Abstract:
Synthesis of highly $^{13}$C isotope enriched azafullerene, C$_{59}$N embedded in C$_{60}$ is reported. $^{13}$C enriched fullerenes, produced with the Kr\"{a}tschmer-Huffmann process, were subject to a N$_{2}$ discharge that produces C$_{59}$N with a low probability. Raman spectroscopy indicates a homogeneous $^{13}$C distribution. Electron spin resonance measurement (ESR) proves that the C$_{59}$N concentration, 0.2 %, is similar as in non-enriched fullerenes. The ESR spectrum is simulated accurately with the known $^{14}$N and $^{13}$C hyperfine coupling constants. The material enables the nuclear spin-labelling of heterofullerene complexes with a potential for biological applications. It might also find applications as a building element for quantum computation.

Abstract:
The $SL(2,\R)$ WZNW $\rightarrow$ Liouville reduction leads to a nontrivial phase space on the classical level both in $0+1$ and $1+1$ dimensions. To study the consequences in the quantum theory, the quantum mechanics of the $0+1$ dimensional, point particle version of the constrained WZNW model is investigated. The spectrum and the eigenfunctions of the obtained---rather nontrivial---theory are given, and the physical connection between the pieces of the reduced configuration space is discussed in all the possible cases of the constraint parameters.

Abstract:
We study some reparametrization invariant theories in context of the BRST-co-BRST quantization method. The method imposes restrictions on the possible gauge fixing conditions and leads to well defined inner product states through a gauge regularisation procedure. Two explicit examples are also treated in detail.

Abstract:
The aim of the current research is to clarify the concept of corporate governance as we believe it is a relatively new concept at national level. At the same time, our analysis focused on the manner in which the principle of transparency has been incorporated into the recommendations and regulations/provisions of the Bucharest Stock Exchange (Romanian: BVB) and how this principle has been applied by the companies listed with the BVB. In order to accomplish the objectives of our research, we adopted a deductive approach, from general to specific, by means of which we were able to combine qualitative with quantitative studies. Therefore, our approach started from the definition found within the principles of OECD according to which corporate governance is the system by which companies are run and controlled. In Romania, the concept of corporate governance was first advanced in 1999 by the Strategic Alliance of the Business Associations (Romanian: ASAA), which drew up a Voluntary code of corporate governance in association with the Confederation of Private Entrepreneurs in Timis county and the Chamber of Commerce and Industry of Romania and Bucharest. Another facet of our research is the principle of transparency and the manner in which entities should put it to practice in order to ensure efficient corporate governance. To this effect, since the beginning of 2009 the entities listed with the BVB have been under obligation to report which recommendations of the new Corporate Governance Code have actually been implemented by the company in the current financial year by disclosing to BVB the Comply or Explain Statement. The findings of our research show that the concept of corporate governance has lately been a matter for intense debate due to the famous financial failures in recent years. In 2009, Transelectrica was the only company in tier I of the BVB which filled in and submitted the Comply or Explain Statement. Therefore, we believe that Transelectrica should serve as a fine example for the entities listed with the BVB as regards the filling in and submitting of the said Statement.The aim of the current research is to clarify the concept of corporate governance as we believe it is a relatively new concept at national level. At the same time, our analysis focused on the manner in which the principle of transparency has been incorporated into the recommendations and regulations/provisions of the Bucharest Stock Exchange (Romanian: BVB) and how this principle has been applied by the companies listed with the BVB. In order to accomplish the objectives of our

Abstract:
The stability properties of a class of dissipative quantum mechanical systems are investigated. The nonlinear stability and asymptotic stability of stationary states (with zero and nonzero dissipation respectively) is investigated by Liapunov's direct method. The results are demonstrated by numerical calculations on the example of the damped harmonic oscillator.

Abstract:
A weakly nonlocal extension of ideal fluid dynamics is derived from the Second Law of thermodynamics. It is proved that in the reversible limit the additional pressure term can be derived from a potential. The requirement of the additivity of the specific entropy function determines the quantum potential uniquely. The relation to other known derivations of Schr\"odinger equation (stochastic, Fisher information, exact uncertainty) is clarified.

Abstract:
Boundary effects in quantum mechanics are examined by considering a partition wall inserted at the centre of a harmonic oscillator system. We put an equal number of particles on both sides of the impenetrable wall keeping the system under finite temperatures. When the wall admits distinct boundary conditions on the two sides, then a net force is induced on the wall. We study the temperature behaviour of the induced force both analytically and numerically under the combination of the Dirichlet and the Neumann conditions, and determine its scaling property for two statistical cases of the particles: fermions and bosons. We find that the force has a nonvanishing limit at zero temperature T = 0 and exhibits scalings characteristic to the statistics of the particles. We also see that for higher temperatures the force decreases according to 1/sqrt{T}, in sharp contrast to the case of the infinite potential well where it diverges according to sqrt{T}. The results suggest that, if such a nontrivial partition wall can be realized, it may be used as a probe to examine the profile of the potentials and the statistics of the particles involved.

Abstract:
Defects or junctions in materials serve as a source of interactions for particles, and in idealized limits they may be treated as singular points yielding contact interactions. In quantum mechanics, these singularities accommodate an unexpectedly rich structure and thereby provide a variety of physical phenomena, especially if their properties are controlled properly. Based on our recent studies, we present a brief review on the physical aspects of such quantum singularities in one dimension. Among the intriguing phenomena that the singularities admit, we mention strong vs weak duality, supersymmetry, quantum anholonomy (Berry phase), and a copying process by anomalous caustics. We also show that a partition wall as a singularity in a potential well can give rise to a quantum force which exhibits an interesting temperature behavior characteristic to the particle statistics.

Abstract:
The quantum dynamics of a free particle on a circle with point interaction is described by a U(2) family of self-adjoint Hamiltonians. We provide a classification of the family by introducing a number of subfamilies and thereby analyze the spectral structure in detail. We find that the spectrum depends on a subset of U(2) parameters rather than the entire U(2) needed for the Hamiltonians, and that in particular there exists a subfamily in U(2) where the spectrum becomes parameter-independent. We also show that, in some specific cases, the WKB semiclassical approximation becomes exact (modulo phases) for the system.

Abstract:
Motivated by a novel method for granular segregation, we analyze the one dimensional drift-diffusion between two absorbing boundaries. The time evolution of the probability distribution and the rate of absorption are given by explicit formulae, the splitting probability and the mean first passage time are also calculated. Applying the results we find optimal parameters for segregating binary granular mixtures.