In this paper we study controllability properties for semilinear degenerate parabolic equations with nonlinearities involving the first derivative in a bounded domain of R. Due to degeneracy, classical null controllability results do not hold in general. Thus we investigate results of ’regional null controllability’, showing that we can drive the solution to rest at time T on a subset of the sp...

Low-temperature photoluminescence-excitation spectra are studied in an n-type modulation-doped T-shaped single quantum wire with a gate to tune electron densities. With a nondegenerate one-dimensional (1D) electron gas, the band-edge absorption exhibits a sharp peak structure induced by the 1D density of states. When the dense 1D electron gas is degenerate at a low temperature, we observe a Fer...

We investigate stochastic homogenization for some degenerate quasilinear parabolic PDEs. The underlying nonlinear operator degenerates along the space variable, uniformly in the nonlinear term: the degeneracy points correspond to the degeneracy points of a reference diffusion operator on the random medium. Assuming that this reference diffusion operator is ergodic, we can prove the homogenizati...

An ultrahigh-Q, tunable optical filter with a FWHM bandwidth of 41 MHz is demonstrated. The filtering is produced by nondegenerate phase conjugation through four-wave mixing in atomic-sodium vapor. The filter is observed to have a maximum quantum efficiency of 4 x 10(-3). However, degenerate phase-conjugation experiments in sodium suggest that a quantum efficiency of greater than unity can be a...

A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. We say that a sweeping automaton is degenerate if the automaton has no left-moving transitions. We show that for each positive integer n, there is a nondeterministic finite automaton An over a two-letter alphabet such that An has n states, whereas the smallest equivalent nondegenerate swee...

In a nondegenerate system, the abelian Berry’s phase will never cause transitions among the Hamiltonian’s eigenstate. However, in a degenerate system, it is well known that the state transition can be caused by the non-abelian Berry phase. Actually, in a such a system, the phase factor is not always nonabelian. Even in the case that the phase is a nondiagonal matrix, it still can be an abelian ...

We analyze gene coexpression network under the random matrix theory framework. The nearest-neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral rigidity test follows random matrix prediction for a certain range and deviates afterwards. Eigenvector analysis of the network using inverse participation r...

Let {Xj} be a collection of real vector fields with C∞ coefficients, defined in a neighborhood of a point x0 ∈ R. Consider a second order differential operator L = − ∑ j X 2 j + ∑ j αjXj + β where αj, β are C ∞ real coefficients. A well known sufficient condition [17] for L to be C∞ hypoelliptic is that the Lie algebra generated by {Xj} should span the tangent space to R at x0. This bracket con...

The two-photon absorption, 2PA, cross sections of PbS quantum dots, QDs, are theoretically and experimentally investigated and are shown to be enhanced with increasing quantum confinement. This is in contrast to our previous results for CdSe and CdTe QDs where the reduced density of states dominated and resulted in a decrease in 2PA with a decrease in QD size. Qualitatively this trend can be un...