Polynomial maps attached to polynomials of an Ore extension are naturally defined. In this setting we show the importance of pseudo-linear transformations and give some applications. In particular, factorizations of polynomials in an Ore extension over a finite field Fq[t; θ], where θ is the Frobenius automorphism, are translated into factorizations in the usual polynomial ring Fq[x].

Gold-catalyzed reactions, which have been widely explored over the past several years, are powerful tools in organic synthesis to access complex molecular frameworks, and some corresponding excellent reviews have been reported. However, little attention has been paid to summarize the reactions of strained small-ring-containing molecules catalyzed by gold. This critical review mainly puts its em...

As an environmentally-green technology, thermal catalytic oxidation of octachloronaphthalene (CN-75) over anatase TiO2 nanomaterials was investigated at 300 °C. A wide range of oxidation intermediates, which were investigated using various techniques, could be of three types: naphthalene-ring, single-benzene-ring, and completely ring-opened products. Reactive oxygen species on anatase TiO2 surf...

Haptens with bridge at the 2-position have not yet been explored. Radioimmunoassays with antibodies directed against 2 alpha-alkyl bridged steroid haptens are expected to be highly specific due to greater topographical exposure and similarity in conformation to the native steroid. The 2 alpha-alkyl bridged haptens were synthesized by first adding a cyclopropane ring to 2-methylene-4-en-3-one. S...

A series of previously unavailable derivatives of 2-alkyland 2-benzylderivatives of oxazolo[3,2-a]pyridines III were obtained via tandem ring opening and ring closure from stable mesoionic 3-acyloxazolo[3,2-a]pyridinium-2-olates I. The key intermediates of this tandem transformation are N-(b-oxoethyl)pyridones-2 II obtained by Dakin-West acylation of (pyridone-2-yl-1)acetic acid. An example of ...

Organocatalysis, now running its second decade of life, is being considered one of the main tools a synthetic chemist has to perform asymmetric catalysis. In this review the synthesis of six-membered rings, that contain multiple chiral centers, either by a ring closing process or by a functionalization reaction on an already existing six-membered ring, utilizing bifunctional (thio)ureas will be...

Fourteen different genes included in a DNA fragment of 18 kb are involved in the aerobic degradation of phenylacetic acid by Pseudomonas putida U. This catabolic pathway appears to be organized in three contiguous operons that contain the following functional units: (i) a transport system, (ii) a phenylacetic acid activating enzyme, (iii) a ring-hydroxylation complex, (iv) a ring-opening protei...

In this paper, we propose an algorithm for wavelet based spatio-temporal data compression in wireless sensor networks. By employing a ring topology, the algorithm is capable of supporting a broad scope of wavelets that can simultaneously explore the spatial and temporal correlations among the sensory data. Furthermore, the ring based topology is in particular effective in eliminating the “borde...

MacWilliams’ equivalence theorem states that Hamming isometries between linear codes extend to monomial transformations of the ambient space. One of the most elegant proofs for this result is due to K. P. Bogart et al. (1978, Inform. and Control 37, 19–22) where the invertibility of orthogonality matrices of finite vector spaces is the key step. The present paper revisits this technique in orde...

In this paper we show that any hypersurface singularities of germs of varieties in positive characteristic can be resolved by iterated monoidal transformations with centers in smooth subvarieties, if we have a valuation ring of iterated divisor type associated with the germ. Besides, we introduce fundamental concepts for the study of resolution of singularities of germs such as space germs, ite...