A Unified Constructive Algorithm For Second- Order Curves’ Foci Creation

2018 ◽  
Vol 6 (2) ◽  
pp. 47-54 ◽  
Author(s):  
Д. Волошинов ◽  
Denis Voloshinov
Keyword(s):  
Geometric Modeling ◽  
Second Order ◽  
Geometric Constructions ◽  
Practical Applications ◽  
Geometric Problems ◽  
Geometric Concepts ◽  
Unified Algorithm ◽  
To Come ◽  
Scientific Value ◽  
Practical Feasibility

While using conventional tools for solving geometric problems, it is difficult to obtain and analyze results where imaginary geometric images appear. Despite the recognition of legitimacy and scientific value of imaginary solutions presenting in geometric constructions, the question on such solutions’ appropriateness and practical feasibility remains no completely clear up till now. That’s why, for most practitioners imaginary solutions are presented as something unattainable or unimportant. However, the introduction of imaginary geometric images into the practice of geometric modeling makes it possible to obtain solutions in an exhaustiveness, to develop unified algorithms for solving problems that were usually presented as either not solvable or reduced to solutions in partial settings. The use of computer technologies and the paradigm of constructive geometric modeling allow eliminate this problem’s acuteness, and direct efforts both at geometric theory’s improvement and introduction of scientific achievements in this area at the field of practical applications. Automation means for geometric experiment make it possible to find new regularities in seemingly well-known mathematical facts, to come to more general understanding of geometric concepts and images. This paper is devoted to analysis of some geometric schemes and to discussion of arising from it questions related to the theory of second-order curves creation by the methods of constructive synthesis. In the paper it has been demonstrated that the currently used definitions of second-order curves’ center and diameters contradict the principle of conics indistinguishability in projective geometry. The ways for eliminating of these contradictions have been proposed, and a unified algorithm for the second-order curves’ foci creation has been developed based on these ways.

Social Science Theory for Environmental Sustainability

2018 ◽  
Author(s):  
Marc J. Stern
Keyword(s):  
Social Science ◽  
Environmental Sustainability ◽  
Persuasive Communication ◽  
Practical Applications ◽  
Social Science Theory ◽  
Science Theory ◽  
The Social ◽  
Communication Conflict ◽  
To Come ◽  
Sustainability Challenges

Social science theory for environmental sustainability: A practical guide makes social science theory accessible and usable to anyone interested in working toward environmental sustainability at any scale. Environmental problems are, first and foremost, people problems. Without better understandings of the people involved, solutions are often hard to come by. This book answers calls for demonstrating the value of theories from the social sciences for solving these types of problems and provides strategies to facilitate their use. It contains concise summaries of over thirty social science theories and demonstrates how to use them in diverse contexts associated with environmental conflict, conservation, natural resource management, and other environmental sustainability challenges. The practical applications of the theories include persuasive communication, conflict resolution, collaboration, negotiation, enhancing organizational effectiveness, working across cultures, generating collective impact, and building more resilient governance of social-ecological systems. Examples throughout the book and detailed vignettes illustrate how to combine multiple social science theories to develop effective strategies for environmental problem solving. The final chapter draws out key principles for enhancing these efforts. The book will serve as a key reference for environmental professionals, business people, students, scientists, public officials, government employees, aid workers, or any concerned citizen who wants to be better equipped to navigate the social complexities of environmental challenges and make a meaningful impact on any environmental issue.

scholarly journals Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mehwish Bari ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Computer Graphics ◽  
Geometric Modeling ◽  
Tension Control ◽  
Free Form ◽  
Subdivision Surfaces ◽  
Smooth Curves ◽  
Practical Applications ◽  
Tension Parameter ◽  
Exact Reproduction ◽  
Free Form Surfaces

AbstractSubdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having $C^{1}$ C 1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.

A Torus Patch Approximation Approach for Point Projection on Implicit Surfaces

2011 ◽  
Vol 346 ◽  
pp. 259-265
Author(s):  
Xiao Ming Liu ◽  
Lei Yang ◽  
Qiang Hu ◽  
Jun Hai Yong
Keyword(s):  
Iterative Algorithm ◽  
Geometric Modeling ◽  
Second Order ◽  
Implicit Surfaces ◽  
Implicit Surface ◽  
Approximation Approach ◽  
Initial Values ◽  
Point Projection

Point projection on an implicit surface is essential for the geometric modeling and graphics applications of it. This paper presents a method for computing the principle curvatures and principle directions of an implicit surface. Using the principle curvatures and principle directions, we construct a torus patch to approximate the implicit surface locally. The torus patch is second order osculating to the implicit surface. By taking advantage of the approximation torus patch, this paper develops a second order geometric iterative algorithm for point projection on the implicit surface. Experiments illustrate the efficiency and less dependency on initial values of our algorithm.

scholarly journals DIFFERENTIATION OF POLYNOMIALS IN SEVERAL VARIABLES OVER GALOIS FIELDS OF FUZZY CARDINALITY AND APPLICATIONS TO REED-MULLER CODES

2018 ◽  
Vol 18 (3) ◽  
pp. 339-348
Author(s):  
V. M. Deundyak ◽  
N. S. Mogilevskaya
Keyword(s):  
Coding Theory ◽  
Communication Systems ◽  
Communication Channels ◽  
Galois Field ◽  
Second Order ◽  
Galois Fields ◽  
Practical Applications ◽  
Several Variables ◽  
Confidential Data ◽  
Partial Distortion

Introduction. Polynomials in several variables over Galois fields provide the basis for the Reed-Muller coding theory, and are also used  in a number of cryptographic problems. The properties of such polynomials specified over the derived Galois fields of fuzzy cardinality are studied. For the results obtained,  two  real-world  applications  are  proposed: partitioning scheme and Reed-Muller code decoder.Materials and Methods. Using linear algebra, theory of Galois fields, and general theory of polynomials in several variables, we have obtained results related to the differentiation and integration  of polynomials  in  several  variables  over  Galois fields of fuzzy cardinality. An analog of the differentiation operator is constructed and studied for vectors.Research Results. On the basis of the obtained results on the differentiation and integration of polynomials, a new decoder for Reed-Muller codes of the second order is given, and a scheme for organizing the partitioned transfer of confidential data is proposed. This is a communication system in which the source data on the sender is divided into several parts and, independently of one  another,  transmitted  through  different communication channels, and then, on the receiver, the initial data is restored of the parts retrieved. The proposed scheme feature is that it enables to protect data, both from the nonlegitimate access, and from unintentional errors; herewith, one  and  the  same  mathematical  apparatus  is  used  in  both cases. The developed decoder for the second-order Reed-Muller codes prescribed over the derived odd Galois field may have a constraint to the recoverable error level; however, its use is advisable for a number of the communication channels.Discussion    and    Conclusions.    The    proposed    practical applications   of   the   results   obtained   are   useful   for   the organization of reliable communication systems. In future, it is planned  to  study  the  restoration  process  of  the  original polynomial by its derivatives, in case of their partial distortion, and the development of appropriate applications.

A Discriminative Ontology for Future Selves

2021 ◽  
Vol 30 (4) ◽  
pp. 372-381
Author(s):  
Juraj Odorčák ◽  
Keyword(s):  
Second Order ◽  
Practical Advantage ◽  
Future Selves ◽  
The Future ◽  
Future Self ◽  
The Right ◽  
Practical Feasibility

The article presents a critique of the commonly held assumption about the practical advantage of endurantism over perdurantism regarding the problem of future-directed self-concern of a person. The future-directed self-concern of a person crucially depends on the possibility of the right differentiation of diverging futures of distinct persons, therefore any theory of persistence that does not entail a special nonbranching relation of a person to only their future self seems to be counterintuitive or unrealistic for practical purposes of personal persistence. I argue that this pragmatic rationale about future-directed self-concern is equally challenging for both theories of persistence. Moreover, I indicate, that both of these theories fall and stand on the practical feasibility of hidden ontological presuppositions about specific second-order notions of concerns of persons for their future.

Features of Distance Learning in Geometric and Graphic Disciplines Using Methods of Constructive Geometric Modeling

2021 ◽  
pp. 46-56
Author(s):  
E. Boyashova
Keyword(s):  
Distance Learning ◽  
Geometric Modeling ◽  
Information Technologies ◽  
Graphical Representation ◽  
Teaching Experience ◽  
Educational Process ◽  
Descriptive Geometry ◽  
Geometric Constructions ◽  
Professional Activities

The article is devoted to the peculiarities of teaching the discipline "Descriptive geometry" in the conditions of distance learning, it examines the application of information technologies in the educational process in geometric and graphic disciplines. Increasing the speed of information processes, reducing the number of hours for mastering the discipline. the conditions of distance learning set new tasks for teachers and dictate their requirements for teaching graphic disciplines and the use of teaching experience in a new reality; there is a need to introduce and develop new forms of education without losing the quality of education. Geometric-graphic disciplines occupy one of the important places in technical education, the complexity of the study of which lies in the development of a graphical representation of phenomena, objects and processes by methods of constructive geometric modeling. The knowledge and skills acquired by students contribute to the development of spatial, imaginative and rational thinking, which is necessary for future professional activities. Descriptive geometry is a discipline that is not easy to master on your own without a conscious understanding of the logic and sequence of geometric constructions, without deep knowledge of theoretical foundations and constant, repeated implementation of practical tasks. The acquisition of practical skills in mastering the methods of discipline has become more difficult in the current epidemiological situation. In modern conditions of distance learning, the use of the Simplex geometric modeling system made it possible to develop and propose a new concept of geometric-graphic interaction, which significantly reduced the time for completing and checking educational tasks in real time. The proposed technology reveals the deep informational essence of the studied discipline "Descriptive Geometry" and becomes a powerful research tool for students. The integration of traditional teaching methods in the graphic preparation of students with computer and communication facilities increases the possibilities of communication and improves the quality of teaching.

Biquadratic Digital Phase-Compensator Design with Stability-Margin Controllability

2019 ◽  
Vol 28 (04) ◽  
pp. 1950068 ◽  
Author(s):  
Tian-Bo Deng
Keyword(s):  
Stability Margin ◽  
Transformation Method ◽  
Second Order ◽  
Approximation Accuracy ◽  
Parameter Transformation ◽  
Practical Applications ◽  
Compensator Design ◽  
Novel Method ◽  
Design Idea ◽  
The Stability

This paper proposes a novel method for the design of a recursive second-order (biquadratic) all-pass phase compensator with controllable stability margin. The design idea stems from the generalized stability triangle (GST) derived by the author for the second-order biquadratic digital filter. Based on the GST, a parameter-transformation method is proposed on the transformations of the denominator coefficients of the transfer function of the biquadratic phase compensator. The transformations convert the original denominator coefficients to other new parameters, and any values of those new parameters can guarantee that the GST condition is always satisfied. Optimizing the new parameters yields a biquadratic phase compensator that definitely meets a prespecified stability margin. That is, a biquadratic all-pass phase compensator can be designed to have an arbitrarily specified stability margin. This in turn avoids the occurrence that a recursive phase compensator may become unstable in the practical applications. Thus, the resulting biquadratic phase compensator has robust stability, which is extremely important during the practical filtering operations. A design example is given to show the stability margin guarantee as well as the approximation accuracy.

Producing Curved Surfaces in the Octahedron: Enrichment for Junior High School Students

1986 ◽  
Vol 34 (3) ◽  
pp. 30-33
Author(s):  
Victoria Pohl
Keyword(s):  
High School ◽  
High School Students ◽  
Junior High School ◽  
Junior High ◽  
Learning Experience ◽  
Junior High School Students ◽  
Curved Surfaces ◽  
Geometric Constructions ◽  
School Students ◽  
Geometric Concepts

String art on an octahedron provides a viable way to teach and illustrate geometric concepts to junior high school students. This learning experience also furnihes an opportunity to correlate mathematics and art. Furthermore, artistic geometric constructions often stimulate junior high school students, particularly those who do not fare well in other areas of mathematics. After completing the following construction, students and teache rs should agree that learning can be fun.

About Prospects of Development of Geometry and Its Tools

10.12737/3844 ◽  
2014 ◽  
Vol 2 (1) ◽  
pp. 15-21 ◽  
Author(s):  
Волошинов ◽  
Denis Voloshinov
Keyword(s):  
Geometric Modeling ◽  
Practical Applications ◽  
Geometric Methods ◽  
Development Methods

This paper is devoted to development of new tools implementing methods of constructive geometric modeling. Such tools’ development methods on a base of discrete electronic programmable devices’ use have been proposed. It has been shown that such tools can serve as a base for an enhanced implementation of geometric methods in practical applications.

MANAGEMENT OF ON-FARM YIELD TRIALS FOR TESTING ADAPTABILITY OF CROP VARIETIES

2005 ◽  
Vol 41 (2) ◽  
pp. 245-254
Author(s):  
D. SUMITH de Z. ABEYSIRIWARDENA
Keyword(s):  
Management Practices ◽  
Research Management ◽  
Rice Varieties ◽  
Research Personnel ◽  
Crop Varieties ◽  
Farmer Management ◽  
Recommended Practices ◽  
Scientific Value ◽  
On Farm ◽  
Practical Feasibility

Farmers themselves are allowed to manage on-farm variety adaptability trials (VATs), to represent farmer management practices in preference to research management. In this approach, within-trial uniformity and thus the scientific value of VATs will be lost. A study was conducted using rice to ascertain whether representation of farmer management in VATs is necessary and to test an approach that represents farmer management without losing within-trial uniformity and the scientific value of VATs. In the proposed approach, both the representation of farmer management and within-trial uniformity are reasonably assured through implementation of site-specific farmer practices by research personnel. This approach was compared with complete research management using recommended practices in a VAT conducted with five rice varieties in six farmers' fields over two seasons. When farmer management was implemented by research personnel, popular varieties among farmers were judged most adaptable. However, when VATs were managed using recommended practices, popular varieties among farmers were judged least adaptable. This provided direct evidence to show the usefulness of representation of farmer management and the validity and practical feasibility of the proposed approach in managing VATs.

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