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...
is a purely mathematical construction, such that the concept of past, present and future is exclusively a consequence of the perception of this sequence of states. Which means that the only physical reality would be the state
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 ...
For GUE, which is a continuous matrix ensemble, one can also define for distinct as the unique quantity such that the probability that there is an eigenvalue in each of the intervals is in the limit . As is well known, the GUE process is a determinantal point process, which means that ...
The next step (following some ideas we found in a paper of Zhan) is to rewrite this estimate not in terms of the exponential sums , but rather in terms of the Dirichlet polynomial . After a certain amount of computation (including some oscillatory integral estimates arising from stationary pha...
in analysis, special case of the mean-value theorem of differential calculus. Rolle's theorem states thatif a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ ...
Gamma () is a term that shows up a lot in special relativity, and describes how much things get messed up by moving fast (time dilation, length contraction, mass increase, …). It’s fairly easy (pre-calculus easy) to show that . Notice from the graph below ...
1. Definition of Intensity: The intensity of a wave refers to the amount of energy that the wave carries per unit area in a specific amount of time. 2. Energy Transfer: When a wave travels through a medium, it transports energy. This energy is not concentrated in one spot but is distri...
Understanding a dataset, calledtime series analysis, can help to make better predictions, but is not required and can result in a large technical investment in time and expertise not directly aligned with the desired outcome, which is forecasting the future. ...
Recall that the time derivative of the velocity is acceleration. The information provided gives us the acceleration with appropriate initial conditions, so we just need to get the velocity function, then use the following formula for the dis...