The Darling-Erdős theorem for sums of I.I.D. random variables

Summary We obtain a general Darling-Erds type theorem for the maximum of appropriately normalized sums of i.i.d. mean zero r.v.'s with finite variances. We infer that the Darling-Erds theorem holds in its classical formulation if and only ifE[X ² 1 {|X|t}]=o((loglogt)^-1) ast. Our method is based on an extension of the truncation techniques of Feller (1946) to non-symmetric r.v.'s. As a by-product we are able to reprove fundamental results of Feller (1946) dealing with lower and upper classes in the Hartman-Wintner LIL.     

Synthesis of one‐, two‐ and three‐ring macrocyclic,bifunctional compounds for use in radiolabelling monoclonal antibodies

The synthesis of new linked bis‐ and tris‐ring tetraazamacrocyclic (bifunctional) reagents for use in an alternative strategy for radiolabelling antibodies is described. For comparison with the above systems, a new single ring bifunctional system incorporating a dioxocyclam ring is also reported.     

Molecular rearrangements of 5-azido substituted 1,2,3-triazoles

5-Azido-4-methoxycarbonyl-1-phenyl-1,2,3-triazole ($\text{8a}$) and its phenyl substituted derivatives $\text{8b}$,$\text{c}$ rearrange at 60–80°C to give tetrazolyldiazoacetates $\text{9}$, which have been isolated. When the reactions are allowed to go to completion, products derived from the diazo compounds are obtained; i.e. norcaradienes ($\text{10}$) from benzene solutions and imidazotetrazoles ($\text{12}$) from nitrite solutions. The latter decompose photochemically into diazacyclopentadienonimines ($\text{13}$). A kinetic study of the rearrangement $\text{8}$ → $\text{9}$ has been carried out and the mechanism (Scheme VI) is discussed in comparison with the Dimroth rearrangement.     

HIV-1 gp120 V3 loop for structure-based drug design

HIV-1 cell entry is mediated by sequential interactions of the envelope protein gp120 with the receptor CD4 and a coreceptor, usually CCR5 or CXCR4, depending on the individual virion. Considerable efforts on exploiting the HIV coreceptors as drug targets have led to the new class of coreceptor antagonists. While these antiretroviral drugs aim at preventing virus/coreceptor interaction by binding to host proteins, neutralizing antibodies directed against the coreceptor-binding sites on gp120 have attracted attention as possible vaccine candidates. However, both approaches are complicated by the multiple protective mechanisms of gp120 which allow for rapid escape from selective pressures exerted by drugs or antibodies. Thus, advances in rational drug and vaccine design rely heavily on improved insights into the relation between genotype and phenotype, the evolution of coreceptor usage, and, ultimately the structural biology of coreceptor usage and inhibition. The third variable (V3) loop of gp120, crucially involved in all these aspects, will be a major focus of this review.     

Tetronic acids and derivatives. Part V. Synthesis of 5-hydroxy-1H-pyrazoles via 4-hydrazino-5H-furan-2-ones. Reaction of hydrazines on tetronic acids

The conversion of tetronic acids 1 to 3(1-hydroxy alkyl)-5-hydroxy-1H-pyrazole derivatives 3, 5, 7 and 12 is described. The formation is shown to proceed via base-catalyzed rearrangement of the intermediate 4-hydrazino-5H-furan-2-one derivatives.     

Synthesis of some 3-acetyl-5-arylmethyl- or arylaminomethyltetronic acids from 4-ethoxycarbonyl-3-(2H)furanone precursors

The synthesis of a series of tetronic acids was accomplished by ring opening of new 4-ethoxycarbonyl-3(2H) furanones.     

Acylation reaction of γ,β-unsaturated β-keto esters and of ethyl hydrogen malonate. Synthesis of 6-alkenyl-5-ethoxycarbonyl-2,3-dihydro-4H-pyran-4-ones and 4,5-dioxo-2,3,7,8-tetrahydro-4H,5H-pyrano[4,3-b]pyran derivatives

The syntheses of 6-alkenyl-5-ethoxycarbonyl-2,3-dihydro-4H-pyran-4-one derivatives by acylation of γ,β-unsaturated β-keto esters or by diacylation of ethyl hydrogen malonate with α,β-unsaturated acyl chlorides are described. These compounds were converted to 4,5-dioxo-2,3,7,8-tetrahydro-4H,5H-pyrano[4,3-b]pyran derivatives.     

Molecular rearrangements of 4-iminomethyl-1,2,3-triazoles. Replacement of 1-aryl substituents in 1H-1,2,3-triazole-4-carbaldehydes

The two structural isomers, 4 and 5 , of 1-substituted-4-iminomethyl-1,2,3-triazoles are interconvertible when heated in dimethyl sulfoxide at 80°. The equilibrium position depends on the electronic properties of the R-substituent, favoring 5 for R = alkyl, benzyl and anisyl, and 4 for p-chlorophenyl and p-nitrophenyl. An interesting application is the synthesis of 1-alkyl-1,2,3-triazole-4-carbaldehydes from 1-phenyl-1,2,3-triazole-4-carbaldehyde by Scheme I. The hydrazones 4ij and the oxime 4k do not rearrange due to an unfavorable Z-configuration around the C ? N bond, whereas the acyloximino derivative 4m is converted into the nitrile 11 . The structures of the products have been fully characterized by ¹³C nmr spectroscopy and the mechanistic details of the rearrangement are discussed.     

3-butenyl esters as convenient protecting groups for carboxylic acids

Carboxylic acids were protected as their corresponding 3-butenyl esters. Deprotection was carried out via ozonolysis and β-elimination of the resultant 3-acyloxypropanal.     

Jusanin,a New Flavonoid from Artemisia commutata with an In Silico Inhibitory Potential against the SARS-CoV-2 Main Protease

A new flavonoid, Jusanin, (1) has been isolated from the aerial parts of Artemisia commutata. The chemical structure of Jusanin has been elucidated using 1D, 2D NMR, and HR-Ms spectroscopic methods to be 5,2′,4′-trihydroxy-6,7,5′-trimethoxyflavone. Being new in nature, the inhibition potential of 1 has been estimated against SARS-CoV-2 using different in silico techniques. Firstly, molecular similarity and fingerprint studies have been conducted for Jusanin against co-crystallized ligands of eight different SARS-CoV-2 essential proteins. The studies indicated the similarity between 1 and X77, the co-crystallized ligand SARS-CoV-2 main protease (PDB ID: 6W63). To confirm the obtained results, a DFT study was carried out and indicated the similarity of (total energy, HOMO, LUMO, gap energy, and dipole moment) between 1 and X77. Accordingly, molecular docking studies of 1 against the target enzyme have been achieved and showed that 1 bonded correctly in the protein’s active site with a binding energy of −19.54 Kcal/mol. Additionally, in silico ADMET in addition to the toxicity evaluation of Jusanin against seven models have been preceded and indicated the general safety and the likeness of Jusanin to be a drug. Finally, molecular dynamics simulation studies were applied to investigate the dynamic behavior of the M^pro-Jusanin complex and confirmed the correct binding at 100 ns. In addition to 1, three other metabolites have been isolated and identified to be сapillartemisin A (2), methyl-3-[S-hydroxyprenyl]-cumarate (3), and β-sitosterol (4).