The use of high energy laser-plasma sources in soft X-ray contact microscopy of living biological samples

In this paper the results of an experiment on soft X-ray contact microscopy using a laser-plasma source are presented. A resolution of 50 nm has been achieved imaging pig sperm cells, while other specimens, such as algae and yeast cells, showed internal details, proving the technique to be a powerful tool for biological investigations. Original biological information has been obtained and the conditions for optimal image formation have been studied. Received 5 June 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: batani@mib.infn.it     

A note on lattice congruence regularization

We give an example that answers in the negative Problem 11 of G. Gr?tzer and E. T. Schmidt, Regular congruence-preserving extensions of lattices. Received November 24, 1999; accepted in final form October 16, 2000.     

Stress Tensor Fluctuations and Stochastic Spacetimes

The physics of the quantum stress tensor operator is discussed. Although theproblem of defining the expectation values of this operator is reasonably wellunderstood, the fluctuations around the mean value are not so well understood.It is shown that the stress tensor correlation function can be decomposed intothree parts, one of which is finite and state dependent, one which is infinite inthe coincidence limit but state independent, and a cross term which is both statedependent and infinite in the coincidence limit. Possible physical interpretationsof each part are discussed. The fluctuations of the stress tensor in turn inducefluctuations of the spacetime geometry. The terms in the correlation functionwhich are singular in the coincidence limit seem to produce drastic fluctuationsof the geometry, leading to a stochastic spacetime. Whether these fluctuationsare observable is an unanswered question.     

J-Inner matrix functions, interpolation and inverse problems for canonical systems, II: The inverse monodromy problem

This is the second of a planned sequence of papers on inverse problems for canonical systems of differential equations. It is devoted to the inverse monodromy problem for canonical integral and differential systems. In this part, which focuses on the case of a diagonal signature matrixJ, a parametrization is obtained of the set of all solutionsM (t) for the inverse problem for integral systems in terms of two chains of entire matrix valued inner functions. Special classes of solutions correspond to special choices of these chains. This theme will be elaborated upon further in a third part of this paper which will be published in a subsequent issue of this journal. There the emphasis will be on symmetries and growth conditions all of which serve to specify or restrict the chains alluded to above, from the outside, so to speak.     

On a pair of axisymmetric forces inside a sphere

In this paper, the stresses in a sphere under a pair of concentrated forces acting axisymmetrically inside the sphere are solved by using a Love's stress function. The method of solution is also applied to solve the problem of a pair of ring forces acting axisymmetrically inside the sphere. In either problem, the solution covers the limiting case in which the pair of forces or ring forces is acting on the sphere.     

Combinatorial proof of the inversion formula on the Kazhdan–Lusztig R-polynomials

In this paper, we present a combinatorial proof of the inversion formula on the Kazhdan–Lusztig \(R\) -polynomials. This problem was raised by Brenti. As a consequence, we obtain a combinatorial interpretation of the equidistribution property due to Verma stating that any nontrivial interval of a Coxeter group in the Bruhat order has as many elements of even length as elements of odd length. The same argument leads to a combinatorial proof of an extension of Verma’s equidistribution to the parabolic quotients of a Coxeter group obtained by Deodhar. As another application, we derive a refinement of the inversion formula for the symmetric group by restricting the summation to permutations ending with a given element.     

Lithium cluster anions: photoelectron spectroscopy and ab initio calculations

Structural and energetic properties of small, deceptively simple anionic clusters of lithium, Li(n)(-), n = 3-7, were determined using a combination of anion photoelectron spectroscopy and ab initio calculations. The most stable isomers of each of these anions, the ones most likely to contribute to the photoelectron spectra, were found using the gradient embedded genetic algorithm program. Subsequently, state-of-the-art ab initio techniques, including time-dependent density functional theory, coupled cluster, and multireference configurational interactions methods, were employed to interpret the experimental spectra.     

The Reaction of P2I4 and N,N-dimethylformamide

P₂I₄ readily reacts with DME to give dimethyl-dodomethy leneammonium iodide, a compound of limited utility as a formylating agent.

Although diphosphorus tetraiodide (P₂I₄) has been known for many years, it has only recently sparked interest among organic chemists for use as a synthetic reagent. We initially became interested in P₂I₄ from a report that it cleanly reduced sulfoxides to sulfides.¹     

Novel Chiral,Sulfur-Containing Heteroarotinoids with Liquid Crystal Properties

Synthetic methods were developed to prepare ethyl (E)-4-[2-(3,4-dihydro-2-n-octyl-1-oxy-2H-1-benzothio-pyran-6-yl)-1-propenyl]benzoate ( 1 ) and ethyl (E)-4-[2-(3,4-dihydro-2-n-octyl-2H-1-benzothiopyran-6-yl)-1-propenyl]benzoate ( 10 ). These are the first examples of heteroarotinoids which possess properties of liquid crystals. The properties were evaluated using differential scanning calorimetry and by use of polarizing micrography. Both displayed textures which are typical of a smectic or cholesteric phase.