On reinforcing effect of birefringent coatings on plate structures

A mathematical model is introduced and used to obtain a correction factor of the reinforcing effect of birefringent coatings on structures. The bending effect introduced to the coated structure due to the shifting of neutral surface is considered in the derivation of the correction factor. The photoelastic data corrected by this correction factor are found to be in good agreement with the theoretical calculations.     

Triangulations of the sphere,bitrades and abelian groups

Let \(\mathcal{G}\) be a triangulation of the sphere with vertex set V, such that the faces of the triangulation are properly coloured black and white. Motivated by applications in the theory of bitrades, Cavenagh and Wanless defined \(\mathcal{A}_W\) to be the abelian group generated by the set V, with relations r+c+s = 0 for all white triangles with vertices r, c and s. The group \(\mathcal{A}_B\) can be de fined similarly, using black triangles. The paper shows that \(\mathcal{A}_W\) and \(\mathcal{A}_B\) are isomorphic, thus establishing the truth of a well-known conjecture of Cavenagh and Wanless. Connections are made between the structure of \(\mathcal{A}_W\) and the theory of asymmetric Laplacians of finite directed graphs, and weaker results for orientable surfaces of higher genus are given. The relevance of the group \(\mathcal{A}_W\) to the understanding of the embeddings of a partial latin square in an abelian group is also explained.     

The Synthesis and Evaluation of Quaternary Pyridinium Bisphosphonates as Potent Anti-Resorptives

Abstract

Several novel quaternary pyridinium bisphosphonates have been synthesised and their efficacy as potential anti-resorptive bone agents have been tested in Dictyostelium discoideum. This assay has been shown to accurately reflect the potency of a bisphosphonic acid as an anti-resorptive compound. All the quaternary bisphosphonates are very potent growth inhibitors but results indicate that the more potent compounds are those containing hydrophobic, bulky groups.     

Studies on Bis(5′-Adenosyl)-P1, P4-Tetraphosphate,Appppa, and Some Synthetic Isosteric and Isopolar Phosphonate Analogues Using the Specific Appppaases from Artemia and Lupin

Abstract

We have recently reported the synthesis and separation of three diastereoisomers of diadenosine 5′, 5″-P¹,P⁴-(P¹, P⁴-dithiO-P², P³-methylene)-tetraphosphate, (Ap₅pCH₂pp₅A), and demonstrated their resistance to hydrolysis by and competitive inhibition of the asymmetrica1 NppppNase from Artemia (1), while Guranowski et al.(2) have studied the ability of four phosphonate analogues of AppppA to act as substrates and inhibitors of the lupin and E. coli NppppNases, lupin phosphodiesterase I, and the yeast AppppA phosphorylase.     

Suzuki-Miyaura cross-coupling of aryl carbamates and sulfamates: experimental and computational studies

The first Suzuki-Miyaura cross-coupling reactions of the synthetically versatile aryl O-carbamate and O-sulfamate groups are described. The transformations utilize the inexpensive, bench-stable catalyst NiCl(2)(PCy(3))(2) to furnish biaryls in good to excellent yields. A broad scope for this methodology has been demonstrated. Substrates with electron-donating and electron-withdrawing groups are tolerated, in addition to those that possess ortho substituents. Furthermore, heteroaryl substrates may be employed as coupling partners. A computational study providing the full catalytic cycles for these cross-coupling reactions is described. The oxidative addition with carbamates or sulfamates occurs via a five-centered transition state, resulting in the exclusive cleavage of the aryl C-O bond. Water is found to stabilize the Ni-carbamate catalyst resting state, which thus provides rationalization of the relative decreased rate of coupling of carbamates. Several synthetic applications are presented to showcase the utility of the methodology in the synthesis of polysubstituted aromatic compounds of natural product and bioactive molecule interest.     

A Note on Sequences with the Shift and Add Property

A sequence of elements from a finite field satisfies the shift and add property if the componentwise sum of any two shifts of the sequence is either a shift of the sequence or the all zero sequence. A sequence whose elements lie in an arbitrary group satisfies the shift and multiply property if the componentwise product of any two shifts of the sequence is either a shift of the sequence or the all identity sequence. The paper classifies sequences which have the shift and add property or the shift and multiply property.