Monte carlo techniques

Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring probability density functions.     

Renormalized Solutions of Nonlinear Parabolic Equations in Weigthed Variable-Exponent Space

This article is devoted to study the existence of renormalized solutions for the nonlinear p(x)-parabolic problemin the Weighted-Variable-Exponent Sobolev spaces, without the sign condition and the coercivity condition.     

Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space

In this article, we study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion $β(u)-div(a(x,Du)+F(u)) ∋ f$ in $Ω$ where $f ∈ L^1(Ω).$ A vector field $a(.,.)$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the framework of weighted variable exponent Sobolev spaces, we prove existence of renormalized solutions for general $L^1$-data.     

Effect of phosphatidylserine content on the partition coefficients of diazepam and flurazepam between phosphatidylcholine-phosphatidylserine bilayer of small unilamellar vesicles and water studied by second derivative spectrophotometry

The affinity of the psychotropic benzodiazepine drugs diazepam (DZ) and flurazepam (FZ) to phosphatidylserine (PS) was examined since PS is abundantly contained in brain membranes. The effect of PS content on the partition coefficients (K(p)s) of these drugs between phosphatidylcholine (PC)-PS bilayer membranes of small unilamellar vesicles (SUV) and water was measured using second derivative spectrophotometry. The second derivative spectra of DZ and FZ measured in the solutions containing various amounts of PC-PS SUV clearly showed derivative isosbestic points and a distinct derivative intensity change depending on the amount of the SUV added. The derivative intensity differences (AD) of the drugs before and after addition of the SUV suspension were measured at a specific wavelength. Using the AD values, the Kp values were calculated and obtained with relative standard deviation of below 10%. The Kp values of both drugs increased according to the PS content in the PS-PC bilayer membranes of the SUV proving that both have higher affinity to the PC-PS bilayer membranes than to PC membranes. The effect was much larger for FZ, i.e., the Kp value of FZ at 30 mol% PS content increased to about five times the value for the PC SUV. This can be explained by the fact that at the experimental pH of 7.4, 80% of FZ molecules are in a cationic form (pKa=8.1), so that these molecules are highly accessible to the negatively charged PS molecules. The results support the rapid and high distribution of DZ and FZ in the central nervous system after their administration.     

The microdetermination of certain pyrimidine derivatives

N-Bromosuccinimide has been used in a new titrimetric method for the microdetermination of uracil, thymine, and sulfadiazine. The reaction between these compounds and N-bromosuccinimide in dilute aqueous solutions is discussed. The determination is carried out within the limits of 10 mg to 100 μg where the experimental error did not exceed ±2%.     

Factorial preservation

Let A be a Dedekind domain with finite residue fields and with a finite unit group. Let S be an infinite subset of A and f be a polynomial with coefficients in the quotient field of A. We show that if the subsets S and f (S) have the same factorials (in Bhargavas sense), then f is of degree 1. In particular, we answer Gilmer and Smiths question [10] if S and f (S) are polynomially equivalent (in McQuillans sense), then f is of degree 1.Received: 29 March 2004     

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.