We consider linear overdetermined systems of partial differential equations. We show that the introduction of weights classically used for the definition of ellipticity is not necessary, as any system that is elliptic with respect to some weights becomes elliptic without weights during its completion to involution. Furthermore, it turns out that there are systems which are not elliptic for any ...

Optical-window birefringence is frequently a major obstacle in experiments measuring changes in the polarization state of light traversing a sample under investigation. It can contribute a signal indistinguishable from that due to the sample and complicate the analysis. Here, we explore a method to measure and compensate for the birefringence of an optical window using the reflection from the l...

We address theoretically and numerically the possibility of observing ellipticity in high-order harmonic generation (HHG) from aligned molecules driven by linearly polarized fields—a subject of controversy in the recent literature with significant implications. To that end we develop a numerical method for solution of the electronic dynamics and extend a recently developed theory of HHG from al...

Optical-window birefringence is frequently a major obstacle in experiments measuring changes in the polarization state of light traversing a sample under investigation. It can contribute a signal indistinguishable from that due to the sample and complicate the analysis. Here, we explore a method to measure and compensate for the birefringence of an optical window using the reflection from the l...

Thermal denaturation of chromatin is observed by simultaneously monitoring absorption and circular dichroism at 276 nm as functions of temperature. Either observation indicates that sheared chromatins shows less thermal stability than native chromatin. The temperature-dependent ellipticities at 276 nm of these chromatins show features not seen in the absorption curves: the ellipticity of unshea...

The properties of the Cosmic Microwave Background (CMB) maps carry valuable cosmological information. Here we report the results of the analysis of ellipticity of the hot and cold CMB anisotropy spots in the BOOMERanG 150 GHz map. We carried out this analysis for the map obtained by summing independent measurement channels (signal plus noise map) and for a comparison map (noise only map) obtain...

Among known strongly lensed quasar systems, ~25% have gravitational potentials sufficiently flat (and sources well aligned) to produce four images rather than two. The projected flattening of the lensing galaxy and tides from neighboring galaxies both contribute potential's quadrupole. Witt's hyperbola Wynne's ellipse permit determination overall quadrupole positions images. position resolves d...

Abstract Using the CO molecule as target, we investigate high-order harmonic generation by a bichromatic elliptically polarized laser field. This field consists of two components with commensurable frequencies and mutually orthogonal semi-major axes. Both odd even harmonics are emitted their ellipticity can be large depending on values laser-field parameters. It is often case that subsequent su...