06 Here's a cool non linear differential equation【这是一个很酷的非线性微分方程】 10:04 The trig integral of your dreams (or nightmares)【你梦(或噩梦)的三角积分】 14:35 两个最酷的积分 12:36 let's solve an impossible integral【让我们解决一个不可能的积分】 13:37 An incredible integral...
uses a set of up to 32 previous symbols as context to predict the most probable next symbol and thus effectively assigns a probability \(p\left({t}_{N}={s}_{j}|{t}_{1}^{N-1}\right)\) for any symbol type \({s}_{j}\in \mathcal{V}\) based on the text it has already ...
It would be reasonable to check Shinobu‘s expedition once a day, as 20 hours is close to 24. With Sara’s 15, however, you could do a 2-1 cycle: on the first day, check right when you wake up and right before bed (as most people are awake 16 hours), and then the next day ...
The t-test is one of the most fundamental forms of statistical analysis. Its goal is to determine whether the means (averages) of two sets of numbers are equal when you only have samples of the two sets. The idea is best explained by example. Suppose you’re investigating the mathematical...
Most importantly, the D-Wave quantum annealer and the associated hybrid solvers are no universal quantum computers. Therefore, we can only perform the QA algorithm on the hardware. In return, this means that we cannot use the ability of quantum computers to represent extensive data with ...
It is impossible to calculate Equation (17) for n → ∞ because different estimation methods have been proposed, such as approximate entropy [61] and Rényi entropy [62], and compression [63]. The Kolmogorov-Sinai entropy and conditional entropy coincide for a stochastic process X, where X n...
Euler's Identity is a remarkable equation that comprises the five most important mathematical constants.
Georgiev, V., Venkov, G.: On uniqueness for the generalized Choquard equation. In: Advances in Harmonic Analysis and Partial Differential Equations, Trends Math., pp. 263–278. Birkhäuser/Springer, Cham (2020) Ghimenti, M., Moroz, V., Van Schaftingen, J.: Least action nodal solutions ...
Equation (is of rectangular shape; representations, (s) are special subcases. Generalisation to arbitrary representations is known [72]. One can set the proportionality factor to be equal to one when, which fixes this factor for other values ofAandIdue to the relations (2.17). It is explicitl...
Forest-grassland mosaic ecosystems can exhibit alternative stables states, whereby under the same environmental conditions, the ecosystem could equally well reside either in one state or another, depending on the initial conditions. We develop a mathemat