Covering pairs by quintuples with index λ  0 (mod 4)

A (v, k. λ) covering design of order v, block size k, and index λ is a collection of k-element subsets, called blocks, of a set V such that every 2-subset of V occurs in at least λ blocks. The covering problem is to determine the minimum number of blocks, α(v, k, λ), in a covering design. It is well known that $ \alpha \left({\nu,\kappa,\lambda } \right) \ge \left\lceil {\frac{\nu}{\kappa}\left\lceil {\frac{{\nu - 1}}{{\kappa - 1}}\lambda} \right\rceil} \right\rceil = \phi \left({\nu,\kappa,\lambda} \right) $, where [χ] is the smallest integer satisfying χ ≤ χ. It is shown here that α (v, 5, λ) = ?(v, 5, λ) + ? where λ ≡ 0 (mod 4) and e= 1 if λ (v?1)≡ 0(mod 4) and λv (v?1)/4 ≡ ?1 (mod 5) and e= 0 otherwise With the possible exception of (v,λ) = (28, 4). © 1993 John Wiley & Sons, Inc.     

Souslin trees at successors of regular cardinals

We present a weak sufficient condition for the existence of Souslin trees at successor of regular cardinals. The result is optimal and simultaneously improves an old theorem of Gregory and a more recent theorem of the author.     

Identification of Potential SARS-CoV-2 Main Protease and Spike Protein Inhibitors from the Genus Aloe: An In Silico Study for Drug Development

Severe acute respiratory syndrome coronavirus (SARS-CoV-2) disease is a global rapidly spreading virus showing very high rates of complications and mortality. Till now, there is no effective specific treatment for the disease. Aloe is a rich source of isolated phytoconstituents that have an enormous range of biological activities. Since there are no available experimental techniques to examine these compounds for antiviral activity against SARS-CoV-2, we employed an in silico approach involving molecular docking, dynamics simulation, and binding free energy calculation using SARS-CoV-2 essential proteins as main protease and spike protein to identify lead compounds from Aloe that may help in novel drug discovery. Results retrieved from docking and molecular dynamics simulation suggested a number of promising inhibitors from Aloe. Root mean square deviation (RMSD) and root mean square fluctuation (RMSF) calculations indicated that compounds 132, 134, and 159 were the best scoring compounds against main protease, while compounds 115, 120, and 131 were the best scoring ones against spike glycoprotein. Compounds 120 and 131 were able to achieve significant stability and binding free energies during molecular dynamics simulation. In addition, the highest scoring compounds were investigated for their pharmacokinetic properties and drug-likeness. The Aloe compounds are promising active phytoconstituents for drug development for SARS-CoV-2.     

Tuning protonation states of tripelennamine antihistamines by cucurbit[7]uril

The formation of host–guest complexes of cucurbit[7]uril (CB7) with the antihistamine drug tripelennamine (TRP) was studied by optical and NMR spectroscopy. The experimental and computational results are consistent with inclusion of a single TRP molecule in CB7. Addition of CB7 has tuned drug protonation states associated with (de)protonation of the ethyldimethylammonium and exocyclic nitrogens with an increase in the associated pK_a values by 1.5 and 2.5 units, respectively. The incorporation of antihistamines drugs such as TRP in cucurbiturils could be utilized for switching their capability for selective binding to histamine H₁‐receptors, in the future. Copyright © 2015 John Wiley & Sons, Ltd.     

A Tandem In Situ Peptide Cyclization through Trifluoroacetic Acid Cleavage

We present a new approach for peptide cyclization during solid phase synthesis under highly acidic conditions. Our approach involves simultaneous in situ deprotection, cyclization and trifluoroacetic acid (TFA) cleavage of the peptide, which is achieved by forming an amide bond between a lysine side chain and a succinic acid linker at the peptide N‐terminus. The reaction proceeds via a highly active succinimide intermediate, which was isolated and characterized. The structure of a model cyclic peptide was solved by NMR spectroscopy. Theoretical calculations support the proposed mechanism of cyclization. Our new methodology is applicable for the formation of macrocycles in solid‐phase synthesis of peptides and organic molecules.     

Tower techniques for cosimplicial resolutions

Let be a simplicial model category and J : a simplicial coaugmented functor. Given an object X, the assignment nJⁿ⁺¹X defines a cofacial resolution (an augmented cosimplicial space without its codegeneracy maps). Following Bousfield and Kan we define J^sX = tot^s([n] Jⁿ⁺¹X). An object X is called J-injective if it is a retract of JX in Ho() via the natural map. We show that certain homotopy limits of J-injective objects are J_s-injective. Our method is to use the notion of pro-weak equivalences which was first introduced in a different language and context by David Edwards and Harold Hastings. The key observation is that a cofacial resolution X (-1) X which admits a left contraction gives rise to a pro-weak equivalence of towers {X(-1)}_s0{tot^SX}_{s 0}.The first author was supported in part by National Science Foundation grant DMS-0296117     

A doubling subset of L_p for p>2 that is inherently infinite dimensional

It is shown that for every \(p\in (2,\infty )\) there exists a doubling subset of \(L_p\) that does not admit a bi-Lipschitz embedding into \(\mathbb R^k\) for any \(k\in \mathbb N\) .     

Application of a process friendly morpholine synthesis to (S,S)-Reboxetine

We report our results on the construction of a morpholine ring system from the corresponding epoxide and amino alcohol. From this study, we were able to convert a previous four-step synthesis into a more efficient two-step process.