A new continuous dependence result for impulsive retarded functional differential equations

We consider a large class of impulsive retarded functional differential equations (IRFDEs) and prove a result concerning uniqueness of solutions of impulsive FDEs. Also, we present a new result on continuous dependence of solutions on parameters for this class of equations. More precisely, we consider a sequence of initial value problems for impulsive RFDEs in the above setting, with convergent right-hand sides, convergent impulse operators and uniformly convergent initial data. We assume that the limiting equation is an impulsive RFDE whose initial condition is the uniform limit of the sequence of the initial data and whose solution exists and is unique. Then, for sufficient large indexes, the elements of the sequence of impulsive retarded initial value problem admit a unique solution and such a sequence of solutions converges to the solution of the limiting Cauchy problem.     

Chemical Analysis and In Vitro Bioactivity of Essential Oil of Laurelia sempervirens and Safrole Derivatives against Oomycete Fish Pathogens

In this study, the essential oil (EO) from Laurelia sempervirens was analyzed by GC/MS and safrole (1) was identified as the major metabolite 1, was subjected to direct reactions on the oxygenated groups in the aromatic ring and in the side chain, and eight compounds (4 to 12) were obtained by the process. EO and compounds 4–12 were subjected to biological assays on 24 strains of the genus Saprolegnia, specifically of the species 12 S. parasitica and 12 S. australis. EO showed a significant effect against Saprolegnia strains. Compound 6 presents the highest activity against two resistant strains, with minimum inhibitory concentration (MIC) and minimum oomyceticidal concentration (MOC) values of 25 to 100 and 75 to 125 µg/mL, respectively. The results show that compound 6 exhibited superior activities compared to the commercial controls bronopol and azoxystrobin used to combat these pathogens.     

Non-Toxic Dimeric Peptides Derived from the Bothropstoxin-I Are Potent SARS-CoV-2 and Papain-like Protease Inhibitors

The COVID-19 outbreak has rapidly spread on a global scale, affecting the economy and public health systems throughout the world. In recent years, peptide-based therapeutics have been widely studied and developed to treat infectious diseases, including viral infections. Herein, the antiviral effects of the lysine linked dimer des-Cys¹¹, Lys¹²,Lys¹³-(pBthTX-I)₂K ((pBthTX-I)₂K)) and derivatives against SARS-CoV-2 are reported. The lead peptide (pBthTX-I)₂K and derivatives showed attractive inhibitory activities against SARS-CoV-2 (EC₅₀ = 28–65 µM) and mostly low cytotoxic effect (CC₅₀ > 100 µM). To shed light on the mechanism of action underlying the peptides’ antiviral activity, the Main Protease (M^pro) and Papain-Like protease (PL^pro) inhibitory activities of the peptides were assessed. The synthetic peptides showed PL^pro inhibition potencies (IC₅₀s = 1.0–3.5 µM) and binding affinities (K_d = 0.9–7 µM) at the low micromolar range but poor inhibitory activity against M^pro (IC₅₀ > 10 µM). The modeled binding mode of a representative peptide of the series indicated that the compound blocked the entry of the PL^pro substrate toward the protease catalytic cleft. Our findings indicated that non-toxic dimeric peptides derived from the Bothropstoxin-I have attractive cellular and enzymatic inhibitory activities, thereby suggesting that they are promising prototypes for the discovery and development of new drugs against SARS-CoV-2 infection.     

Effect of Perylene as Electron Acceptor and poly(tetrabromo-p-phenylene Diselenide) as “Buffer Layer” on Heterojunction Solar Cells Performances

Summary : Perylene derivatives, that behave as liquid crystal and might be used as electron acceptors, and poly(tetrabromo-p-phenylenediselenide) (PTBrPDSe) were synthesized with the purpose of using the polymer as buffer layer in solar cells. It was demonstrated that perylene compounds of N,N′-diheptyl-3,4,9,10-perylentetracarboxyldiimide (PTCDI-C7) and N,N′-diundecyl-3,4,9,10-perylentetracarboxyldiimide (PTCDI-C11) enabled obtaining photovoltaic effect when coupled with copper phthalocyanine (CuPc). The power conversion efficiency of the cells prepared from these perylenes is similar, whatever the x value. However this efficiency is smaller than the one achieved when the couple CuPc/C₆₀ (fullerene) is used. More precisely, the best efficiency was obtained when a PTBrPDSe/Au buffer layer is introduced between the ITO anode and the CuPc. It was established that the presence of the thin PTBrPDSe layer allows improving the shunt resistance and consequently the cells performance.     

Characterization of must and wine of six varieties of grapes by direct infusion electrospray ionization mass spectrometry

Samples of must derived from six different varieties of grapes taken during the fermentation process, as well as the respective wine samples directly after the end of the malolactic fermentation, were analyzed by direct infusion negative ion mode electrospray ionization mass spectrometry (ESI-MS). Diagnostic ions for must were different from those of wine samples, although small variations for each of the grape varieties were also detected. The addition of unfermented must or sugar to wine could also be clearly detected. The spectra were acquired in a few minutes per sample, indicating that ESI-MS can be used for high-throughput analysis of samples and should prove useful for quality control during and after the fermentation process.     

Enantioselective organocatalytic oxyamination of unprotected 3-substituted oxindoles

An enantioselective α-oxyamination of unprotected 3-substituted oxindoles with nitrosobenzene catalyzed by tertiary amine-thiourea bifunctional organocatalysts has been developed and affords the corresponding 3-amino-2-oxindole derivatives in good yields and with moderate to excellent enantioselectivities (up to > 99.9?:?0.1 er when the product is isolated by direct filtration from the reaction mixture). The absolute configuration of the major enantiomers of the products has been established both by chemical correlation and by comparison between the theoretically calculated and the experimental ECD.     

On a class of bivariate second-order linear partial difference equations and their monic orthogonal polynomial solutions

In this paper we classify the bivariate second-order linear partial difference equations, which are admissible, potentially self-adjoint, and of hypergeometric type. Using vector matrix notation, explicit expressions for the coefficients of the three-term recurrence relations satisfied by monic orthogonal polynomial solutions are obtained in terms of the coefficients of the partial difference equation. Finally, we make a compilation of the examples existing in the literature belonging to the class analyzed in this paper, namely bivariate Charlier, Meixner, Kravchuk and Hahn orthogonal polynomials.     

Generalized homogeneous functions and the two-body problem

IntroductionInthispaper,wegeneralizetheclassicconceptofhomogeneousfunctionofdegreeαandwestudytherelationbetweenthehomogeneousfunctionconceptandthemovementofabodythatsatisfiestheKepler’ssecondlaw .Asanapplicationoftheinvolvedtechniquesthatwereused ,wepresentasolutionofthetwo_bodyproblem ,givingawaytoobtainatimeequationforthebodythatrotatesaroundtheother,usingtheconceptofhomogeneousfunction .WeobtainedaserieslikeasthatwaspresentedinRef.[1 ] .1　GeneralizedHomogeneousFunctionsLetUbeanopensub…