Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

Integral completeness of locally convex spaces

A locally convex space X is said to be integrally complete if each continuous mapping f: [0, 1] --> X is Riemann integrable. A criterion for integral completeness is established. Readily verifiable sufficient conditions of integral completeness are proved.

On stratifiable locally convex spaces

In the present paper we prove several results on the stratifiability of locally convex spaces. In particular, we show that a free locally convex sum of an arbitrary set of stratifiable LCS is a stratifiable LCS, and that all locally convex F'-spaces whose bounded subsets are metrizable are stratifiable. Moreover, we prove that a strict inductive limit of metrizable LCS is stratifiable and establish the stratifiability of many important general and specific spaces used in functional analysis. We also construct some examples that clarify the relationship between the stratifiability and other properties.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Laser-Driven Proton Beams: Acceleration Mechanism, Beam Optimization, and Radiographic Applications

This paper reviews recent experimental activity in the area of optimization, control, and application of laser accelerated proton beams, carried out at the Rutherford Appleton Laboratory and the Laboratoire pour l’Utilisation des Lasers Intenses 100 TW facility in France. In particular, experiments have investigated the role of the scale length at the rear of the plasma in reducing target-normal-sheath-acceleration acceleration efficiency. Results match with recent theoretical predictions and provide information in view of the feasibility of proton fast-ignition applications. Experiments aiming to control the divergence of the proton beams have investigated the use of a laser-triggered microlens, which employs laser-driven transient electric fields in cylindrical geometry, enabling to focus the emitted
protons and select monochromatic beam lets out of the broad spectrum beam. This approach could be advantageous in view
of a variety of applications. The use of laser-driven protons as a particle probe for transient field detection has been developed and
applied to a number of experimental conditions. Recent work in this area has focused on the detection of large-scale self-generated magnetic fields in laser-produced plasmas and the investigation of fields associated to the propagation of relativistic electron both on the surface and in the bulk of targets irradiated by high-power laser pulses.

Performance projections and design optimization of planar double gate SOI MOSFETs for logic technology applications

In this paper, by investigating the influence of source/drain extension region engineering (also known as gate-source/drain underlap) in nanoscale planar double gate (DG) SOI MOSFETs, we offer new insights into the design of future nanoscale gate-underlap DG devices to achieve ITRS projections for high performance (HP), low standby power (LSTP) and low operating power (LOP) logic technologies. The impact of high-kappa gate dielectric, silicon film thickness, together with parameters associated with the lateral source/drain doping profile, is investigated in detail. The results show that spacer width along with lateral straggle can not only effectively control short-channel effects, thus presenting low off-current in a gate underlap device, but can also be optimized to achieve lower intrinsic delay and higher on-off current ratio (I-on/I-off). Based on the investigation of on-current (I-on), off-current (I-off), I-on/I-off, intrinsic delay (tau), energy delay product and static power dissipation, we present design guidelines to select key device parameters to achieve ITRS projections. Using nominal gate lengths for different technologies, as recommended from ITRS specification, optimally designed gate-underlap DG MOSFETs with a spacer-to-straggle (s/sigma) ratio of 2.3 for HP/LOP and 3.2 for LSTP logic technologies will meet ITRS projection. However, a relatively narrow range of lateral straggle lying between 7 to 8 nm is recommended. A sensitivity analysis of intrinsic delay, on-current and off-current to important parameters allows a comparative analysis of the various design options and shows that gate workfunction appears to be the most crucial parameter in the design of DG devices for all three technologies. The impact of back gate misalignment on I-on, I-off and tau is also investigated for optimized underlap devices.

Design and optimization of FinFETs for ultra-low-voltage analog applications

In this paper, we analyze the enormous potential of engineering source/drain extension (SDE) regions in FinFETs for ultra-low-voltage (ULV) analog applications. SDE region design can simultaneously improve two key analog figures of merit (FOM)-intrinsic de gain (A(vo)) and cutoff frequency (f(T)) for 60 and 30 nm FinFETs operated at low drive current (J(ds) = 5 mu A/mu m). The improved Avo and fT are nearly twice compared to those of devices with abrupt SDE regions. The influence of the SDE region profile and its impact on analog FOM is extensively analyzed. Results show that SDE region optimization provides an additional degree of freedom apart from device parameters (fin width and aspect ratio) to design future nanoscale analog devices. The results are analyzed in terms of spacer-to-straggle ratio a new design parameter for SDE engineered devices. This paper provides new opportunities for realizing future ULV/low-power analog design with FinFETs.