Use of the perturbation theory in the study of attributes of elastic waves propagating in weakly anisotropic media leads to approximate but transparent and simple formulas, which have many applications in forward and inverse wave modeling. We present and study such formulas. We show that all studied attributes depend on elements of a matrix linearly dependent on parameters of a medium. We study...

The topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of mic...

In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact, real analytic Riemannian manifold. Motivated by the “complexifier” approach of T. Thiemann as well as certain formulas of V. Guillemin and M. Stenzel, we obtain the polarization associated to the adapted complex structure by applying the “imaginary...

In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact, real-analytic Riemannian manifold. Motivated by the “complexifier” approach of T. Thiemann as well as certain formulas of V. Guillemin and M. Stenzel, we obtain the polarization associated to the adapted complex structure by applying the “imaginary...

Abstract We generalize Smirnov’s formula for the elliptic stable envelopes of Hilbert scheme points in $\mathbb {C}^2$ to case affine type $A$ Nakajima quiver varieties constructed with positive stability condition. allow arbitrary choices polarization and a fairly general choice chamber. This paper is companion Maple code developed by author, which implements formulas described this paper.

We calculate the vacuum polarization-induced ellipticity acquired by a linearly polarized laser beam of angular frequency ω̄ on traversing a region containing a transverse magnetic field rotating with a small angular velocity Ω around the beam axis. The transmitted beam contains the fundamental frequency ω̄ and weak sidebands of frequency ω̄±2Ω, but no other sidebands. To first order in small quan...

In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact, real analytic Riemannian manifold. Motivated by the “complexifier” approach of T. Thiemann as well as certain formulas of V. Guillemin and M. Stenzel, we obtain the polarization associated to the adapted complex structure by applying the “imaginary...

Abstract: Phase matching between the fundamental TE and TM modes is an essential condition for complete polarization rotation in magnetooptic waveguides with longitudinally directed magnetization. This condition can be satisfied with embedded square waveguides or with raised strip waveguides, provided that the core dimensions are suitably chosen. Based on coupled mode theory for the vectorial m...

Last decade improvement of the experimental facilities provided means of exploring the polarization phenomena in deep inelastic collisions and also gave rise to a still existing need for a suitable theory. From the first paper [-1] many theoretical works dealing with the spin alignment and polarization effects in heavy ion reactions have been done (see [-2] and references therein). A variety of...