Molecules of Post algebras

Following A. Abian, we define amolecule of a partially ordered set to be any nonzero elementm with the property that any two nonzero elements less than or equal tom have a nonzero lower bound. In a Boolean algebra an element is a molecule iff it is an atom; however, in an arbitrary distributive lattice the notion of a molecule is too general to permit explicit characterization. In this note we examine the molecules in a coproduct of two distributive lattices and use our results to show that molecules play the same role in Post algebras as atoms do in Boolean algebras.Presented by R. S. Pierce.I would like to thank the referee for helpful comments that resulted in simplifying a number of proofs in this paper.     

Greedy linear extensions for minimizing bumps

Let P be a finite poset and let L={x ₁<...n} be a linear extension of P. A bump in L is an ordered pair (x _i , x _i+1) where x _ii+1 in P. The bump number of P is the least integer b(P), such that there exists a linear extension of P with b(P) bumps. We call L optimal if the number of bumps of L is b(P). We call L greedy if x _{i j} for every j>i, whenever (x _i, x _i+1) is a bump. A poset P is called greedy if every greedy linear extension of P is optimal. Our main result is that in a greedy poset every optimal linear extension is greedy. As a consequence, we prove that every greedy poset of bump number k is the linear sum of k+1 greedy posets, each of bump number zero.This research (Math/1406/31) was supported by the Research Center, College of Science, King Saud University, Riyadh, Saudi Arabia.     

Efficient and accurate Car-Parrinello-like approach to Born-Oppenheimer molecular dynamics

We present a new method which combines Car-Parrinello and Born-Oppenheimer molecular dynamics in order to accelerate density functional theory based ab initio simulations. Depending on the system a gain in efficiency of 1 to 2 orders of magnitude has been observed, which allows ab initio molecular dynamics of much larger time and length scales than previously thought feasible. It will be demonstrated that the dynamics is correctly reproduced and that high accuracy can be maintained throughout for systems ranging from insulators to semiconductors and even to metals in condensed phases. This development considerably extends the scope of ab initio simulations.     

Hybrid of the 1,2,3-triazole nucleus and sesquiterpene skeleton as a potential antitumor agent: Hemisynthesis,molecular structure,Hirshfeld surface analysis,density functional theory,and in vitro cytotoxic and apoptotic effects

A new 1,2,3-triazole sesquiterpenic named (4aR,5aS,7aR,10aR,10bR)-10-benzyl-5,5-dichloro-1,1,4a,7a-tetramethyl-1,2,3,4,4a,5,7a,10,10a,10b decahydrocyclopropa[2′,3′]cyclohepta [1′,2′:3,4]benzo[1,2-d][1,2,3]triazol-7(6H)-one was synthesized by a dipolar cycloaddition 1,3 between benzyl azide and α,β-unsaturated sesquiterpene ketone catalyzed by titanium tetrachloride TiCl₄. It was obtained with a good yield and characterized using single-crystal X-ray diffraction technique, infra red (IR) spectroscopy, High Resolution Mass Spectrometry (HRMS), UV-Visible, and ¹H and ¹³C NMR spectroscopies. The optimization by the density functional theory (DFT) method was carried out to study the formation mechanism of the derivative. The selected compounds 1 – 4 exhibited anticancer activities in vitro against namely fibrosarcoma (HT-1080), lung carcinoma (A-549), and breast (MCF-7 and MDA-MB-231 cell lines with IC₅₀ in the range of 10.02–44.71 μM). In addition to using flow cytometry and the apoptosis assay, cell cycle arrest at the S phase (10 μM) and G2/M arrest in (5 and 10 μM) was performed for compound 4 in fibrosarcoma (HT-1080) cancer cells. Results suggested that compound 4 test with good activity against HT-1080 cells with IC₅₀ value from 10.02 μM and induced the apoptotic effect. Theoretical studies were realized to estimate the molecular proprieties that lead to a high potential of cytotoxic effect, which is in agreement with the experimental results.     

Correlation Between Chemical Shifts (31P) and Steric Parameters of Phosphametallacycloalkanes

Abstract

The X-ray structures of the phosphametallacycloalkanes 1¹

were investigated to understand the anomalous chemical shift behavior of the phosphorus incorporated in the ringsystem. The ³¹P chemical shifts could not be related to bond angles and to Tolman angles. An electronic contribution to the δP value could be excluded, while the torsional angle effect proved to be the dominant factor.     

1,2,3-Triazolyl-tetrahydropyrimidine Conjugates as Potential Sterol Carrier Protein-2 Inhibitors: Larvicidal Activity against the Malaria Vector Anopheles arabiensis and In Silico Molecular Docking Study

Alteration of insect growth regulators by the action of inhibitors is becoming an attractive strategy to combat disease-transmitting insects. In the present study, we investigated the larvicidal effect of 1,2,3-triazolyl-pyrimidinone derivatives against the larvae of the mosquito Anopheles arabiensis, a vector of malaria. All compounds demonstrated insecticidal activity against mosquito larvae in a dose-dependent fashion. A preliminary study of the structure–activity relationship indicated that the electron-withdrawing substituent in the para position of the 4-phenyl-pyrimidinone moiety enhanced the molecules’ potency. A docking study of these derivatives revealed favorable binding affinity for the sterol carrier protein-2 receptor, a protein present in the intestine of the mosquito larvae. Being effective insecticides against the malaria-transmitting Anopheles arabiensis, 1,2,3-triazole-based pyrimidinones represent a starting point to develop novel inhibitors of insect growth regulators.     

Synthesis and study of poly(ethylene oxide) membranes obtained from homopolymerization of peo macromonomers

Hydrogels were obtained by free-radical polymerization of bifunctional macromonomers. This reaction can be conducted in water solution or in organic solvent. The k_p value is yet strongly depending on the solvent used. The properties of these networks will be compared to those of networks obtained by end-linking procedures. These materials were also used as a semi-permeable membrane in the conception of an artificial pancreas.