Nebo - P1 - Page 1 Greetings all ! I start with a couple of ideas about life ! what is life ? In its simplest form , life is nothing more than a way of decreasing entropy in expanse of producing heat . Hence , it's just another way of contributing heat death of universe . is it ok to live forever ? we loose the urgency of doing things . we will have always tomorrow , why to get up even ? So we cant achive nothing . even if we do things their value will drop by time . If given enough time you can achive anything . Now , lets do some math This is famous Parseval 's theorem : if you expand a function in a complete orthtonormal set than their square 's are related . Complete set can be Fourier , Legendre , Bessel etc . This is very useful . It can be even used to define completeness . Let 's
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Nebo - New 9 - Page 1 Happy new year blog On the last day of 2019 Lets solve some problems so that we prepare for 2019 . Did you know that there is no explicit formula for the indefinite integral : ∫ e - x 2 dx = ? But we have a value for definite integral ∫ 0 ∞ e - x 2 dx = π 2 Do you use the symmetry while solving definite integrals ? That is a useful trick ; any function can be written as g x = g e x
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Greetings all Recently I am asked about a hypothetical question, what changes if gravitation is nonexistent? It's always pleasure for me to think about the hypotetical questions since creative answers follow and profound description of real situation becomes available. We have to leave the comfortable zone of usual situations and have to think about from start by considering unusual first. gravitationless life • lets start from simple. No gravity means no gravitational force to hold us to the ground and no normal forces so no friction. If no friction we can't walk. • Momentum conservation helps we can move due to action-reaction by pulling and pushing around. • Your analog watch won't work since there is no gravity. Any device with a pendulum in it wont work. • Buoyoncy will be an issue. Convective heating will not happen. If you heat one part that heat wont propagate other parts. • Swimming wont be possible due to surface tension of water and the absence of
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Hello earthlings ! Last month of 2018 is upon us. Today, I would like to discuss "what life is" in terms of physics. In physics, a rock is not different than a kitten. The closest we got is nonlinear statistical mechanical theories of life. Prof. ilya prigogine was the frontier in this area. He got nobel prise in non equilibrium statistical mechanics. His work mainly consist of trying to show ordered structure can happen even if no equilibrium achived. Life itself is a non equilibrium phenomena, so there is some connection. Nowaday people are excited to do work in this area and try to describe life. As a matter of fact, I just started working in this area. you may check my old blogs about my preliminary work. It is also my privillage to do my phd in the ilya prigogine center of complex system while I was in UT austin. I attended Ilya prigogine's and coworkers seminars. I was asking so many questions in these seminars, one day he called me in his office and told me like
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Nebo - New5 - Page 1 Random variables , sure variables stochastic process → time evolution of random variables X(t) deterministic process → time evolution of sure variables . X ( t ) Assigning probability → statistical or frequency inductive - equal a priori independent event . expected values moments ⟨ X ⟩ = ∑ i x i P x i Probabilities → mean ( sure variables ) Mean(first moment ), Variance ( 2nd moment); skewness ( 3rd moment); kurtosis ( 4th moment ) v a r X = ⟨ X - ⟨ X ⟩ 2 ⟩ = ⟨