scholarly journals Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Agustín Pérez-Ramírez ◽  
Julian Guerrero Juk ◽  
Rafael Sanchez-Lara ◽  
Joel Antonio Trejo-Sánchez ◽  
Lelio de la Cruz-May
Keyword(s):  
Group Theory ◽  
Sparse Matrices ◽  
Point Sources ◽  
Multiplicative Complexity ◽  
Binary Images ◽  
Symmetry Properties ◽  
Digital Holograms ◽  
Additive Complexity ◽  
Symmetrical Group ◽  
The Creation

This work presents an algorithm to reduce the multiplicative computational complexity in the creation of digital holograms, where an object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image. The image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity (k-1)N2 for the case of sparse matrices or binary images, where k is the number of pixels other than zero and N2 is the total of points in the image.

Symmetrical group theory for mathematical complexity reduction of digital holograms

2017 ◽  
Vol 24 (5) ◽  
pp. 647-652
Author(s):  
A. Perez-Ramirez ◽  
J. Guerrero-Juk ◽  
R. Sanchez-Lara ◽  
M. Perez-Ramirez ◽  
M. A. Rodriguez-Blanco ◽  
...  
Keyword(s):  
Group Theory ◽  
Complexity Reduction ◽  
Digital Holograms ◽  
Symmetrical Group

Elements of Group Theory

2021 ◽  
pp. 51-110
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Group Theory ◽  
Lie Groups ◽  
Lorentz Group ◽  
Unitary Representations ◽  
Compact Groups ◽  
Mathematical Language ◽  
Group Representations ◽  
Infinite Groups ◽  
Infinite Dimensional ◽  
Symmetry Properties

The mathematical language which encodes the symmetry properties in physics is group theory. In this chapter we recall the main results. We introduce the concepts of finite and infinite groups, that of group representations and the Clebsch–Gordan decomposition. We study, in particular, Lie groups and Lie algebras and give the Cartan classification. Some simple examples include the groups U(1), SU(2) – and its connection to O(3) – and SU(3). We use the method of Young tableaux in order to find the properties of products of irreducible representations. Among the non-compact groups we focus on the Lorentz group, its relation with O(4) and SL(2,C), and its representations. We construct the space of physical states using the infinite-dimensional unitary representations of the Poincaré group.

The symmetry of electron diffraction zone axis patterns

1976 ◽  
Vol 281 (1301) ◽  
pp. 171-194 ◽  
Keyword(s):  
Electron Microscopy ◽  
Group Theory ◽  
Graphical Representation ◽  
Zone Axis ◽  
Fast Electrons ◽  
Extinction Contour ◽  
Symmetry Properties ◽  
Point Groups ◽  
Diffraction Patterns ◽  
Convergent Beam

The convergent beam and bend extinction contour techniques of electron microscopy are capable of providing much more information than can be obtained from conventional diffraction patterns and it is the objective of this work to examine the symmetry properties of each of these patterns. The diffraction of fast electrons by a thin parallelsided slab has been studied by group theory and by a graphical construction. We find that the pattern symmetries may be described by thirty-one diffraction groups and that each of these diffraction groups is isomorphic to one of the point groups of diperiodic plane figures and to one of the thirty-one Shubnikov groups of coloured plane figures. A graphical representation of each diffraction group is given, together with tables showing how the diffraction groups are related to the specimen point groups and under certain assumptions to the crystal point groups. These tables assume the symmetric Laue condition and ignore the presence of irreducible lattice translations normal to the slab. By using the tables, crystal point groups can be obtained from convergent beam or bend contour patterns. The method is demonstrated by experiments on several materials, but particularly on germanium and gallium-arsenide specimens since the similarity of these materials exemplifies the sensitivity of the technique.

scholarly journals Every Outcome Counts

2020 ◽  
Vol 3 ◽  
pp. 24-31
Author(s):  
Jeden O. Tolentino
Keyword(s):  
Probability Theory ◽  
Graph Theory ◽  
Group Theory ◽  
Visual Art ◽  
Home Country ◽  
The Philippines ◽  
The Creation ◽  
Young Immigrants

I approached the creation of these four graphics as a convergence of the skills and knowledge that I brought from my home country, the Philippines, and those that I have acquired in Canada. Combining abstract mathematics and visual art, I used concepts from graph theory, group theory, and probability theory to show a pictorial flow comparing the muddled situation in which young immigrants to Canada find themselves to the “optimal” albeit assimilated situation of those who have had time to settle (in multiple senses) into their new lives.

scholarly journals Calculation of One-Electron Wave Functions and Energy Levels of N-Butane Molecule on the Basis of Slater Atomic Orbitals

2021 ◽  
Vol 75 (3) ◽  
pp. 229-233
Author(s):  
Faig Pashaev ◽  
Arzuman Gasanov ◽  
Musaver Musaev ◽  
Ibrahim Abbasov
Keyword(s):  
Group Theory ◽  
Energy Levels ◽  
Wave Functions ◽  
Electron Wave ◽  
Hamilton Operator ◽  
Atomic Orbitals ◽  
Symmetry Properties ◽  
Symmetry Transformations ◽  
Space Symmetry ◽  
Polyatomic Systems

Abstract It is known that the application of the group theory greatly simplifies the problems of polyatomic systems possessing to any space symmetry. The symmetry properties of such systems are their most important characteristics. In such systems, the Hamilton operator is invariant under unitary symmetry transformations and rearrangements of identical particles in the coordinate system. This allows to obtain information about the character of one-electron wave functions — molecular orbitals — the considered system, i.e. to symmetrise the original wave functions without solving the Schrödinger equation.

scholarly journals Mapping Light Pollution, a CubeSat

2019 ◽  
Author(s):  
Anil Kumar Bheemaiah
Keyword(s):  
Imaging System ◽  
Point Sources ◽  
Pollution Monitoring ◽  
Light Pollution ◽  
Light Sources ◽  
Dual Use ◽  
Far Right ◽  
Delta Sleep ◽  
The Creation ◽  
Night Sky

Abstract:A key addition to the series of papers on non - lethal and reversible weapons, as a trail to peace, creating confidence through technocracy, this paper is on the design of linear light pollution monitoring satellites for combating the ugly menace of night sky pollution and towards PID roles in the creation of DSS support based on SaaS services for precision use of EMI based sleep inducing payloads in very light drones, potentially replacing inaccurate drone bombing.Keywords: PID systems, GIS, Cognitive Geography, Panoptic segmentation, Mapillary, DSS systems, SaaS, EMI Delta Sleep,LiFi, Integration filters(™).What: A dual use technology based on SaaS computing to map point sources of light pollution on the surface of the Earth with filters to distinguish stationary and moving sources. Dual use of this technology in remedying light pollution of the night sky for minimal circadian rhythm disruption and allied health disorders, and in the creation of filters for PID systems , useful in use cases, of anti insurgency strategy, with sleep weapon EMI integration as drone payloads.(Bheemaiah, n.d.)How:Light pollution is mapped using a cubesat imaging system originally developed for LiFi last mile connectivity from street lamps for 6G networking, but instead adopted on the trail-map to peace as a Peace Weapon(™) in anti insurgency strategy.Why:PID systems using moving light sources are critical in detecting insurgency across the pakistan India border, the LOC can be monitored using the above cubesat for confidence building measures as a PID system, to deter infiltration by subversives, preventing expensive disruption by infiltration of sabotage minded subversives.(“[No Title]” n.d.), Similar conflicts calling for peaceful resolution by reversible lethality is called for in technocracy, an apolitical far right strategy towards lasting peace, as endowed by K.O.D(™) or the King Of Doves(™), a symbol of peace.

Symmetry Properties in the Symmetry-Breaking of Nonsmooth Dynamical Systems

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
Alessio Ageno ◽  
Anna Sinopoli
Keyword(s):  
Group Theory ◽  
Stability Analysis ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Simply Supported ◽  
Symmetry Properties ◽  
Existence Conditions ◽  
Asymmetric Responses ◽  
The Stability ◽  
Nonsmooth Dynamical Systems

In this paper, the block simply supported on a harmonically moving ground is assumed as a system well representing a typical nonsmooth dynamical behavior. The aim of the work is to carry out the existence conditions of asymmetric responses; an analysis that comes first in any stability investigation. By using simple definitions belonging to the symmetry group theory, it is possible to completely clarify the relationships between the various initial conditions that allow simple asymmetric responses, and to develop tools, which will be very useful in the stability analysis of more complex asymmetric responses.

scholarly journals Orthonormalized basic of fractal stepped multiwavelets – a new multiwavelet technology for signal and image processing

2021 ◽  
pp. 91-95
Author(s):  
Lev Hnativ
Keyword(s):  
Image Processing ◽  
Computational Complexity ◽  
Classical Method ◽  
Multiplicative Complexity ◽  
New Class ◽  
Step Functions ◽  
Multiwavelet Transform ◽  
Additive Complexity ◽  
Linear And Nonlinear ◽  
Discrete Multiwavelet Transform

A new class of fractal step functions with linear and nonlinear changes in values is described, and on their basis a recurrent method for constructing functions of a new class of fractal step multiwavelets (FSMW) of various shapes with linear and nonlinear changes in values is developed. A method and an algorithm for constructing a whole family of basic FSMW systems have been developed. An algorithm for calculating the coefficients of a discrete multiwavelet transform based on a multiwavelet packet without performing convolution and decimated sampling operations, in contrast to the classical method, is presented. A method and algorithm for fast multiwavelet transform of low computational complexity has been developed, which, in comparison with the well-known classical Mall's algorithm, is 70 times less in multiplicative complexity, and 20 times less in additive complexity.

scholarly journals Space structures processed by the group supermatrix procedure

2011 ◽  
Vol 3 (3) ◽  
pp. 92-101
Author(s):  
Đorđe Zloković
Keyword(s):  
Mathematical Modeling ◽  
Group Theory ◽  
Space Structures ◽  
Symmetry Groups ◽  
Geometrical Configuration ◽  
Qualitative And Quantitative ◽  
Symmetry Properties ◽  
Conventional Methods

The shapes of natural and technical space structures may have geometrical configuration with symmetry properties that can be analyzed by superior mathematical modeling of the group theory, which has been shown in this paper by some aspects and results of the Author's group supermatrix procedure using the group supermatrix chain of the symmetry groups C2, D2, D2h and linear, rectangular, hexahedral and icosahedral configurations. This procedure formulates the analysis of structures composed according to definite space patterns with simple and complex symmetries, as well as symmetrized nonsymmetrical patterns, providing many qualitative and quantitative advantages in comparison with conventional methods.

The role of affect in feelings of obligation

2020 ◽  
Vol 43 ◽  
Author(s):  
Stefen Beeler-Duden ◽  
Meltem Yucel ◽  
Amrisha Vaish
Keyword(s):  
Positive Emotions ◽  
The Creation ◽  
Sense Of Obligation

Abstract Tomasello offers a compelling account of the emergence of humans’ sense of obligation. We suggest that more needs to be said about the role of affect in the creation of obligations. We also argue that positive emotions such as gratitude evolved to encourage individuals to fulfill cooperative obligations without the negative quality that Tomasello proposes is inherent in obligations.

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