High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens

Recently, Dorn et al. [Phys. Rev. Lett. 91, 233901 (2003)] demonstrated the significance of radially polarized doughnut beams in obtaining very small focal spots (with an area of approximately 0.26 lambda2) with high-numerical-aperture (NA) aplanatic microscope objectives. We propose two simple alternative ways to focus such radially polarized beams: a parabolic mirror and a flat diffractive lens. Because of their large apodization factor for a high NA, a significant further reduction in spot area (up to a factor of 1.76 at a NA of 1) compared with the aplanatic system can be achieved.     

Baryogenesis at low reheating temperatures

We note that the maximum temperature during reheating can be much greater than the reheating temperature T(r) at which the universe becomes radiation dominated. We show that the standard model anomalous (B+L)-violating processes can therefore be in thermal equilibrium for 1 GeV less, similarT(r)<100 GeV. Electroweak baryogenesis could work and the traditional upper bound on the Higgs mass coming from the requirement of the preservation of the baryon asymmetry may be relaxed. Alternatively, the baryon asymmetry may be reprocessed by sphaleron transitions either from a (B-L) asymmetry generated by the Affleck-Dine mechanism or from a chiral asymmetry between e(R) and e(L) in a B-L = 0 universe.     

Tracking X‐ray‐derived redox changes in crystals of a methylamine dehydrogenase/amicyanin complex using single‐crystal UV/Vis microspectrophotometry

X‐ray exposure during crystallographic data collection can result in unintended redox changes in proteins containing functionally important redox centers. In order to directly monitor X‐ray‐derived redox changes in trapped oxidative half‐reaction intermediates of Paracoccus denitrificans methylamine dehydrogenase, a commercially available single‐crystal UV/Vis microspectrophotometer was installed on‐line at the BioCARS beamline 14‐BM‐C at the Advanced Photon Source, Argonne, USA. Monitoring the redox state of the intermediates during X‐ray exposure permitted the creation of a general multi‐crystal data collection strategy to generate true structures of each redox intermediate.     

A three dimensional dark focal spot uniformly surrounded by light

A new technique is proposed for generating a tight dark focal spot surrounded by uniform light intensity in all directions. It is based on a single focusing lens illuminated from one side, hence the alignment sensitivities associated with 4π methods are eliminated. Such a beam can be useful, e.g. as a dark atomic trap, and as the erase beam in three dimensional super-resolution fluorescence microscopy.     

Asymptotic infiltration into a soil which contains cracks or holes but whose surface is otherwise impermeable

An asymptotic, one-dimensional Green-Ampt model is derived for infiltration into a soil whose surface is impermeable except for regularly spaced vertical cracks, and infiltration into a cylindrical soil column whose top surface is also impermeable except for a central hole. The model is valid at times when the wetting front has become horizontal and corresponds to one-dimensional infiltration initiated from a plane lying above or below the soil surface, depending on the crack spacing/depth ratio (or column radius/hole depth ratio). When applicable, asymptotic Green-Ampt solutions are shown to agree well, in selected cases, with corresponding finite difference solutions of the saturated-unsaturated flow equations.     

PH-Bestimmungsmethoden

Ohne Zusammenfassung     

Synthesis of simplified analogues of eleutherobin via a Claisen rearrangement/RCM strategy

The enantioselective synthesis of a number of simplified analogues of the cytotoxic natural product eleutherobin is reported.     

Stereoselective synthesis of d-desosamine and related glycals via tungsten-catalyzed alkynol cycloisomerization

Stereoselective synthesis of d-desosamine diacetate ester (iii, R = Ac) was achieved from the glycal (ii). generated by tungsten carbonyl-catalyzed cycloisomerization of the corresponding amino-alkynol (i). A wide variety of N-substituents (R, R') are compatible with the cycloisomerization, provided that at least one R or R' is an acyl derivative.     

Curves of positive solutions of boundary value problems on time-scales

Let TR be a time-scale, with a=infT, b=supT. We consider the nonlinear boundary value problem

(2)

(4)

u(a)=u(b)=0,