Weighted Elliptic Systems of Lane–Emden Type in Unbounded Domains

We study the existence of weak solutions for a nonlinear elliptic system of Lane-Emden type $$\left\{\begin{array}{ll} -\Delta u \; = \; {\rm sgn}(v)|v|^{p-1} & {\rm in}\;\mathbb{R}^N, \\ -\Delta v \; = \; -\rho(x){\rm sgn}(u)|u|^{\frac{1}{p-1}} + f(x, u) & {\rm in}\;\mathbb{R}^N, \\ u, v \to 0 \quad {\rm as} \quad |x| \to +\infty, \end{array}\right.$$ by means of the Mountain Pass Theorem and some compact imbeddings in weighted Sobolev spaces.     

New synthetic approach to paullones and characterization of their SIRT1 inhibitory activity

A series of 7,12-dihydroindolo[3,2-d][1]benzazepine-6(5H)-ones (paullones) substituted at C9/C10 (Br) and C2 (Me, CF(3), CO(2)Me) have been synthesized by a one-pot Suzuki-Miyaura cross-coupling of an o-aminoarylboronic acid and methyl 2-iodoindoleacetate followed by intramolecular amide formation. Other approaches to the paullone scaffold based on Pd-catalyzed C-H activation were unsuccessful. In vitro enzymatic assay with recombinant human SIRT-1 indicated a strong inhibitory profile for the series, in particular the analogue with a methoxycarbonyl group at C2 and a bromine at C9. These compounds are, in general, inducers of granulocyte differentiation of the U937 acute leukemia cell line and cause a marked increase in pre-G1 of the cell cycle.     

Hybrid ligand-alkylating agents targeting telomeric G-quadruplex structures

The synthesis, physico-chemical properties and biological effects of a new class of naphthalene diimides (NDIs) capable of reversibly binding telomeric DNA and alkylate it through an electrophilic quinone methide moiety (QM), are reported. FRET and circular dichroism assays showed a marked stabilization and selectivity towards telomeric G4 DNA folded in a hybrid topology. NDI-QMs' alkylating properties revealed a good reactivity on single nucleosides and selectivity towards telomeric G4. A selected NDI was able to significantly impair the growth of melanoma cells by causing telomere dysfunction and down-regulation of telomerase expression. These findings points to our hybrid ligand-alkylating NDIs as possible tools for the development of novel targeted anticancer therapies.     

Water soluble extended naphthalene diimides as pH fluorescent sensors and G-quadruplex ligands

Extended naphthalene diimides (NDIs) fused to 1,4-dihydropyrazine-2,3-dione, containing two solubilizing moieties, have been synthesized. Fluorescence spectra of the new NDIs were remarkably affected by pH, as the second deprotonation of the dihydropyrazinedione moiety (pK(a) 6.9) switched off the emission. Binding to a G-quadruplex folded oligonucleotide and stoichiometry were evaluated by FRET melting assay and CD analysis. G-quadruplex binding was strongly enhanced shifting from pH 7.4 to pH 6.0 as a consequence of the dihydropyrazinedione moiety protonation. Cytotoxicity studies using two human telomerase-positive cell lines (HT29 and A549) revealed that the best G-quadruplex ligand was very active against the colon cell line, with an EC(50) of 300 nM.     

Iron(II) complexes of new hexadentate 1,1,1-tris-(iminomethyl)ethane podands, and their 7-methyl-1,3,5-triazaadamantane rearrangement products

New iron(II) podand complexes have been prepared, by condensation of 2-(aminomethyl)-2-methyl-1,3-diaminopropane with 3 equiv of a heterocyclic aldehyde in the presence of hydrated Fe[BF(4)](2) or Fe[ClO(4)](2) as templates. The 2-(aminomethyl)-2-methyl-1,3-diaminopropane is prepared in situ by deprotonation of its trihydrochloride salt. The chloride must be removed from these reactions by precipitation with silver, to avoid the formation of the alternative 2,4,6-trisubstituted-7-methyl-1,3,5-triazaadamantane condensation products, or their FeCl(2) adducts. The crystal structures of two 2,4,6-tri(pyridyl)-7-methyl-1,3,5-triazaadamantane-containing species are presented, and contain two different geometric isomers of this tricyclic ring with three equatorial, or two equatorial and one axial, pyridyl substituents. Both structures feature strong C-HX (X = Cl or F) hydrogen bonding from the aminal C-H groups in the triazaadamantane ring. Five iron(II) podand complexes were successfully obtained, all of which contain low-spin iron centres.     

Photoreduction of mesoporous In2O3: mechanistic model and utility in gas sensing

A model is proposed for the drop in electronic resistance of n-type semiconducting indium oxide (In(2)O(3)) upon illumination with light (350?nm, 3.5?eV) as well as for the (light-enhanced) sensitivity of In(2)O(3) to oxidizing gases. Essential features of the model are photoreduction and a rate-limiting oxygen-diffusion step. Ordered, mesoporous In(2)O(3) with a high specific surface area serves as a versatile system for experimental studies. Analytical techniques comprise conductivity measurements under a controlled atmosphere (synthetic air, pure N(2)) and temperature-resolved in-situ Fourier transform infrared (FTIR) spectroscopy. IR measurements reveal that oxygen vacancies form a donor level 0.18?eV below the conduction band.     

Decatungstate as photoredox catalyst: benzylation of electron-poor olefins

Excited tetrabutylammonium decatungstate (TBADT), known to activate a variety of compounds via hydrogen atom transfer (HAT), has now been applied as a photoredox catalyst for the effective oxidative cleavage of benzyl silanes and radical benzylation of reducible olefins occurring in isolated yields from poor to excellent.     

Role of quaternary ammonium salts as new additives in the enantioselective organocatalytic β-benzylation of enals

We report herein the efficiency of quaternary ammonium salts as co-catalysts in organocatalytic Michael reactions involving iminium activation of α,β-unsaturated aldehydes. The enantioselective formal benzylation of these substrates has been optimized and used to rationalize the role of the ammonium salts in these processes.     

A non-standard finite difference method to solve a model of HIV–Malaria co-infection

In this paper, we design and analyse a non-standard finite difference numerical scheme for the numerical solution of the HIV–malaria co-infection model with a distributed delay representing the incubation period of malaria parasite in the mosquitoes vector. To come up with the efficient numerical method for the full co-infection model, we study a number of qualitative properties of sub-models and then use the information while designing the numerical methods for these sub-models. One of the salient features of these methods is that they preserve positivity of the solution which is very essential while studying epidemiological models. We also present numerical simulations to confirm the theoretical findings.