The way of Diophantus: Some clarifications on Diophantus' method of solution

In the introduction of the Arithmetica Diophantus says that in order to solve arithmetical problems one has to “follow the way he (Diophantus) will show.” The present paper has a threefold objective. Firstly, the meaning of this sentence is discussed, the conclusion being that Diophantus had elaborated a program for handling various arithmetical problems. Secondly, it is claimed that what is analyzed in the introduction is definitions of several terms, the exhibition of their symbolism, the way one may operate with them, but, most significantly, the main stages of the program itself. And thirdly, it is argued that Diophantus' intention in the Arithmetica is to show the way the stages of his program should be practically applied in various arithmetical problems.     

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.     

Détermination des perturbations induites aux extrémités d’une ligne blindée soumise à une excitation ponctuelle de courant

This article allows the determination of the induced perturbations at the ends of the coaxial line in wide frequency band enough. The perturbation source is a current direct point injection into the cable screen in any position. For this, we have applied the theory of the state variables, with foundation of the quasi-TEM approximation, in order to simulate the coaxial line above a ground level that has a finished conductivity. This allows us to supply the current and voltage expressions at the ends of the line as their analytic forms for any conditions of charge. Next, the elaborate objective is to verify experimentally on concrete applications if the test obtained results confirm the theoretical expectations supplied by calculation code finalizing.     

Quaternionic-Kähler manifolds and conformal geometry

Research funded in part by NSF grant DMS-8704401     

Modélisation et analyse temporelle d’un bus d’interconnexion en technologie GaAs

The author presents the theoretical methods for modeling and transient analysis of coupled transmission lines. For an interconnecting bus used in GaAs technology with a 30 ps rise time activating signal and 3 mm length, he shows the great importance of coupling: signal distortion on the activated lines and parasiting on the unactivated ones. He studies the reduction of these phenomena with use of earth lines or addition of a second ground plane over the lines.     

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.     

Mlcrolasers based on silica microspheres

Light can be confined efficiently in the high-Q, small-volume whispering-gallery-modes observed in silica microspheres. By coupling these microspheres to eroded optical fibers and fiber tips, direct mapping of the whispering-gallery modes has been achieved and the mode numbers have been assessed. The properties of these modes have allowed us to obtain laser action with very low thresholds in Nd-doped silica microspheres. Further projects in the field of non-linear optics and cavity quantum electrodynamics are described.