Model-Free Analysis of Mixtures by NMR Using Blind Source Separation

The concept of blind source separation is described and examples of its use in 1D and 2D NMR spectroscopy are presented. The goal of this data processing method is to extract the spectra of components molecules when only mixtures are available.     

Time-of-flight secondary ion mass spectrometry imaging demonstrates the specific localization of deca-bromo-diphenyl-ether residues in the ovaries and adrenal glands of exposed rats

Deca-bromo-diphenyl ether (DBDE) is one of the most efficient brominated flame retardant (BFR) available on the market. We recently demonstrated that when administered to female rat by oral route, DBDE is efficiently absorbed, with the highest residual concentrations found in two endocrine glands, namely the adrenal glands and the ovaries. Tinie-of-flight secondary ion mass spectrometry (TOF-SIMS) imaging, a technique usually used for the study of endogenous compounds, was applied for the first time to a persistent organic pollutant, allowing to detect and to precisely localize DBDE residues in these two target tissues. The detection of the bromide ion (⁸¹Br isotope) by TOF-SIMS mass spectrometry imaging allowed us to demonstrate a marked cortical tropism of DBDE residues for the adrenal glands in female rats dosed per os 2 mg · kg⁻¹ DBDE, daily, over 96 h. In ovaries, DBDE residues were found to be concentrated in spots corresponding to part of the corpora lutea. Hepatic residues of DBDE were found to be homogeneously distributed. Due to the intrinsic toxicity of DBDE, its accumulation in the adrenal glands and the ovaries may be connected to the mechanisms of actions by which DBDE could trigger endocrine disruption in mammals.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.