1,354,509 research outputs found
Vacuum Einstein metrics with bidimensional Killing leaves. II-Global aspects
No full textAbstractA formalism (ζ-complex analysis), allowing one to construct global Einstein metrics by matching together local ones described in the papers [G. Sparano, G. Vilasi, A.M. Vinogradov, Differential Geom. Appl. 16 (2002) 95–120; Phys. Lett. B 513 (2001) 142–146], is developed. With this formalism the singularities of the obtained metrics are described naturally as well
Comparison of 1H-NMR spectra by normalisation algorithms for studying amyloid toxicity in cells
No full textA range of debilitating human diseases is associated with the formation of stable, highly organised, protein aggregates, the amyloid fibrils. Substantial evidence suggests that Prefibrillar Oligomeric Aggregates (PFAs), preceding mature fibrils formation, are the crucial species in the onset of the neuronal degeneration even if with mechanisms to be further cleared. In this work, we show how 1H-NMR cell spectral analysis methods can prove to be very effective tools to clear the PFAs amyloid cytotoxicity mechanisms. Following the same method shown by Vilasi, we apply a new 1H-NMR analysis algorithm to identify the metabolites significantly varied in cells incubated with toxic oligomers from the amyloidogenic W7FW14F mutant of apomyoglobin. Our main aim is to confirm the results obtained by Vilasi et al.,
normalising a set of different data spectra with the new PRICONA algorithm
here described, thus contributing to strengthen the general framework of
metabolites and proteins involved in cellular amyloid toxicity
Singular pp-waves, Junction conditions and BPS states
No full textA simple model to study the collision of PP waves via the Israel junction conditions is proposed. The junction conditions are interpreted as topological conservation laws, and the relation with BPS states is shortly described
Hamiltonian dynamics
No full textThis is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a
Integrable Hamiltonian Hierarchies
No full textPreface
In the past decades now a famous class of evolution equations has been discovered and intensively studied, a class including the nowadays celebrated Korteweg-de Vries equation, sine-Gordon equation, nonlinear Schr ̈odinger
equation, etc. The equations from this class are known also as the soliton equations or equations solvable by the so- called Inverse Scattering Transform Method. They possess a number of interesting properties, probably the most interesting from the geometric point of view of being that most of them are Liouville integrable Hamiltonian systems. Because of the importance of the soliton equations, a dozen monographs have been devoted to them. However, the great variety of approaches to the soliton equations has led to the
paradoxical situation that specialists in the same field sometimes understand each other with difficulties. We discovered it ourselves several years ago during a number of discussions the three of us had. Even though by friendship binds us, we could not collaborate as well as we wanted to, since our individual approach to the field of integrable systems (finite and infinite dimensional) is quite different. We have become aware that things natural in one approach are difficult to understand for people using other approaches, though the objects are the same, in our case – the Recursion (generating) Operators and their applications to finite and infinite dimensional (not necessarily integrable) Hamiltonian systems. Since even between us, in order to overcome our differences, we needed some serious efforts, we decided that it was time to bring together the analytic and geometric aspects, if not of the theory of the soliton equations (this would be too ambitious) but at least the analytic and the
geometric aspects of the so-called Recursion Operators, which are among the powerful tools for the study of soliton equations. We had to do it in such a way, that a specialist in one of the approaches can read and understand the value of the other approach. However, the material we started to collect soon began growing rapidly, and we realized that a book should be written on this topic. The realization of the book project took longer than we expected – more than six years. But now we are happy that we are able to present a text which in our opinion reflects our original ideas.
The book has two parts, the first is dedicated to the analytic approach to the Recursion operators, the second, to the geometric nature of these operators, that is, to their interpretation as mixed tensor fields with special geometric properties over the manifold of potentials.
As we mentioned, we expect that the book will be useful to specialists in the Recursion Operator approach to the soliton equations. However, with an intent to target a larger audience, we have included some other important topics, such as the construction of the soliton solutions, for example. We have tried to develop the material in such a way that the book proves useful for graduate students who want to enter this interesting field of research.
The present book is based on some material that has become already classical, as well as on some of our works. The last few have been written in collaboration with many other friends and colleagues, namely:
Sergio De Filippo, Giuseppe Marmo, Mario Salerno, Giovanni Landi, Yanus Grabowski, Andrei Borowiz, Giovanni Sparano, Alexandre Vinogradov, Patrizia Vitale, Fabrizio Canfora, Luca Parisi, Boris Florko, Ljudmila Bordag, Peter Kulish, Evgenii Khristov, David Kaup, Evgenii Doktorov, Mikhail Ivanov, Yordan Vaklev, Marco Boiti, Flora Pempinelli, Nikolay
Kostov, Ivan Uzunov, Evstati Evstatiev, Georgi Diankov, Rossen Ivanov, Rossen Dandoloff, Georgi Grahovski, Assen Kyuldjiev, Viktor Enol’skii, Bakhtiyor Baizakov, Vladimir Konotop, Jianke Yang, Adrian Constantin, Tihomir Valchev, Victor Atanasov. We would like to extend our thanks to all of them.
We are grateful to Evgenii Doktorov, Nikolay Kostov, David Kaup, Georgi Grahovski, Rossen Ivanov for careful reading of the manuscript and for the many useful discussions we had with them.
A crucial factor which helped us complete the book was the financial support of Istituto Nazionale di fisica Nucleare, Gruppo Collegato di Salerno, and of Dipartimento di Fisica “E.R.Caianiello” at the University of Salerno, Italy. We would also like to thank the Institute for Nuclear Research and Nuclear energy, Sofia and the University of Cape Town for their organizational and financial support, as well as the National science foundation of Bulgaria (contract No. 1410).
Sofia, Salerno, Cape Town
Vladimir Stefanov Gerdjikov
Gaetano Vilasi
Alexander Yanovski
http://www.springer.com/978-3-540-77053-
Gravitational fields with 2-dimensional Killing leaves and the gravitational interaction of Light
No full textIs the Light too light?
No full textThe gravitational interaction of light is analyzed considering its dual characteristic nature, i.e. as an (electromagnetic) wave or as a particle (photon). Considered as an electromagnetic wave, the light can be source of gravitational waves belonging to the larger class of exact solutions of Einstein field equations which are invariant for a non-Abelian two-dimensional Lie algebra of Killing fields. It is shown that in the would be quantum theory of gravity they correspond to spin-1 massless particles
An integrable model in general relativity
No full textIt is shown that gravitational fields invariant for a
non Abelian 2-dimensional Lie algebra of Killing fields are
parameterized either by solutions of a transcendental equation
(the tortoise equation) or by solutions of a linear second
order partial differential equation (the Laplace equation
or the Darboux equation) on the plane. Those determined
via Laplace or Darboux equations are exact nonlinear gravitational
waves obeying to two nonlinear superposition laws
On the gravity of light
No full textA solution of the old problem raised by Tolman, Ehrenfest, Podolsky and
Wheeler, concerning the lack of attraction of two light pencils ‘moving parallel’,
is proposed, considering that the light can be a source of nonlinear gravitational
waves corresponding (from a quantum point of view) to spin-1 massless
particles
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