The S′-convolution with singular kernels in the Euclidean case and the product domain case

We characterize those tempered distributions which are S′-convolvable with a given class of singular convolution kernels. We study both, the Euclidean case and the product domain case. In the Euclidean case, we consider a class of kernels that includes Riesz kernels, Calderón–Zygmund singular convolution kernels, finite part distributions defined by hypersingular convolution kernels, and Hörmander multipliers. In the product domain case, we consider a class of singular kernels introduced by Fefferman and Stein as a generalization of the n-dimensional Hilbert kernel.     

Regioselective formation of N-alkyl-3,5-pyrazole derived ligands. A synthetic and computational study

New N-alkyl-3,5-pyrazole derived ligands were synthesized by reaction between 3,5-pyrazole derived ligands and the appropriate haloalkane in toluene or THF using NaOEt or NaH as base. When the precursor ligand bears a pyridyl substituent the alkylation reaction presents a large regioselectivity. Theoretical calculations have been carried out to rationalize the experimental observations. It has been shown that regioselectivity is governed by the formation of Na⁺-pyrazolide chelate complexes.     

Perron’s Method and Wiener’s Theorem for a Nonlocal Equation

We study the Dirichlet problem for non-homogeneous equations involving the fractional p-Laplacian. We apply Perron’s method and prove Wiener’s resolutivity theorem.     

Synthesis and structure of ruthenium(IV) complexes featuring N-heterocyclic ligands with an N-H group as the hydrogen-bond donor: hydrogen interactions in solution and in the solid state

The synthesis and characterization of novel ruthenium(IV) complexes [Ru(η(3):η(3)-C(10)H(16))Cl(2)L] [L = 3-methylpyrazole (2b), 3,5-dimethylpyrazole (2c), 3-methyl-5-phenylpyrazole (2d), 2-(1H-pyrazol-5-yl)phenol (2e), 6-azauracile (3), and 1H-indazol-3-ol (4)] are reported. Complex 2e is converted to the chelated complex [Ru(η(3):η(3)-C(10)H(16))Cl(κ(2)-N,O-2-(1H-pyrazol-3-yl)phenoxy)] (5) by treatment with an excess of NaOH. All of the ligands feature N-H, O-H, or C═O as the potential hydrogen-bonding group. The structures of complexes 2a-2c, 2e, 3, and 5 in the solid state have been determined by X-ray diffraction. Complexes 2a-2c and 3, which contain the pyrazole N-H group, exhibit intra- and intermolecular hydrogen bonds with chloride ligands [N-H···Cl distances (?): intramolecular, 2.30-2.78; intermolecular, 2.59-2.77]. Complexes 2e and 3 bearing respectively O-H and C═O groups also feature N-H···O interactions [intramolecular (2e), 2.27 ?; intermolecular (3), 2.00 ?]. Chelated complex 5, lacking the O-H group, only shows an intramolecular N-H···Cl hydrogen bonding of 2.42 ?. The structure of complex 3, which turns out to be a dimer in the solid state through a double intermolecular N-H···O hydrogen bonding, has also been investigated in solution (CD(2)Cl(2)) by NMR diffusion studies. Diffusion-ordered spectroscopy experiments reveal an equilibrium between monomer and dimer species in solution whose extension depends on the temperature, concentration, and coordinating properties of the solvent. Preliminary catalytic studies show that complex 3 is highly active in the redox isomerization of the allylic alcohols in an aqueous medium under very mild reaction conditions (35 °C) and in the absence of a base.     

Quinic acids from Aster caucasicus and from transgenic callus expressing a beta-amyrin synthase

Several different classes of secondary metabolites, including flavonoids, triterpenoid saponins and quinic acid derivatives, are found in Aster spp. (Fam. Asteraceae). Several Aster compounds revealed biological as well as pharmacological activities. In this work, a phytochemical investigation of A. caucasicus evidenced the presence of quinic acid derivatives, as well as the absence of triterpene saponins. To combine in one species the production of different phytochemicals, including triterpenes, an Agrobacterium-mediated transformation of A. caucasicus was set up to introduce A. sedifolius beta-amyrin synthase (AsOXA1)-encoding gene under the control of the constitutive promoter CaMV35S. The quali-quantitative analysis of transgenic calli with ectopic expression of AsOXA1 showed, in one sample, a negligible amount of triterpene saponins combined with higher amount of quinic acid derivatives as compared with the wild type callus.     

Phenotypic and Target-Directed Screening Yields New Acaricidal Alternatives for the Control of Ticks

Rhipicephalus microplus, the “common cattle tick”, is the most important ectoparasite in livestock worldwide due to the economic and health losses it produces. This tick is a vector for pathogens of several tick-borne diseases. In Latin American countries, damages reach approximately USD 500 million annually due to tick infections, as well as tick-borne diseases. Currently, resistant populations for every chemical group of acaricides have been reported, posing a serious problem for tick control. This study aims to find new alternatives for controlling resistant ticks with compounds derived from small synthetic organic molecules and natural origins. Using BME26 embryonic cells, we performed phenotypic screening of 44 natural extracts from 10 Mexican plants used in traditional medicine, and 33 compounds selected from our chemical collection. We found 10 extracts and 13 compounds that inhibited cell growth by 50% at 50 µg/mL and 100 µM, respectively; the dose-response profile of two of them was characterized, and these compounds were assayed in vitro against different life stages of Rhipicephalus microplus. We also performed a target-directed screening of the activity of triosephosphate isomerase, using 86 compounds selected from our chemical collection. In this collection, we found the most potent and selective inhibitor of tick triosephosphate isomerase reported until now. Two other compounds had a potent acaricidal effect in vitro using adults and larvae when compared with other acaricides such as ivermectin and Amitraz. Those compounds were also selective to the ticks compared with the cytotoxicity in mammalian cells like macrophages or bovine spermatozoids. They also had a good toxicological profile, resulting in promising acaricidal compounds for tick control in cattle raising.     

Click and count: specific detection of acid ceramidase activity in live cells

The use of intact cells in medical research offers a number of advantages over employing cell-free systems. In diagnostics, cells isolated from liquid biopsies can be directly used, speeding up the time of analysis and diminishing the risk of protein degradation by sample manipulation. In drug discovery, studies in live cells take into account aspects neglected in cell-free systems, such as uptake, metabolization, and subcellular concentration by compartmentalization of potential drug candidates. Therefore, probes for studies in cellulo are of paramount importance. Acid ceramidase (AC) is a lysosomal enzyme that hydrolyses ceramides into sphingoid bases and fatty acids. The essential role of this enzyme in the outburst and progress of several diseases, some of them still incurable, is well sustained. Despite the great clinical relevance of AC as a biomarker and therapeutic target, the specific monitoring of AC activity in live cells has remained elusive due to the concomitant existence of neutral and alkaline ceramidases. In this work, we report that 1-deoxydihydroceramides are exclusively hydrolysed by AC. Using N-octanoyl-18-azidodeoxysphinganine as a probe and a BODIPY-substituted bicyclononyne, we show the click-reliant predominant staining of lysosomes, with extra-lysosomal labeling also occurring in some cells. Importantly, using pharmacological and genetic tools together with high resolution mass spectrometry, we demonstrate that both lysosomal and extra-lysosomal staining are AC-dependent. These findings are translated into the specific flow cytometry monitoring of AC activity in intact cells, which fills an important gap in the field of diseases linked to altered AC activity.

The use of intact cells in medical research offers a number of advantages over employing cell-free systems.     

A novel synthesis of 3-cyanoindoles and a new route to indole-3-carboxylic acid derivatives

2-Alkyl-3-cyanoindoles are obtained when 1-alkylmethyl-2-chloro-(or 2-phenylsulfonyl)-3-phenylsulfonylindoles are reacted with excess azide ion (90°/DMF). The reaction is considered to occur by a fragmentation recombination process in which the Schiff's base $\text{12}$ is of central importance. This proposal is supported by the formation of 2-substituted indole-3-carboxylates $\text{17}$ from aldehydes and the α-phenylsulfonyl-$\text{o}$-aminophenylacetic acid ester derivative $\text{16}$.     

Banach Spaces of Solutions of the Helmholtz Equation in the Plane

The purpose of this article is to study the Hilbert space W²\mathcal{ W}^2 consisting of all solutions of the Helmholtz equation Du+u=0\Delta u+u=0 in \BbbR²\Bbb{R}^2 that are the image under the Fourier transform of L²L^2 densities in the unit circle. We characterize this space as a close subspace of the Hilbert space H²\mathcal{ H}^2 of all functions belonging to L²( | x | ^-3dx) L^2( | x | ^{-3}dx) jointly with their angular and radial derivatives, in the complement of the unit disk in \BbbR²\Bbb{R}^2. We calculate the reproducing kernel of W²\mathcal{ W}^2 and study its reproducing properties in the corresponding spaces H^p\mathcal{H}^p, for $p>1$p>1.     

Activity coefficients at infinite dilution for surfactants

A new alternative is presented for activity coefficients at infinite dilution determination via surface tension data of low vapour pressure substances. It was found that experimental data for surfactants follows Volmer's surface equation of state behaviour over the diluted region until the critical micelle concentration. The key operations are: the choice of the same standard conditions for the bulk and the surface phases, the combination of Gibbs and Volmer equations and the use of the symmetric activity coefficients convention. An exact relation between the activity coefficient at infinite dilution and the reciprocal of the critical micelle mole fraction was found which allowed us the verification of the model.