Creation of a sharper focus by using a rectified TEMp0 beam

The superresolution technique is usually used in optical imaging for its ability to make the central diffractive spot smaller than the Airy spot. In this paper, we apply the superresolution technique for transforming a symmetrical TEM_p0 Laguerre-Gauss beam into a Gaussian intensity distribution in the plane of a converging lens. The beam shaping is achieved by an annular binary Diffractive Optical Element having a transmittance, alternatively equal to −1 or + 1, modelled on the p light rings of the incident beam. It is observed that the rectified TEM₃₀ beam at focus has a focal volume 170 times smaller than that of a Gaussian beam.     

Absolute configuration of N-[(–)-2-(7-methoxy-1,2,3,4-tetra­hydro­-1-naphthyl)­ethyl]­cyclo­propyl­carbox­amide,a highly potent and selective melatonin analogue

The title compound, C₁₇H₂₃NO₂, a tetra­hydro­naphthalenic analogue of melatonin, crystallizes in the monoclinic space group P2₁ with one mol­ecule in the asymmetric unit. The crystal structure has been determined by X-ray analysis at room temperature. The absolute configuration of this compound was determined unambiguously as R at the chiral naphthalene C-1 position.     

Mixed Spin-1/2 and Spin-5/2 Model by Renormalization Group Theory: Recursion Equations and Thermodynamic Study

Using the renormalization group approximation, specifically the Migdal-Kadanoff technique, we investigate the Blume-Capel model with mixed spins S = 1/2 and S = 5/2 on d-dimensional hypercubic lattice. The flow in the parameter space of the Hamiltonian and the thermodynamic functions are determined. The phase diagram of this model is plotted in the (anisotropy, temperature) plane for both cases d = 2 and d = 3 in which the system exhibits the first and second order phase transitions and critical end-points. The associated fixed points are drawn up in a table, and by linearizing the transformation at the vicinity of these points, we determine the critical exponents for d = 2 and d = 3. We have also presented a variation of the free energy derivative at the vicinity of the first and second order transitions. Finally, this work is completed by a discussion and comparison with other approximation.     

Natural convection of non-Newtonian power law fluids in a shallow horizontal rectangular cavity uniformly heated from below

Analytical and numerical study is conducted for two-dimensional steady-state buoyancy driven flow of a non-Newtonian power law fluid confined in a shallow rectangular horizontal cavity uniformly heated from below, while its short vertical rigid sides are considered adiabatic. The effect of the non-Newtonian behaviour on the onset of convection, fluid flow, temperature field, and heat transfer is examined. A closed approximate analytical solution is developed on the basis of the parallel flow assumption and the obtained results are validated numerically by solving the full governing equations.     

Régio et périsélectivité de réactions de diels-alder et des cycloadditions dipolaires-1,3 avec une triazépine-1,2,4: Approche théorique

e.s The cycloaddition of 1,3-dipoles (mesitonitrile, C,N-dimethylnitrone) and various dienophiles (DMAD, maleic anhydride) to 1,2,4-triazepine 1 are peri and regiospecific. Nitrone excepted the preferred orientation of addition is predicted correctly by FMO/MNDO calculation.