PROBABILITY: A NOTE

2020 ◽  
Author(s):  
JAYDIP DATTA
Keyword(s):  
Wave Function ◽  
Partition Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Probabilistic Approach ◽  
Wave Functions ◽  
P Wave ◽  
Multiplicative Rule

Wave Function , Probability Density Function , Multiplicative Probability , Partition function .In this note we correlate a quantum normalized probabilistic approach with Algebric approach of Probability . The Probability Density [ Shi ]^2 may be equated as additive wave functions ie [Shi A] +[ Shi B ] . In real probability algebra we also know that P(A) +P(B )= P ( A*B ) . This is termed as multiplicative rule of Probability . Greater is P ( A*B ) = [ Shi ] ^2 greater will be the Probability Density F( x ) .

scholarly journals WAVE FUNCTION TO PARTITION FUNCTION: A CORRELATION

2021 ◽  
Author(s):  
JAYDIP DATTA
Keyword(s):  
Wave Function ◽  
Partition Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Statistical Thermodynamics ◽  
Mathematical Probability ◽  
Function Correlation

In this note the statistical thermodynamics is correlated to wave function through mathematical probability. The note can be subdivided into two following portions.STATISTICS -THE BASIC OF STATISTICAL THERMODYNAMICS: A CORRELATION and PROBABILITY -A THE BASICS OF WAVE FUNCTION .Randomisation , Wave Function , Probability Density Function , Multiplicative Probability , Partition function , Correlation ( K.P ) coefficient , Probability , Weights , Stirring’s Approximation

A Method to Estimate Operational Fatigue Life of Aeronautical Structural Components and Experimental Verification Thereof - An Outline

2008 ◽  
Vol 23 (1) ◽  
pp. 77-88
Author(s):  
Henryk Tomaszek ◽  
Józef Żurek ◽  
Sylwester Kłysz
Keyword(s):  
Fatigue Life ◽  
Probability Density Function ◽  
Crack Length ◽  
Probability Density ◽  
Density Function ◽  
Experimental Verification ◽  
Probabilistic Approach ◽  
Structural Components ◽  
Load Spectrum ◽  
Applied Method

A Method to Estimate Operational Fatigue Life of Aeronautical Structural Components and Experimental Verification Thereof - An OutlineThe study presents an attempt to estimate fatigue life of structural components with further verification of the applied method by means of testing the specimens taken. Therefore, it has been assumed that a specimen subjected to tests is a structural component of a real system, and operational loads have been simulated in the form of a predefined loading scheme. All parameters necessary for the method have been derived from the analyses of both the specimens subjected to tests and properties of the preset load spectrum.The applied method of fatigue life estimation represents a probabilistic approach based on the Paris formula for the crack growth rate, and on difference equations that after some transformation result in an equation of the Fokker-Planck type. A probability density function of a crack length is a solution to this equation and depends on either the total time of operating the component in question or the number of load cycles applied.The probability density function of a crack length has been used to find out a formula for the probability of not exceeding the permissible crack length against the number of load cycles. The derived relationship has been applied after normalization to estimate fatigue life as based on results of experimental examination of specimens made from titanium alloy.The nomenclature of the aeronautical engineering is used throughout the paper due to the assumption that the component exposed to tests represents a part of an aircraft. This, in turn, has been intended to show some specific application(s) of the formulated model.

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