Search results for "Mathematica"
showing 10 items of 7971 documents
Ionization and scintillation response of high-pressure xenon gas to alpha particles
2013
High-pressure xenon gas is an attractive detection medium for a variety of applications in fundamental and applied physics. In this paper we study the ionization and scintillation detection properties of xenon gas at 10 bar pressure. For this purpose, we use a source of alpha particles in the NEXT-DEMO time projection chamber, the large scale prototype of the NEXT-100 neutrinoless double beta decay experiment, in three different drift electric field configurations. We measure the ionization electron drift velocity and longitudinal diffusion, and compare our results to expectations based on available electron scattering cross sections on pure xenon. In addition, two types of measurements add…
New techniques for classification of multigerms
2018
Abstract The goal of these notes is to give an overview of the state of the art in classification of multigerms. We have tried to make them self-contained but certainly not extensive. The results included here scope most of the research on classification of multigerms carried out in the last 15 years with special emphasis on recent results by the authors of these notes and their collaborators.
Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem
2011
Abstract We determine the shape which minimizes, among domains with given measure, the first eigenvalue of a nonlocal operator consisting of a perturbation of the standard Dirichlet Laplacian by an integral of the unknown function. We show that this problem displays a saturation behaviour in that the corresponding value of the minimal eigenvalue increases with the weight affecting the average up to a (finite) critical value of this weight, and then remains constant. This critical point corresponds to a transition between optimal shapes, from one ball as in the Faber–Krahn inequality to two equal balls.
Review of Classical Non-self-adjoint Spectral Theory
2019
The first section of this chapter deals with Fredholm theory in the spirit of Appendix A in Helffer and Sjostrand (Mm Soc Math Fr (NS) 24–25:1–228, 1986), see also an appendix in Melin and Sjostrand (Asterique 284:181–244, 2003) and Sjostrand and Zworski (Ann Inst Fourier 57:2095–2141, 2007). The remaining sections give a brief account of the very beautiful classical theory of non-self-adjoint operators, taken from a section in Sjostrand (Lectures on Resonances) which is a brief account of parts of the classical book by Gohberg and Krein (Introduction to the Theory of Linear Non-Selfadjoint Operators. Translations of Mathematical Monographs, vol 18. AMS, Providence, 1969).
Quasi-Modes and Spectral Instability in One Dimension
2019
In this section we describe the general WKB construction of approximate “asymptotic” solutions to the ordinary differential equation $$\displaystyle P(x,hD_x)u=\sum _{k=0}^m b_k(x)(hD_x)^ku=0, $$ on an interval α < x < β, where we assume that the coefficients bk ∈ C∞(]α, β[). Here h ∈ ]0, h0] is a small parameter and we wish to solve (above equation) up to any power of h. We look for u in the form $$\displaystyle u(x;h)=a(x;h)e^{i\phi (x)/h}, $$ where ϕ ∈ C∞(]α, β[) is independent of h. The exponential factor describes the oscillations of u, and when ϕ is complex valued it also describes the exponential growth or decay; a(x;h) is the amplitude and should be of the form $$\displaystyle a(x;h…
*-Representations of Partial *-Algebras
2002
This chapter is devoted to *-representations of partial *-algebras. We introduce in Section 7.1 the notions of closed, fully closed, self-adjoint and integrable *-representations. In Section 7.2, the intertwining spaces of two *-representations of a partial *-algebra are defined and investigated, and using them we define the induced extensions of a *-representation. Section 7.3 deals with vector representations for a *-representation of a partial *-algebra, which are the appropriate generalization to a *-representation of the notion of generalized vectors described in Chapter 5. Regular and singular vector representations are defined and characterized by the properties of the commutant, and…
Effects of the Best Possible Self intervention: A systematic review and meta-analysis
2019
The Best Possible Self (BPS) exercise promotes a positive view of oneself in the best possible future, after working hard towards it. Since the first work that attempted to examine the benefits of this intervention in 2001, studies on the BPS have grown exponentially and, currently, this is one of the most widely used Positive Psychology Interventions. However, little is yet known about its overall effectiveness in increasing wellbeing outcomes. Thus, the aim of this meta-analysis is to shed light on this question. A systematic literature search was conducted, and 29 studies (in 26 articles) met the inclusion criteria of empirically testing the intervention and comparing it to a control con…
Quantum Hopfield Model
2020
We find the free-energy in the thermodynamic limit of a one-dimensional XY model associated to a system of N qubits. The coupling among the &sigma
Analysis of a parabolic cross-diffusion population model without self-diffusion
2006
Abstract The global existence of non-negative weak solutions to a strongly coupled parabolic system arising in population dynamics is shown. The cross-diffusion terms are allowed to be arbitrarily large, whereas the self-diffusion terms are assumed to disappear. The last assumption complicates the analysis since these terms usually provide H 1 estimates of the solutions. The existence proof is based on a positivity-preserving backward Euler–Galerkin approximation, discrete entropy estimates, and L 1 weak compactness arguments. Furthermore, employing the entropy–entropy production method, we show for special stationary solutions that the transient solution converges exponentially fast to its…
Module categories of finite Hopf algebroids, and self-duality
2017
International audience; We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.