Let u(x, t) be the solution of the Schrödinger or wave equation with L 2 initial data. We provide counterexamples to plausible conjectures involving the decay in t of the BMO norm of u(t, ·). The proofs make use of random methods, in particular, Brownian motion.

We consider solutions of the Schrödinger equation with a weak time-dependent random potential. It is shown that when the two-point correlation function of the potential is rapidly decaying then the Fourier transform ζ̂ε(t, ξ) of the appropriately scaled solution converges point-wise in ξ to a deterministic limit, exponentially decaying in time. On the other hand, when the two-point correlation f...

The aim of this study was to evaluate how fish locomote at different muscle temperatures. Sarcomere length excursion and muscle shortening velocity, V, were determined from high-speed motion pictures of carp, Cyprinus carpio (11-14 cm), swimming steadily at various sustained speeds at 10, 15 and 20 degrees C. In the middle and posterior regions of the carp, sarcomeres of the lateral red muscle ...

Theories on visual awareness claim that predicted stimuli reach awareness faster than unpredicted ones. In the current study, we disentangle whether prior information about the upcoming stimulus affects visual awareness of stimulus location (i.e., individuation) by modulating processing efficiency or threshold setting. Analogous research on stimulus identification revealed that prior informatio...

We prove a representation for the average wave function of the Schrödinger equation with a white noise potential in d = 1, 2, in terms of the renormalized self-intersection local time of a Brownian motion.

The effective dynamics of solitons for the generalized nonlinear Schrödinger equation in a random potential is rigorously studied. It is shown that when the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is almost surely described by Hamilton’s equations for a classical particle in the random potential, plus error terms d...

The basic aspects of the momentum picture of motion in Lagrangian quantum field theory are given. Under some assumptions, this picture is a 4-dimensional analogue of the Schrödinger picture: in it the field operators are constant, spacetime-independent, while the state vectors have a simple, exponential, spacetime-dependence. The role of these assumptions is analyzed. The Euler-Lagrange equatio...

This article describes the case of Cinema Fantasma, a Mexican Stop Motion animation studio. It presents process by which this firm designed and matured its business model, creative process, as well current methods creation production, prop character development. The research for study was made through use personal interviews with founders past employees; fieldwork research. main findings are fo...

The architectural curriculum has been based on the design studio class model which focuses on learning by doing and all processes and procedures of problem solving are transmitting trough lectures and critique sessions. The tutorial system in design studio classes is same as masterApprentice. So students learn during a communication between students and teachers and also between students. By th...