A Holographic Prism Based on Photo-Thermo-Refractive Glass: Requirements and Possibilities

A technology for multivalued holographic measurement of a plane angle—a holographic prism, which serves as the basis for a device for calibrating the testing tools for navigational equipment under rolling— has been developed. The holographic prism is a miniature sample of photosensitive material, which contains a system of superimposed holographic gratings, and a laser the radiation of which passes through gratings to form a fan of diffracted beams. The fan in a prism based on a calcium fluoride (fluorite) crystal with color centers contained six out-of-plane beams radiating from a region with a hard-to-localize center. This fact hindered calibration of the measure and its application in the testing device. The use of photothermo-refractive glass as a material for preparing a sample and recording a system of holograms in it makes it possible to eliminate the drawbacks of fluorite-based prism. The number of holograms rises up to 21, the fan becomes in-plane, and its center is localized in a small region, with a size of several tenths of the sample thickness (1–2 mm). The fan beams are energetically homogeneous, and each can be identified when using the fan in a testing device.     

Euler characteristic in percolation theory

The notion of the Euler characteristic is introduced in percolation theory, which, in fact, was implicitly used from the very beginning of studying percolation problems. An exact formula is given for the case of the ball problem, along with some of its generalizations.     

Neutrino exchange and asymptotic behaviour of weak interaction cross sections

It is argued that total cross sections cannot increase asymptotically as a power of energy even in the presence of massless particle exchange. Elastic νν scattering is considered as an example. The properties of s- and t-channel partial waves are analysed and it is shown that the above statement is true if the amplitude is bounded by a polynomial in s for s→∞ and t>0 and if its singularity at t=0 is dominated by two-particle exchange.     

Aleksei Borisovich Kaidalov (July 20, 1940–July 25, 2010)

Physics of Atomic Nuclei -     

On the article of G. Gamow, D. Ivanenko, and L. Landau “World Constants and Limiting Transition”

This brief preface explains why the editorial board of the journal Yadernaya Fizika (Physics o f Atomic Nuclei) decided to reprint the article of the three authors, which was published in 1928 and which is hardly accessible to the present-day reader; tells briefly the history of its creation; and traces, from 1881 to 2001, the fate of the questions discussed in it and the impact of this article on modern fundamental physics.     

A remark on KL → 2μ decay and possible existence of new particles

The possibility of production of new particles in yet unobserved decay channels of the K_L meson is discussed in connection with the K_L → 2μ puzzle. Experimental possibilities of searching for these particles are considered.     

Measurement of bile acid CoA esters by high-performance liquid chromatography-electrospray ionisation tandem mass spectrometry (HPLC-ESI-MS/MS)

The novel and rapid assay presented here combines high-performance liquid chromatography and electrospray ionisation tandem mass spectrometry (HPLC-ESI-MS/MS) to directly measure and quantify the CoA esters of 3alpha,7alpha,12alpha-trihydroxy- and 3alpha,7alpha-dihydroxy-5beta-cholestan-26-oic acid (THCA and DHCA). The latter are converted inside peroxisomes to the primary bile acids, cholic and chenodeoxycholic acids, respectively. Prior to MS/MS, esters were separated by reversed-phase HPLC on a C(18) column using an isocratic mobile phase (acetonitrile/water/2-propanol) and subsequently detected by multiple reaction monitoring. For quantification, the CoA ester of deuterium-labelled 3alpha,7alpha,12alpha-trihydroxy-5beta-cholan-24-oic acid (d(4)-CA) was used as internal standard. To complete an assay took less than 8 min.To verify the validity of the assay, the effect of peroxisomal proteins on the efficacy of extraction of the CoA esters was tested. To this end, variable amounts of the CoA esters were spiked with a fixed amount of either intact peroxisomes or peroxisomal matrix proteins and then extracted using a solid-phase extraction system. The CoA esters could be reproducibly recovered in the range of 0.1-4 micromol l(-1) (linear correlation coefficient R(2) > 0.99), with a detection limit of 0.1 micromol l(-1).In summary, electrospray ionization tandem mass spectrometry combined with HPLC as described here proved to be a rapid and versatile technique for the determination of bile acid CoA esters in a mixture with peroxisomal proteins. This suggests this technique to become a valuable tool in studies dealing with the multi-step biosynthesis of bile acids and its disturbances in disorders like the Zellweger syndrome.     

Threshold intensity and coefficient of raman scattering amplification in a high-<Emphasis Type=Italic>Q</Emphasis> bilayer microresonator during the formation of internal and external submicron photonic jets: A photonic nanojet in the near field

Using quantum and semiclassical approaches, the energy excitation threshold for induced Raman scattering is estimated and a relationship between the excitation threshold and the concentration of optically active molecules in a bilayer microresonator is established. Estimates are made during the formation of specially configured optical fields: internal and external photonic nanojets. Based on the amount of stored energy per mode and the value of the threshold intensity, an additional generalized selection rule for whispering gallery modes is suggested. It is shown that the bilayer microresonator can focus incident radiation (laser pumping) into a submicron focal volume at a low threshold intensity.     

The strong Atiyah conjecture for right-angled Artin and Coxeter groups

We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.