Invariant measures and regularity properties of perturbed Ornstein-Uhlenbeck semigroups

This paper deals with perturbations of the Ornstein-Uhlenbeck operator on L²-spaces with respect to a Gaussian measure μ. We perturb the generator of the Ornstein-Uhlenbeck semigroup by a certain unbounded, non-linear drift, and show various properties of the perturbed semigroup such as compactness and positivity. Strong Feller property, existence and uniqueness of an invariant measure are discussed as well.     

Gas chromatographic properties of two thermotropic Poly(L-glutamates) with long alkyl side chains

Summary Comparative gas chromatographic properties of two thermotropic Poly(L-glutamates) with long alkyl side chains (10 and 16 carbons called Poly 10 and Poly 16 respectively) are studied.Their thermal properties were established with differential scanning calorimetry (DSC) and gas chromatography. They present a cholesteric liquid crystal in a large temperature range.The chromatographic separation abilities of the two polymers in the liquid crystal state were studied using capillary glass columns. Interesting analytical performances were obtained in different fields: isomeric separation of alkanes, aromatics, polyaromatics, volatile aroma compounds and cis and trans isomers. Some differences were noticed in their behaviours; 2 and 3-methyloctane and xylene isomers are separated only on Poly 10 while limonene and eucalyptol are separated only on Poly 16.     

Quasistatic frictional thermo‐piezoelectric contact problem

We consider here a mathematical model describing the bilateral frictional contact between a thermo‐piezoelectric body and a thermally conductive foundation. We model the behavior of the material with a linear thermo‐electro‐elastic constitutive law. The process is assumed to be quasistatic and the contact is modeled with a nonlocal version of Coulomb's dry friction law, in which the frictional heat generated in the process, is taken into account. We drive a variational formulation of the problem and establish the existence of its weak solution.     

Representation of infinite-dimensional neutral non-autonomous control systems

This paper studies the well-posedness of a class of non-autonomous neutral control systems in Banach spaces. We prove that such systems are represented by absolutely regular non-autonomous linear systems in the sense of Schnaubelt [R. Schnaubelt, Feedback for non-autonomous regular linear systems, SIAM J. Control Optim. 41 (2002) 1141-1165]. This paper can be considered as the non-autonomous version of the work presented in [H. Bounit, S. Hadd, Regular linear systems governed by neutral FDEs, J. Math. Anal. Appl. 320 (2006) 836-858].     

Improved moment estimates for invariant measures of semilinear diffusions in Hilbert spaces and applications

We study regularity properties for invariant measures of semilinear diffusions in a separable Hilbert space. Based on a pathwise estimate for the underlying stochastic convolution, we prove a priori estimates on such invariant measures. As an application, we combine such estimates with a new technique to prove the L¹-uniqueness of the induced Kolmogorov operator, defined on a space of cylindrical functions. Finally, examples of stochastic Burgers equations and thin-film growth models are given to illustrate our abstract result.     

Fluorinated resveratrol and pterostilbene

A general method for the synthesis of polyhydroxylated stilbene monofluorinated on the central double bond based on the Suzuki reaction between a bromofluoroolefin and a phenylboronic acid is described. Synthesis of fluorinated analogues of resveratrol and pterostilbene was achieved using this strategy.     

Positivity of Perturbed Ornstein-Uhlenbeck Semigroups on Cb(H)

In this paper we further develop the abstract theory of bi-continuous semigroups by combining perturbation and approximation techniques. The results are then applied to show the positivity for a class of perturbed Ornstein-Uhlenbeck semigroups on the Banach lattice C_b(H) of bounded continuous functions on a separable Hilbert space H.     

Ethnobotanical study of some aromatic and medicinal plants in the Middle Atlas mountains of Morocco

By the diversity of its soil and climatic factors, Morocco offers a flora particularly rich in aromatic and medicinal plants (MAP). In order to obtain the most information about the flora (flowering times, fruiting, harvesting and their main uses in traditional medicine), a study was conducted in the mountainous Khenifra region. A survey of users of MAP (rural population, herbalists arborists) has been undertaken and was completed by field observations and sampling at different stages of growth. The results showed a range of indigenous and diversified MAP belonging to 10 botanical families (Lamiaceae, Asteraceae, Rosaceae, Chenopodiaceae, Papaveraceae, Caryophyllaceae, Cupressaceae, Rutaceae, Anacardiaceae and Zygophyllaceae). The flowering period of all species, according to the local community surveyed, spread from February (2%) to September (12%), with a significant concentration from April to June (65%).The highest rate of fructification occurred in June-July (64%). The harvesting period of the main MAP from this mountain area stretches mainly from March to April (61%). The mode of propagation stated varied among species, and concerned mainly replication by seeds (53%) and cuttings (24%). Regarding the use of these indigenous MAP as traditional medicines, all plant parts are used, especially leaves, flowers and stems.     

Polyfunctional fused heterocyclic compounds via indene‐1,3‐diones

2‐Dimethylaminomethylene‐ and 2‐ethoxymethylene‐1,3‐indendione 1a,b react with 6‐amino‐2‐thioxopyrimidin‐4(3H)‐one 2 in boiling acetic acid to give 2‐thioxo‐1,3‐dihydroindeno[3,2‐d]pyrimidino[4,5‐b]pyridine‐4,9‐dione ( 4 ). The latter compound reacts with hydrazonoyl chlorides 5a–c to afford products 12a–c . Formamidine 15 reacts with indene‐1,3‐dione in boiling ethanol to give acyclic compound 16 , which cyclizes to 12a in boiling glacial acetic acid. Also, enaminone 1a reacts with heterocyclic amines 17a–e in boiling ethanol, affording the corresponding substitution products 18a–c , respectively. The latter products 18a–c cyclize in glacial acetic acid to give 19a–c , respectively. The structures of the newly synthesized compounds are established on the basis of chemical and spectroscopic evidence. © 2003 Wiley Periodicals, Inc. Heteroatom Chem 14:491–497, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10166