A magnetic lens for cold atoms controlled by a rf field

We report on a new type of magnetic lens that focuses atomic clouds using a static inhomogeneous magnetic field in combination with a radio-frequency (rf) field. The experimental study is performed with a cloud of cold cesium atoms. The rf field adiabatically deforms the magnetic potential of a coil and therefore changes its focusing properties. The focal length can be tuned precisely by changing the rf frequency value. Depending on the rf antenna position relative to the dc magnetic profile, the focal length of the atomic lens can be either decreased or increased by the rf field. PACS 39.25.+k; 37.10.Gh     

Na10(Na,Mn)7Mn43(PO4)36: a new synthetic fillowite‐type phosphate

Na₁₀(Na,Mn)₇Mn₄₃(PO₄)₃₆ (sodium manganese phosphate) was synthesized hydrothermally at 873 K and 0.35 GPa. The complex crystal structure is almost identical to that of natural fillowite‐type phosphates and can be described as a hexagonal packing of three types of rods parallel to the c axis. The rods are constituted by an alternation of five‐ to seven‐coordinated Mn sites [average Mn—O = 2.243 (3) Å], of six‐ to nine‐coordinated Na sites [average Na—O = 2.590 (3) Å], of PO₄ tetrahedra [average P—O = 1.548 (3) Å] and of cation vacancies.     

Single-molecule stochastic times in a reversible bimolecular reaction

In this work, we consider the reversible reaction between reactants of species A and B to form the product C. We consider this reaction as a prototype of many pseudobiomolecular reactions in biology, such as for instance molecular motors. We derive the exact probability density for the stochastic waiting time that a molecule of species A needs until the reaction with a molecule of species B takes place. We perform this computation taking fully into account the stochastic fluctuations in the number of molecules of species B. We show that at low numbers of participating molecules, the exact probability density differs from the exponential density derived by assuming the law of mass action. Finally, we discuss the condition of detailed balance in the exact stochastic and in the approximate treatment.     

Discerning matrix-cluster peaks in matrix-assisted laser desorption/ionization time-of-flight mass spectra of dilute peptide mixtures

Matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry is widely used for the analysis of peptide mixtures such as those resulting from protein digestion. Among several useful peptide matrices, alpha-cyano-4-hydroxycinnamic acid (4-HCCA) appears to be the most popular. This matrix does not generally give matrix-cluster peaks at the mass region covered by enzyme-digested peptides (i.e., m/z above approximately 500). However, when an analyte mixture is very dilute and/or the sample contains a large amount of salts, ion peaks from matrix clusters can be quite intense, compared to peptide peaks. This matrix-cluster interference becomes more pronounced as the amount of analyte decreases. In this paper, a simple scheme for matrix-cluster identification is reported. It is shown that matrix-cluster formation follows a systematic pattern, although the relative intensities of these cluster ions cannot be predicted. Discerning the matrix-cluster peaks from the peptide peaks is found to be critical in analyzing dilute peptide mixtures with both conventional and microspot MALDI-TOF techniques.     

Desingularizations of quiver Grassmannians via graded quiver varieties

Inspired by recent work of Cerulli, Feigin and Reineke on desingularizations of quiver Grassmannians of representations of Dynkin quivers, we obtain desingularizations in considerably more general situations and in particular for Grassmannians of modules over iterated tilted algebras of Dynkin type. Our desingularization map is constructed from Nakajima's desingularization map for graded quiver varieties.     

A note on the Entropy/Influence conjecture

The Entropy/Influence conjecture, raised by Friedgut and Kalai (1996) [9], seeks to relate two different measures of concentration of the Fourier coefficients of a Boolean function. Roughly saying, it claims that if the Fourier spectrum is “smeared out”, then the Fourier coefficients are concentrated on “high” levels. In this note we generalize the conjecture to biased product measures on the discrete cube.