Search results for "FACTORIZATION"
showing 10 items of 221 documents
Isometric factorization of vector measures and applications to spaces of integrable functions
2022
Let $X$ be a Banach space, $\Sigma$ be a $\sigma$-algebra, and $m:\Sigma\to X$ be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pelczýnski factorization procedure that there exist a reflexive Banach space $Y$, a vector measure $\tilde{m}:\Sigma \to Y$ and an injective operator $J:Y \to X$ such that $m$ factors as $m=J\circ \tilde{m}$. We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pelczýnski factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on $L_1(m)$ is weakly compact, t…
Suffixes, Conjugates and Lyndon Words
2013
In this paper we are interested in the study of the combinatorial aspects connecting three important constructions in the field of string algorithms: the suffix array, the Burrows-Wheeler transform (BWT) and the extended Burrows-Wheeler transform (EBWT). Such constructions involve the notions of suffixes and conjugates of words and are based on two different order relations, denoted by $\plex$ and $\pom$, that, even if strictly connected, are quite different from the computational point of view. In this study an important role is played by Lyndon words. In particular, we improve the upper bound on the number of symbol comparisons needed to establish the $\pom$ order between two primitive wo…
Quantification of melanin and hemoglobin in humain skin from multispectral image acquisition: use of a neuronal network combined to a non-negative ma…
2012
International audience; This article presents a multispectral imaging system which, coupled with a neural network-based algorithm, reconstructs reflectance cubes. The reflectance spectra are obtained using artificial neural-netwok reconstruction which generates reflectance cubes from acquired multispectral images. Then, a blind source separation algorithm based on Non-negative Matrix Factorization is used for the decomposition of human skin absorption spectra in its main pigments: melanin and hemoglobin. The analysis is performed on reflectance spectra. The implemented source separation algorithm is based on a multiplicative coefficient upload. The goal is to represent a given spectrum as t…
First observation of a baryonic Bc+ decay
2014
A baryonic decay of the $B_c^+$ meson, $B_c^+\to J/\psi p\overline{p}\pi^+$, is observed for the first time, with a significance of $7.3$ standard deviations, in $pp$ collision data collected with the LHCb detector and corresponding to an integrated luminosity of $3.0$ fb$^{-1}$ taken at center-of-mass energies of $7$ and $8$ $\mathrm{TeV}$. With the $B_c^+\to J/\psi \pi^+$ decay as normalization channel, the ratio of branching fractions is measured to be \begin{equation*} \frac{\mathcal{B}(B_c^+\to J/\psi p\overline{p}\pi^+)}{\mathcal{B}(B_c^+\to J/\psi \pi^+)} = 0.143^{\,+\,0.039}_{\,-\,0.034}\,(\mathrm{stat})\pm0.013\,(\mathrm{syst}). \end{equation*} The mass of the $B_c^+$ meson is dete…
Power Corrections to Event Shapes with Mass-Dependent Operators
2013
We introduce an operator depending on the "transverse velocity'' r that describes the effect of hadron masses on the leading 1/Q power correction to event-shape observables. Here, Q is the scale of the hard collision. This work builds on earlier studies of mass effects by Salam and Wicke [J. High Energy Phys. 05 (2001) 061] and of operators by Lee and Sterman [Phys. Rev. D 75, 014022 (2007)]. Despite the fact that different event shapes have different hadron mass dependence, we provide a simple method to identify universality classes of event shapes whose power corrections depend on a common nonperturbative parameter. We also develop an operator basis to show that at a fixed value of Q, the…
A QCD analysis of LHCb D-meson data in p plus Pb collisions
2020
We scrutinize the recent LHCb data for D$^0$-meson production in p+Pb collisions within a next-to-leading order QCD framework. Our calculations are performed in the SACOT-$m_{\rm T}$ variant of the general-mass variable-flavour-number scheme (GM-VFNS), which has previously been shown to provide a realistic description of the LHC p+p data. Using the EPPS16 and nCTEQ15 nuclear parton distribution functions (PDFs) we show that a very good agreement is obtained also in the p+Pb case both for cross sections and nuclear modification ratios in the wide rapidity range covered by the LHCb data. Encouraged by the good correspondence, we quantify the impact of these data on the nuclear PDFs by the Hes…
Long range two-particle rapidity correlations in collisions from high energy QCD evolution
2009
Long range rapidity correlations in A+A collisions are sensitive to strong color field dynamics at early times after the collision. These can be computed in a factorization formalism \cite{GelisLV5} which expresses the $n$-gluon inclusive spectrum at arbitrary rapidity separations in terms of the multi-parton correlations in the nuclear wavefunctions. This formalism includes all radiative and rescattering contributions, to leading accuracy in $\alpha_s\Delta Y$, where $\Delta Y$ is the rapidity separation between either one of the measured gluons and a projectile, or between the measured gluons themselves. In this paper, we use a mean field approximation for the evolution of the nuclear wav…
Exclusive heavy vector meson electroproduction to NLO in collinear factorisation
2021
We compute the exclusive electroproduction, $\gamma^* p \rightarrow V p$, of heavy quarkonia $V$ to NLO in the collinear factorisation scheme, which has been formally proven for this process. The inclusion of an off-shell virtuality $Q^2$ carried by the photon extends the photoproduction phase space of the exclusive heavy quarkonia observable to electroproduction kinematics. This process is relevant for diffractive scattering at HERA and the upcoming EIC, as well as at the proposed LHeC and FCC.
Exact relativistic beta decay endpoint spectrum
2007
5 pages, 3 figures.-- PACS nrs.: 14.60.Pq; 13.30.-a; 23.40.-s; 23.40.Bw.-- ISI Article Identifier: 000250620900070.-- ArXiv pre-print available at: http://arxiv.org/abs/0706.0897
The LHC p+Pb run from the nuclear PDF perspective
2014
The p+Pb and Pb+Pb runs at the LHC have opened a possibility to investigate the validity of collinear factorization in a clearly higher center-of-mass energy scale than earlier in nuclear collisions. Indeed, some processes that have been measured routinely in p+p(p) collisions and utilized for years in free proton PDF fits, can now finally be reached also in the nuclear case. Such new data are expected to provide conclusive answers concerning the universality of the nuclear PDFs. In this talk, I will contrast some of the first p+Pb and Pb+Pb measurements to the predictions based on the nuclear PDFs.