The Campbell-Hausdorff formula and invariant hyperfunctions

Toeplitz operators on strictly pseudo-convex boundaries of complex domains are defined; they behave like pseudo-differential operators. An extension of the Atiyah-Singer formula is proved for elliptic systems of such operators.     

Debromodispacamides B and D: isolation from the marine sponge Agelas mauritiana and stereoselective synthesis using a biomimetic proline route

New debromopyrrole-2-aminoimidazolones, debromodispacamide B (1) and debromodispacamide D (2) were isolated from the sponge Agelas mauritiana, collected in the Solomon Islands. A biomimetic one-step reaction from pseudopeptides 5 and 13 in presence of air oxygen and guanidine gave the chiral form of the natural product stereoselectively.     

MALDI-TOF/TOF CID study of 4-alkyl-substituted polystyrene fragmentation reactions

MALDI-TOF/TOF CID experiments were conducted on a variety of hydrogen-terminated poly(4-methylstyrene), hydroxylated poly(t-butylstyrene), and polystyrene precursor ions: n = 10, 15, 20, 25, and 30, where the number of repeat units n corresponds to the oligomer mass number. The influences of structure, molecular weight, and effective collision kinetic energy on degradation mechanisms were examined to test the generality of our multi-chain fragmentation model developed for polystyrene. Each depolymerization mechanism is presented in detail with experimental and computational data to justify/rationalize its occurrence and effective kinetic energy dependence. These processes show the complex interrelationship between the various pathways along with preferred production of secondary radicals, which suppresses the appearance of primary radicals. Additionally, Py-GC/MS experimental data are presented, for comparison of the multimolecular free radical reactions in pyrolysis with the unimolecular fragmentation reactions of MS/MS. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Correlations between chemical composition and provenance of Justino site ceramics by INAA

Instrumental neutron activation analysis (INAA), have been used for the definition of compositional groups of potteries from Justino site, Brazil, according to the chemical similarities of ceramic paste. The outliers were identified by means of robust Mahalanobis distance. The temper effect in the ceramic paste was studied by means of modified Mahalanobis filter. The results were interpreted by means of cluster, principal components, and discriminant analyses. This work provides contributions for the reconstruction of the prehistory of baixo São Francisco region, and for the reconstitution of the Brazilian Northeast ceramist population of general frame.     

Computation of the Highest Coefficients of Weighted Ehrhart Quasi-polynomials of Rational Polyhedra

This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient algorithm for computing the highest degree coefficients of the weighted Ehrhart quasi-polynomial for a rational simple polytope in varying dimension, when the weights of the lattice points are given by a polynomial function h. Our technique is based on a refinement of an algorithm of A.?Barvinok in the unweighted case (i.e., h≡1). In contrast to Barvinok’s method, our method is local, obtains an approximation on the level of generating functions, handles the general weighted case, and provides the coefficients in closed form as step polynomials of the dilation. To demonstrate the practicality of our approach, we report on computational experiments which show that even our simple implementation can compete with state-of-the-art software.     

Regulators of membrane trafficking and Mycobacterium tuberculosis phagosome maturation block

The biogenesis and maturation of phagosomes is an area of study which has been employing aspects of proteomic analyses and variations on that theme by identifying components on isolated organelles and following their dynamic changes and interactions with the endocytic pathway. In the case of Mycobacterium tuberculosis phagosome, the arrest of its maturation in infected macrophages, referred to in classical texts as the inhibition of phagosome-lysosome fusion, represents a phenomenon that is used to functionally dissect the phagosomal maturation pathway. In this review, we summarize the recent studies on regulators of membrane trafficking and other organelle components in the context of phagosomal biogenesis and mycobacterial phagosome maturation arrest.     

Vector partition functions and index of transversally elliptic operators

This is the first of a series of papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index theory are in [4], while in [5] and [6] we shall investigate the cohomological formulas generated by this theory.