scholarly journals Absolute Hidden Symmetry in Time and Absolute Asymmetry in Mass and Velocity between a Particle and Its Anti-Particle

2019 ◽  
Vol 11 (2) ◽  
pp. 43
Author(s):  
Eyal Brodet
Keyword(s):  
Cp Violation ◽  
Complex Number ◽  
Parity Violation ◽  
Hidden Variables ◽  
Neutral Kaon ◽  
Complex Numbers ◽  
Absolute Position ◽  
Mass Asymmetry ◽  
Hidden Symmetry ◽  
Energy And Momentum

In this paper we will the discuss possible hidden symmetry in time and the possible asymmetry in mass and velocity between a particle and its anti-particle. Possible hidden symmetry in time between a particle and its anti-particle manifested in their corresponding possible hidden variables in time, fr and -fr  was first discussed in Brodet (2017b). In this paper we will extend the discussion and discuss how the above possible hidden symmetry in time and its corresponding possible symmetry in absolute position, energy and momentum, may yield an asymmetry in mass and velocity of a particle and its corresponding anti-particle. We will deconstruct the particle’s and anti-particle’s absolute position, into three complex number describing the particle/anti-particle time, velocity and mass. The particle/anti-particle symmetry and asymmetry of the above complex numbers will be discussed in the context of parity violation and the known asymmetry in angular production of particles and anti-particles. Moreover, the possible mass asymmetry will be used to explain the CP violation in the neutral kaon system. Finally, experimental ways to investigate and test the above are presented.

scholarly journals Winding Numbers, Unwinding Numbers, and the Lambert W Function

2021 ◽  
Author(s):  
A. F. Beardon
Keyword(s):  
Complex Plane ◽  
Complex Number ◽  
Lambert W Function ◽  
Complex Numbers ◽  
Winding Number ◽  
Line Integral ◽  
Complex Functions

AbstractThe unwinding number of a complex number was introduced to process automatic computations involving complex numbers and multi-valued complex functions, and has been successfully applied to computations involving branches of the Lambert W function. In this partly expository note we discuss the unwinding number from a purely topological perspective, and link it to the classical winding number of a curve in the complex plane. We also use the unwinding number to give a representation of the branches $$W_k$$ W k of the Lambert W function as a line integral.

Encircling Graphs

2017 ◽  
Author(s):  
Arthur Benjamin ◽  
Gary Chartrand ◽  
Ping Zhang
Keyword(s):  
Nineteenth Century ◽  
Real Number ◽  
Traveling Salesman Problem ◽  
Complex Number ◽  
Traveling Salesman ◽  
Complex Numbers ◽  
Real Numbers ◽  
Hamiltonian Graphs ◽  
The World ◽  
The Traveling Salesman Problem

This chapter considers Hamiltonian graphs, a class of graphs named for nineteenth-century physicist and mathematician Sir William Rowan Hamilton. In 1835 Hamilton discovered that complex numbers could be represented as ordered pairs of real numbers. That is, a complex number a + b i (where a and b are real numbers) could be treated as the ordered pair (a, b). Here the number i has the property that i² = -1. Consequently, while the equation x² = -1 has no real number solutions, this equation has two solutions that are complex numbers, namely i and -i. The chapter first examines Hamilton's icosian calculus and Icosian Game, which has a version called Traveller's Dodecahedron or Voyage Round the World, before concluding with an analysis of the Knight's Tour Puzzle, the conditions that make a given graph Hamiltonian, and the Traveling Salesman Problem.

scholarly journals The generalized criterion of multiaxial random fatigue based on conception proposed by prof. Macha

2019 ◽  
Vol 300 ◽  
pp. 15001
Author(s):  
Tadeusz Łagoda ◽  
Marta Kurek ◽  
Karolina Łagoda
Keyword(s):  
Shear Stress ◽  
Complex Number ◽  
Mathematical Problem ◽  
Equivalent Stress ◽  
Complex Stress ◽  
Complex Numbers ◽  
Pure Bending ◽  
Pure Torsion ◽  
Special Cases ◽  
Random Fatigue

This criterion has been repeatedly verified, analyzed and special cases of this criterion reducing complex stress to equivalent uniaxial were taken into account. Since both normal and shear stress are vectors, we encounter the mathematical problem of adding these vectors, and the question arises how to understand the obtained equivalent stress, because two perpendicular vectors are added with weighting factors. Therefore, in this work it was proposed to adopt a system of complex numbers. Normal stress was defined as the real part and shear stress as imaginary part. As a result, on the basis of the defined complex number and basing on pure bending and pure torsion after transformations, the expression for equivalent stress was identical to the previously proposed criteria defined on the basis of the concept of prof. Macha.

Measurement of the CP-Violation Parameterη+−γin Neutral Kaon Decays

1993 ◽  
Vol 70 (17) ◽  
pp. 2529-2532 ◽  
Author(s):  
E. J. Ramberg ◽  
G. J. Bock ◽  
R. Coleman ◽  
J. Enagonio ◽  
Y. B. Hsiung ◽  
...  
Keyword(s):  
Cp Violation ◽  
Neutral Kaon ◽  
Kaon Decays

scholarly journals Complex Number Vedic Multiplier and its Implementation in a Filter

2018 ◽  
Vol 7 (2.24) ◽  
pp. 336
Author(s):  
N Saraswathi ◽  
Lokesh Modi ◽  
Aatish Nair
Keyword(s):  
Complex Number ◽  
Digital Signal ◽  
Digital Signal Processors ◽  
Complex Numbers ◽  
Fast Speed ◽  
Vedic Multiplier ◽  
X 32 ◽  
Signal Processors ◽  
Complex Multiplier ◽  
Mathematical Process

Complex numbers multiplication is a fundamental mathematical process in systems like digital signal processors (DSP). The main     objective of complex number multiplication is to perform operations at lightning fast speed with less intake of power. In this paper, the best possible architecture is designed for a Real vedic multiplier based on the ancient Indian mathematical procedure known as URDHVA TIRYAKBHYAM SUTRA i.e. the structure of a MxM Vedic real multiplier architecture is developed. Then, a Vedic real multiplier solution of a complex multiplier is presented and its simulation results are obtained. The MxM Vedic real multiplier architecture, architecture of the Real Vedic  multiplier solution for 32 x 32 bit complex numbers multiplication of complex multiplier and the architecture of a FIR filter has been code in Verilog and implementation is done through Modelsim 5.6 and Xilinx ISE 7.1 navigator. 

scholarly journals On lp-Complex Numbers

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 877
Author(s):  
Wolf-Dieter Richter
Keyword(s):  
Symmetry Group ◽  
Complex Number ◽  
Common Property ◽  
Complex Numbers ◽  
Trigonometric Functions ◽  
Absolute Value ◽  
Basic Properties ◽  
The Common

Dispensing with the common property of distributivity and replacing classical trigonometric functions with their l p -counterparts in Euler’s trigonometric representation of complex numbers, classes of l p -complex numbers are introduced and some of their basic properties are proved. The collection of all points that leave the l p -absolute value of each l p -complex number invariant under l p -complex numbers multiplication is shown to be a group of elements that have l p -absolute value one but not the symmetry group.

scholarly journals Beyond Google’s PageRank: Complex Number-based Calculations for Node Ranking

2019 ◽  
pp. 1-12
Author(s):  
K. Sugihara
Keyword(s):  
Complex Number ◽  
Link Analysis ◽  
Complex Numbers ◽  
Damping Factor ◽  
Node Ranking ◽  
Alternative Algorithm ◽  
Centrality Score

This study is focused on a proposed alternative algorithm for Google's PageRank, named Hermitian centrality score, which employs complex numbers for scoring a node of the network to overcome the issues of PageRank’s link analysis. This study presents the Hermitian centrality score as a solution for the problems of PageRank, which are associated with the damping factor of Google’s algorithm. The algorithm for Hermitian centrality score is designed to be free from a damping factor, and it reproduces PageRank results well. Moreover, the proposed algorithm can mathematically and systematically change the point of a node of a network.

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