Abstract:
The world economic crisis was a major factor that caused industrial production and trade over the globe decrease. It closed millions of working places and effected fear of political instability to spread even over the states that have been considered as stable. Economies all over the world face with wide range recessions, that will lead to the 3% to 7% GNP drop with respect to the last decade increasing trend. In such uncertainty conditions, where authorities are not sure about crisis development and duration, banner task is imposed: uncertainty must be passed. In Serbian economy, good model for crisis overcoming is agriculture strategic development and especially within it, the safe food production. One of guidelines of Serbian agriculture development is modernization and change of production structure towards stronger market orientation and improvement of alimentary industry total efficiency. Increased productively technological restructuring achieving increased efficiency, as well as greater competitiveness at domestic and foreign markets should be based on economical, ecological and energy criterions. Also, applied scientific research papers should allow significant increase of size and competitiveness of Serbian agriculture production.

Abstract:
Let $G$ be a connected undirected graph with $n$, $n\ge 3$, vertices and $m$ edges. Denote by $\rho_1 \ge \rho_2 \ge \cdots > \rho_n =0$ the normalized Laplacian eigenvalues of $G$. Upper and lower bounds of $\rho_i$, $i=1,2,\ldots , n-1$, are determined in terms of $n$ and general Randi\' c index, $R_{-1}$.

Abstract:
This paper describes the selection of parameters neccessary for the calculation of minimal representative quantity of coal sample for various investigations in the field of mineral processing. The procedure is illustrated on the example case of the Drmno coal field, from where the coal is delivered to the thermal power plant Kostolac. Two primary samples of coal, crushed down to different sizes and prepared (homogenized and divided), are analyzed for the ash content and the results were statisticaly processed. The analytical results are statistically processed. Analytical and graphical solutions, at the lowest sampling error, give an optimum range of the representative minimal sample mass for the given coal size. The coefficient of proportionality, k, which characterizes the kind of mineralization in the given material, and α exponent for the Drmno coal type, are determined.

Abstract:
We argue that the naively expected singularities of the Fermi surface, in the mixed composite boson - composite fermion states proposed [S.H. Simon et al., PRL 91, 046803(2003)] for the evolution of \nu = 1 bilayer quantum Hall system with distance, are obliterated. Our conclusion is based on a careful analysis of the momentum distribution in \nu = 1/2 single-layer composite-fermion state. We point out to a possibility of the phenomenon hitherto unknown outside Kondo lattice systems when, in a translationally invariant system, Fermi-liquid-like portion of electrons enlarges its volume.

Abstract:
We describe the invariant structure common to abelian fractional quantum Hall systems with spin. It appears in a generalization of the lattice description of the polarized hierarchy that encompasses both partially polarized and unpolarized ground state systems. We formulate, using the spin-charge decomposition, conditions that should be satisfied so that the description is SU(2) invariant. In the case of the spin- singlet hierarchy construction, we find that there are as many SU(2) symmetries as there are levels in the construction. We show the existence of a spin and charge lattice for the systems with spin. The ``gluing'' of the charge and spin degrees of freedom in their bulk is described by the gluing theory of lattices.

Abstract:
The Hilbert spaces of the edge excitations of several ``paired'' fractional quantum Hall states, namely the Pfaffian, Haldane-Rezayi and 331 states, are constructed and the states at each angular momentum level are enumerated. The method is based on finding all the zero energy states for those Hamiltonians for which each of these known ground states is the exact, unique, zero-energy eigenstate of lowest angular momentum in the disk geometry. For each state, we find that, in addition to the usual bosonic charge-fluctuation excitations, there are fermionic edge excitations. The edge states can be built out of quantum fields that describe the fermions, in addition to the usual scalar bosons (or Luttinger liquids) that describe the charge fluctuations. The fermionic fields in the Pfaffian and 331 cases are a non-interacting Majorana (i.e., real Dirac) and Dirac field, respectively. For the Haldane-Rezayi state, the field is an anticommuting scalar. For this system we exhibit a chiral Lagrangian that has manifest SU(2) symmetry but breaks Lorentz invariance because of the breakdown of the spin statistics connection implied by the scalar nature of the field and the positive definite norm on the Hilbert space. Finally we consider systems on a cylinder where the fluid has two edges and construct the sectors of zero energy states, discuss the projection rules for combining states at the two edges, and calculate the partition function for each edge excitation system at finite temperature in the thermodynamic limit. It is pointed out that the conformal field theories for the edge states are examples of orbifold constructions.

Abstract:
We propose an effective low-energy theory for ferromagnetic Hall states. It describes the charge degrees of freedom, on the edge, by a (1 + 1) dimensional chiral boson theory, and the spin degrees of freedom by the (2 + 1)dimensional quantum ferromagnet theory in the spin-wave approximation. The usual chiral boson theory for spinless electrons is modified to include the charge degrees of freedom with spin. Our total, bulk plus edge, effective action is gauge invariant and we find a generalized "chiral anomaly" in this case. We describe two, charged and neutral, sets of edge spin-wave solutions. The spreading of these waves is much larger than the one for the charge (edge) waves and they have linear dispersion relations.

Abstract:
We systematically discuss candidate wave functions for the ground state of the bilayer \nu = 1 as the distance between the layers is varied. Those that describe increased intralayer correlations at finite distance show a departure from the superflid description for smaller distances. They may support finite energy meron excitations and a dissipative collective mode in the place of the Goldstone mode of the ordered phase i.e. describe a vortex metal phase, or imply even an incompressible, pseudospin liquid, behavior. Therefore they describe possible outcomes of quantum disordering at finite distance between the layers. The vortex metal phase may show up in experiments in the presence of disorder at lower temperatures and explain the observed "imperfect superfluidity", and the pseudospin liquid phase may be the cause of the thermally activated (gapped) behavior of the longitudinal and Hall resistances at higher temperatures in counterflow experiments.

Abstract:
The optimal wavelet basis is used to develop quantitative, experimentally applicable criteria for self-organization. The choice of the optimal wavelet is based on the model of self-organization in the wavelet tree. The framework of the model is founded on the wavelet-domain hidden Markov model and the optimal wavelet basis criterion for self-organization which assumes inherent increase in statistical complexity, the information content necessary for maximally accurate prediction of the system's dynamics. At the same time the method, presented here for the one-dimensional data of any type, performs superior denoising and may be easily generalized to higher dimensions.

Abstract:
We study the edge--states excitations of a droplet of quantum Hall liquid embedded in an electron (Wigner) solid. The presence of strong correlations between the liquid and solid sectors in the ground state is shown to be reflected in the density of states $D(E)$, associated with the excitations of the liquid--solid interface. We find that the prominent effect of these correlations is a suppression of $D(E)$ with respect to its value ($D_0(E)$) in the absence of the Wigner solid environment: $D(E) \sim e^{-\alpha |E|}D_0(E)$. The coefficient $\alpha$ (which is shown to vanish for a perfectly regular distribution of electron sites in the solid), is evaluated for two different realizations of an irregular distribution. We conclude that probing this effect (e.g. in a tunneling experiment), can provide evidence for correlated liquid--solid mixture states in quantum dots, or disordered samples, in very strong magnetic fields.