Theoretical investigations of the processes of laser interaction with ocular tissues for laser applications in ophthalmology

Theoretical investigations and the results of computer modeling of the optical, thermophysical, and thermochemical processes during laser interaction with ocular tissues are reviewed in this paper. Physical-mathematical models and results of numerical simulation of the processes are presented. The computer modeling was applied for investigations of laser heating and coagulation of ocular tissues for treatment of retina diseases and intraocular tumors, cyclophotocoagulation of the ciliary body for treatment of glaucoma, and laser thermal keratoplasty of the cornea. The influence of radiation parameters on the selectivity of laser coagulation of laminated ocular tissues is considered. The results obtained are of essential interest for laser applications in ophthalmology and can be used for investigation of heating and coagulation of tissues in different fields of laser medicine.     

On the Weak Invariance Principle for Stationary Sequences under Projective Criteria

In this paper, we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables with respect to the distant past. The results contribute to the clarification of the central limit question for stationary sequences. Magda Peligrad is supported in part by a Charles Phelps Taft research support grant at the Univeristy of Cincinnati and the NSA grant H98230-05-1-0066.     

More compact invariant manifolds appearing in the non-linear coupling of oscillators

Near partially elliptic rest points of generic families of vector fields or transformations, many types of normally hyperbolic invariant compact manifolds can appear, diffeomorphic to intersections of quadrics. To cite this article: M. Chaperon et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Regularization procedures of mixed finite element approximations of the stokes problem

We propose a theoretical framework for the study of regularization of the Stokes problem. This enables us to perform a general error analysis and to apply it to known schemes as well as to a new one pertaining to the use of the P1-P1 element. Finally we show that in the P1-case the theory can also be used to get convergence results for elements obtained by addition of bubble functions, without using the usual mixed finite element machinery.     

Numerical and theoretical study of a Dual Mesh Method using finite volume schemes for two phase flow problems in porous media

Summary. In this paper we are interested in two phase flow problems in porous media. We use a Dual Mesh Method to discretize this problem with finite volume schemes. In a simplified case (elliptic - hyperbolic system) we prove the convergence of approximate solutions to the exact solutions. We use the Dual Mesh Method in physically complex problems (heterogeneous cases with non constant total mobility). We validate numerically the Dual Mesh Method on practical examples by computing error estimates for different test-cases. Received March 21, 1997 / Revised version received October 13, 1997     

Synthesis of new 7-aminosterol squalamine analogues with high antimicrobial activities through a stereoselective titanium reductive amination reaction

A series of 7-amino- and polyaminosterol analogues of squalamine and trodusquemine were synthesized involving a new stereoselective titanium reductive amination reaction in high chemical yields of up to 95% in numerous cases. These derivatives were evaluated for their in vitro antimicrobial properties against human pathogens. All the compounds present excellent activities against Gram-positive bacteria exhibiting similar results against Staphylococcus aureus and Streptococcus faecalis with minimum inhibitory concentrations (MICs) varying from 2.5 to 10 μg/mL. Numerous derivatives possess also MICs against Gram-negative Escherichia coli bacteria (MICs varying from 2.5 to 10 μg/mL) suggesting that nature of the amino group attached to the sterol moiety plays an important role on the activities of such products.     

Polygermoxanes suitable for biochemical purposes. Part I. Digermoxanes (low-viscosity oils)

In order to replace silicones in some of their biomedical applications, e.g. syringe lubrication, implants ets., a series of digermoxanes (R¹R²R³Ge)₂O (R = n–alkyl, aryl) were synthesized. These compounds are thermally stable oils; their viscosities, depending on the nature of substituents, lie in the range 1–72 cPo (mPa s) at 20°C.