceptual model of data architecture and a documentation workflow model for FMCG chain retailing companies.Methods. This study represents the general documentation workflow system of FMCG chain retailing companies as three subsystems (external, internal, and supporting workflow). The authors examine the major channels of interaction between chain retailing companies and such interested parties as government authorities, suppliers, consumers, and third-party organizations. Based on the analysis of the elements of the workflow system, this study builds a top-level documentation workflow model and presents a conceptual model of data architecture for FMCG chain retailing companies with allowance for the above-mentioned entities. The model uses UML notation, which makes it possible to reflect key classes and relationships and to identify relationships that need to be simplified.Results. The study examines the process of improving documentation workflow in FMCG chain retailing companies in the context of active implementation of new IT solutions and automation of business processes to reduce costs and increase sales. The authors show the general documentation workflow system of FMCG chain retailing companies, identifying the major interested parties — participants of external workflow — and analyzing certain types of internal workflow. According to the results of the study, a top-level documentation workflow model for FMCG chain retailing companies is developed based on data architecture design.Conclusions. Large FMCG chain retailing companies are actively implementing new IT solutions and automate business processes to reduce costs and increase sales. Optimal documentation support for FMCG chain retailing companies is impossible without generating huge amounts of data. Methods of data storage and processing have a direct impact on the speed and quality of business processes. In order to improve documentation workflow, it is becoming increasingly important to develop and optimize data architecture. Data architecture is one of the fundamental models of company operation in terms of comprehensive digitalization. The obtained data model can be considered universal for FMCG chain retailing companies since it makes it possible to organize management in such a way as to ensure the development and efficient functioning of the architecture of chain retailing companies.

A MATHEMATICAL ANALYSIS OF THE DISTRIBUTION IN MAIZE OF HELIOTHIS ARMIGERA Hb. (OBSOLETA F.)

1942 ◽  
Vol 20d (8) ◽  
pp. 235-261 ◽  
Author(s):  
Marjory G. Walker
Keyword(s):  
Mathematical Analysis ◽  
Mathematical Theory ◽  
Random Distribution ◽  
Heliothis Armigera ◽  
The Other ◽  
Good Representation ◽  
Poisson Series ◽  
Egg Distribution ◽  
Rough Approximation ◽  
Maize Plants

The distribution among maize plants of the eggs of the American boll-worm, Heliothis armigera Hb., is discussed and analysed.The problem is considered in relation lo what is known of the connection between the state of development of maize plants and their attractiveness to ovipositing boll-worm moths. The actual frequency distribution of the eggs suggests a random as opposed to a uniform distribution, but it is shown that the conditions required for a pure mathematical random distribution cannot be satisfied. Because the maize plants differ from one another in absolute degree of attractiveness at any one time, and in relative degree of attractiveness with the passing of time, it is not true that every plant has the same chance of receiving any given egg.It is demonstrated that a mathematical theory, which is eventually one of random distribution, but which incorporates a modification to allow for the varying degrees of attractiveness of the plants, gives a fairly good representation of the egg distribution found in the field.Theoretical distributions to fit the data are calculated by two methods. One is a discontinuous process which is presented as only a rough approximation of what it is intended lo express. The other uses the compound Poisson series of Greenwood and Yule. The continuous variation in nature both in space and time, which is the essential difficulty of the problem, is discussed.

Geometric Simulation and Descriptive Geometry

2016 ◽  
Vol 4 (4) ◽  
pp. 31-40 ◽  
Author(s):  
Сальков ◽  
Nikolay Sal'kov
Keyword(s):  
Mathematical Model ◽  
Graphical Models ◽  
Graphical Model ◽  
Geometric Model ◽  
Descriptive Geometry ◽  
Geometric Figure ◽  
Geometric Figures ◽  
Geometric Simulation ◽  
The Mathematical Model ◽  
Special Case

Geometric simulation is creation of a geometric model, whose properties and characteristics in a varying degree determine the subject of investigation’s properties and characteristics. The geometric model is a special case of the mathematical model. The feature of the geometric model is that it will always be a geometric figure, and therefore, by its very nature, is visual. If the mathematical model is a set of equations, which says little to an ordinary engineer, the geometric model as representation of the mathematical model and as the geometric figure itself, enables to "see" this set. Any geometric model can be represented graphically. Graphical model of an object is a mapping of its geometric model onto a plane (or other surface). Therefore, the graphical model can be considered as a special case of the geometric model. Graphical models are very various – these are graphics, and graphical structures of immense complexity, reflecting spatial geometric figures. These are drawings of geometric figures, simulating processes of all kinds. The simulation goes on as follows. According to known geometric and differential criteria the geometric model is executed. Then a mathematical model is composed based on the geometric model, finally a computer program is compiled on the mathematical model. As a result of consideration in this paper the process of obtaining the geometric models of surface and linear forms for auto-roads it is possible to make a following conclusion. For geometric simulation and the consequent mathematical one the descriptive geometry involvement is vital. Just the descriptive geometry is used both on the initial and final stages of design.

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