A Kato's second type representation theorem for solvable sesquilinear forms

Kato's second representation theorem is generalized to solvable sesquilinear forms. These forms need not be non-negative nor symmetric. The representation considered holds for a subclass of solvable forms (called hyper-solvable), precisely for those whose domain is exactly the domain of the square root of the modulus of the associated operator. This condition always holds for closed semibounded forms, and it is also considered by several authors for symmetric sign-indefinite forms. As a consequence, a one-to-one correspondence between hyper-solvable forms and operators, which generalizes those already known, is established.Comment: 20 page

A Survey on Solvable Sesquilinear Forms

The aim of this paper is to present a unified theory of many Kato type representation theorems in terms of solvable forms on Hilbert spaces. In particular, for some sesquilinear forms $\Omega$ on a dense domain $\mathcal{D}$ one looks for an expression $$\Omega(\xi,\eta)=\langle T\xi , \eta\rangle, \qquad \forall \xi\in D(T),\eta \in \mathcal{D},$$ where $T$ is a densely defined closed operator with domain $D(T)\subseteq \mathcal{D}$. There are two characteristic aspects of solvable forms. Namely, one is that the domain of the form can be turned into a reflexive Banach space need not be a Hilbert space. The second one is the existence of a perturbation with a bounded form which is not necessarily a multiple of the inner product.Comment: 11 page

Highlights on beauty detection in nucleus-nucleus collisions with ALICE

We describe a strategy for the detection of open beauty in the semi-electronic channel with ALICE evaluating the expected S/(S+B) ratio.Comment: 3 pages, 2 figures, published in "Proceedings of the 5th international conference 'Quark confinement and hadron spectrum'" (Gargnano, Brescia, Italy, 10-14 Sep 2002), August 2003, World Scientifi

Optimal control of partially observable linear quadratic systems with asymmetric observation errors

This paper deals with the optimal quadratic control problem for non-Gaussian discrete-time stochastic systems. Our main result gives explicit solutions for the optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. For this purpose an asymmetric version of the Kalman filter based on asymmetric least squares estimation is used. We illustrate the applicability of our approach with numerical results

Nonlocality threshold for entanglement under general dephasing evolutions: A case study

Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal demonstration, a closed formula of the Bell function, witnessing nonlocality, as a function of the concurrence, quantifying entanglement, valid for a system of two noninteracting qubits initially prepared in extended Werner-like states undergoing any local pure-dephasing evolution. This formula allows for finding nonlocality thresholds for the concurrence depending only on the purity of the initial state. We then utilize these thresholds in a paradigmatic system where the two qubits are locally affected by a quantum environment with an Ohmic class spectrum. We show that steady entanglement can be achieved and provide the lower bound of initial state purity such that this stationary entanglement is above the nonlocality threshold thus guaranteeing the maintenance of nonlocal correlations.Comment: 7 pages, 4 figures. Revised versio

Hierarchical Structure in Financial Markets

I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between all pairs of stocks of the portfolio by considering the synchronous time evolution of the difference of the logarithm of daily stock price. The hierarchical tree of the subdominant ultrametric space associated with the graph provides information useful to investigate the number and nature of the common economic factors affecting the time evolution of logarithm of price of well defined groups of stocks.Comment: 11 pages, 3 figures with 7 panel

The Tenth Article of Ettore Majorana

This year is the centenary of the birth of Ettore Majorana, one of the major Italian physicists of all times. In this note we briefly sketch a few biographical details about Ettore Majorana and introduce and discuss the main points of Majorana's 10th article. In his article Majorana explicitly considers quantum mechanics as an irreducible statistical theory because the theory is not able to describe the time evolution of a single particle or atom in a precise environment at a deterministic level. This lack of determinism at the level of an elementary physical system motivated him to suggest a formal analogy between statistical laws observed in physics and in the social sciences. We hope the occasion of the centenary of the birth of Ettore Majorana will be useful to remember and to reconsider not only his exceptional achievements in theoretical physics but also his fresh and original views on the role of statistical laws in physics and in other disciplines such as the social sciences.Comment: 3 pages, to appear in Europhysics News 37/4 July/August 200

Building Community: Making Space for Art

Examines the role of the arts in communities; artists working in community development, education, health, or environmental fields; and contemporary art spaces in community planning and revitalization strategies

Asegúrate: an intervention program against cyberbullying based on teachers' commitment and on design of its instructional materials

This article presents the impact on cyberbullying of the Asegúrate program. This educational program is based on the theory of normative social behavior, self-regulation skills,and the beliefs held by adolescents and consists in a whole package of strategies and resources to help teachers to include in the ordinary curricula. The evaluation of Asegúrate was carried out with a sample of 4779 students (48.9% girls) in 5th and 6th grade in primary education and compulsory secondary education (M = 12.76; SD = 1.67) through a quasi-experimental methodology, with two measures over time. The instrument used was the European Cyberbullying Intervention Project Questionnaire. The results show that the involvement in cyberbullying as cyber-victim,cyber-aggressor, and cyber-bully-victim increase without intervention, whereas it diminishes when intervention is carried out by the teachers who have received specific training and have used the didactic Asegúrate package. Additionally, the impact of the intervention on the different types of behaviors was analyzed, and the results show that Asegúrate is more effective with some forms than with others. Consequently, the Asegúrate program is effective for decreasing the prevalence of cyberbullying, but some modifications need to be made to impact on all the different forms it can take.Gobierno de España PSI2017-86723-RGobierno de España PSI2016-74871-