Variational Convergence for Nonlinear Shell Models with Directors and Related Semicontinuity and Relaxation Results

We use a variational convergence method to study the consistency of various Cosserat hypotheses in shell theory with the limit nonlinear membrane model derived from three-dimensional elasticity. In the course of the analysis, we introduce a generalization of quasiconvexity that is suitable for problems of the calculus of variations with two vectorial unknowns, one of which appears through its gradient, the other one through its value, in a weak W ^{1, p} ×L ^p framework. (Accepted: October 1, 1999)?Published online August 21, 2000     

Multivariate orthogonal polynomials, homogeneous Padé approximants and Gaussian cubature

The connection between orthogonal polynomials, Padé approximants and Gaussian quadrature is well known and will be repeated in section 1. In the past, several generalizations to the multivariate case have been suggested for all three concepts [4,6,9,...], however without reestablishing a fundamental and clear link. In sections 2 and 3 we will elaborate definitions for multivariate Padé and Padé-type approximation, multivariate polynomial orthogonality and multivariate Gaussian integration in order to bridge the gap between these concepts. We will show that the new m-point Gaussian cubature rules allow the exact integration of homogeneous polynomials of degree 2m−1, in any number of variables. A numerical application of the new integration rules can be found in sections 4 and 5. This revised version was published online in June 2006 with corrections to the Cover Date.     

Electron transfer processes involving ferrocenes. Electrogeneration and reactivity of an unusual species,the monocyclopentadienyliron radical

The very reactive cyclopentadienyliron species, (RC₅H₄)Fe, are relatively easily generated by electrochemical reduction of appropriately substituted and readily available ferrocenes. Thus (MeCOC₅H₄)Fe has been generated by monoelectronic reduction of (MeCOC₅H₄)₂Fe; it reacts with CO leading, after further reduction, to the acetyl cyclopentadienyldicarbonyliron anion. Reactions of this anion give ring-substituted cyclopentadienyldicarbonyliron derivatives containing the electron-withdrawing MeCO substituent.     

On the reversibility of the first electron transfer involving titanocene dichloride

The 1e reduction of titanocene dichloride (Cp₂TiCl₂) in DMF has been examined in detail. The reaction is reversible, in contradiction of a recent report.     

Transposition de neber en série tétrahydropyrannone

The Neber rearrangement applied to the oxime tosylates of the 4- and 3-tetrahydropyranones gives the α-aminoacetals 5 and 20 , as well as 3-amino-4,4-diethoxy and 2-amino-3,3-diethoxy-tetrahydropyranes. The hydrolysis of the former gives the pyrazine 6 and the latter gives the aminoketone 21. On the other hand the aminoacetal 5 allows one to obtain the 4-acetoxy-3-trimethylammonium tetrahydropyran iodide ( 12 ) with a preferential cis axial acetoxy equatorial trimethylammonium conformation. The oxime tosylate of the 3-tetrahydropyranone readily undergoes the Beckman rearrangement into lactam 18 whose open chain product is the (3-aminopropoxy)acetic acid ( 19 ).     

Active inductor shunt peaking in high-speed VCSEL driver design

An all-transistor active-inductor shunt-peaking structure has been used in a prototype of 8 Gbps high- speed VCSEL driver which is designed for the optical link in ATLAS liquid Argon calorimeter upgrade. The VCSEL driver is fabricated in a commercial 0.25 p~m Silicon-on-Sapphire （SOS） CMOS process for radiation tolerant purpose. The all-transistor active-inductor shunt-peaking is used to overcome the bandwidth limitation from the CMOS pro- cess. The peaking structure has the same peaking effect as the passive one, but takes a small area, does not need linear resistors and can overcome the process variation by adjust the peaking strength via an external control. The design has been taped out, and the prototype has been proven by the preliminary electrical test results and bit error ratio test results. The driver achieves 8 Gbps data rate as simulated with the peaking. We present the all-transistor active-inductor shunt-peaking structure, simulation and test results in this paper.