Maximal operators and differentiation theorems for sparse sets

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Two weight inequalities for discrete positive operators

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Two weight inequalities for maximal truncations of dyadic Calderón-Zygmund operators

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Morphologic and morphometric aspects of oenocytes of Apis mellifera queens and workers in different phases of life

Oenocytes of adult workers and queens of Apis mellifera L. were studied in different ages or life stages, by means of morphometric and histologic techniques. In workers, the oenocytes were found in the head, near the mandibles and in the abdomen, immersed in the parietal fat body mainly below the sterna, close to the wax gland. In queens, two populations of oenocytes different in size and localization were found within the parietal and visceral fat body, respectively. The oenocytes of workers and queens show the presence of acid lipids and acid phosphatase. The role of these cells in the castes differences is discussed.

Coefficients of Drinfeld modular forms and Hecke operators

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The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Spectrum of Morphologic Changes of Lymph Nodes in HIV Infection

Cervical lymph nodes biopsies from 31 HIV positive patients (with or without AIDS) were studied by histologic methods and immunohistochemistry (StreptABC staining of paraffin sections) to identify cellular and extracellular matrix components. The results were the following: (1) the biopsies were included in the stages of follicular hyperplasia without fragmentation FH-FF (4 cases); follicular hyperplasia with follicular fragmentation FH+FF (16 cases); follicular involution FI (6 cases) and diffuse pattern DP (5 cases); (2) the most important alteration was the germinal centers disruption due to follicle lysis, which began in the light zone; (3) there was coincidence between intrafollicular hemorrhages and segmental hyaline mycroangiopathy; (4) during the progression of the disease occurred: (a) an increase in the number of mast cells, CD68+ and Mac387+ macrophages; (b) a diffuse augment of collagen III, elastic fibers, laminin, fibronectin and proteoglycans; (c) maintenance of Factor VIII - related antigens in the vascular endothelial cells, with decrease in the expression of Ulex-Europeus I lectin. Follicular hyperplasia (FH-FF or FH+FF) was the most common histologic pattern recognized in the lymph nodes of patients without AIDS and follicular involution and difuse pattern were seen in those who had AIDS. The results indicate that the lymph node biopsies may provide important information about the evolutive stage of the disease and its prognosis.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

Hankel operators on holomorphic Hardy-Orlicz spaces

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Morphologic aspects of Tetratrichomonas didelphidis isolated from opossums Didelphis marsupialis and Lutreolina crassicaudata

Tetratrichomonas didelphidis (Hegner & Ratcliffe, 1927) Andersen & Reilly, 1965 is a flagellate protozoan found in the intestine, cecum, and colon of Didelphis marsupialis. The parasitic protozoa used in this study was found and isolated in the intestine of opossums in Pavlova starch-containing medium in Florianópolis, State of Santa Catarina, Brazil, from D. marsupialis and Lutreolina crassicaudata. The strains were cultivated in Diamond medium without maltose and with starch solution, pH 7.5 at 28°C. The specimens were stained by the Giemsa method and Heidenhain's iron hematoxylin. The light microscopy study of the trophozoites revealed the same morphologic characteristics as specimens previously described.

Complex and real Hausdorff operators

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Moduli of smoothness and rate of a.e. convergence for some convolution operators

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Reduction theorems for operators on the cones of monotone functions

For a quasilinear operator on the semiaxis a reduction theorem is proved on the cones of monotone functions in Lp - Lq setting for 0 < q < ∞, 1<= p < ∞. The case 0 < p < 1 is also studied for operators with additional properties. In particular, we obtain critera for three-weight inequalities for the Hardy-type operators with Oinarov' kernel on monotone functions in the case 0 < q < p <= 1.