The first cohomology group of leaves and local stability of compact foliations

A foliation with all leaves compact (compact foliation) is called locally stable if every leaf has a basis of neighborhoods which are unions of leaves. We study the relationship between the first real cohomology group of leaves and the local stability of compact foliations. We show by example that the topology of the typical leaves (i.e. leaves with zero holonomy) has no influence on the local stability of the foliation while — at least for small codimensions — (less than 4 in general or less than 5 for foliations on compact minifolds) — a locally unstable foliation has a leaf F with infinite holonomy and a finite covering F' of F such that H¹(F'; IR) O. We also prove a related structural stability result for fibre bundles.     

Singularity-Free Two-Body Equation with Confining Interactions in Momentum Space

We are developing a covariant model for all mesons that can be described as quark-antiquark bound states in the framework of the Covariant Spectator Theory (CST) in Minkowski space. The kernel of the bound-state equation contains a relativistic generalization of a linear confining potential which is singular in momentum space and makes its numerical solution more difficult. The same type of singularity is present in the momentum-space Schrödinger equation, which is obtained in the nonrelativistic limit. We present an alternative, singularity-free form of the momentum-space Schrödinger equation which is much easier to solve numerically and which yields accurate and stable results. The same method will be applied to the numerical solution of the CST bound-state equations.     

Ultrasensitive method for the determination of 4-hydroxy-1-(3-pyridyl)-1-butanone-releasing DNA adducts by gas chromatography–high resolution mass spectrometry in mucosal biopsies of the lower esophagus

4-Hydroxy-1-(3-pyridyl)-1-butanone (HPB)-releasing DNA adducts are formed by metabolic activation of the tobacco-specific nitrosamines 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) and N′-nitrosonornicotine (NNN). NNK and NNN are considered carcinogenic to humans by the International Agency for Research on Cancer. Existing analytical methods for determination of HPB-releasing DNA adducts require 0.3–2.0 g of human target tissues such as lung and esophagus. For adduct determination in milligram amounts of biopsy samples, an ultrasensitive and specific method is presented using capillary gas chromatography coupled to a high-resolution mass spectrometer operated in the negative chemical ionization mode (GC-NCI-HRMS). The method has a limit of detection of 4.6 fmol HPB, a limit of quantification of 14.9 fmol HBP and a recovery of 45 ± 15%. Intra- and inter-day imprecision for N = 6 samples were calculated with coefficients of variation of <3.1%. Method applicability was evaluated with biopsies of esophageal mucosa (N = 14) yielding 5.6 ± 1.9 mg tissue and a mean adduct level of 6.13 ± 9.35 pmol HPB/mg DNA.     

Index theory for boundary value problems via continuous fields of -algebras

We prove an index theorem for boundary value problems in Boutet de Monvel's calculus on a compact manifold X with boundary. The basic tool is the tangent semi-groupoid generalizing the tangent groupoid defined by Connes in the boundaryless case, and an associated continuous field of C^*-algebras over [0,1]. Its fiber in =0, , can be identified with the symbol algebra for Boutet de Monvel's calculus; for ≠0 the fibers are isomorphic to the algebra of compact operators. We therefore obtain a natural map . Using deformation theory we show that this is the analytic index map. On the other hand, using ideas from noncommutative geometry, we construct the topological index map and prove that it coincides with the analytic index map.     

Synthesis and antigenic analysis of the BclA glycoprotein oligosaccharide from the Bacillus anthracis exosporium

The glycoprotein BclA is an important constituent of the exosporium of Bacillus anthracis spores. This glycoprotein is substituted with an oligosaccharide composed of a beta-L-rhamnoside substituted with the previously unknown terminal saccharide, 2-O-methyl-4-(3-hydroxy-3-methylbutanamido)-4,6-dideoxy-D-glucopyranose, also referred to as anthrose. Anthrose has not been found in spores of B. cereus and B. thuringiensis, making it a potential species-specific marker for B. anthracis. In order to study the antigenicity of anthrose, efficient syntheses of an anthrose-containing trisaccharide and a series of structurally related analogues were developed. The analogues lacked either the methyl ether at C-2 or contained modified C-4 amino functionalities of anthrose. The synthetic compounds were equipped with an aminopropyl spacer to facilitate conjugation to the carrier proteins mariculture Keyhole Limpet Hemocyanin (mcKLH) and bovine serum albumin (BSA). Serum antibodies of rabbits immunized with live or irradiated spores of B. anthracis Sterne 34F(2) were able to recognize the synthetic trisaccharide-mcKLH conjugate. The specificity of the interaction was confirmed by competitive inhibition with the free- and BSA-conjugated trisaccharides. Inhibition using the trisaccharide analogues demonstrated that the isovaleric acid moiety of anthrose is an important structural motif for antibody recognition. These data demonstrate that 1) anthrose is a specific antigenic determinant of the B. anthracis Sterne spore; 2) this antigen is presented to the immune system of rabbits receiving the anthrax live-spore vaccine; 3) synthetic analogues of the oligosaccharide retain the antigenic structure; and 4) the antigenic region is localized to specific terminal groups of the oligosaccharide. Collectively these data provide an important proof-of-concept step in the synthesis and development of spore-specific reagents for detection and targeting of non-protein structures in B. anthracis.     

Temperature dependent thermodynamic model of the system H(+)-NH₄(+)-Na(+)-SO₄²⁻-NO₃⁻-Cl⁻-H₂O

A thermodynamic model of the system H(+)-NH?(+)-Na(+)-SO?2?-NO??-Cl?-H?O is parametrized and used to represent activity coefficients, equilibrium partial pressures of H?O, HNO?, HCl, H?SO?, and NH?, and saturation with respect to 26 solid phases (NaCl(s), NaCl·2H?O(s), Na?SO?(s), Na?SO?·10H?O(s), NaNO?·Na?SO?·H?O(s), Na?H(SO?)?(s), NaHSO?(s), NaHSO?·H?O(s), NaNH?SO?·2H?O(s), NaNO?(s), NH?Cl(s), NH?NO?(s), (NH?)?SO?(s), (NH?)?H(SO?)?(s), NH?HSO?(s), (NH?)?SO?·2NH?NO?(s), (NH?)?SO?·3NH?NO?(s), H?SO?·H?O(s), H?SO?·2H?O(s), H?SO?·3H?O(s), H?SO?·4H?O(s), H?SO?·6.5H?O(s), HNO?·H?O(s), HNO?·2H?O(s), HNO?·3H?O(s), and HCl·3H?O(s)). The enthalpy of formation of the complex salts NaNH?SO?·2H?O(s) and Na?SO?·NaNO?·H?O(s) is calculated. The model is valid for temperatures < or approximately 263.15 up to 330 K and concentrations from infinite dilution to saturation with respect to the solid phases. For H?SO?-H?O solutions the degree of dissociation of the HSO?? ion is represented near the experimental uncertainty over wide temperature and concentration ranges. The parametrization of the model for the subsystems H(+)-NH?(+)-NO??-SO?2?-H?O and H(+)-NO??-SO?2?-Cl?-H?O relies on previous studies (Clegg, S. L. et al. J. Phys. Chem. A 1998, 102, 2137-2154; Carslaw, K. S. et al. J. Phys. Chem. 1995, 99, 11557-11574), which are only partly adjusted to new data. For these systems the model is applicable to temperatures below 200 K, dependent upon liquid-phase composition, and for the former system also to supersaturated solutions. Values for the model parameters are determined from literature data for the vapor pressure, osmotic coefficient, emf, degree of dissociation of HSO??, and the dissociation constant of NH? as well as measurements of calorimetric properties of aqueous solutions like enthalpy of dilution, enthalpy of solution, enthalpy of mixing, and heat capacity. The high accuracy of the model is demonstrated by comparisons with experimentally determined mean activity coefficients of HCl in HCl-Na?SO?-H?O solutions, solubility measurements for the quaternary systems H(+)-Na(+)-Cl?-SO?2?-H?O, Na(+)-NH?(+)-Cl?-SO?2?-H?O, and Na(+)-NH?(+)-NO??-SO?2?-H?O as well as vapor pressure measurements of HNO?, HCl, H?SO?, and NH?.