Physics Commons^™

Measurement Of Geometric Fractals On The Basis Of Hausdorf-Bezikovich And Minkovsky-Buligan Measurements, Anorova Amanbaevna Shaxzoda, Jabborov Sindorovich Jamoliddin, Meliyev Fattoevich Farxod

Scientific Bulletin. Physical and Mathematical Research

This article is devoted to the study of the future position of fractal measurements. Different methods of computer modeling of a wide range of classes of fractal geometric objects are described in detail, as well as the main methods of mathematical analysis of fractal size of virtual and real fractals are described. The article explains the differences between the concept of fractals, their properties, B. Mandelbrot's tariff, Hausdorf-Bezikovich scale, Minkowski-Buligan scale, topological measurement, the concept of fractal measurement and measurement in Euclidean geometry. This article provides basic information about fractals. A detailed description of the various methods of computer modeling …

Electromagnetic Properties Of Fractal Antennas, Jordan Jeffrey Ewing

Browse all Theses and Dissertations

Finite element method analysis is used to conduct electromagnetic simulations to characterize fractal antennas. This work considers wire (1D) antennas such as the triadic Koch curve, zig zag, and quadratic Koch curve of varying heights, iterations, and cross-sectional areas. Carpet (2D) antennas, including the Sierpinksi carpet, of varying heights, iterations, and deterministic and stochastic iterations are analyzed. The antenna shapes were generated in MATLAB and then modeled with finite element analysis using COMSOL Multiphysics®. The focus of this study is to determine what role various fractal patterns and iterations have on the S11 return loss and far field radiation patterns. …

Theoretical Investigation Of Interactions And Relaxation In Biological Macromolecules, Koki Yokoi

Theses and Dissertations

One of the major challenges posed to our quantitative understanding of structure, dynamics, and function of biological macromolecules has been the high level of complexity of biological structures. In the present work, we studied interactions between G protein-coupled receptors (GPCRs), and also introduced a theoretical model of relaxation in complex systems, in order to help understand interactions and relaxation in biological macromolecules.

GPCRs are the largest and most diverse family of membrane receptors that play key roles in mediating signal transduction between outside and inside of a cell. Oligomerization of GPCRs and its possible role in function and signaling currently …

Universal Scaling And Intrinsic Classification Of Electro-Mechanical Actuators, Sambit Palit, Ankit Jain, Muhammad A. Alam

Birck and NCN Publications

Actuation characteristics of electromechanical (EM) actuators have traditionally been studied for a few specific regular electrode geometries and support (anchor) configurations. The ability to predict actuation characteristics of electrodes of arbitrary geometries and complex support configurations relevant for broad range of applications in switching, displays, and varactors, however, remains an open problem. In this article, we provide four universal scaling relationships for EM actuation characteristics that depend only on the mechanical support configuration and the corresponding electrode geometries, but are independent of the specific geometrical dimensions and material properties of these actuators. These scaling relationships offer an intrinsic classification for …

The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun

Xiao-Jun Yang

The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform, used in Yang-Fourier transform in fractal space. This paper points out new standard forms of discrete Yang-Fourier transforms (DYFT) of fractal signals, and both properties and theorems are investigated in detail.

A Short Introduction To Local Fractional Complex Analysis, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent’s series of complex functions in complex fractal space, and generalized residue theorems are investigated.

A New Viewpoint To The Discrete Approximation: Discrete Yang-Fourier Transforms Of Discrete-Time Fractal Signal, Yang Xiao-Jun

Xiao-Jun Yang

It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated in detail.

Local Fractional Functional Analysis And Its Applications, Yang Xiao-Jun

Xiao-Jun Yang

Local fractional functional analysis is a totally new area of mathematics, and a totally new mathematical world view as well. In this book, a new approach to functional analysis on fractal spaces, which can be used to interpret fractal mathematics and fractal engineering, is presented. From Cantor sets to fractional sets, real line number and the spaces of local fractional functions are derived. Local fractional calculus of real and complex variables is systematically elucidated. Some generalized spaces, such as generalized metric spaces, generalized normed linear spaces, generalized Banach's spaces, generalized inner product spaces and generalized Hilbert spaces, are introduced. Elemental …

Local Fractional Integral Transforms, Yang X

Xiao-Jun Yang

Over the past ten years, the local fractional calculus revealed to be a useful tool in various areas ranging from fundamental science to various engineering applications, because it can deal with local properties of non-differentiable functions defined on fractional sets. In fractional spaces, a basic theory of number and local fractional continuity of non-differentiable functions are presented, local fractional calculus of real and complex variables is introduced. Some generalized spaces, such as generalized metric spaces, generalized normed linear spaces, generalized Banach’s spaces, generalized inner product spaces and generalized Hilbert spaces, are introduced. Elemental introduction to Yang-Fourier transforms, Yang-Laplace transforms, local …