Highly Efficient,Four Component,One-pot Synthesis of Tetrasubstituted Imidazoles Using a Catalytic Amount of FeCl<Subscript>3</Subscript> · 6H<Subscript>2</Subscript>O

Summary. An efficient and improved procedure for the synthesis of tetrasubstituted imidazoles by FeCl₃ · 6H₂O catalyzed four-component one-pot synthesis in refluxing ethanol is described.     

Bounding the performance of tandem queues with finite buffer spaces

We consider a queueing system with three single servers in tandem with two intermediate buffer storages of finite capacity. The processing times are exponentially distributed and the first server has unlimited number of customers in front of it. Using a negative dependence property between the number of customers at the first and second buffer storages we show that a popular form of decomposition approach applied to this model, indeed, provides a lower bound for its performance. The approach used here to establish the bound is new and could be extended to establish bounds for other types of tandem queues with finite buffer spaces.     

Preparation of Co3O4 nanoparticles by nonhydrolytic thermolysis of [Co(Pht)(H2O)]n polymers

Benzenedicarboxylate complexes, especially phthalate ones, can be significant precursors for the preparation of nano-sized metal and metal oxides. The injection of organic surfactants such as oleic acid (OA) and triphenylphosphine into molecular precursors has yielded samples with size control, narrow size distributions and crystallinity of individual nanocrystals. Fourier transform infrared and X-ray photoelectron spectroscopy revealed that the OA molecules were adsorbed on the ferromagnetic nanoparticles by chemisorption. The temperature-dependent magnetization curve in zero-field-cooled and field-cooled exhibit weak ferromagnetism of the Co₃O₄ nanoparticles. At 300 K the remanent magnetization is 0.02 emu/g, the coercive field is 441 Oe and the magnetization at saturation is 1.05 emu/g.     

Tunable optical filter based on Sagnac phase-shift using single optical ring resonator

In this paper, a single optical ring resonator connected to a Sagnac loop is used to demonstrate theoretically a novel narrow band optical filter response that is based on Sagnac phase-shift Δφ. The given filter structure permits the Sagnac rotation to control the filter response. It is shown that by changing the Sagnac rotation rate, we can tune the filter response for desired bandwidths. To increase the wavelength selectivity of the filter, the Sagnac phase-shift should be as small as possible that is limited by the loop length. For Δφ=0.1 rad, the obtained FWHM is 2.63 MHz for tuning loop length of 2 m. The simulation response agrees fairly with the recently reported experimental result.     

Some generalizations of torsion-free Crawley groups

In this paper we investigate two new classes of torsion-free Abelian groups which arise in a natural way from the notion of a torsion-free Crawley group. A group G is said to be an Erd?s group if for any pair of isomorphic pure subgroups H,K with G/H ? G/K, there is an automorphism of G mapping H onto K; it is said to be a weak Crawley group if for any pair H,K of isomorphic dense maximal pure subgroups, there is an automorphism mapping H onto K. We show that these classes are extensive and pay attention to the relationship of the Baer-Specker group to these classes. In particular, we show that the class of Crawley groups is strictly contained in the class of weak Crawley groups and that the class of Erd?s groups is strictly contained in the class of weak Crawley groups.     

On the Apéry sets of monomial curves

In this paper, we use the Apéry table of the numerical semigroup associated to an affine monomial curve in order to characterize arithmetic properties and invariants of its tangent cone. In particular, we precise the shape of the Apéry table of a numerical semigroup of embedding dimension 3, when the tangent cone of its monomial curve is Buchsbaum or 2-Buchsbaum, and give new proofs for two conjectures raised by Sapko (Commun. Algebra 29:4759–4773, 2001) and Shen (Commun. Algebra 39:1922–1940, 2001). We also provide a new simple proof in the case of monomial curves for Sally’s conjecture (Numbers of Generators of Ideals in Local Rings, 1978) that the Hilbert function of a one-dimensional Cohen-Macaulay ring with embedding dimension three is non-decreasing. Finally, we obtain that monomial curves of embedding dimension 4 whose tangent cones are Buchsbaum, and also monomial curves of any embedding dimensions whose numerical semigroups are balanced, have non-decreasing Hilbert functions. Numerous examples are provided to illustrate the results, most of them computed by using the NumericalSgps package of GAP (Delgado et al., NumericalSgps-a GAP package, 2006).     

Powers of the Vertex Cover Ideal of a Chordal Graph

In this article, Cohen–Macaulay chordal graphs and generalized star graphs are studied to show that all powers of the vertex cover ideal of such graphs have linear quotients. Moreover, it is shown that the Alexander dual of the clique complex of any chordal graph is vertex decomposable.     

Fuzzy quasi C*-algebra

At the present paper, the new concepts of fuzzy quasi norm, fuzzy Banach space, fuzzy quasi continuity and fuzzy quasi boundedness is introduced. Furthermore, we define the fuzzy quasi operator norm and also it is shown that the set all of fuzzy quasi bounded operator from X to Y is fuzzy quasi Banach space. Finally, we have introduced and investigated some notions and some results on *-algebra theory.