Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces

Finsler and Lagrange spaces can be equivalently represented as almost Kahler manifolds enabled with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to perform a natural Fedosov-type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental Finsler functions on tangent bundles.Comment: the latex 2e variant of the manuscript accepted for JMP, 11pt, 23 page

Comparison of Recombinant Human Haptocorrin Expressed in Human Embryonic Kidney Cells and Native Haptocorrin

Haptocorrin (HC) is a circulating corrinoid binding protein with unclear function. In contrast to transcobalamin, the other transport protein in blood, HC is heavily glycosylated and binds a variety of cobalamin (Cbl) analogues. HC is present not only in blood but also in various secretions like milk, tears and saliva. No recombinant form of HC has been described so far. We report the expression of recombinant human HC (rhHC) in human embryonic kidney cells. We purified the protein with a yield of 6 mg (90 nmol) per litre of cell culture supernatant. The isolated rhHC behaved as native HC concerning its spectral properties and ability to recognize both Cbl and its baseless analogue cobinamide. Similar to native HC isolated from blood, rhHC bound to the asialoglycoprotein receptor only after removal of terminal sialic acid residues by treatment with neuraminidase. Interestingly, rhHC, that compared to native HC contains four excessive amino acids (…LVPR) at the C-terminus, showed subtle changes in the binding kinetics of Cbl, cobinamide and the fluorescent Cbl conjugate CBC. The recombinant protein has properties very similar to native HC and although showing slightly different ligand binding kinetics, rhHC is valuable for further biochemical and structural studies

A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope

A derivation of the Ces\`aro-Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-linear boundaries. Several results are obtained that relate the coefficients, $b_i$, in the Shephard-Todd polynomial to the geometry of the fundamental domain. For the 3-sphere we show that $b_4$ is given by the ratio of the volume of the fundamental tetrahedron to its Schl\"afli reciprocal.Comment: Plain TeX, 26 pages (eqn. (86) corrected

Cohomologies of the Poisson superalgebra

Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on $R^{2n}$ ($C^{2n}) are investigated under suitable continuity restrictions on cochains. The first and second cohomology spaces in the trivial representation and the zeroth and first cohomology spaces in the adjoint representation of the Poisson superalgebra are found for the case of a constant nondegenerate Poisson superbracket for arbitrary n>0. The third cohomology space in the trivial representation and the second cohomology space in the adjoint representation of this superalgebra are found for arbitrary n>1.Comment: Comments: 40 pages, the text to appear in Theor. Math. Phys. supplemented by computation of the 3-rd trivial cohomolog

Fluorescent angiography of chicken embryo and photobleaching velocimetry

Fluorescent angiography approach in application to a living chicken embryo is discussed. It provides precise vessel wall detection and demonstrates usefulness for real time monitoring of vasoconstriction and vasodilatation related to self regulation of vascular network as well as to response to external factors. On the other hand, high stability of fluorescence and long period of dye elimination makes variations of fluorescent intensity practically independent from fast variations of blood flow rate. Therefore, we proposed the improvement of fluorescent angiography technique by introduction of photobleaching fluorescent velocimetry approach. We have developed the imaging system for intravital microscopic photobleaching velocimetry and tested it by using a glass capillary tube as a model of blood vessel. We demonstrated high potential of the technique for instant flow velocity distribution profile measurement with high spatial and temporal resolution up to 2 μm and 60 ms, respectively

Traces for star products on the dual of a Lie algebra

In this paper, we describe all traces for the BCH star-product on the dual of a Lie algebra. First we show by an elementary argument that the BCH as well as the Kontsevich star-product are strongly closed if and only if the Lie algebra is unimodular. In a next step we show that the traces of the BCH star-product are given by the \ad-invariant functionals. Particular examples are the integration over coadjoint orbits. We show that for a compact Lie group and a regular orbit one can even achieve that this integration becomes a positive trace functional. In this case we explicitly describe the corresponding GNS representation. Finally we discuss how invariant deformations on a group can be used to induce deformations of spaces where the group acts on.Comment: 18 pages, LaTeX2e. Updated reference

Uniformization and an Index Theorem for Elliptic Operators Associated with Diffeomorphisms of a Manifold

We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely differential operators with shifts induced by the action of an isometric diffeomorphism. The key to the solution is the method of uniformization: We assign to the nonlocal problem a pseudodifferential operator with the same index, acting in sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah-Singer index theorem.Comment: 16 pages, no figure

Formality theorems for Hochschild chains in the Lie algebroid setting

In this paper we prove Lie algebroid versions of Tsygan's formality conjecture for Hochschild chains both in the smooth and holomorphic settings. In the holomorphic setting our result implies a version of Tsygan's formality conjecture for Hochschild chains of the structure sheaf of any complex manifold and in the smooth setting this result allows us to describe quantum traces for an arbitrary Poisson Lie algebroid. The proofs are based on the use of Kontsevich's quasi-isomorphism for Hochschild cochains of R[[y_1,...,y_d]], Shoikhet's quasi-isomorphism for Hochschild chains of R[[y_1,...,y_d]], and Fedosov's resolutions of the natural analogues of Hochschild (co)chain complexes associated with a Lie algebroid.Comment: 40 pages, no figure

Miscellaneous notes on the genus Forsstroemia in Russia (Neckeraceae, Bryophyta)

Molecular phylogenetic analysis supports the position on the species known as Neckera konoi in the genus Forsstroemia, therefore it is transferred to this genus with a new combination, F. konoi (Broth.) Enroth, Fedosov & Ignatov. Molecular data also confirm the position of F. stricta Laz. described from the Russian Far East in F. producta, a pantropical species. Forstroemia neckeroides is reported from Russia, Primorsky Territory, for the first time.Peer reviewe

Lagrange-Fedosov Nonholonomic Manifolds

We outline an unified approach to geometrization of Lagrange mechanics, Finsler geometry and geometric methods of constructing exact solutions with generic off-diagonal terms and nonholonomic variables in gravity theories. Such geometries with induced almost symplectic structure are modelled on nonholonomic manifolds provided with nonintegrable distributions defining nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and Fedosov nonholonomic manifolds provided with almost symplectic connection adapted to the nonlinear connection structure. We investigate the main properties of generalized Fedosov nonholonomic manifolds and analyze exact solutions defining almost symplectic Einstein spaces.Comment: latex2e, v3, published variant, with new S.V. affiliatio