Propagation of generalized Mathieu–Gauss beams through paraxial misaligned optical systems

Based on the generalized diffraction integral, we derive an analytical formula for generalized Mathieu–Gauss beams (gMGBs) passing through an apertured misaligned optical system. Furthermore, we use the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions to establish an approximate propagation equation of gMGBs through paraxial circularly apertured optical system. As an example, the propagation of ordinary and modified zeroth order MGBs through a misaligned thin lens is studied numerically.     

Flat-topped Mathieu-Gauss beam and its transformation by paraxial optical systems

In order to avoid the severe axial intensity oscillations which appear when an ideal Mathieu beam is truncated, we propose to modulate it by a flattened multi-Gaussian envelope. The obtained beam, which is referred as flattened Mathieu-Gauss (FTMG) beam, can be expanded into a finite series of Mathieu-Gauss beams with various waists. The propagation study of this beam reveals that the axial intensity is unchanged within a certain propagation distance as for super-Gaussian-Bessel beams or Gori’s flattened Bessel beams. By using Collins formula, we derive closed-form expressions of FTMG beam propagating through a paraxial axisymmetric ABCD optical system. Some numerical calculations and discussions are also given.     

Finite rank perturbations of contractions

We study finite rank perturbations of contractions of classC _.0 with finite defect indices. The completely nonunitary part of such a perturbation is also of classC _.0, while the unitary part is singular. When the defect indices of the original contraction are not equal, it can be shown that almost always (with respect to a suitable measure) the perturbation has no unitary part.     

A detailed study of Mathieu-Gauss beams propagation through an apertured ABCD optical system

Using Collins formula and the expansion of Mathieu beams in terms of Bessel beams we derive the exact propagation equations of Mathieu-Gauss beams through an apertured paraxial ABCD optical system. A comparison between the exact propagation equations and the approximated ones, which are derived by expanding the circ function into a finite sum of Gaussian functions, is presented. The propagation characteristics of zeroth-order Mathieu-Gauss beams in (y-z) and (x-z) planes are analyzed with detailed numerical calculations. It is found that the profile of the propagated Mathieu-Gauss beam is similar to that of Bessel-Gauss beam. Furthermore, the focalization of the Mathieu-Gauss beams through a thin lens is illustrated and analyzed with numerical results.     

Characteristic Functions for Multicontractions and Automorphisms of the Unit Ball

A multicontraction on a Hilbert space is an n-tuple of operators T = (T₁,..., T_n) acting on , such that . We obtain some results related to the characteristic function of a commuting multicontraction, most notably discussing its behaviour with respect to the action of the analytic automorphisms of the unit ball.     

New approach to the stereoselective synthesis of the [4.5] spiroketal moiety of papulacandins

An efficient approach for the stereoselective construction of the spiroketal moiety of papulacandins, based on the condensation of the protected derivative of D-arabino-1,4-lactone 2 with the α-lithiated carbanion of β-phenylsulfonyl dihydrofuran 1, is described.     

Inhibitory effect of a new isoniazid derivative as an effective inhibitor for mild steel corrosion in 1.0 M HCl: combined experimental and computational study

Research on Chemical Intermediates - Controlling corrosion of metals such as mild steel (MS), which is extensively employed in various industrial fields, is a topic of great interest for...     

Stereodynamics of Ar–CO rotation and conformational preferences of 2-amino-3-(2,4-difluorobenzoyl)-imidazo[1,2-a]pyridine

The dynamic NMR analysis of 2, a subunit of a new class of cyclic-dependent kinase inhibitors, reveals that the compound exists as two conformational isomers, Z and E, in acetone, as a consequence of the restricted rotation about the imidazopyridine–carbonyl bond. The less hindered Z-rotamer is the most abundant conformer (85:15 Z/E at 233 K) and the free energy of activation of the interconversion is 13.2 kcal mol⁻¹. The rotamer ratio and the interconversion barrier are similar in other solvents, such as CD₃OD and CDCl₃.     

Numerical Ranges of <Emphasis Type="Italic">C</Emphasis><Subscript>0</Subscript>(<Emphasis Type="Italic">N</Emphasis>) Contractions

A conjecture of Halmos proved by Choi and Li states that the closure of the numerical range of a contraction on a Hilbert space is the intersection of the closure of the numerical ranges of all its unitary dilations. We show that for C ₀(N) contractions one can restrict the intersection to a smaller family of dilations. This generalizes a finite dimensional result of Gau and Wu.     

Aluthge transforms of unbounded weighted composition operators in L2-spaces

We describe the Aluthge transform of an unbounded weighted composition operator acting in an L²-space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize p-hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation. We show that the only fixed points of the Aluthge transformation on weighted composition operators are quasinormal ones.