The problem of determining the degree of C-sufficiency s(f) of a given analytic function germ f : (C, 0) → (C, 0) is well known in singularity theory. There is some previous work which gives an upper estimate for this number (see Section 2 for its definition). For instance, in the paper [Lichtin 81], the case n = 2 is considered. In the paper [Fukui 91], an estimate for the degree of C-sufficie...

In the framework of the minimal supersymmetric standard model with an R-parity breaking coupling of the scalar top quark (stop) we investigate production processes and decay properties of the stop at HERA energies. The model is characterized by a light stop possibly lighter than the other squarks. We show that the stop could be singly produced not only in the neutral current processes but also ...

Background: Understanding of the gut-liver axis is important for the up-to-date management of liver cirrhosis, and changes of intestinal functions form the core of this interesting research field. Summary: Most investigators noted small intestinal dysmotility in their patients with liver cirrhosis. Marked changes in the contraction pattern were observed in early manometric studies. The orocecal...

OBJECTIVE To investigate the relationship between axial length, myopia of the eye, and the severity of lens opacity at the time of cataract surgery. METHODS We retrospectively reviewed a consecutive series of 198 eyes of patients aged older than 50 years at Fukui University Hospital (Fukui, Japan) from June 2004 to December 2005. Patient age at the time of surgery, axial length, spherical equ...

The free-energy profile of a reaction can be estimated in a molecular-dynamics approach by imposing a mechanical constraint along a reaction coordinate (RC). Many recent studies have shown that the temperature can greatly influence the path followed by the reactants. Here, we propose a practical way to construct the minimum-energy path directly on the free-energy surface at a given temperature....

In this work, the theoretical description of the 4- and 3-substituted-cinnamic acid esterification with different electron donating and electron withdrawing groups was performed at the B3LYP and M06-2X levels, as a two-step process: the O-protonation and the nucleophile attack by ethanol. In parallel, an experimental work devoted to the synthesis and characterization of the substituted-cinnamat...