Abstract:
The Peierls structural transition in quasi-one-dimensional organic crystals of TTF-TCNQ is investigated in the frame of a more complete physical model. The two most important electron-phonon interaction mechanisms are taken into account simultaneously. One is similar of that of deformation potential and the other is of polaron type. For simplicity, the 2D crystal model is considered. The renormalized phonon spectrum and the phonon polarization operator are calculated in the random phase approximation for different temperatures. The effects of interchain interaction on renormalized acoustic phonons and on the Peierls critical temperature are analyzed.

Abstract:
We investigate the metal-insulator transition in quasi-one-dimensional organic crystals of tetrathiotetracene-iodide, TTT_{2}I_{3}, in the 2D model. A crystal physical model is applied which takes into account two the most important hole-phonon interaction mechanisms. One is similar to that of deformation potential and the other is of polaron type. The scattering on defects is also considered and it is crucial for the explanation of the transition. The phonon polarization operator and the renormalized phonon spectrum are calculated in the random phase approximation for different temperatures applying the method of Green functions. We show that the transition is of Peierls type. The effect of lattice distortion on the dispersion of renormalized acoustic phonons is analyzed.

Abstract:
The phenomenon of money laundering affects in great part each state that is both a member ofthe European community and is placed outside its frontiers. The adoption of some efficient measures offighting money laundering represents an international prerogative and in any way a particular one of everystate since the sovereignty of a country does not find recognition and respect among the criminals andother ethnicities that practice destroying activities towards the policy of society development. Theintensification of the stopping of this phenomenon appears as a logical necessity of the protecting of theeconomy of each state both separately and of the whole community of states. The adhesion to theinternational standards, confirmed in treaties implies the assumption of some engagements by each statewith regards to the implementation of the efficient strategies that would annihilate the danger of the realimentation” of the criminal activity and of the neglecting of state as independent subject in theformation and guaranteeing of the law.

Abstract:
This paper concerns the long-term behavior of population systems, and in particular of chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two important open problems in the field of Chemical Reaction Network Theory, the Persistence Conjecture and the Global Attractor Conjecture. We study the persistence of a large class of networks called lower-endotactic and in particular, we show that in weakly reversible mass-action systems with two-dimensional stoichiometric subspace all bounded trajectories are persistent. Moreover, we use these ideas to show that the Global Attractor Conjecture is true for systems with three-dimensional stoichiometric subspace.

Abstract:
The making of complex researches of resistance and compactproperties of concrete on the base of limestone offal that contains a huge pitch of concrete components on the base of nominal materials. They studied three types of concrete based on residue from crushing limestone: concrete on small particles as filler in concrete were used to crushing limestone residues career Mic uti; carbonate concrete, the coarse-grained aggregate as they used limestone gravel career low, and as small aggregate - residues from crushing limestone in the same career; cheramzit concrete on gravel and waste from crushing limestone. These studies reveal general rules of these properties of concrete according to their characteristic structure.

Abstract:
Decisions about supplied goods depend of used technologies, of possibilities to acquire necessary factors, of quality of products, of demand level etc. Usually, firms cannot get a 100% level of qualitative goods, dividing them in some groups or categories. We research three generalizations of the classical model, where expected profit depends of quantity of good of first quality, of prices for each category, of demand level. We propose to solve described models using method of projection of generalized gradient. There are present some experimental results for different demand behavior.

Abstract:
The author tackles the issue of competition between penal norms and nonpenal norms in theprocess of defending the order of right against the illegality related to the crediting process. The interferenceof penal right spheres and the ones of other branches of law (firstly the civil right) is specific for the processof defending against the economic offences. Or, to obtain and grant a credit firstly constitute the settlementobject of the civil law. The author analyzes different situations and underlines that the civic responsibilitydoesn’t automatically exclude the possibility of applying the penal responsibility. Also, the banking”responsibility that is specific to the banking law is analyzed and its relation with the other responsibilities isrevealed. The author comes to the conclusion that it is not necessary to unincriminate the deeds stipulated inart.238 and 239 of the Criminal Code of Republic of Moldova. An evident social necessity for juridical-penaldefence of the rights and interests of honest participants at crediting relations exists. The existence andapplication of these norms constitus a guarantee of preventing and combating the illegalities related tocrediting, characterized by a high prejudicial level, that are commited by the dishonest participants. Theprejudicial level is the criterion that permits the application by itself either of the banking” responsibility orpenal responsibility. In the same time, each of the specified juridical responsibility forms may beaccomapnied by the civic responsibility.

Abstract:
The paper concerns the topology of an isospectral real smooth manifold for certain Jacobi element associated with real split semisimple Lie algebra. The manifold is identified as a compact, connected completion of the disconnected Cartan subgroup of the corresponding Lie group $\tilde G$ which is a disjoint union of the split Cartan subgroups associated to semisimple portions of Levi factors of all standard parabolic subgroups of $\tilde G$. The manifold is also related to the compactified level sets of a generalized Toda lattice equation defined on the semisimple Lie algebra, which is diffeomorphic to a toric variety in the flag manifold ${\tilde G}/B$ with Borel subgroup $B$ of $\tilde G$. We then give a cellular decomposition and the associated chain complex of the manifold by introducing colored-signed Dynkin diagrams which parametrize the cells in the decomposition.

Abstract:
The paper concerns a compactification of the isospectral varieties of nilpotent Toda lattices for real split simple Lie algebras. The compactification is obtained by taking the closure of unipotent group orbits in the flag manifolds. The unipotent group orbits are called the Peterson varieties and can be used in the complex case to describe the quantum cohomology of Grassmannian manifolds. We construct a chain complex based on a cell decomposition consisting of the subsystems of Toda lattices. Explicit formulae for the incidence numbers of the chain complex are found, and encoded in a graph containing an edge whenever an incidence number is non-zero. We then compute rational cohomology, and show that there are just three different patterns in the calculation of Betti numbers. Although these compactified varieties are singular, they resemble certain smooth Schubert varieties e.g. they both have a cell decomposition consiting of unipotent group orbits of the same dimensions. In particular, for the case of a Lie algebra of type $A$ the rational homology/cohomology obtained from the compactified isospectral variety of the nilpotent Toda lattice equals that of the corresponding Schubert variety.

Abstract:
This paper concerns the topology of isospectral real manifolds of certain Jacobi elements associated with real split semisimple Lie algebras. The manifolds are related to the compactified level sets of the generalized (nonperiodic) Toda lattice equations defined on the semisimple Lie algebras. We then give a cellular decomposition and the associated chain complex of the manifold by introducing colored Dynkin diagrams which parametrize the cells in the decomposition. We also discuss the Morse chain complex of the manifold.