1,721,003 research outputs found
Criteria for the reality of the spectrum of PT-symmetric Schroedinger operators and for the existence of PT-symmetric phase transitions
No full textA major mathematical problem in PT-symmetric quantum mechanics is to determine whether or not the spectrum of any given non self-adjoint but PT-symmetric Schroedinger operator is real. In this case the PT-symmetry is called "proper". Clearly in this connection an equally important issue is the spontaneous violation of the PT-symmetry which might occur in a PT-symmetric operator family. The spontaneous violation of the PT-symmetry is defined as the transition from real values of the spectrum to complex ones at the variation of the parameter labeling the family. Its occurrence is referred to also as the -symmetric phase transition.
This chapter intends to present a review of recent results concerning these two mathematical points, within the standard notions of spectral theory for Hilbert space operators. The main technical instrument is represented by perturbation theory
Convex Replica Simmetry Breaking from Positivity and Thermodynamic Limit
No full textConsider a correlated Gaussian random energy model built by successively adding one particle (spin) into the system and imposing the positivity of the associated covariance matrix. We show that the validity of a recently isolated condition ensuring the existence of the thermodynamic limit forces the covariance matrix to exhibit the Parisi replica symmetry breaking scheme with a convexity conditions on the matrix elements
Max Abraham's and Tullio Levi-Civita's approach to Einstein Theory of Relativity
No full textThis work deals with the theory of Relativity and its diffusion in Italy in the first decades of the XX century. Not many scientists belonging to Italian universities were active in understanding Relativity, but two of them, Max Abraham and Tullio Levi-Civita left a deep mark.
Max Abraham engaged a substantial debate against Einstein between 1912 and 1914 about electromagnetic and gravitation aspects of the theories.
Levi-Civita played a fundamental role in giving Einstein the correct mathematical instruments for the General Relativity formulation since 1915.
This work, which doesn't have the aim of a mere historical chronicle of the events, wants to highlight two particular perspectives:
on one hand, the importance of Abraham-Einstein debate in order to clarify the basis of Special Relativity, to observe the rigorous logical structure resulting from a fragmentary reasoning sequence and to understand Einstein's thinking;
on the other hand, the originality of Levi-Civita's approach, quite different from the Einstein's one, characterized by the introduction of a method typical of General Relativity even to Special Relativity and the attempt to hide the two Einstein Special Relativity postulates
Some aspects of the theory of Schrödinger operators
No full textIn these notes, we will survey a part of theory of the operator -Δ + V. More extensive surveys can be found in [1,2,3] and in [4]
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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