Euler-Lagrange equations for composition functionals in calculus of variations on time scales

In this paper we consider the problem of the calculus of variations for a functional which is the composition of a certain scalar function $H$ with the delta integral of a vector valued field $f$, i.e., of the form $H(\int_{a}^{b}f(t,x^{\sigma}(t),x^{\Delta}(t))\Delta t)$. Euler-Lagrange equations, natural boundary conditions for such problems as well as a necessary optimality condition for isoperimetric problems, on a general time scale, are given. A number of corollaries are obtained, and several examples illustrating the new results are discussed in detail.Comment: Submitted 10-May-2009 to Discrete and Continuous Dynamical Systems (DCDS-B); revised 10-March-2010; accepted 04-July-201

Transversality Conditions for Infinite Horizon Variational Problems on Time Scales

We consider problems of the calculus of variations on unbounded time scales. We prove the validity of the Euler-Lagrange equation on time scales for infinite horizon problems, and a new transversality condition.Comment: Submitted 6-October-2009; Accepted 19-March-2010 in revised form; for publication in "Optimization Letters"

R-matrix approach to integrable systems on time scales

A general unifying framework for integrable soliton-like systems on time scales is introduced. The $R$-matrix formalism is applied to the algebra of $\delta$-differential operators in terms of which one can construct infinite hierarchy of commuting vector fields. The theory is illustrated by two infinite-field integrable hierarchies on time scales which are difference counterparts of KP and mKP. The difference counterparts of AKNS and Kaup-Broer soliton systems are constructed as related finite-field restrictions.Comment: 21 page

Parametrization of Scale-Invariant Self-Adjoint Extensions of Scale-Invariant Symmetric Operators

On a Hilbert space H, we consider a symmetric scale-invariant operator with equal defect numbers. It is assumed that the operator has at least one scale invariant self-adjoint extension in H. We prove that there is a one-to-one correspondence between (generalized) resolvents of scale-invariant extensions and solutions of some functional equation. Two examples of Dirac-type operators are considered

A Charge-Sensitive Amplifier Associated with APD or PMT for Positron Emission Tomography Scanners

to be presented at the 32nd International Convention MIPRO (Microeectronics, Electronics, and Electronic Technology (MEET)), Opatija, Croatia, May 25-29 2009We present a Charge-Sensitive Amplifier (CSA) to be coupled with a 511-KeV 2-photon detector for positron emission tomography scanners. The circuit has been designed to be associated with an Avalanche Photodiode (APD) or Photo-Multiplier Tube (PMT) with large capacitance. It is a two-stage structure. The input stage consists of a foldedcascode fully-differential part and a common-mode feedback (CMFB) circuit. The output stage employs complementary source followers. The amplifier has been designed in a 0.35μm BiCMOS process with optimization of noise and speed performances to meet specific constraints. Its main characteristics evaluated by post-layout simulations are: 70-dB DC gain, 4.6-GHz GBW, 20-ns peaking time for pulsed stimulus, 3900-electron equivalent input noise charge (ENC), 135-mW power consumption at 3.5 V supply

Contribution of HEP electronics techniques to the medical imaging field

présenté par P.-E. Vert, proceedings sous forme de CD Imagerie Médical

The 8 bits 100 MS/s Pipeline ADC for the INNOTEP Project – TWEPP-09

This paper describes the Analog to Digital Converter developed for the front end electronic of the IN2P3 INNOTEP project by the “pole microelectronique Rhone-Auvergne”. (Collaboration between LPC Clermont-Ferrand and IPNL Lyon). This ADC is a 4 stages 2.5 bits per stage pipe line with open loops track and holds and amplifiers. It runs at 100MSamples/s and has 8 bits resolution. The stages used two lines, the gain line and the comparison line, with most operators running in current. The main idea of this current line is to make a first step toward an all in current structure. Currently, this ADC is designed with a 0,35μm SiGe technology