Raman scattering plays a key role in unraveling the quantum dynamics of graphene, perhaps the most promising material of recent times. It is crucial to correctly interpret the meaning of the spectra. It is therefore very surprising that the widely accepted understanding of Raman scattering, i.e., Kramers-Heisenberg-Dirac theory, has never been applied to graphene. Doing so here, a remarkable me...

This paper presents the analysis, design, and characterization of the thirty gigahertz instrument receiver developed for the Q-U-I Joint Tenerife experiment. The receiver is aimed to obtain polarization data of the cosmic microwave background radiation from the sky, obtaining the Q, U, and I Stokes parameters of the incoming signal simultaneously. A comprehensive analysis of the theory behind t...

Restricted open-shell Kohn-Sham (ROKS) theory provides a powerful computational tool for calculating singlet excited state energies and dynamics. However, the possibility of multiple solutions to the ROKS equations - with the associated difficulty of automatically selecting the physically meaningful solution - limits its usefulness for intensive applications such as long-time Born-Oppenheimer m...

In this paper, a unified analytical approach is proposed to investigate vibrational behavior of functionally graded shells. Theoretical formulation is established based on Sanders’ thin shell theory. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stokes transformation. Material properties are assumed to be graded in...

The article surveys the application of complex ray theory to the scalar Helmholtz equation in two dimensions. The rst objective is to motivate a framework within which complex rays may be used to make predictions about waveeelds in a wide variety of geometrical conngurations. A crucial ingredient in this framework is the r^ ole played by Stokes' phenomenon in determining the regions of existenc...

The equation for evolution of the four-component Stokes vector in weakly anisotropic and smoothly inhomogeneous media is derived on the basis of a quasi-isotropic approximation of the geometrical optics method, which provides the consequent asymptotic solution of Maxwell's equations. Our equation generalizes previous results obtained for the normal propagation of electromagnetic waves in strati...

Given a nonstationary trajectory of the Navier–Stokes system, a finitedimensional feedback boundary controller stabilizing locally the system to the given solution is constructed. Moreover the controller is supported in a given open subset of the boundary of the domain containing the fluid and acts normal to the boundary. In a first step a controller is constructed that stabilizes the linear Os...

Last week we studied the key concepts of Finite Element Methods, in the context of solving the Laplace equation. We saw the …nite element method arise naturally as an instance of the Galerkin method, a discretization procedure for the corresponding weak formulation. Finally, we learned about error estimates, examples of elements and implementation practices. This week, our main objective is to ...

Combinatorics of complexes plays an important role in topology, nonlinear analysis, game theory, and mathematical economics. In 1967, Ky Fan used door-to-door principle to prove a combinatorial Stokes’ theorem on pseudomanifolds. In 1993, Shih and Lee developed the geometric context of general position maps, π-balanced and π-subbalanced sets and used them to prove a combinatorial formula for mu...