37 research outputs found
MR3631681 Reviewed Nigsch, E. A.(A-WIENM) On a nonlinear Peetre's theorem in full Colombeau algebras. (English summary) Comment. Math. Univ. Carolin. 58 (2017), no. 1, 69–77. 46F30 (46M20)
No full textColombeau algebras are defined as quotients of spaces containing the representatives of generalized functions given by smooth mappings: R:C∞(Ω,D(Ω))→C∞(Ω), where Ω is an open subset of Rn. In this paper the notion of locality defined by the author for a representative R of a nonlinear generalized function is characterized in such a way that the representative depends only on its ∞-jet. Finally, the author examines the possibility of defining a notion of order for the mapping R
Vacancy-engineering implants for high boron activation in silicon on insulator
No full textThe formation of boron interstitial clusters is a key limiting factor for the fabrication of highly-conductive ultrashallow doped regions in future silicon-based device technology. Optimized vacancy engineering strongly reduces boron clustering, enabling low-temperature electrical activation to levels rivalling what can be achieved with conventional pre-amorphization and solid-phase epitaxial regrowth. An optimized 160-keV silicon implant in a 55/145nm silicon-on-insulator structure enables stable activation of a 500eV boron implant to a concentration ~ 5x1020cm-3
Issues with n-type Dopants in Germanium
No full textThe last decade has seen considerable experimental and theoretical work towards the use of germanium for high-speed low-power electronics. Despite the demonstration of high performance p-channel Ge transistors in planar and non-planar device technology, fabrication of n-channel Ge transistors faces a number of scientific and technological challenges, which hinder the development of CMOS logic circuits based entirely on Ge. Major challenge constitutes the control of fast n-type dopant (out-/in-)diffusion in Ge, which prevents the formation of ultra-shallow and highly activated n+/p junctions necessary for n-channel Ge MOSFET’s enhanced performance. The paper focuses on parameters affecting n-type dopant diffusion in Ge and the attempts to suppress it, with particular emphasis on the action of nitrogen as phosphorous diffusion blocker
Interactions entre défauts étendus et anomalies de diffusion des dopants dans le silicium : modèle physique et simulations prédictives
No full textTOULOUSE3-BU Sciences (315552104) / SudocSudocFranceF
Generalized Functions and Multiplication of Distributions on C∞ Manifolds
No full textAbstractAn improvement in definition permits us to make invariant under the action of C∞ diffeomorphisms a concept of generalized functions introduced by the first author to define arbitrary products of distributions
Holomorphic maps with a given asymptotic expansion at a boundary point
No full textAbstractThe following result has been known for a long time: let 0 < α < 2π and let S be the sector {z ≠ 0 and arg z ≠ α(+ 2kπ)} of the complex plane; let (un) be a given infinite sequence of complex numbers; then there exists a holomorphic function on S which admits the formal power series ∑+∞n = 0 unzn as asymptotic expansion at the origin. A first generalization of this result to the infinite dimensional case is given by the author (A result of existence of holomorphic maps which admit a given asymptotic expansion, in “Advances in Holomorphy” (J. A. Barroso, Ed.), in press). We give here an improvement of this last result, based upon a different proof. Then we give two counterexamples showing that our assumptions on the spaces are essential
Holomorphic generalized functions
No full textAbstractIn the new theory of generalized functions introduced by one author we study the generalized functions G on open sets of Cn solutions of the equation ∂G = 0. These generalized functions—which cannot be distributions except if they are usual holomorphic functions—have many properties of the usual holomorphic functions but they present also serious differences in relation with the analytic continuation
Large deviations principles of Non-Freidlin-Wentzell type
No full textoai:arXiv.org:0803.2072Generalized Large deviation principles was developed for Colombeau-Ito SDE
with a random coefficients. We is significantly expand the classical theory of
large deviations for randomly perturbed dynamical systems developed by Freidlin
and Wentzell.Using SLDP approach, jumps phenomena, in financial markets, also
is considered. Jumps phenomena, in financial markets is explained from the
first principles, without any reference to Poisson jump process. In contrast
with a phenomenological approach we explain such jumps phenomena from the first
principles, without any reference to Poisson jump process.Comment: 189 pages. arXiv admin note: substantial text overlap with
arXiv:math/0411386 by other author
Discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations
No full textAbstractNonlinear nonstationary problems, arising in elastodynamics, have naturally a nonconservative form. For these systems it is not possible to define a weak solution according to distribution theory: in order to define the concept of discontinuous solutions for these systems, one is confronted with multiplications of distributions. This is unavoidable from a physical viewpoint since discontinuous solutions are needed to represent shock waves. The theory of generalized functions of the second author, in which one may multiply arbitrary distributions, gives a concept of generalized solutions that may be discontinuous functions. Existence of such global solutions of the Cauchy problem for a system of two equations is proved by a compactness argument from a convergent numerical scheme. In the case under consideration, the generalized solutions are bounded variation functions. The results thus obtained agree with the results expected by the engineers and lead to the development of new numerical schemes
