Synthesis and Reactions of Some New Pyrrolylfuro[2,3‐d]Pyrimidines and Pyrrolopyrazinofuropyrimidines

5‐Amino‐4‐methyl‐2‐phenyl‐6‐substitutedfuro[2,3‐d]pyrimidines ( 2a‐c ) were reacted with 2,5‐dimethoxytetrahydrfuran to afford the pyrrolyl derivatives 3a‐c . Compound 3a was chosen as intermediate for the synthesis of poly fused heterocycles incorporated furopyrimidines moiety 4–11 . Some of the synthesized compounds were screened for their antibacterial and antifungal activities.     

Sparse polynomials, redundant bases, gauss periods, and efficient exponentiation of primitive elements for small characteristic finite fields

Gauss periods give an exponentiation algorithm that is fast for many finite fields but slow for many other fields. The current paper presents a different method for construction of elements that yield a fast exponentiation algorithm for finite fields where the Gauss period method is slow or does not work. The basic idea is to use elements of low multiplicative order and search for primitive elements that are binomial or trinomial of these elements. Computational experiments indicate that such primitive elements exist, and it is shown that they can be exponentiated fast.     

Effects of annealing conditions on the electrical properties of Bi4-xNdxTi3O12 (x = 0.46) thin films processed at low temperature

Neodymium-substituted Bi₄Ti₃O₁₂ (BNdT) thin films were prepared by a chemical solution deposition technique on platinum- coated silicon substrates. All of the samples were annealed at the relatively low temperature of 600 °C by a rapid thermal annealing process in different atmospheres, such as O₂, air, and nitrogen, and vacuum. Irrespective of different annealing atmospheres, all of the BNdT thin films exhibit good ferroelectric properties, such as a saturated hysteresis loop, good fatigue endurance, and low leakage current density. A large remanent polarization (P_r) of ∼48 μC/cm² with an electric field of 240 kV/cm was observed from the BNdT thin film annealed in O₂ atmosphere. The BNdT thin films annealed in nitrogen and vacuum, at reduced oxygen partial pressures, exhibit smaller P_r than that annealed in oxygen. The difference of P_r of the BNdT thin films annealed in different atmospheres may originate from differences in the grain sizes and the number of oxygen vacancies. PACS 77.55.+f; 77.80.-e; 77.80.Fm; 81.15.-z     

Some formulae for the q-Bernoulli and Euler polynomials of higher order

The purpose of this paper is to give a proof of Kummer type congruence for the q-Bernoulli numbers of higher order, which is an answer to a part of the problem in a previous publication (see Indian J. Pure Appl. Math. 32 (2001) 1565-1570).     

Three New Polyoxygenated Steroids from Two Species of the South China Sea Gorgonian Muricella flexuosa and Menella verrucosa Brundin

Three new polyoxygenated steroids, muricesteroid ( 1 ), and menellsteroids A ( 2 ) and B ( 3 ), were isolated from two species of the South China Sea gorgonian Muricella flexuosa and Menella verrucosa Brundin , respectively. The structures of these new compounds were elucidated on the basis of extensive spectroscopic analysis, chemical methods and comparison with known related compounds.     

Asymmetric synthesis of homo-apioneplanocin A from d-ribose

Homo-apioneplanocin A was efficiently synthesized via stereoselective hydroxymethylation, regio- and chemoselective hydroboration, and chemoselective oxidation as key steps from d-ribose.     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Novel route to 5-position vinyl derivatives of thiolactomycin: Olefination vs. deformylation

Vinyl and diene derivatives of thiolactomycin have been prepared via Horner-Wadsworth-Emmons olefination from protected 5-formyl-3,5-dimethylthiotetronic acid. Several 4-position protecting groups and a variety of phosphonates were evaluated, with MOM protection and β-ketophosphonates yielding the highest ratio of the desired product to deformylated product.     

Fuzzy convex sets in median algebras

The fuzzification of convex sets in median algebras is considered, and some of their properties are investigated. A characterization of finite valued fuzzy convex set is given.