Experimental control of pattern formation by photonic lattices

We study the control of modulational instability and pattern formation in a nonlinear dissipative feedback system with a periodic modulation of the material refractive index. We use a one-dimensional photonic lattice in a single-mirror feedback configuration and identify three mechanisms for pattern control: bandgap suppression of instability modes, periodicity induced pattern modes, and orientational pattern control.The authors acknowledge the support of the Conseil Régional de Lorraine, the bilateral FrenchAustralian Science and Technology program, and the Australian Research Council through Discovery projects

Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media

The authors study experimentally the transverse second-harmonic generation of counterpropagating pulses by a quasi-phase-matching in a medium with a random ferroelectric domain structure. The authors show that this parametric process results in a direct realization of the cross correlation of two optical signals and, therefore, it can be employed for direct characterizations of ultrashort pulses including their temporal structure and pulse front tilt.The authors acknowledge the support of the Australian Research Council

Universal subspaces for compact Lie groups

For a representation of a connected compact Lie group G in a finite dimensional real vector space U and a subspace V of U, invariant under a maximal torus of G, we obtain a sufficient condition for V to meet all G-orbits in U, which is also necessary in certain cases. The proof makes use of the cohomology of flag manifolds and the invariant theory of Weyl groups. Then we apply our condition to the conjugation representations of U(n), Sp(n), and SO(n) in the space of $n\times n$ matrices over C, H, and R, respectively. In particular, we obtain an interesting generalization of Schur's triangularization theorem.Comment: 20 page

Yang-Mills fields on CR manifolds

We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR manifold.Comment: 52 page

Some Grüss' Type Inequalities in 2-Inner Product Spaces and Applications for Determinantal Integral Inequalities

Some new Grüss type inequalities in 2-inner product spaces are given. Using this framework, some determinantal integral inequalities for synchronous functions are also derived

An HST/STIS Optical Transmission Spectrum of Warm Neptune GJ 436b

GJ 436b is a prime target for understanding warm Neptune exoplanet atmospheres and a target for multiple JWST GTO programs. Here, we report the first space-based optical transmission spectrum of the planet using two HST/STIS transit observations from 0.53-1.03 microns. We find no evidence for alkali absorption features, nor evidence of a scattering slope longward of 0.53 microns. The spectrum is indicative of moderate to high metallicity (~100-1000x solar) while moderate metallicity scenarios (~100x solar) require aerosol opacity. The optical spectrum also rules out some highly scattering haze models. We find an increase in transit depth around 0.8 microns in the transmission spectra of 3 different sub-Jovian exoplanets (GJ 436b, HAT-P-26b, and GJ 1214b). While most of the data come from STIS, data from three other instruments may indicate this is not an instrumental effect. Only the transit spectrum of GJ 1214b is well fit by a model with stellar plages on the photosphere of the host star. Our photometric monitoring of the host star reveals a stellar rotation rate of 44.1 days and an activity cycle of 7.4 years. Intriguingly, GJ 436 does not become redder as it gets dimmer, which is expected if star spots were dominating the variability. These insights into the nature of the GJ 436 system help refine our expectations for future observations in the era of JWST, whose higher precision and broader wavelength coverage will shed light on the composition and structure of GJ 436b's atmosphere.Comment: 20 pages, 11 figures, 5 tables, Accepted to AJ. A full version of table 1 is included as table1_mrt.tx

Trapezoidal type inequalities related to h-convex functions with applications

A mapping M(t) is considered to obtain some preliminary results and a new trapezoidal form of Fejer inequality related to the h-convex functions. Furthermore the obtained results are applied to achieve some new inequalities in connection with special means, random variable and trapezoidal formula