Roughly speaking, their argument proceeds by a multiscale construction, in which the solution is set up to eventually have some presence at a spatial scale , which is conducive to generating an exponential “stretching” of a small forcing term at a much higher spatial scale , which one then...
Work is done when the form of energy changes. A. False B. True Is it possible to convert energy to 100% work? What is the construction and working of an electric motor? Evaluate the integral: int 0 infty (sin (3x) + 2) d/dx delta (x - pi) x. ...
Theorem 3 The partition of a random monic polynomial of degree converges in distribution to the partition of a random permutation of length , in the limit where is fixed and the characteristic goes to infinity. We can quickly prove this theorem as follows. We first need a basic fact: Lem...
As it is shown in the first part of this short essay, duality plus conservation laws allow the violation of Bell’s inequalities for any spatio-temporal separation. To dig deeper into particle dualism, in the second part, a class of models is proposed as a working framework. It encompasses...
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This is a geometric series, which can also be written as Given that , we can take the limit as approaches infinity, giving us the following expression for the total duration of the bounces: The term in (1) comes from the fact that there’s also some time before the first bounce. ⁂...
1. What is meant by luxury apartment? Luxury apartment is a high-end residence that emphasises superior construction, refined amenities, and premium location to provide an elevated living experience. 2. How do luxury apartments differ from regular apartments?
Emojis have become an integral part of our messaging experience, be it on WhatsApp, Snapchat, or Instagram. It helps us fill in many emotional and expressive cues, which are otherwise not available through texts. Over the years, many emojis covering life’s aspects have been added. However,...
An elliptic curve is a group of points of the form P=(x,y) and a special point "at infinity" that is an honorary member of the curve. These points satisfy some equations and most importantly, one can add two points on the curve to get another and this addition makes the curve into...
Because of the -spread hypothesis, it is hard for to contain any fixed large set. If we could apply this observation in the contrapositive to we could hope to get a good upper bound on the size of and hence on thanks to (4). One can also hope to improve such an upper bound by al...