Divergence & Probability Density : A Hypothesis

The earlier work by Datta et al ( 1 ) the note has been made with the algebraic properties of Probability ie P (A) +P(B )= P ( A*B ) . This is termed as multiplicative rule of Probability. By multiplication rule any number say a can be first diverged through a series of a ( pow ) x , Where x is an integer like 0 to n . REF :PROBABILITY & WAVEFUNCTION : A NOTE November 2019 DOI: 10.31219/osf.io/awk96

PROBABILITY: A NOTE

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 ) .

The Risks of Associated Use of Alcohool and Tabaco: A Functional Learning and Its Limits

Drinking alcohol and smoking tobacco commonly occur together. Young adults, middleaged adults, elderly people, and very elderly people perceive the combined effects on health of drinking and smoking as sub-additive. This model bears little resemblance to what is expected on the basis of epidemiological studies. The health risks of combining drinking and smoking, particularly the risk of cancer is multiplicative. This article reviews studies showing that learning the multiplicative relationship between daily intakes of alcohol and tobacco, and the risk of esophageal cancer is effective, even in 75 aged people, provided that participants receive outcome feedback through functional learning. This learning persists at least one month. This learning has limitations due to the decline of executive functioning that is associated with aging. The very old people have difficulty in learning the multiplicative rule. Instead, they learn an additive rule. Other studies are required. Because of the nature of the risks for esophageal cancer, specific groups should be targeted, those who drink and smoke heavily, and for whom esophageal cancer looms as an important personal threat.

A note on a breakdown of the multiplicative composition of inner and outer expansions

It is shown that the multiplicative rule of the method of matched asymptotic expansions fails under certain conditions. The velocity distribution in front of an elliptic airfoil is given as an example. The reason for the breakdown is explained by inspecting the usual formal justification of multiplicative composition.