Recurrence relations for orthogonal rational functions

It is well known that members of families of polynomials, that are orthogonal with respect to an inner product determined by a nonnegative measure on the real axis, satisfy a three-term recursion relation. Analogous recursion formulas are available for orthogonal Laurent polynomials with a pole at the origin. This paper investigates recursion relations for orthogonal rational functions with arbitrary prescribed real or complex conjugate poles. The number of terms in the recursion relation is shown to be related to the structure of the orthogonal rational functions.     

Atomic decompositions for tensor products and polynomial spaces

We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product , for any symmetric tensor norm μ. In addition, the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained. Finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on X.     

Gender effect on neurodegeneration and myelin markers in an animal model for multiple sclerosis

Background  

Multiple sclerosis (MS) varies considerably in its incidence and progression in females and males. In spite of clinical evidence, relatively few studies have explored molecular mechanisms possibly involved in gender-related differences. The present study describes possible cellular- and molecular-involved markers which are differentially regulated in male and female rats and result in gender-dependent EAE evolution and progression. Attention was focused on markers of myelination (MBP and PDGFαR) and neuronal distress and/or damage (GABA synthesis enzymes, GAD65 and GAD67, NGF, BDNF and related receptors), in two CNS areas, i.e. spinal cord and cerebellum, which are respectively severely and mildly affected by inflammation and demyelination. Tissues were sampled during acute, relapse/remission and chronic phases and results were analysed by two-way ANOVA.     

Non-negatively constrained image deblurring with an inexact interior point method

Nonlinear image deblurring procedures based on probabilistic considerations have been widely investigated in the literature. This approach leads to model the deblurring problem as a large scale optimization problem, with a nonlinear, convex objective function and non-negativity constraints on the sign of the variables. The interior point methods have shown in the last years to be very reliable in nonlinear programs. In this paper we propose an inexact Newton interior point (IP) algorithm designed for the solution of the deblurring problem. The numerical experience compares the IP method with another state-of-the-art method, the Lucy Richardson algorithm, and shows a significant improvement of the processing time.     

Investigation of catalytic activities by differential thermal analysis

A calorimetric method is proposed to evaluate the catalytic activity of a solid catalyst with respect to the exothermic oxidation of Volatile Organic Compounds (VOC).This method employs a differential thermal analyzer in which an inert reference and a catalytically active sample are both fluxed at a constant rate with a reactive gaseous mixture composed of an inert gas (N₂ 90% vol.), oxygen and VOC, the last typically 900 to 5000 ppm. While the temperature is varied according to a predefined cycle, the output signal due to the exothermic reaction on the catalyst is continuously recorded. The design of the test chamber, the amount of catalyst, the shape of the holders and finally the flow rate and composition of the gaseous mixture should be carefully selected in order to achieve reproducible results.     

Highly Enantioselective Construction of Tricyclic Derivatives by the Desymmetrization of Cyclohexadienones

The asymmetric synthesis of tricyclic compounds by the desymmetrization of cyclohexadienones is presented. The reaction tolerated a large variety of substituents at different positions of the cyclohexadienone, and heterocyclic rings of different sizes were accessible. Density functional theory calculations showed that the reaction proceeds through an asynchronous [4+2] cycloaddition.     

Alkylation of aryl 3-oxopropanedithioate and 3-amino-1-aryl-3-thioxo-1-propanones as an effective tool for the construction of differently substituted thiophenes and annulated thiophenes

The alkylation of aryl 3-oxopropanedithioate with α-haloketones under different reaction conditions afforded substituted aryl[2-(methylsulfanyl)-4-phenyl-3-thienyl]methanones and [3-aryl-5-(methylsulfanyl)-2-thienyl](phenyl)methanones. The same strategy was extended to 3-amino-1-aryl-3-thioxo-1-propanones to afford aryl[2-amino-4-phenyl-3-thienyl]methanones and ethyl 3-phenyl-5-piperidino-2-thiophene carboxylate.     

A new zirconium inorganic building brick forming metal organic frameworks with exceptional stability

Porous crystals are strategic materials with industrial applications within petrochemistry, catalysis, gas storage, and selective separation. Their unique properties are based on the molecular-scale porous character. However, a principal limitation of zeolites and similar oxide-based materials is the relatively small size of the pores, typically in the range of medium-sized molecules, limiting their use in pharmaceutical and fine chemical applications. Metal organic frameworks (MOFs) provided a breakthrough in this respect. New MOFs appear at a high and an increasing pace, but the appearances of new, stable inorganic building bricks are rare. Here we present a new zirconium-based inorganic building brick that allows the synthesis of very high surface area MOFs with unprecedented stability. The high stability is based on the combination of strong Zr-O bonds and the ability of the inner Zr6-cluster to rearrange reversibly upon removal or addition of mu3-OH groups, without any changes in the connecting carboxylates. The weak thermal, chemical, and mechanical stability of most MOFs is probably the most important property that limits their use in large scale industrial applications. The Zr-MOFs presented in this work have the toughness needed for industrial applications; decomposition temperature above 500 degrees C and resistance to most chemicals, and they remain crystalline even after exposure to 10 tons/cm2 of external pressure.     

Progress in drug delivery to the central nervous system by the prodrug approach

This review describes specific strategies for targeting to the central nervous system (CNS). Systemically administered drugs can reach the brain by crossing one of two physiological barriers resistant to free diffusion of most molecules from blood to CNS: the endothelial blood-brain barrier or the epithelial blood-cerebrospinal fluid barrier. These tissues constitute both transport and enzymatic barriers. The most common strategy for designing effective prodrugs relies on the increase of parent drug lipophilicity. However, increasing lipophilicity without a concomitant increase in rate and selectivity of prodrug bioconversion in the brain will result in failure. In these regards, consideration of the enzymes present in brain tissue and in the barriers is essential for a successful approach. Nasal administration of lipophilic prodrugs can be a promising alternative non-invasive route to improve brain targeting of the parent drugs due to fast absorption and rapid onset of drug action. The carrier-mediated absorption of drugs and prodrugs across epithelial and endothelial barriers is emerging as another novel trend in biotherapeutics. Several specific transporters have been identified in boundary tissues between blood and CNS compartments. Some of them are involved in the active supply of nutrients and have been used to explore prodrug approaches with improved brain delivery. The feasibility of CNS uptake of appropriately designed prodrugs via these transporters is described in detail.