Search results for "7a"
showing 10 items of 161 documents
The Tan 2Θ Theorem in fluid dynamics
2017
We show that the generalized Reynolds number (in fluid dynamics) introduced by Ladyzhenskaya is closely related to the rotation of the positive spectral subspace of the Stokes block-operator in the underlying Hilbert space. We also explicitly evaluate the bottom of the negative spectrum of the Stokes operator and prove a sharp inequality relating the distance from the bottom of its spectrum to the origin and the length of the first positive gap.
Maximal Operators with Respect to the Numerical Range
2018
Let $\mathfrak{n}$ be a nonempty, proper, convex subset of $\mathbb{C}$. The $\mathfrak{n}$-maximal operators are defined as the operators having numerical ranges in $\mathfrak{n}$ and are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the $\mathfrak{n}$-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.
Study of the Ti-44(alpha, p)V-47 reaction and implications for core collapse supernovae
2014
The underlying physics triggering core collapse supernovae is not fully understood but observations of material ejected during such events helps to solve this puzzle. In particular, several satellite based γ -ray observations of the isotope 44Ti have been reported recently. Conveniently, the amount of this isotope in stellar ejecta is thought to depend critically on the explosion mechanism. The most influential reaction to the amount of 44Ti in supernovae is 44Ti(α, p)47V. Here we report on a direct study of this reaction conducted at the REX-ISOLDE facility, CERN. The experiment was performed with a 44Ti beam at Elab = 2.16 MeV/u, corresponding to an energy distribution, for reacting α-par…
Continuous frames for unbounded operators
2021
Few years ago G\u{a}vru\c{t}a gave the notions of $K$-frame and atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$ in order to decompose $\mathcal{R}(K)$, the range of $K$, with a frame-like expansion. These notions are here generalized to the case of a densely defined and possibly unbounded operator on a Hilbert space $A$ in a continuous setting, thus extending what have been done in a previous paper in a discrete framework.
Interior Eigenvalue Density of Jordan Matrices with Random Perturbations
2017
International audience; We study the eigenvalue distribution of a large Jordan block subject to a small random Gaussian perturbation. A result by E. B. Davies and M. Hager shows that as the dimension of the matrix gets large, with probability close to 1, most of the eigenvalues are close to a circle.We study the expected eigenvalue density of the perturbed Jordan block in the interior of that circle and give a precise asymptotic description.; Nous étudions la distribution de valeurs propres d’un grand bloc de Jordan soumis à une petite perturbation gaussienne aléatoire. Un résultat de E. B. Davies et M. Hager montre que quand la dimension de la matrice devient grande, alors avec probabilité…
Hom-Lie quadratic and Pinczon Algebras
2017
ABSTRACTPresenting the structure equation of a hom-Lie algebra 𝔤, as the vanishing of the self commutator of a coderivation of some associative comultiplication, we define up to homotopy hom-Lie algebras, which yields the general hom-Lie algebra cohomology with value in a module. If the hom-Lie algebra is quadratic, using the Pinczon bracket on skew symmetric multilinear forms on 𝔤, we express this theory in the space of forms. If the hom-Lie algebra is symmetric, it is possible to associate to each module a quadratic hom-Lie algebra and describe the cohomology with value in the module.
The 30 Year Search for the Compact Object in SN 1987A
2018
Despite more than 30 years of searches, the compact object in Supernova (SN) 1987A has not yet been detected. We present new limits on the compact object in SN 1987A using millimeter, near-infrared, optical, ultraviolet, and X-ray observations from ALMA, VLT, HST, and Chandra. The limits are approximately 0.1 mJy ($0.1\times 10^{-26}$ erg s$^{-1}$ cm$^{-2}$ Hz$^{-1}$) at 213 GHz, 1 Lsun ($6\times 10^{-29}$ erg s$^{-1}$ cm$^{-2}$ Hz$^{-1}$) in optical if our line-of-sight is free of ejecta dust, and $10^{36}$ erg s$^{-1}$ ($2\times 10^{-30}$ erg s$^{-1}$ cm$^{-2}$ Hz$^{-1}$) in 2-10 keV X-rays. Our X-ray limits are an order of magnitude less constraining than previous limits because we use a…
Search for heavy neutrinos with the T2K near detector ND280
2019
This paper reports on the search for heavy neutrinos with masses in the range 140<MN<493 MeV/c2 using the off-axis near detector ND280 of the T2K experiment. These particles can be produced from kaon decays in the standard neutrino beam and then subsequently decay in ND280. The decay modes under consideration are N→ℓ±απ∓ and N→ℓ+αℓ−β(−)ν(α,β=e,μ). A search for such events has been made using the Time Projection Chambers of ND280, where the background has been reduced to less than two events in the current dataset in all channels. No excess has been observed in the signal region. A combined Bayesian statistical approach has been applied to extract upper limits on the mixing elements of heav…
On several notions of complexity of polynomial progressions
2021
For a polynomial progression $$(x,\; x+P_1(y),\; \ldots,\; x+P_{t}(y)),$$ we define four notions of complexity: Host-Kra complexity, Weyl complexity, true complexity and algebraic complexity. The first two describe the smallest characteristic factor of the progression, the third one refers to the smallest-degree Gowers norm controlling the progression, and the fourth one concerns algebraic relations between terms of the progressions. We conjecture that these four notions are equivalent, which would give a purely algebraic criterion for determining the smallest Host-Kra factor or the smallest Gowers norm controlling a given progression. We prove this conjecture for all progressions whose ter…