scholarly journals On Three Constructions of Nanotori

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2036
Author(s):  
Vesna Andova ◽  
Pavel Dimovski ◽  
Martin Knor ◽  
Riste Škrekovski
Keyword(s):  
Computer Science ◽  
Explicit Form ◽  
Topological Indices ◽  
The Other ◽  
Explicit Formulas ◽  
Extra Parameter

There are three different approaches for constructing nanotori in the literature: one with three parameters suggested by Altshuler, another with four parameters used mostly in chemistry and physics after the discovery of fullerene molecules, and one with three parameters used in interconnecting networks of computer science known under the name generalized honeycomb tori. Altshuler showed that his method gives all non-isomorphic nanotori, but this was not known for the other two constructions. Here, we show that these three approaches are equivalent and give explicit formulas that convert parameters of one construction into the parameters of the other two constructions. As a consequence, we obtain that the other two approaches also construct all nanotori. The four parameters construction is mainly used in chemistry and physics to describe carbon nanotori molecules. Some properties of the nanotori can be predicted from these four parameters. We characterize when two different quadruples define isomorphic nanotori. Even more, we give an explicit form of all isomorphic nanotori (defined with four parameters). As a consequence, infinitely many 4-tuples correspond to each nanotorus; this is due to redundancy of having an “extra” parameter, which is not a case with the other two constructions. This result significantly narrows the realm of search of the molecule with desired properties. The equivalence of these three constructions can be used for evaluating different graph measures as topological indices, etc.

scholarly journals Polynomials and General Degree-Based Topological Indices of Generalized Sierpinski Networks

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Chengmei Fan ◽  
M. Mobeen Munir ◽  
Zafar Hussain ◽  
Muhammad Athar ◽  
Jia-Bao Liu
Keyword(s):  
Complex Systems ◽  
Computer Science ◽  
Topological Indices ◽  
Fractal Nature ◽  
Similar Nature ◽  
Zagreb Index ◽  
Recursive Sequences ◽  
And Mathematics

Sierpinski networks are networks of fractal nature having several applications in computer science, music, chemistry, and mathematics. These networks are commonly used in chaos, fractals, recursive sequences, and complex systems. In this article, we compute various connectivity polynomials such as M -polynomial, Zagreb polynomials, and forgotten polynomial of generalized Sierpinski networks S k n and recover some well-known degree-based topological indices from these. We also compute the most general Zagreb index known as α , β -Zagreb index and several other general indices of similar nature for this network. Our results are the natural generalizations of already available results for particular classes of such type of networks.

Abstrakcja, obiekty i cywilizacja globalna

1970 ◽  
Vol 9 (1) ◽  
pp. 203-216
Author(s):  
Robert Janusz
Keyword(s):  
Complex Systems ◽  
Computer Science ◽  
Logical Analysis ◽  
The Other ◽  
Analysis And Design ◽  
Other Hand ◽  
Exact Description

The article is about an interaction between philosophy and informatics. The discussion is based on a complex example - a country, which has an evolving domain. In contemporary computer science very complex systems are modeled. However it would be impossible to model such systems with every detail, because it would be too difficult, it would be as complex as the reality itself. Frequently complex domains don't have an exact description of their behavior: some have an inadequate description, some have a contradictory one. To model such complex domains a computer science specialist acts like a philosopher: makes classifications, explanations, etc. On the other hand there have to be some philosophical presuppositions - a conviction that a logical analysis and design will work in the domain being modeled: a postulate is introduced that logos is able to capture-in the reality. The descriptions are continuously purified from irrational influences.

Professionalising Natural Science Education and Multipronged Open Distance Learning

2012 ◽  
pp. 306-320 ◽  
Author(s):  
B. PanduRanga Narasimharao
Keyword(s):  
Biological Sciences ◽  
Public Policy ◽  
Computer Science ◽  
Natural Science ◽  
The Other ◽  
Science Journalism ◽  
Physical Sciences ◽  
Master's Programs ◽  
Natural Science Education ◽  
And Training

Tobias et al. (1995) postulated in their book on “Rethinking Science as a Career” that Master’s programs could produce graduates who provide the same level of expertise and leadership as professionals do in other fields. They say that they would do so by having the ability to use the products of scholarship in their work and by being familiar with the practical aspects of emerging problem areas. If we consider natural science consisting of physical sciences, biological sciences, mathematics, geosciences, and computer science, degrees in computer science and geosciences served as credentials for practice, whereas physics, chemistry, and biological sciences served as classical graduate education. Robbins-Roth (2006) collected 22 career descriptions for science graduates ranging from public policy to investment banking, and from patent examining to broadcast science journalism. There are several sectors of the society where the principles and knowledge of these science disciplines are used. On the other hand, there are many of the graduates in these disciplines who either are working in areas completely unrelated to their education and training or are unemployable. The need for preparing the science graduates professionally is well recognized (Schuster, 2011; Vanderford, 2010; Narasimharao, Shashidhara Prasad and Nair, 2011; Chuck, 2011).

Two Case Studies of Online Discussion Use in Computer Science Education

2020 ◽  
pp. 409-434
Author(s):  
Gokce Akcayir ◽  
Zhaorui Chen ◽  
Carrie Demmans Epp ◽  
Velian Pandeliev ◽  
Cosmin Munteanu
Keyword(s):  
Science Education ◽  
Computer Science ◽  
Mixed Methods Research ◽  
Online Discussion ◽  
Online Discussions ◽  
Asynchronous Discussion ◽  
The Other ◽  
Course Content ◽  
Integration Strategies ◽  
Deep Integration

In this chapter, two cases that include computer science (CS) instructors' integration of an online discussion platform (Piazza) into their courses were examined. More specifically, the instructors' perspectives and role in these cases were explored to gain insight that might enable further improvements. Employing a mixed methods research design, these cases were investigated with text mining and qualitative data analysis techniques with regard to instructors' integration strategies and students' reactions to them. The results of the study showed that among these cases, one entailed a deep integration (Case 1) and the other a shallow one (Case 2). Instructors' presence and guidance through their posting behaviors had a bigger effect than the nature of the course content. Additionally, TA support in online discussions helped address the limitations of the asynchronous discussion when the TAs had the maturity to only respond to questions for which they were adequately prepared.

Partner Relationship Management

2011 ◽  
pp. 158-170
Author(s):  
Diego Jiménez-López ◽  
Marcos Ruano-Mayoral ◽  
Joaquín Fernández-González ◽  
Fernando Cabezas Isla
Keyword(s):  
Decision Support ◽  
Computer Science ◽  
Customer Relationship Management ◽  
Relationship Management ◽  
The Other ◽  
Customer Relationship ◽  
Marketing Communication ◽  
Semantic Technologies ◽  
Partner Relationship ◽  
The One

R&D activities normally require consortium formation due to the different areas of expertise involved in such activities. On the one hand, it is not trivial for a R&D entity to decide in which projects it should participate, or which are the adequate partners to form a consortium. On the other hand, acceptation of the Customer Relationship Management (CRM) Systems has become a reality for the industry and researchers in areas, such as marketing, communication, or computer science. These tools contain in their basic packages features to manage key company actives, including partners and clients. However, R&D environments involve special characteristics and traits, which require an extension of functionalities in order to be accurately covered. The increasing strength and usefulness of semantic technologies have led to innovative decision support processes and management of partners and R&D call for proposals. This work introduces an architecture that integrates R&D processes with the CRM philosophy.

Professionalising Natural Science Education and Multipronged Open Distance Learning

2015 ◽  
pp. 138-152
Author(s):  
B. PanduRanga Narasimharao
Keyword(s):  
Biological Sciences ◽  
Public Policy ◽  
Computer Science ◽  
Natural Science ◽  
The Other ◽  
Science Journalism ◽  
Physical Sciences ◽  
Master's Programs ◽  
Natural Science Education ◽  
And Training

Tobias et al. (1995) postulated in their book on “Rethinking Science as a Career” that Master's programs could produce graduates who provide the same level of expertise and leadership as professionals do in other fields. They say that they would do so by having the ability to use the products of scholarship in their work and by being familiar with the practical aspects of emerging problem areas. If we consider natural science consisting of physical sciences, biological sciences, mathematics, geosciences, and computer science, degrees in computer science and geosciences served as credentials for practice, whereas physics, chemistry, and biological sciences served as classical graduate education. Robbins-Roth (2006) collected 22 career descriptions for science graduates ranging from public policy to investment banking, and from patent examining to broadcast science journalism. There are several sectors of the society where the principles and knowledge of these science disciplines are used. On the other hand, there are many of the graduates in these disciplines who either are working in areas completely unrelated to their education and training or are unemployable. The need for preparing the science graduates professionally is well recognized (Schuster, 2011; Vanderford, 2010; Narasimharao, Shashidhara Prasad and Nair, 2011; Chuck, 2011).

Multichannel Modality in Displaying Information

2013 ◽  
Vol 4 (1) ◽  
pp. 60-79 ◽  
Author(s):  
Elisa Benetti ◽  
Gianluca Mazzini
Keyword(s):  
Computer Science ◽  
Public Administration ◽  
The Other ◽  
Public Institution ◽  
Automated System ◽  
Government Services ◽  
Physical Location ◽  
The Past ◽  
Different Types ◽  
The One

Computer science and telecommunications are increasingly important in society and this leads also public administrations to take advantage of ICT, in order to communicate with citizens in a more rapid and simpler way than the complex and paper-based bureaucracy of the past. While on the one hand the use of these technologies responds to the duty of any public institution to involve the largest number of addressees, on the other hand, society must also consider the limitations of these technologies. Firstly not everybody is so familiar in their use. Moreover, the digital administration thus becomes virtual, accessible only through technological devices and not present in a physical location, and is therefore essential to ensure full coverage of the territory, which is currently not always possible. The main novelty of this paper is the implementation of an automated system capable of adapting different types of government services to multiple communication media. The joint exploitation of multiple technologies allows to use the strengths of one of them when are found the limits of another, making this multichannel modality the solution to the requirement of ICT in public administration.

scholarly journals On distances in Sierpiński graphs: Almost-extreme vertices and metric dimension

2013 ◽  
Vol 7 (1) ◽  
pp. 72-82 ◽  
Author(s):  
Sandi Klavzar ◽  
Sara Zemljic
Keyword(s):  
Computer Science ◽  
Metric Dimension ◽  
Fractal Nature ◽  
Explicit Formulas ◽  
Arbitrary Vertex ◽  
Tower Of Hanoi ◽  
Sierpiński Graphs ◽  
Total Distance

Sierpi?ski graphs Sn p form an extensively studied family of graphs of fractal nature applicable in topology, mathematics of the Tower of Hanoi, computer science, and elsewhere. An almost-extreme vertex of Sn p is introduced as a vertex that is either adjacent to an extreme vertex of Sn p or is incident to an edge between two subgraphs of Sn p isomorphic to Snp-1. Explicit formulas are given for the distance in Sn p between an arbitrary vertex and an almostextreme vertex. The formulas are applied to compute the total distance of almost-extreme vertices and to obtain the metric dimension of Sierpi?ski graphs.

scholarly journals Discussion of “Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” by DejanBrkić; and Pavel Praks, Mathematics 2019, 7, 34; doi:10.3390/math7010034

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 253 ◽  
Author(s):  
Lotfi Zeghadnia ◽  
Bachir Achour ◽  
Jean Robert
Keyword(s):  
Friction Factor ◽  
The Other ◽  
Maximum Deviation ◽  
Explicit Formulas ◽  
Flow Friction ◽  
Complex Equation ◽  
Other Hand

The Colebrook-White equation is often used for calculation of the friction factor in turbulent regimes; it has succeeded in attracting a great deal of attention from researchers. The Colebrook–White equation is a complex equation where the computation of the friction factor is not direct, and there is a need for trial-error methods or graphical solutions; on the other hand, several researchers have attempted to alter the Colebrook-White equation by explicit formulas with the hope of achieving zero-percent (0%) maximum deviation, among them Dejan Brkić and Pavel Praks. The goal of this paper is to discuss the results proposed by the authors in their paper:” Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” and to propose more accurate formulas.

scholarly journals Period polynomials and explicit formulas for Hecke operators on Γ0(2)

2009 ◽  
Vol 146 (2) ◽  
pp. 321-350 ◽  
Author(s):  
SHINJI FUKUHARA ◽  
YIFAN YANG
Keyword(s):  
Vector Space ◽  
Explicit Form ◽  
Congruence Subgroup ◽  
Bernoulli Polynomials ◽  
Affirmative Answer ◽  
Hecke Operators ◽  
Cusp Forms ◽  
Isomorphism Theorem ◽  
Explicit Formulas ◽  
Space Of Cusp Forms

AbstractLet Sw+2(Γ0(N)) be the vector space of cusp forms of weight w + 2 on the congruence subgroup Γ0(N). We first determine explicit formulas for period polynomials of elements in Sw+2(Γ0(N)) by means of Bernoulli polynomials. When N = 2, from these explicit formulas we obtain new bases for Sw+2(Γ0(2)), and extend the Eichler–Shimura–Manin isomorphism theorem to Γ0(2). This implies that there are natural correspondences between the spaces of cusp forms on Γ0(2) and the spaces of period polynomials. Based on these results, we will find explicit form of Hecke operators on Sw+2(Γ0(2)). As an application of main theorems, we will also give an affirmative answer to a speculation of Imamoglu and Kohnen on a basis of Sw+2(Γ0(2)).

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