GENERALIZED EXCITED NEGATIVE BINOMIAL STATES OF ELECTROMAGNETIC FIELD AND SOME OF THEIR NON-CLASSICAL PROPERTIES

2003 ◽  
Vol 17 (07) ◽  
pp. 1071-1086 ◽  
Author(s):  
H. H. SALAH ◽  
M. DARWISH ◽  
A.-S. F. OBADA
Keyword(s):  
Electromagnetic Field ◽  
Correlation Function ◽  
Probability Distribution ◽  
Wigner Function ◽  
Coherent States ◽  
Negative Binomial ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
New States ◽  
Q Function

New states of electromagnetic field, generalized excited negative binomial states are introduced here. These states interpolate between the superposition of two excited coherent states and number states. The non-classical properties for these states are discussed, such as, second order correlation function, squeezing phenomena [normal squeezing and amplitude squared squeezing], phase properties in Pegg–Barnett formalism and the quasi-probability distribution functions (Q-function and Wigner function).

scholarly journals Definite Probabilities from Division of Zero by Itself Perspective

2020 ◽  
pp. 1-26
Author(s):  
Wangui Patrick Mwangi
Keyword(s):  
Probability Distribution ◽  
Negative Binomial ◽  
Random Variable ◽  
Distribution Functions ◽  
Point Of View ◽  
Basic Knowledge ◽  
Probability Distribution Functions ◽  
New Findings ◽  
Wide Range ◽  
New Finding

Over the years, the issues surrounding the division of zero by itself remained a mystery until year 2018 when the mystery was solved in numerous ways. Afterwards, the same solutions provided opened many other doors in academic space and one of the applications is in sure probabilities. This research is all about the sure probabilities computed from the zero divided by itself point of view. The solutions obtained in the computations are in harmony with logic and basic knowledge. A wide range of already existing probability distribution functions has been applied in different scenarios to compute the sure probabilities unanimously and new findings have also been encountered along the way. Some of the discrete and continuous probability distribution functions involved are the binomial, hypergeometric, negative binomial, Poisson, normal and exponential among others. It has been found in this work that sure probabilities can be evaluated from the division of zero by itself perspective. Another new finding is that in case of combinatorial, if the numerator is smaller than the denominator, then the solutions tend to zero when knowledge in gamma functions, integrations and factorials is applied. Again, if the case of continuous pdf involves integration and random variable specified in the direction of the parameter, then indirect computation of such probabilities should be applied. Finally, it has been found that the expansion of the domains of some of the parameters in some existing probability distribution functions can be considered and the restriction in conditional probabilities can be revised.

Probability Distribution Functions for the Random Forced Burgers Equation

1997 ◽  
Vol 78 (10) ◽  
pp. 1904-1907 ◽  
Author(s):  
Weinan E ◽  
Konstantin Khanin ◽  
Alexandre Mazel ◽  
Yakov Sinai
Keyword(s):  
Probability Distribution ◽  
Burgers Equation ◽  
Distribution Functions ◽  
Probability Distribution Functions

SOME FEATURES OF SQUEEZED NEGATIVE BINOMIAL STATE

1992 ◽  
Vol 06 (03n04) ◽  
pp. 409-415 ◽  
Author(s):  
AMITABH JOSHI ◽  
S. V. LAWANDE
Keyword(s):  
Electromagnetic Field ◽  
Density Matrix ◽  
Wigner Function ◽  
Negative Binomial ◽  
Thermal State ◽  
Photon Number ◽  
Binomial State ◽  
Relationship Of ◽  
The Relationship ◽  
Photon Number Distribution

Properties of electromagnetic field in the squeezed negative binomial state are investigated in terms of photon number distribution and Wigner function. The relationship of the density matrix of the squeezed negative binomial state to the density matrix of the squeezed thermal state is shown explicitly. The possibility of generation of the negative binomial state is also discussed.

Exploring probability distribution functions best-fitting the kinetic energy of coarse particles at above threshold flow conditions

2021 ◽  
Author(s):  
Hamed Farhadi ◽  
Manousos Valyrakis
Keyword(s):  
Probability Distribution ◽  
Kinetic Energy ◽  
Test Section ◽  
Particle Transport ◽  
River Flow ◽  
Distribution Functions ◽  
Transport Processes ◽  
Flow Conditions ◽  
Probability Distribution Functions ◽  
Transport Regime

<p>Applying an instrumented particle [1-3], the probability density functions of kinetic energy of a coarse particle (at different solid densities) mobilised over a range of above threshold flow conditions conditions corresponding to the intermittent transport regime, were explored. The experiments were conducted in the Water Engineering Lab at the University of Glasgow on a tilting recirculating flume with 800 (length) × 90 (width) cm dimension. Twelve different flow conditions corresponding to intermittent transport regime for the range of particle densities examined herein, have been implemented in this research. Ensuring fully developed flow conditions, the start of the test section was located at 3.2 meters upstream of the flume outlet. The bed surface of the flume is flat and made up of well-packed glass beads of 16.2 mm diameter, offering a uniform roughness over which the instrumented particle is transported. MEMS sensors are embedded within the instrumented particle with 3-axis gyroscope and 3-axis accelerometer. At the beginning of each experimental run, instrumented particle is placed at the upstream of the test section, fully exposed to the free stream flow. Its motion is recorded with top and side cameras to enable a deeper understanding of particle transport processes. Using results from sets of instrumented particle transport experiments with varying flow rates and particle densities, the probability distribution functions (PDFs) of the instrumented particles kinetic energy, were generated. The best-fitted PDFs were selected by applying the Kolmogorov-Smirnov test and the results were discussed considering the light of the recent literature of the particle velocity distributions.</p><p>[1] Valyrakis, M.; Alexakis, A. Development of a “smart-pebble” for tracking sediment transport. In Proceedings of the International Conference on Fluvial Hydraulics (River Flow 2016), St. Louis, MO, USA, 12–15 July 2016.</p><p>[2] Al-Obaidi, K., Xu, Y. & Valyrakis, M. 2020, The Design and Calibration of Instrumented Particles for Assessing Water Infrastructure Hazards, Journal of Sensors and Actuator Networks, vol. 9, no. 3, 36.</p><p>[3] Al-Obaidi, K. & Valyrakis, M. 2020, Asensory instrumented particle for environmental monitoring applications: development and calibration, IEEE sensors journal (accepted).</p>

Design for Project Change Management: Part 2 — Attribute Design

2004 ◽  
Author(s):  
D. Xue ◽  
S. Y. Cheing ◽  
P. Gu
Keyword(s):  
Optimal Design ◽  
Probability Distribution ◽  
Taguchi Method ◽  
Systematic Approach ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
Construction Tasks ◽  
Design Attribute ◽  
Value Changes ◽  
Design Aspect

This research introduces a new systematic approach to identify the optimal design configuration and attributes to minimize the potential construction project changes. The second part of this paper focuses on the attribute design aspect. In this research, the potential changes of design attribute values are modeled by probability distribution functions. Attribute values of the design whose construction tasks are least sensitive to the changes of these attribute values are identified based upon Taguchi Method. In addition, estimation of the potential project change cost due to the potential design attribute value changes is also discussed. Case studies in pipeline engineering design and construction have been conducted to show the effectiveness of the introduced approach.

Sign in / Sign up

Export Citation Format

Share Document