scholarly journals Partial Covering of a Circle by 6 and 7 Congruent Circles

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2133
Author(s):  
Zsolt Gáspár ◽  
Tibor Tarnai ◽  
Krisztián Hincz
Keyword(s):  
Unit Circle ◽  
Numerical Solutions ◽  
Numerical Data ◽  
The Self ◽  
Covering Problem ◽  
Tabular Form ◽  
Geometrical Problem ◽  
Tensegrity Structure ◽  
Different Types ◽  
Partial Covering

Background: Some medical and technological tasks lead to the geometrical problem of how to cover the unit circle as much as possible by n congruent circles of given radius r, while r varies from the radius in the maximum packing to the radius in the minimum covering. Proven or conjectural solutions to this partial covering problem are known only for n = 2 to 5. In the present paper, numerical solutions are given to this problem for n = 6 and 7. Method: The method used transforms the geometrical problem to a mechanical one, where the solution to the geometrical problem is obtained by finding the self-stress positions of a generalised tensegrity structure. This method was developed by the authors and was published in an earlier publication. Results: The method applied results in locally optimal circle arrangements. The numerical data for the special circle arrangements are presented in a tabular form, and in drawings of the arrangements. Conclusion: It was found that the case of n = 6 is very complicated, whilst the case n = 7 is very simple. It is shown in this paper that locally optimal arrangements may exhibit different types of symmetry, and equilibrium paths may bifurcate.

Simulating Self-Regeneration and Self-Replication Processes Using Movable Cellular Automata with a Mutual Equilibrium Neighborhood

2020 ◽  
Vol 29 (4) ◽  
pp. 741-757
Author(s):  
Kateryna Hazdiuk ◽  
◽  
Volodymyr Zhikharevich ◽  
Serhiy Ostapov ◽  
◽  
...  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Three Dimensional ◽  
Computer Models ◽  
The Self ◽  
Model Construction ◽  
Natural Phenomena ◽  
Different Types ◽  
Movable Cellular Automata ◽  
Self Replication

This paper deals with the issue of model construction of the self-regeneration and self-replication processes using movable cellular automata (MCAs). The rules of cellular automaton (CA) interactions are found according to the concept of equilibrium neighborhood. The method is implemented by establishing these rules between different types of cellular automata (CAs). Several models for two- and three-dimensional cases are described, which depict both stable and unstable structures. As a result, computer models imitating such natural phenomena as self-replication and self-regeneration are obtained and graphically presented.

Gathering Evidence: The Basics

2018 ◽  
Author(s):  
Jacqueline M. Dewar
Keyword(s):  
Teaching And Learning ◽  
Qualitative Data ◽  
Numerical Data ◽  
Scholarship Of Teaching ◽  
What Works ◽  
Starting Point ◽  
Different Types ◽  
Gathering Data

Chapter 4 provides an introduction to gathering data for scholarship of teaching and learning (SoTL) investigations, including the importance of triangulation, that is, collecting several different types of evidence. Examples are given of typical kinds of quantitative (numerical) and qualitative (non-numerical) data that might be used in a SoTL study. That quantitative and qualitative data are more closely related than it might seem at first is discussed. The taxonomy of SoTL questions—What works? What is? What could be?—provides a starting point for considering what type of data to collect. Suggestions are offered for ways to design assignments so that the coursework students produce can also serve as evidence, something that benefits both students and their instructor.

Nanocomposite Photocatalyst Based on Layered Double Hydroxides (LDHs) Associated with TiO2

2014 ◽  
Vol 92 ◽  
pp. 100-109 ◽  
Author(s):  
Jonjaua Ranogajec ◽  
Andrijana Sever-Skapin ◽  
Ognjen Rudic ◽  
Snezana Vucetic
Keyword(s):  
Photocatalytic Activity ◽  
Layered Double Hydroxides ◽  
Direct Contact ◽  
Building Materials ◽  
Specific Problem ◽  
The Self ◽  
Different Types ◽  
Double Hydroxides ◽  
Positive Effect ◽  
Material Porosity

The surfaces of building materials are constantly exposed to the actions of environmental factors, pollutants of inorganic and organic origin as well as to microorganisms, which significantly contribute to corrosion phenomena.The application of coatings decreases the negative action of the pollutants minimizing their direct contact with the substrate. Different types of coatings with additional functions have been developed. A specific problem of these applications is the lack of compatibility of the photocatalysts with the surface of the building materials and the detachment of potentially toxic TiO2nanoparticles. In the present study, this problem was solved by the proper immobilization of TiO2nanoparticles onto the photocatalyst support, layered double hydroxides (LDHs). The newly formed coating possesses acceptable porosity for a porous building material (porosity within the range of 30-46 %) and satisfied photocatalytic activity, as well as mineralogical compatibility with the substrates (mortars, renders, bricks). Additionally, a positive effect considering the self-cleaning phenomenon was attained.

On one method of solving the partial covering problem

Cybernetics ◽  
1989 ◽  
Vol 25 (1) ◽  
pp. 122-125
Author(s):  
V. A. Roshchin ◽  
I. V. Sergienko
Keyword(s):  
Covering Problem ◽  
Partial Covering

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

scholarly journals Analysis of the self-similar solutions of a generalized Burger's equation with nonlinear damping

2001 ◽  
Vol 7 (3) ◽  
pp. 253-282 ◽  
Author(s):  
Ch. Srinivasa Rao ◽  
P. L. Sachdev ◽  
Mythily Ramaswamy
Keyword(s):  
Initial Conditions ◽  
Nonlinear Damping ◽  
Nonlinear Ordinary Differential Equation ◽  
The Self ◽  
Similar Reduction ◽  
Generalized Burgers Equation ◽  
Different Types ◽  
Self Similar ◽  
Parameter Ranges ◽  
Similar Solutions

The nonlinear ordinary differential equation resulting from the self-similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming initial conditions at the origin we observe a wide variety of solutions – (positive) single hump, unbounded or those with a finite zero. The existence and nonexistence of positive bounded solutions with different types of decay (exponential or algebraic) to zero at infinity for specific parameter ranges are proved.

scholarly journals Self-assessed attitudes of adolescents towards learning

2021 ◽  
Vol 1 (1) ◽  
pp. 53-66
Author(s):  
Viorica Goras-Postica
Keyword(s):  
Organization Culture ◽  
Educational Process ◽  
The Self ◽  
Online Questionnaire ◽  
Self Assessment ◽  
Culture Of Learning ◽  
Essential Aspect ◽  
Teacher Student ◽  
Different Types ◽  
Institutional Process

The article presents the results of a pedagogical study, recently conducted on a group of over 8 thou- sand adolescents on the self-assessment of attitudes towards learning. As technologies have shifted many points of focus in addressing learning as an essential aspect of the educational process, the author intended to analyze the representations of adolescents from the knowledge and information century, administering an online questionnaire consisting of different types of questions. The results revealed diverse and mature perceptions, problems of teacher-student, student-student relations, of the institutional process of organization / culture of learning, but also of its results, as perceived by the main actors of the educational act.

scholarly journals Post-Traumatic Growth in Cancer Survivors: Narrative Markers and Functions of The Experience's Transformation

2016 ◽  
Author(s):  
Maria Luisa Martino ◽  
Maria Francesca Freda
Keyword(s):  
Cancer Survivors ◽  
Mixed Method ◽  
The Self ◽  
Traumatic Experience ◽  
Post Traumatic Growth ◽  
The World ◽  
Different Types ◽  
Post Traumatic ◽  
Transformative Function ◽  
The Relationship

The concept that a traumatic experience, such as a cancer, can lead to a positive change and transformation of self, life and relationships was named as post-traumatic growth (PTG). A large amount of research measured PTG in cancer survivors arguing an interpretation of the construct as an outcome. Recently, qualitative research shows different types of narrative of PTG, but the narrative markers and their functions of transformation remain still unclear. Within a mixed-method, we aim to highlight the narrative markers and their transformative functions, underlying the PTG, within 12 cancer survivors’ narratives with medium/high and medium/low level of PTG. A redemptive sequence analysis was carried out. In the narratives with high/medium PTG we find a specific transformative function on-thinking focused transformation founded on the change/expansion of the own internal criteria to interpret the relationship with the world centralizing the self in the present and future; in the narratives with medium/low PTG we find an on-acting focused transformation, founded on the change of the operational procedures aimed to live centered on the present and on its moments.

Impact of a Mass on a Damped Elastically Supported Beam

1948 ◽  
Vol 15 (2) ◽  
pp. 125-136
Author(s):  
W. H. Hoppmann
Keyword(s):  
Differential Equation ◽  
Elastic Foundation ◽  
Forced Vibration ◽  
Numerical Solutions ◽  
Coefficient Of Restitution ◽  
Tabular Form ◽  
Single Degree Of Freedom ◽  
Simply Supported ◽  
Single Degree ◽  
Elastically Supported

Abstract In this paper a study is made of the problem of the central impact of a mass on a simply supported beam on an elastic foundation with considerations of internal and external damping. The differential equation for the forced vibration of the beam is developed. It is solved for the case in which the force is a function of time and is concentrated at the center of the beam. Formulas are obtained for the deflections. An expression is developed for the coefficient of restitution which is essential in determining the deflections and the strains. Criteria are devised for determining the cases in which the beam may be considered as a single-degree-of-freedom system when damping and an elastic foundation are considered. The importance of these criteria is discussed. A numerical example illustrating the theory developed in the paper is worked out in detail. Results of computations for several numerical solutions are given in tabular form.

An Examination of the Direct and Generalized Effects of a Play-Training and Overcorrection Procedure upon the Self-Stimulatory Behavior of a Profoundly Retarded Boy

AAESPH Review ◽  
1977 ◽  
Vol 2 (3) ◽  
pp. 131-146 ◽  
Author(s):  
Robert C. Kissel ◽  
Thomas L. Whitman
Keyword(s):  
Positive Reinforcement ◽  
Play Behavior ◽  
The Self ◽  
Inappropriate Behavior ◽  
Training Package ◽  
Response Generalization ◽  
Different Types

This study was designed to answer a question posed by Epstein, Doke, Sajwaj, Sorell, and Rimmer (1974) concerning whether an overcorrection technique administered to one inappropriate behavior will also suppress other untreated inappropriate responses. In addition, it examined another often-overlooked question, that is, whether the effects of treatment generalize over situations. The effects of a positive reinforcement and a hand overcorrection training package upon the play and self-stimulatory responses of a 14 year old profoundly retarded boy were examined In three different types of play situations. The design allowed both stimulus and response generalization effects to be assessed. Results indicated that the training procedures increased play behavior and decreased three different self-stimulatory responses. Although there was some evidence that both situational and response generalization effects occurred, these effects were not sufficient to preclude the need for further treatment.

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