The main objective of mathematics is to amuse and delight. However, an interesting, and on occasion useful, byproduct is its capacity to describe, understand and predict natural phenomena and place us at the center of the universe around us.#To achieve these goals, mathematics often relies on...
In our numerical studies, we aim to compare different definitions on bounded domains using a collection of benchmark problems. We consider the fractional Poisson equation with both zero and nonzero boundary conditions, where the fractional Laplacian is defined according to the Riesz definition, the ...
With this type of GAN, a low-resolution image can be changed into a more detailed one. Super-resolution GANs increase image resolution by filling in blurry spots. Laplacian pyramid GAN. This GAN builds an image using several generator and discriminator networks, incorporating different levels of ...
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal r
Very roughly speaking, it asserts that on a regular graph of reasonably controlled growth (e.g. polynomial growth), random walks of length concentrate on the ball of radius or so centred at the origin of the random walk. Proof: Let be the graph Laplacian, thus for any , where is ...
where is a function of both time and space , with being the Laplacian operator. One can generalise this equation in a number of ways, for instance by replacing the spatial domain with some other manifold and replacing the Laplacian with the Laplace-Beltrami operator or adding lower order terms...
What is electromagnetism? Explain it with an example. Define p-n junction? For n \neq -1, what is the Laplacian \nabla^2r^n? What is meant by the dynamical theory of heat? What is the definition of theory? What is the work-energy theorem?
What is the Difference between Galilean/Newtonian physics and special relativity? Who was Newton? What can be concluded from Hubble's law? What is stated in Bernoulli's Theorem? What is the use of Bernoulli's Theorem? For n \neq -1, what is the Laplacian \nabla^2r^n?
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Unsupervised learning is a machine learning branch for interpreting unlabeled data. Discover how it works and why it is important with videos, tutorials, and examples.