Radiative Transfer in a Discrete Random Medium Adjacent to a Half-Space with a Rough Interface

For a macroscopically plane-parallel discrete random medium, the boundary conditions for the specific coherency dyadic at a rough interface are derived. The derivation is based on a modification of the Twersky approximation for a scattering system consisting of a group of particles and the rough surface, and reduces to the solution of the scattering problem for a rough surface illuminated by a plane electromagnetic wave propagating in a discrete random medium with non-scattering boundaries. In a matrix-form setting, the boundary conditions for the specific coherency dyadic imply the boundary conditions for specific intensity column vectors which in turn, yield the expressions for the reflection and transmission matrices. The derived expressions are shown to be identical to those obtained by applying a phenomenological approach based on a facet model to the solution of the scattering problem for a rough surface illuminated by a plane electromagnetic wave

A Nonlinear Plancherel Theorem with Applications to Global Well-Posedness for the Defocusing Davey-Stewartson Equation and to the Inverse Boundary Value Problem of Calderón

We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in $L^2$ for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calder\'on in dimension $2$, for conductivities \sigma>0 with $\log \sigma \in \dot H^1$. The proof of the nonlinear Plancherel theorem includes new estimates on classical fractional integrals, as well as a new result on $L^2$-boundedness of pseudo-differential operators with non-smooth symbols, valid in all dimensions

Vacuum Polarization on the Schwarzschild Metric with a Cosmic String

We consider the problem of the renormalization of the vacuum polarization in a symmetry space-time with axial but not spherical symmetry, Schwarzschild space-time threaded by an infinite straight cosmic string. Unlike previous calculations, our framework to compute the renormalized vacuum polarization does not rely on special properties of Legendre functions, but rather has been developed in a way that we expect to be applicable to Kerr space-time

Poisson structure and Action-Angle variables for the Camassa-Holm equation

The Poisson brackets for the scattering data of the Camassa-Holm equation are computed. Consequently, the action-angle variables are expressed in terms of the scattering data.Comment: 20 pages, LaTeX. The original publication is available at www.springerlink.co

Hybrid k⋅p\mathbf{k\cdot p}-tight-binding model for intersubband optics in atomically thin InSe films

We propose atomic films of n-doped $\gamma$-InSe as a platform for intersubband optics in the infrared (IR) and far infrared (FIR) range, coupled to out-of-plane polarized light. Depending on the film thickness (number of layers) of the InSe film these transitions span from $\sim 0.7$ eV for bilayer to $\sim 0.05$ eV for 15-layer InSe. We use a hybrid $\mathbf{k} \cdot \mathbf{p}$ theory and tight-binding model, fully parametrized using density functional theory, to predict their oscillator strengths and thermal linewidths at room temperature

Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid

We describe an instability of viscoelastic Couette-Taylor flow that is directly analogous to the magnetorotational instability (MRI) in astrophysical magnetohydrodynamics, with polymer molecules playing the role of magnetic field lines. By determining the conditions required for the onset of instability and the properties of the preferred modes, we distinguish it from the centrifugal and elastic instabilities studied previously. Experimental demonstration and investigation should be much easier for the viscoelastic instability than for the MRI in a liquid metal. The analogy holds with the case of a predominantly toroidal magnetic field such as is expected in an accretion disk and it may be possible to access a turbulent regime in which many modes are unstable.Comment: 4 pages, 4 figures, to be published in Physical Review Letter

Binary morphological shape-based interpolation applied to 3-D tooth reconstruction

In this paper we propose an interpolation algorithm using a mathematical morphology morphing approach. The aim of this algorithm is to reconstruct the $n$-dimensional object from a group of (n-1)-dimensional sets representing sections of that object. The morphing transformation modifies pairs of consecutive sets such that they approach in shape and size. The interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation. We prove the convergence of the morphological morphing. The entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets. We apply the interpolation algorithm for 3-D tooth reconstruction

Peran Orang Tua sebagai Pendidik Anak dalam Keluarga

Artikel ini membahas tentang peran orang tua sebagai pendidik anak dalam rumah tangga. Para sarjana Muslim banyak menukil ayat-ayat qur\u27an dan hadis sebagai dasar petingnya pendidikan anak dalam keluarga. Keluarga sebagai instrumen terkecil  dalam masyarakat dan sebagai peletak dasar sekaligus tempat pendidikan awal bagi setiap anak. Peran orang tua sangatlah pentingdalam pendidikan anak. Orang tua yang mampu memposisikan diri sebagai pelindung, pengayom, dan pendidik anak tentunya akan koheren dengan harapan agar mendapat calon generasi penerus yang baik, karena sifat dasar anak adalah membutuhkan kasih sayang dan rhatian dari orang tuanya. Wasiat Lukman al-Hakim dalam Q.S. Luqman ayat 13-19 merupakan manifestasi dari pentingnya pendidikan anak oleh orang tua dalam keluarga. Pendidikan dalam keluarga bukan hanya dibatasi dalam pendidikan agama saja, namun juga memberikan pendidikan akhlaq, kepribadian, dan sosial. Orang tua sepantasnya mampu melaksanakan pendidikan holistik kepada anak dalam keluarga sehingga mampu mewujudkan tujuan pendidikan yaitu menjadikan insan paripurna yang seimbang antara emosi, intelektual, dan spiritual