Muckenhoupt weights with singularities on closed lower dimensional sets in spaces of homogeneous type

We give sufficient conditions on a real number β and on a closed set F   in a general space of homogeneous type (X,d,μ)$(X,d,\mu )$ in such a way that μ(B(x,d(x,F)))^β$\mu {(B(x,d(x,F)))}^{\beta }$ becomes a Muckenhoupt weight. In order to prove our result, we modify the underlying space so that it becomes 1-Ahlfors regular.     

New diterpenoids from Calceolaria polifolia

Four new and seven known diterpenes have been isolated from the dichloromethane extract of the aerial parts of Calceolaria polifolia. The structures of the new compounds were established by spectroscopic evidence.     

Kinetic studies of urban solid residues and leachate from sanitary landfill

Urban solid residues are constituted of food remaining, grass leaves, fruit peelings, paper, cardboard, rubber, plastic, etc. The organic fraction formed represents about 50% during the decomposition yields biogas and leachate, which are sources of pollution. Residue samples were collected from the landfill in different and cells from several ages and the corresponding leachate, both after treatments, were submitted to thermal analysis. Kinetic parameters were determined using Flynn–Wall–Ozawa method. The linear relation between the two kinetic parameters (ln A and E) was verified for organic residue urban’s samples, but not for leachate’s sample. The occurred difference can be attributed to the constituents present in leachate.     

Role of Alginate Composition on Copper Ion Uptake in the Presence of Histidine or Beta-Amyloid

The anomalous interaction between metal ions and the peptide beta-amyloid is one of the hallmarks of Alzheimer’s disease. Metal-binding biopolymers, including polysaccharides, can elucidate the fundamental aspects of metal ions’ interactions with biological tissue and their interplay in Alzheimer’s disease. This work focuses on the role of the alginate composition on Cu(II) adsorption in the presence of histidine or β-amyloid, the peptide associated with the progression of Alzheimer’s disease. Alginate samples with different mannuronic/guluronic (M/G) ratios led to similar Cu(II) adsorption capacities, following the Langmuir isotherm and the pseudo-second-order adsorption kinetic models. Although the presence of histidine produced up to a 20% reduction in the copper adsorption capacity in guluronic-rich alginate samples (M/G~0.61), they presented stable bidentate chelation of the metallic ion. Chemical analyses (FTIR and XPS) demonstrated the role of hydroxyl and carboxyl groups in copper ion chelation, whereas both crystallinity and morphology analyses indicated the prevalence of histidine interaction with guluronic-rich alginate. Similar results were observed for Cu(II) adsorption in alginate beads in the presence of beta-amyloid and histidine, suggesting that the alginate/histidine system is a simple yet representative model to probe the application of biopolymers to metal ion uptake in the presence of biological competitors.     

The modified complex Busemann-Petty problem on sections of convex bodies

The complex Busemann-Petty problem asks whether origin symmetric convex bodies in with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if n ≤ 3 and negative if n ≥ 4. Since the answer is negative in most dimensions, it is natural to ask what conditions on the (n − 1)-dimensional volumes of the central sections of complex convex bodies with complex hyperplanes allow to compare the n-dimensional volumes. In this article we give necessary conditions on the section function in order to obtain an affirmative answer in all dimensions. The result is the complex analogue of [16].