New Raman Spectroscopic Data of the Almahata Sitta Meteorite

The archaeological site of Pintia (Padilla de Duero/Peñafiel, Valladolid), considered one of the first cities on the Iberian Peninsula, has yielded very interesting archaeological records regarding the different functional areas that involve the oppidum. Pottery, metal, and bone/skeletal remains are very well preserved, being optimal for analysis and study of the ancient food contained, such as milk-based products, animal fats, beer, and wine. The combination of Raman Microscopy (RM) with other analytical techniques such as Light Microscopy (LM) and Environmental Scanning Electron Microscopy equipped with Energy Dispersive X-ray Spectroscopy (ESEM-EDX) becomes a powerful tool to obtain information on the possible content in the ceramic receptacles from historical-archaeological heritage. It can lead to an interpretation of their specific use or functionality. In this work, a unique sample preparation was used for all techniques, which lead to a very simple procedure and documentation. The degradation and aging of natural fibers and the presence of organic matter with low crystallinity and calcium oxalate–related residuals can be studied by these combined techniques. The archaeological residuals can be separated from modern contamination coming from agriculture processes, surrounding land minerals, or fresh vegetal matter.     

Algebra Forms with $$d^{N} = 0$$ on Quantum Plane. Generalized Clifford Algebra Approach

We construct a q-analog of exterior calculus with a differential d satisfying d ^N = 0, where N ≥ 2 and q is a primitive Nth root of unity, on a noncommutative space and introduce a notion of a q-differential k-form. A noncommutative space we consider is a reduced quantum plane. Our construction of a q-analog of exterior calculus is based on a generalized Clifford algebra with four generators and on a graded q-differential algebra. We study the structure of the algebra of q-differential forms on a reduced quantum plane and show that the first order calculus induced by the differential d is a coordinate calculus. The explicit formulae for partial derivatives of this first order calculus are found.     

Invariant subsets of rank 1 manifolds

It is proved that for a Riemannian manifold M with nonpositive sectional curvature and finite volume the space of directions at each point in which geodesic rays avoid a sufficiently small neighborhood of a fixed rank 1 vector v∈UM looks very much like a generalized Sierpinski carpet. We also show for nonpositively curved manifolds M with dim M≥ 3 the existence of proper closed flow invariant subsets of the unit tangent bundle UM whose footpoint projection is the whole of M. Received: 6 July 2000 / Revised version: 11 October 2001     

Influence of noncontractile motion of plasmalemma upon cotton fiber cell wall structure

Unusual noncontractile motion in vivo within the fibers growing on cotton ovules was found for four cotton genotypes. Structural investigations have shown that, in addition to the active motion related to fiber cell growth, a simultaneous spiral rotation of the cytoplasmic membrane occurs. Due to translational growth of the fiber cell apices and spiral rotation of plasmalemma, the fibers of cotton cultivars take on a twisted, corkscrew-like external shape. Optical microphotos illustrate the formation process of the fiber cell wall at different stages of growth and noncontractile motion in cotton fiber cells.     

Cohomology of Subregular Tilting Modules for Small Quantum Groups

Let U be a quantumgroup with divid d powers at root ofunity constructed froma rootsystem R .Let u U b th small quantumgroup.Th cohomologyof u with trivial coefficients was computed by Ginzburg and Kumar.It turns out to be isomorphic to the functions algebra of the nilpotent cone of a semisimpl algebraic group with root system R .In this not we calculate cohomology of u with coefficients in simplest reducible tilting modul with nontrivial cohomology.It appears to b isomorphic to th functions algebra of th closure of the subregular nilpotent orbit.     

Research on orotron oscillator with dispersive open resonant system

Theoretical and experimental results of an investigation into a new resonant system have been obtained. This system is named the sphere-corner-echelette open resonator (SCEOR) due to the employment of a mirror that was formed by two echelettes at the angles of 45° to the resonator axis. It turns ont that this resonator is excited on the specific modes not unique to others oscillating systems. There are presented the results of the experimental research of the orotron oscillator with the SCEOR. The spectrum of this device contains only the fundamental modes such as theT E M ₀₀₆,T E M ₀₀₇,T E M ₀₀₈. The efficiency of the orotron is improved, when all other factors are the same the orotron with a much used sphere-cylindrical open resonator.