Studies of the elimination of 4-aryl-3-methyl-4-piperidinols—I The conformation of epimeric 1-alkyl (and aralkyl)-4-aryl-5-methyl-1,2,5-6-tetrahydropyridine hydrochlorides

A detailed study of the products of elimination of some 4-aryl-3-methyl-4-piperidinols has been made and the PMR spectra of derived 1-alkyl (and aralkyl)-4-aryl-5-methyl-1,2,5,6-tetrahydropyridines and the corresponding hydrochloric salts reported and discussed. The 5-methyltetrahydropyridine hydrochlorides are shown to exist in epimeric forms in deuterochloroform and their PMR spectra have been interperted in terms of probable conformations.     

Polynomes a valeurs entieres sur un anneau de pseudovaluation

We study the ring of integral valued polynomials over a pseudovaluation domain A. We entirely determine the set of prime ideals above the maximal ideal M of A: if M is a principal ideal in the valuation domain V associated with A and if its residue field is finite, then this set is in bijection with a topologically complete ring, as in the Noetherian case; if M is principal but of infinite residue field in V, then this set is finite; at last, if M is not principal, then the ring of integral valued polynomials is included in V[X] and has the same set of prime ideals above M.     

Isotope Effects on the Lipophilicity of Deuterated Caffeines

In the present study, it is confirmed that the deuteration of C? H groups is accompanied by a small but genuine decrease in lipophilicity. The lipophilicity of deuterated isotopomers of caffeine was measured by reversed-phase HPLC. Overall, lipophilicity was shown to decrease when going from unlabelled caffeine to the three isomeric trideuterated caffeines, then to the three isomeric hexadeuterated caffeines, and finally to nonadeuterated caffeine. In addition, position-specific effects were also proven. E.g. (7-methyl-²H₃)caffeine experienced a smaller isotope effect than its two positional isomers. Both a cavity factor (decreased volume of deuterated isotopomers) and intramolecular electronic effects are postulated to operate.     

Solvability of some quadratic BSDEs without exponential moments

We establish the existence and uniqueness of square integrable solutions for a class of one-dimensional quadratic backward stochastic differential equations (QBSDEs). This is done with a merely square integrable terminal condition, and in some cases with a measurable generator. This shows, in particular, that neither the existence of exponential moments for the terminal condition nor the continuity of the generator are needed for the existence and/or uniqueness of solutions for quadratic BSDEs. These conditions are used in the previous papers on QBSDEs. To do this, we show that Itô?s formula remains valid for functions having a merely locally integrable second (generalized) derivative. A comparison theorem is also established.     

Besov regularity for the indefinite Skorohod integral with respect to the fractional Brownian motion: The singular case

Using the techniques of the Malliavin calculus and the properties of Gaussian processes, we prove that the paths of the indefinite Skorohod integral with respect to the fractional Brownian motion (fBm) with Hurst parameter less than 1/2 belongs to the Besov space B p , X H , for any p >(1/ H ).     

Regular subsets of valued fields and Bhargava’s v-orderings

We generalize notions and results obtained by Amice for regular compact subsets S of a local field K and extended by Bhargava to general compact subsets of K. Considering any ultrametric valued field K and subsets S that are regular in a generalized sense (but not necessarily compact), we show that they still have strong properties such as having v-orderings ${\{a_n\}_{n\geq0}}$ which satisfy a generalized Legendre formula, which are very well ordered and well distributed sequences in the sense of Helsmoortel and which remain v-orderings when a finite number of the initial terms of the sequence are deleted.