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In this talk we introduce some recent developments of Heisenberg-Pauli-Weyl uncertainty principle in the different settings.
We focus on numerical study of the dynamical Ginzburg-Landau equations under the temporal gauge, and propose a decoupled numerical scheme based on the finite element method. For the variable A, the se...
A new class of high-order maximum principle preserving numerical methods is proposed for solving the semilinear Allen-Cahn equation. We start with the method consists of a $k$th-order multistep expone...
For ergodic SDEs, their ergodic limits are usually approximated by the suitable means of numerical methods. To reveal the numerical asymptotic behavior, we study the large deviations principle (LDP) f...
In this lecture, I will talk about the large deviation problems in random interlacements, in particular the LDP of the occupation measure, and discuss its relations to sharp asymptotic probabilities o...
KPZ limit for one-dimensional weakly asymmetric Ginzburg-Landau model was studied by Diehl-Gubinelli-Perkowski in a setting of martingale (energy) solution. Our goal is to apply a path-wise approach b...
In the waves off Southern California, germ warfare occurs in a struggle as old as life itself. That's where University of Southern California marine biologists recently completed a comprehensive new s...
Geochemists at Indiana University and Virginia Tech have developed and demonstrated a technique for assessing the validity of a principle that has long been important in thermodynamics and chemical ki...
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz.We assume either an appropriate measure growth condition with ...
Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDE’s with a small parameter at the second order derivatives are considered in th...
A dinner table seats k guests and holds n discrete morsels of food. Guests select morsels in turn until all are consumed. Each guest has a ranking of the morsels according to how much he would enjoy e...
Recently, something remarkable happened. The US Congress passed, and President Obama signed into law, five ocean-related bills that were included in the Public Lands Management Act of 2009. These five...
We consider possible violations of the equivalence principle through the exchange of a light “dilaton-like” scalar field. Using recent work on the quark-mass dependence of nuclear binding, we find tha...
Light scalar particles with couplings of sub-gravitational strength, which can generically be called 'dilatons', can produce violations of the equivalence principle. However, in order to understand ex...

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