Abstract:
In the last decades, the financial instruments developed very quickly, the world economy becoming “a paper economy”. The financial innovation transformed the financial system, offers for the financial intermediaries and investors’ new opportunities, but also brings new risks. The financial supervisory authorities passed from the regulation and deregulation process again to the re-regulation process in the intent to insure the stability in the financial markets and a development without the (hidden) dangers that sometimes transformed in financial crisis of financial intermediaries’ bankruptcy.

Abstract:
The goal of this paper is to estimate the inflationary effect of adoption of the Common Agricultural Policy in countries which joined the European Union in 2004, using two approaches. The first one supposes the comparison of consumer food prices before (May-December 2001-2003 and January – April 2002-2004) and after joining the European Union (May – December 2004 and January – April 2005), in all ten states. The second approach consist in the application of a multifactorial regression model for the period 2003-2010 in six countries: the Czech Republic, Hungary, Latvia, Lithuania, Slovakia and Slovenia. The results of the study shows that, contrary to the usual perception, the influence of the agricultural products prices on the food price and, implicitly, on the consumer prices have been relatively low in all the analysed countries, in some countries being counterbalanced by the appreciation of the national currency and the elimination of import custom duties.

Abstract:
In the year 2004 ten states from Central and South-Eastern Europe joined the European Union. The majority of them have registered a significant consumer price increase in the year 2004. The goal of this paper is to examine the fundamental factors that have influenced inflation rate after EU accession and to analyse the causes of the inflation differential in EU member states which acceded in 2004. The impact of EU accession was different in analysed countries, the increasing of inflation rate in accession year being determined by the adoption of the Common Agricultural Policy, the harmonization of the structure and rates of indirect taxes, the introduction of the Common Customs Policy, the free movement of goods, the free movement of capital and the expected inflation. From the analyses we have done, we have remarked that the main cause of inflation differential has been the oil price on the international market, because of the different degree of dependence on oil import of these countries, but also on the different weight of electricity, gases and other fuels in the consumer basket.

Abstract:
No matter how counterintuitive they are, quantum phenomena are all simple consequences of the laws of Quantum Mechanics. It is not needed to extend the theory with hidden mechanisms or additional principles to explain what Quantum Mechanics already predicts. This indubitable fact is often taken as supporting the view that all we can know about the universe comes from the outcomes of the quantum observations. According to this view, we can even learn the physical laws, in particular the properties of the space, particles, fields, and interactions, solely from the outcomes of the quantum observations. In this article it is shown that the unitary symmetry of the laws of Quantum Mechanics imposes severe restrictions in learning the physical laws of the universe, if we know only the observables and their outcomes.

Abstract:
Quantum correlations and other phenomena characteristic to a quantum world can be understood as simply consequences of a principle derived from the postulates of Quantum Mechanics. This explanatory principle states that these phenomena specific to the quantum world are caused by the tension between the constraints, or initial conditions, imposed by incompatible observations. This tension is found to be at the root of Bohr's complementarity, Heisenberg's uncertainty, results concerning nonlocality, contextuality, quantum correlations in time and space. This tension requires the presence of noncommuting observables, but noncommutativity doesn't always lead to the tension, and the two concepts are not exactly the same, as it will be explained and exemplified.

Abstract:
A set endowed with a reflexive relation has surprisingly many features in common with the causal structure of a spacetime in General Relativity. If we identify this relation as the relation between lightlike separated events (the horismos relation), we can construct in a natural way the entire causal structure: causal and chronological relations, causal curves, and a topology. By imposing a simple additional condition, the structure gains a definite number of dimensions. This construction works both with continuous and discrete spacetimes. The dimensionality is obtained with ease also in the discrete case, in contrast with the causal set approach, which starts with a discrete set of events endowed with partial order relation representing the causal relation, but has severe difficulties in recovering the number of dimensions. Other simple conditions make it into a differentiable manifold with a conformal structure (the metric up to a scaling factor) just like in General Relativity. This structure provides a simple and general reconstruction of the spacetime in General Relativity, which normally requires a hierarchy of structures: topological structure, differential structure, geometric structure (which in turn can be decomposed in the conformal structure, giving the causal relations, and the volume element).

Abstract:
The main mystery of quantum mechanics is contained in Wheeler's delayed choice experiment, which shows that the past is determined by our choice of what quantum property to observe. This gives the observer a participatory role in deciding the past history of the universe. Wheeler extended this participatory role to the emergence of the physical laws ("law without law"). Since what we know about the universe comes in yes/no answers to our interrogations, this led him to the idea of "it from bit" (which includes the participatory role of the observer as a key component). The yes/no answers to our observations ("bit") should always be compatible with the existence of at least a possible reality - a global solution ("it") of the Schrodinger equation. I argue that there is in fact an interplay between "it" and "bit". The requirement of global consistency leads to apparently acausal and nonlocal behavior, explaining the weirdness of quantum phenomena. As an interpretation of Wheeler's "it from bit" and "law without law", I discuss the possibility that the universe is mathematical, and that there is a "mother of all possible worlds" - named the "Axiom Zero".

Abstract:
Well-known operations defined on a non-degenerate inner product vector space are extended to the case of a degenerate inner product. The main obstructions to the extension of these operations to the degenerate case are (1) the index lowering operation is not invertible, and (2) we cannot associate to the inner product in a canonical way a reciprocal inner product on the dual of the vector space. This article shows how these obstructions can be avoided naturally, allowing a canonical definition of covariant contraction for some important special cases. The primary motivation of this article is to lay down the algebraic foundation for the construction of invariants in Singular Semi-Riemannian Geometry, especially those related to the curvature. It turns out that the operations discussed here are enough for this purpose (arXiv:1105.0201, arXiv:1105.3404, arXiv:1111.0646). Such invariants can be applied to the study of singularities in the theory of General Relativity (arXiv:1111.4837, arXiv:1111.4332, arXiv:1111.7082, arXiv:1108.5099, arXiv:1112.4508).

Abstract:
We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard operations like covariant contraction, covariant derivative, and constructions like the Riemann curvature are usually prohibited by the fact that the metric is not invertible. The things become even worse at the points where the signature changes. We show that we can still do many of these operations, in a different framework which we propose. This allows the writing of an equivalent form of Einstein's equation, which works for degenerate metric too. Once we make the singularities manageable from mathematical viewpoint, we can extend analytically the black hole solutions and then choose from the maximal extensions globally hyperbolic regions. Then we find space-like foliations for these regions, with the implication that the initial data can be preserved in reasonable situations. We propose qualitative models of non-primordial and/or evaporating black holes. We supplement the material with a brief note reporting on progress made since this talk was given, which shows that we can analytically extend the Schwarzschild and Reissner-Nordstrom metrics at and beyond the singularities, and the singularities can be made degenerate and handled with the mathematical apparatus we developed.

Abstract:
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which, under a set of conditions, allow us to define proper geometric invariants, and to write field equations, including equations which are equivalent to Einstein's at non-singular points, but remain well-defined and smooth at singularities. This class of singularities is large enough to contain isotropic singularities, warped-product singularities, including the Friedmann-Lemaitre-Robertson-Walker singularities, etc. Also a Big-Bang singularity of this type automatically satisfies Penrose's Weyl curvature hypothesis. The Schwarzschild, Reissner-Nordstrom, and Kerr-Newman singularities apparently are not of this benign type, but we can pass to coordinates in which they become benign. The charged black hole solutions Reissner-Nordstrom and Kerr-Newman can be used to model classical charged particles in General Relativity. Their electromagnetic potential and electromagnetic field are analytic in the new coordinates - they have finite values at r=0. There are hints from Quantum Field Theory and Quantum Gravity that a dimensional reduction is required at small scale. A possible explanation is provided by benign singularities, because some of their properties correspond to a reduction of dimensionality.