Self-similar asymptotic behavior for the solutions of a linear coagulation equation

In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law $v^{?\sigma }$. The validity of the equation has been rigorously proved in [22] taking as a starting point a particle model and for values of the exponent $\sigma >3$, but the model can be expected to be valid, on heuristic grounds, for $\sigma >\frac{5}{3}$. The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent σ. Here we show that for $\frac{5}{3}<\sigma <2$ the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable.     

Synthesis of Polysubstituted Symmetrical BODIPYs via Fischer Carbene Complexes: Theoretical,Photophysical and Electrochemical Evaluation

A series of new symmetrical highly substituted BODIPYs 6 a – l was synthesized through a prefunctionalization approach in 35 %–89 % yields from the pyrrole core. This strategy allowed modulation of the substituents at the different positions based on the choice of Fischer's alkynyl carbenes, oxazolones and aldehydes used as precursors. The substituent variation at positions 2, 6, 3 and 5 had the greatest effect on the modulation of their photophysical properties such as absorption (λ_abs) and emission (λ_em) wavelengths, extinction coefficient (ϵ), quantum yields (ϕ), Stokes shifts (Δν), fluorescence decay, radiative (k_rad) and non-radiative (k_nr) constants and the CIE 1931 coordinates. Theoretical calculations allowed to corroborate the effect of the substituents of meso-position on the modification of the dihedral angles. Cyclic voltammetry studies revealed that the BODIPY series presents similar redox potential behavior, being electrochemically active even in successive cycles, which suggests that transport by diffusion is the dominant process.     

A Broad Light-Harvesting Conjugated Oligoelectrolyte Enables Photocatalytic Nitrogen Fixation in a Bacterial Biohybrid

We report a rationally designed membrane-intercalating conjugated oligoelectrolyte (COE), namely COE-IC , which endows aerobic N₂-fixing bacteria Azotobacter vinelandii with a light-harvesting ability that enables photosynthetic ammonia production. COE-IC possesses an acceptor-donor-acceptor (A-D-A) type conjugated core, which promotes visible light absorption with a high molar extinction coefficient. Furthermore, COE-IC spontaneously associates with A. vinelandii to form a biohybrid in which the COE is intercalated within the lipid bilayer membrane. In the presence of L-ascorbate as a sacrificial electron donor, the resulting COE-IC /A. vinelandii biohybrid showed a 2.4-fold increase in light-driven ammonia production, as compared to the control. Photoinduced enhancement of bacterial biomass and production of L-amino acids is also observed. Introduction of isotopically enriched ¹⁵N₂ atmosphere led to the enrichment of ¹⁵N-containing intracellular metabolites, consistent with the products being generated from atmospheric N₂.     

Conformational Effects of Regioisomeric Substitution on the Catalytic Activity of Copper/Calix[8]arene C−S Coupling

Functionalization of the phenolic rim of p-tert-butylcalix[8]arene with phenanthroline to create a cavity leads to formation of two regioisomers. Substitution of positions 1 and 5 produces the known C_2v-symmetric regioisomer 1,5-(2,9-dimethyl-1,10-phenanthroyl)-p-tert-butylcalix[8]arene ( L^1,5 ), while substitution of positions 1 and 4 produces the C_s-symmetric regioisomer 1,4-(2,9-dimethyl-1,10-phenanthroyl)-p-tert-butylcalix[8]arene ( L^1,4 ) described herein. [ Cu(L^1,4)I ] was synthesized from L^1,4 and CuI in good yield and characterized spectroscopically. To evaluate the effect of its cavity on catalysis, Ullmann-type C−S coupling was chosen as proof-of-concept. Selected aryl halides were used, and the results compared with the previously reported Cu(I)/ L^1,5 system. Only highly activated aryl halides generate the C−S coupling product in moderate yields with the Cu(I)/ L^1,4 system. To shed light on these observations, detailed computational investigations were carried out, revealing the influence of the calix[8]arene macrocyclic morphology on the accessible conformations. The L^1,4 regioisomer undergoes a deformation that does not occur with L^1,5 , resulting in an exposed catalytic center, presumably the cause of the low activity of the former system. The 1,4-connectivity was confirmed in the solid-state structure of the byproduct [ Cu(L^1,4 − H) (CH₃CN)₂] that features Cu(I) coordinated inside a cleft defined by the macrocyclic framework.     

Effectiveness of Photodynamic Therapy in Elimination of HPV‐16 and HPV‐18 Associated with CIN I in Mexican Women

This study aimed to determine the effectiveness of photodynamic therapy (PDT), using δ‐aminolevulinic acid (5‐ALA), in the elimination of premalignant cervical lesions in Mexican patients with human papillomavirus (HPV) infection and/or cervical intraepithelial neoplasia (CIN). Thirty women diagnosed with CIN I and/or positive for HPV participated in the study. Topical 6% 5‐ALA in gel form was applied to the uterine cervix; after 4 h, the lesion area was irradiated with a light dose of 200 J cm^?2 at 635 nm. This procedure was performed three times at 48‐h intervals. Clinical follow‐up was performed at 3, 6, and 12 months after the initial PDT administration, by colposcopy, cervical cytology, histopathological analysis, polymerase chain reaction, and hybrid capture. Of HPV‐infected patients without evidence of CIN I, 80% cleared the infection, while HPV associated with CIN I was eliminated in 83% of patients (P < 0.05). At 12 months, CIN I had regressed in 57% of patients, although this response was not statistically significant. PDT using 6% 5‐ALA is concluded to be effective in eliminating HPV infection associated or not with CIN I.     

Lemon Oils Attenuate the Pathogenicity of Pseudomonas aeruginosa by Quorum Sensing Inhibition

The chemical composition of three Citrus limon oils: lemon essential oil (LEO), lemon terpenes (LT) and lemon essence (LE), and their influence in the virulence factors production and motility (swarming and swimming) of two Pseudomonas aeruginosa strains (ATCC 27853 and a multidrug-resistant HT5) were investigated. The main compound, limonene, was also tested in biological assays. Eighty-four compounds, accounting for a relative peak area of 99.23%, 98.58% and 99.64%, were identified by GC/MS. Limonene (59–60%), γ-terpinene (10–11%) and β-pinene (7–15%) were the main compounds. All lemon oils inhibited specific biofilm production and bacterial metabolic activities into biofilm in a dose-dependent manner (20–65%, in the range of 0.1–4 mg mL⁻¹) of both strains. Besides, all samples inhibited about 50% of the elastase activity at 0.1 mg mL⁻¹. Pyocyanin biosynthesis decreases until 64% (0.1–4 mg mL⁻¹) for both strains. Swarming motility of P. aeruginosa ATCC 27853 was completely inhibited by 2 mg mL⁻¹ of lemon oils. Furthermore, a decrease (29–55%, 0.1–4 mg mL⁻¹) in the synthesis of Quorum sensing (QS) signals was observed. The oils showed higher biological activities than limonene. Hence, their ability to control the biofilm of P. aeruginosa and reduce the production of virulence factors regulated by QS makes lemon oils good candidates to be applied as preservatives in the food processing industry.     

An Expedient Method for the Umpolung Coupling of Enols with Heteronucleophiles**

In this paper, we present an unprecedented and general umpolung protocol that allows the functionalization of silyl enol ethers and of 1,3-dicarbonyl compounds with a large range of heteroatom nucleophiles, including carboxylic acids, alcohols, primary and secondary amines, azide, thiols, and also anionic carbamates derived from CO₂. The scope of the reaction also extends to carbon-based nucleophiles. The reaction relies on the use of 1-bromo-3,3-dimethyl-1,3-dihydro-1λ³[d][1,2]iodaoxole, which provides a key α-brominated carbonyl intermediate. The reaction mechanism has been studied experimentally and by DFT, and we propose formation of an unusual enolonium intermediate with a halogen-bonded bromide.