In this paper, the concept of Abramov's method for transferring boundary conditions posed for regular ordinary diierential equations is applied to index 1 DAEs. Having discussed the reduction of inhomogeneous problems to homogeneous ones and analyzed the underlying ideas of Abramov's method, we consider boundary value problems for index 1 linear DAEs both with constant and varying leading matri...

We propose and demonstrate a global and efficient approach for scalar and vectorial beam shaping based on the interaction of circularly polarized light with a single piece of homogeneous anisotropic medium. The main idea is to mimic the behavior of a two-dimensional inhomogeneous birefringent medium with a radial distribution of its optical axis. This is done by transforming an incident Gaussia...

In metric Diophantine approximation there are two main types of approximations: simultaneous and dual for both homogeneous and inhomogeneous settings. The well known measure-theoretic theorems of Khintchine and Jarník are fundamental in these settings. Recently, there has been substantial progress towards establishing a metric theory of Diophantine approximations on manifolds. In particular, bo...

We describe an algorithm for locally-adaptive parameter estimation of spatially inhomogeneous Markov random elds (MRFs). In particular, we establish that there is a unique solution which maximizes the local pseudo-likelihood in the inhomogeneous MRF model. Subsequently we demonstrate how Besag's iterative conditional mode (ICM) procedure can be generalized from homogeneous MRFs to inhomogeneous...

We derive transport theoretic boundary conditions for acoustic wave reflection at a weakly rough boundary in an inhomogeneous half space. We use the Wigner distribution to go from waves to energy transport in the high frequency limit. We generalize known results on the reflection of acoustic plane waves in a homogeneous medium. We analyze higher order corrections, which include a enhanced backs...

A mathematical model of food recruitment and resource exploitation in group-living organisms accounting for direct traffic of individuals between the available sources is developed. It is shown that traffic between sources gives rise to the enhancement of the range of stability of the homogeneous mode of exploitation and of the range of coexistence of homogeneous and semi-inhomogeneous ones, as...

In Diophantine Approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that the inhomogeneous exponent of approximation to a generic point in R by a system of n linear forms is equal to the inverse of the uniform homogeneous exponent...