Stationary points, also known as critical points, are points on a graph where the slope of the tangent line is equal to 0. To find stationary points in a function, you must first take the derivative of the function and set it equal to 0. Then, solve for the values of x that make ...
In this paper we revisit an open problem posed by Aldous on the max-entropy win-probability martingale: given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum entropy and hence gives the most excitement for the spectators?
is equivalent to the assertion that all the Furstenberg limits of Liouville with logarithmic averaging are equivalent to the Bernoulli system. Recently, I was able to prove the two-point version of the logarithmically averaged Chowla conjecture, for any non-zero integer ; this is equivalent to ...
From the semicircle law (and the fundamental theorem of calculus), one expects the eigenvalue spacing to have an average size of . It is thus natural to introduce the normalised eigenvalue spacing and ask what the distribution of is. As mentioned previously, we will focus on the bulk case ...
What Is a Derivative? In calculus, a derivative is the rate of change at a given point in a real-valued function. For example, the derivative f'(x) of function f() for variable x is the rate that the function f() changes at the point x. It might change a lot, e.g. be very...
I was the only one in my engineering math class who passed calculus, first time. Vanadium 50 said: Perhaps more to the point, the gravitational acceleration where the muons interact is only a few percent different that at the surface. Not that different from the poles vs. the equator ...
In the post “What is the nature of time?” the essence of time has been analyzed from the point of view of physics. Several conclusions have been drawn from it, which can be summarized in the following points: Time is an observable that emerges at the classical level from quantum reality...
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But from the fundamental theorem of calculus, the left-hand side can be written as and the claim then follows from the triangle inequality and a routine calculation. We are thus interested in getting good bounds on the sum . More generally, we consider normalised exponential sums of the ...
What does a function is twice differentiable? The function f is twice differentiable on the open set S′⊆ S if it is differentiable at each point in S′. If it is twice differentiable then it is calledsmoothor C2. If f(x) is twice differentiable then. evaluated at . ...