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Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers of the differential operator

D = \frac{d}{dx} \,

and the integration operator J. (Usually J is used in favor of I to avoid confusion with other I-like glyphs and identities) Read the rest of this entry »


Implication A statement of the form :

 If p, then q.

 is called an implication or a conditional statement. 

Mathematicians have agreed that an implication will be called false only when the antecedent is true and the consequent is false.  That is to say when P is true and q  is false.  

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The following link is an abstract of the book by A D Aleksandrov on his view on Mathematics. A D Aleksandrov’s view of Mathematics Which introduce the methods, contents and meaning of mathematics. 

  • How much we know about the related topic which we are going to build new theory on.
  • What information are possibly useful for proving or disproving a new idea. Read the rest of this entry »

In mathematical analysisdistributions (also known as generalized functions) are objects which generalize functions and probability distributions. They extend the concept of derivative to all integrable functions and beyond, and are used to formulate generalized solutions of partial differential equations. They are important in physics and engineering where many non-continuous problems naturally lead to differential equations whose solutions are distributions, such as the Dirac delta distribution.

“Generalized functions” were introduced by Sergei Sobolev in 1935. They were independently introduced in the late 1940s by Laurent Schwartz, who developed a comprehensive theory of distributions.

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Stochastic analysis