Search results for "BERT"

Star-products, spectral analysis, and hyperfunctions

2000

We study the ⋆-exponential function U(t;X) of any element X in the affine symplectic Lie algebra of the Moyal ⋆-product on the symplectic manifold (ℝ × ℝ;ω). When X is a compact element, a natural specific candidate for U (t;X) to be the exponential function is suggested by the study we make in the non-compact case. U (t;X) has singularities in the t variable. The analytic continuation U(z;X),z = t + iy, defines two boundary values δ+ U (t;X) = limy↓0 U(z;X) and δ-(t;X) = limy↑0 U(z; X). δ+ U (t;X) is a distribution while δ- U (t;X) is a Beurling-type, Gevrey-class s — 2 ultradistribution. We compute the Fourier transforms in t of δ± U (t;X). Both Fourier spectra are discrete but different …

Hyper-Entanglement in Time and Frequency

2019

Hyper-entanglement, i.e. entanglement in more than one degree of freedom, enables a multiplicative increase in Hilbert space size. Such systems can be treated as multi-partite even though the number of state particles is not increased, making them highly attractive for applications in high-capacity quantum communications and information processing [1]. Until now, such states have been realized only using combinations of fully independent degrees of freedom, described by commuting operators, such as polarization and optical paths. Time and frequency, in turn, are linked and described by non-commuting operators. Here, using two discrete forms of energy-time entanglement we demonstrate that ti…

2012

We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase space construction, propose a meaningful definition of the Wigner function in this case, and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states, and to their superpositions.

Topologies on Partial O*-Algebras

2002

In this chapter, we introduce some basic locally convex topologies on partial O*-algebras and we establish general properties of these topologies. In Section 4.1, we compare the graph topologies induced by different O-families on the same domain (and the corresponding families of bounded subsets). In the case where the domain D M of an O-family M is a (quasi-) Frechet space, the structure of bounded subsets in D M can be described in a rather explicit way. Section 4.2 and Section 4.3 are devoted to the topologization of (partial) O*-algebras. Section 4.2 deals with locally convex topologies, the so-called uniform topologies τ u , τ u , τ * u and quasiuniform topologies τ qu , and Section 4.…

Zvaigžņotā Debess: 2009, Pavasaris (203)

2009

Contents: E.R.Mustel, President of the Astronomical Council of the USSR Academy of Sciences. Congratulations to Editorial Board of “Zvaigžņotā debess” ; Z.Alksne. Gould’s Belt ; I.Daube. At the Radioastrophysical Observatory of the Latvian Academy of Sciences ; Z.Alksne, A.Alksnis. Lopsided Galaxies ; A.Alksnis. HII Region Gum 29 – a Stellar Nursery ; D.Docenko. On Collision of Asteroid 2008 TC3 with the Earth ; V.Lapoška. On „Leap Second” ; I.Vilks, M.Gills. Beginning of the International Year of Astronomy in Paris: Impressions by Latvian Delegates ; J.Jaunbergs. Equatorial Ridge on Iapetus ; M.Sudārs. Space Shuttle Is Not Likely to Retire Next Year ; I.Vilks. Planet Satellite Names in Lat…

Res sunt ut agas. Scritti per Gianna Petrone

2010

Para regenerar la democracia - ¡Vivan los treinta años de CEISA!

La libertad de la imprenta.

Signat a la fi: José Mor de Fuentes Text a 1 col Sign.: [ ]4

Kiberdrošības politiku salīdzinājums Baltijas valstīs

2017

Darbā tiek aplūkota un salīdzināta Latvijas, Lietuvas un Igaunijas situācija kiberdrošības jomā, lai noskaidrotu, vai un cik lielā mērā starp trim Baltijas valstīm pastāv atšķirības kiberdrošības politikas instrumentu attīstībā. Drošībošanas koncepta ietvaros tiek pārbaudīts, vai 2007. gada kiberuzbrukumus Igaunijai var uzskatīt par sekmīgi veiktu drošībošanas procesu. Izanalizējot pieejamo informāciju, tiek secināts, ka Igaunijas gadījums nav attiecināms uz drošībošanas teorijas ietvaru. Tomēr kiberuzbrukumi Igaunijā ir veicinājuši kiberdrošības koncepta attīstību Igaunijā. Darba nobeigumā tiek secināts, ka nav pamata apgalvot, ka Igaunijā šobrīd ir sasniegts ievērojami lielāks progress ki…

GRADED IDENTITIES FOR THE ALGEBRA OF n×n UPPER TRIANGULAR MATRICES OVER AN INFINITE FIELD

2003

We consider the algebra Un(K) of n×n upper triangular matrices over an infinite field K equipped with its usual ℤn-grading. We describe a basis of the ideal of the graded polynomial identities for this algebra.