This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...

It is shown that if the ring of constants of a restricted differential Lie algebra with a quasi-Frobenius inner part satisfies a polynomial identity (PI) then the original prime ring has a generalized polynomial identity (GPI). If additionally the ring of constants is semiprime then the original ring is PI. The case of a non-quasi-Frobenius inner part is also considered.

It is shown that a commutative Bézout ring R with compact minimal prime spectrum is an elementary divisor ring if and only if so is R/L for each minimal prime ideal L. This result is obtained by using the quotient space pSpec R of the prime spectrum of the ring R modulo the equivalence generated by the inclusion. When every prime ideal contains only one minimal prime, for instance if R is arith...

Let S be a cancellative monoid with quotient group of torsion-free rank a. We show that the monoid ring R[S] is a Hilbert ring if and only if the polynomial ring R[{ X, },s/] is a Hilbert ring, where |/| = a. Assume that R is a commutative unitary ring and G is an abelian group. The first research problem listed in [K, Chapter 7] is that of determining equivalent conditions in order that the gr...

A homemade mitral annular prosthesis has been developed using expanded-polytetrafluoroethylene material. It is safe in that it avoids the risk of prosthesis wrinkle when stitches are tied. Simultaneously, it is strong enough to prevent future stretching and rupture. This device has been implanted in 60 patients with good and stable results at 42 months of follow-up. Our flexible mitral annular ...

PURPOSE To assess the outcomes of intrastromal corneal ring (ISCR) implantation for the treatment of corneal ectasia. METHODS Thirty-five consecutive patients with secondary corneal ectasia treated with keraring intrastromal corneal ring segment implantation aided by intralaser femtosecond technique (K-ICRS-FS) were evaluated. Visual acuity (logMAR), refraction and astigmatism vector analysis...

This lecture defines formally the new concept of "edge of chaos" in a mathematically rigorous, explicit, and easily testable manner. The main result asserts that the edge of chaos is the Holy Grail that both Alan Turing and Stephen Smale had sought in vain. It is in fact the genesis of non-homogeneous spatial-temporal patterns and structures widely reported in complexity theory. 25.05.2012 Begi...

In the larval salivary glands of C. tentans, it is possible to visualize by electron microscopy how Balbiani ring (BR) pre-mRNA associates with proteins to form pre-mRNP particles, how these particles move to and through the nuclear pore, and how the BR RNA is engaged in the formation of giant polysomes in the cytoplasm. Here, we study C. tentans hrp36, an abundant protein in the BR particles, ...

Two decarboxylative methods providing access to N-alkylated α-trihalomethylated heterocyclic amines have been developed. A batch protocol in which methyl trifluoroacetate acts both as a methylating reagent and subsequently as a nucleophilic trifluoromethyl anion precursor upon its addition to (iso)quinoline derivatives. Next, a telescoped continuous flow process, forming the corresponding α-tri...