scholarly journals On the Digital Pontryagin Algebras

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 875 ◽  
Author(s):  
Sunyoung Lee ◽  
Yeonjeong Kim ◽  
Jeong-Eun Lim ◽  
Dae-Woong Lee
Keyword(s):  
Computer Science ◽  
Digital Images ◽  
Base Point ◽  
Fundamental Properties

In the current study, we explore digital homology modules, and investigate their fundamental properties on (pointed) digital images as one of the developments of symmetries. We also examine pointed digital Hopf spaces and base point preserving digital Hopf functions between pointed digital Hopf spaces with suitable digital multiplications, and explore the digital primitive homology classes, digital Pontryagin algebras on digital Hopf spaces as a symmetric phenomenon in mathematics and computer science.

scholarly journals The higher topological complexity in digital images

2020 ◽  
Vol 21 (2) ◽  
pp. 305
Author(s):  
Melih İs ◽  
İsmet Karaca
Keyword(s):  
Lower Bounds ◽  
Algebraic Topology ◽  
Digital Images ◽  
Topological Complexity ◽  
Fundamental Properties ◽  
The Future

Y. Rudyak develops the concept of the topological complexity TC(X) defined by M. Farber. We study this notion in digital images by using the fundamental properties of the digital homotopy. These properties can also be useful for the future works in some applications of algebraic topology besides topological robotics. Moreover, we show that the cohomological lower bounds for the digital topological complexity TC(X,κ) do not hold.

Ontologies for Model-Driven Service Engineering

2008 ◽  
pp. 154-193
Author(s):  
Bill Karakostas ◽  
Yannis Zorgios
Keyword(s):  
Computer Science ◽  
Service Provider ◽  
Universal Service ◽  
Abstract Concept ◽  
Generic Concept ◽  
Service Engineering ◽  
Model Driven ◽  
Fundamental Properties ◽  
Concept Vehicle ◽  
Service Consumer

In Chapter II we discussed the fundamental properties and concepts of a service. Concepts like interface, contract, service provider and service consumer are universal (i.e., they apply to all types of services). However, in as much as they are intuitive and universal, service concepts such as the aforementioned lack widely agreed upon semantics. The term semantics is used by disciplines such as philosophy, mathematics, and computer science to refer to “the meaning of things.” Meaning is usually attributed to a concept via its association with other concepts. In everyday speech, defining, for example, a “car” to be a kind of a “vehicle” is an attempt to attribute meaning to “car” by associating it with another, more abstract concept called “vehicle.” If the recipient of this definition already understands the concept of a vehicle, then he/she can also understand the concept of car via its association with the more abstract/generic concept vehicle.

scholarly journals Coalgebras on Digital Images

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2082
Author(s):  
Sunyoung Lee ◽  
Dae-Woong Lee
Keyword(s):  
Commutative Ring ◽  
Digital Images ◽  
Continuous Functions ◽  
Contravariant Functor ◽  
Fundamental Properties

In this article, we investigate the fundamental properties of coalgebras with coalgebra comultiplications, counits, and coalgebra homomorphisms of coalgebras over a commutative ring R with identity 1R based on digital images with adjacency relations. We also investigate a contravariant functor from the category of digital images and digital continuous functions to the category of coalgebras and coalgebra homomorphisms based on digital images via the category of unitary R-modules and R-module homomorphisms.

scholarly journals Using Digital Images to Teach Abstract Math and Inspire Students towardsCareers in Computer Science and Engineering

2020 ◽  
Author(s):  
Victor Mejia ◽  
Jessica Alvarenga ◽  
Jianyu Dong ◽  
Huiping Guo ◽  
Israel Hernandez ◽  
...  
Keyword(s):  
Computer Science ◽  
Digital Images ◽  
Science And Engineering

scholarly journals Soft rational line integral

2021 ◽  
Vol 31 (4) ◽  
pp. 578-596
Author(s):  
S. Acharjee ◽  
D.A. Molodtsov
Keyword(s):  
Computer Science ◽  
Set Theory ◽  
Soft Set ◽  
Theoretical Development ◽  
Classical Analysis ◽  
Computing Systems ◽  
Line Integral ◽  
Fundamental Properties ◽  
Necessary And Sufficient ◽  
Rational Line

Soft set theory is a new area of mathematics that deals with uncertainties. Applications of soft set theory are widely spread in various areas of science and social science viz. decision making, computer science, pattern recognition, artificial intelligence, etc. The importance of soft set-theoretical versions of mathematical analysis has been felt in several areas of computer science. This paper suggests some concepts of a soft gradient of a function and a soft integral, an analogue of a line integral in classical analysis. The fundamental properties of soft gradients are established. A necessary and sufficient condition is found so that a set can be a subset of the soft gradient of some function. The inclusion of a soft gradient in a soft integral is proved. Semi-additivity and positive uniformity of a soft integral are established. Estimates are obtained for a soft integral and the size of its segment. Semi-additivity with respect to the upper limit of integration is proved. Moreover, this paper enriches the theoretical development of a soft rational line integral and associated areas for better functionality in terms of computing systems.

scholarly journals An extension problem of a connectedness preserving map between Khalimsky spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 15-28 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Computer Science ◽  
Mathematical Morphology ◽  
Digital Images ◽  
Digital Topology ◽  
Extension Problem ◽  
Topological Spaces ◽  
Digital Geometry ◽  
Applied Topology ◽  
Continuous Map ◽  
Connected Sets

The goal of the present paper is to study an extension problem of a connected preserving (for short, CP-) map between Khalimsky (K-for brevity, if there is no ambiguity) spaces. As a generalization of a K-continuous map, for K-topological spaces the recent paper [13] develops a function sending connected sets to connected ones (for brevity, an A-map: see Definition 3.1 in the present paper). Since this map plays an important role in applied topology including digital topology, digital geometry and mathematical morphology, the present paper studies an extension problem of a CP-map in terms of both an A-retract and an A-isomorphism (see Example 5.2). Since K-topological spaces have been often used for studying digital images, this extension problem can contribute to a certain areas of computer science and mathematical morphology.

Taking the Lid off the Utah Teapot

2012 ◽  
Vol 3 (1) ◽  
pp. 169-184 ◽  
Author(s):  
Ann-Sophie Lehmann
Keyword(s):  
Visual Culture ◽  
Computer Science ◽  
Media Studies ◽  
Art History ◽  
Digital Images ◽  
Theoretical Concepts ◽  
The Impact

Der Beitrag stellt die These auf, dass der Einfluss digitaler Bilder auf visuelle Kultur nur verstanden werden kann, wenn die spezifische Materialität dieser Artefakte bedacht wird. Anhand einer Analyse des berühmten Utah teapot werden fünf materiale Schichten unterschieden, darunter Herstellung, Codierung, forensische und epistemische Materialität, sowie der Begriff der Trans-Materialität. Jede Schicht wird in Beziehung zu theoretischen Konzepten von Materialität in Medienwissenschaften, Kunstgeschichte, Computerwissenschaft und Anthropologie diskutiert. </br></br>This article argues that the impact of digital images on visual culture can only be understood if the specific materiality of these artefacts is taken into account. An analysis of the famous distinguishes five material layers, including making, coding, forensic and epistemic materiality, as well as the notion of trans-materiality. Each layer is developed in relation to theoretical concepts of materiality in media studies, art history, computer science, and anthropology.

Research on the Development and Applications of Computer Science and Technology

2014 ◽  
Vol 926-930 ◽  
pp. 2406-2409
Author(s):  
Xiao Guang Li
Keyword(s):  
Computer Science ◽  
Complexity Theory ◽  
Protein Structures ◽  
Computer Memory ◽  
Theory Of Computation ◽  
Access To Information ◽  
Computer Scientist ◽  
Fundamental Properties ◽  
Intractable Problems ◽  
Computational Systems

Computer science (abbreviated CS or CompSci) is the scientific and practical approach to computation and its applications. It is the systematic study of the feasibility, structure, expression, and mechanization of the methodical processes (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to information, whether such information is encoded in bits and bytes in a computer memory or transcribed engines and protein structures in a human cell. A computer scientist specializes in the theory of computation and the design of computational systems. Its subfields can be divided into a variety of theoretical and practical disciplines. The computational complexity theory which explores the fundamental properties of computational and intractable problems, are highly abstract, while fields such as computer graphics emphasize real-world visual applications.

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