Exploring the Essential Spectrum of Normal Vibrations in Internal Waves: Insights from Specific Geometries and Explicit Eigenvalues | Chapter 11 | Research Updates in Mathematics and Computer Science Vol. 3

 Aims: For various models of three-dimensional fluid which describe the flows in the Atmosphere and the Ocean in the gravity field with the stratification of vertical density, we investigate a relation between the essential spectrum of normal vibrations of internal waves and non-uniqueness of the limit amplitude of vibrations induced by external mass forces. To make the study more detailed and descriptive, we find the explicit spectrum for some particular domains.

Methodology: Fourier Transform, Spectral Analysis of Self-Adjoint Operators in Hilbert Spaces.

Results: We establish a direct relation between the frequency of the induced vibrations, the essential spectrum, and the non-uniqueness of the limit amplitude. We also find the explicit eigenfunctions and the eigenvalues of the spectrum for rectangular, spherical and cylindrical domains.

Author(s) Details:

Andrei Giniatoulline,
Los Andes University, Carrera 1 No. 18ª-10, Bogota, Colombia.

Please see the link here: https://stm.bookpi.org/RUMCS-V3/article/view/14042

Educational Software for Analysis of Complex Networks Using the Spectral Graph Theory | Chapter 10 | Innovations in Science and Technology Vol. 3

 This paper presents instructional software for analysing complex networks and visualising algorithms using spectral graph theory. The system was written in the Java programming language and can run as a standalone Java application or a Java applet. A genuine system, such as a web or social network, or an Internet infrastructure network, is often referred to as a network. The mathematical representation of the network is a graph. To comprehend a system, one must first comprehend the graph that represents the system's network. The spectral graph theory explores the relationship between graphs and eigenvalues and eigenvectors. Specific topological aspects of a graph are used to characterise connectivity and have a significant impact on dynamic processes in complex networks. The technology allows for the design of a variety of laboratory tasks that allow students to visually track the processes that occur in complicated networks.

Author(S) Details

Nenad Jovanovic
Faculty of Technical Sciences, University of Pristina, Postal Addresses: Kneza Milosa 7, 38220, Kosovska Mitrovica, Serbia.

View Book:- https://stm.bookpi.org/IST-V3/article/view/5461