Abstract:
We study the class of pulsating strings on AdS4×ℂℙ3. Using a generalized ansatz for pulsating string configurations we find new solutions of this class. Further we quasiclassically quantize the theory and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual 𝒩=6 Chern-Simons theory.

Abstract:
A quantum-kinetic equation accounting for the electron-phonon interaction is solved by a stochastic approach. Analyzed are three analytically equivalent integral formulation of the equation which appear to have different numerical properties. Particularly the path-integral formulation is found to be advantageous for the numerical treatment. The analysis is supported by the presented simulation results. A variety of physical effects such as collisional broadening and collision retardation introduced by the equation are discussed.

Abstract:
Some of the recent important developments in understanding string/ gauge dualities are based on the idea of highly symmetric motion of ``string solitons'' in $AdS_5\times S^5$ geometry originally suggested by Gubser, Klebanov and Polyakov. In this paper we study symmetric motion of certain string configurations in so called Pilch-Warner geometry. The two-form field $A_2$ breaks down the supersymmetry to $\mathcal{N}=1$ but for the string configurations considered in this paper the classical values of the energy and the spin are the same as for string in $AdS\times S^5$. Although trivial at classical level, the presence of NS-NS antisymmetric field couples the fluctuation modes that indicates changes in the quantum corrections to the energy spectrum. We compare our results with those obtained in the case of pp-wave limit in hep-th/0206045.

Abstract:
In this paper we prove some new Stone-type duality theorems for some subcategories of the category $\ZLC$ of locally compact zero-dimensional Hausdorff spaces and continuous maps. These theorems are new even in the compact case. They concern the cofull subcategories $\SkeZLC$, $\QPZLC$, $\OZLC$ and $\OPZLC$ of the category $\ZLC$ determined, respectively, by the skeletal maps, by the quasi-open perfect maps, by the open maps and by the open perfect maps. In this way, the zero-dimensional analogues of Fedorchuk Duality Theorem and its generalization are obtained. Further, we characterize the injective and surjective morphisms of the category $\HLC$ of locally compact Hausdorff spaces and continuous maps, as well as of the category $\ZLC$, and of some their subcategories, by means of some properties of their dual morphisms. This generalizes some well-known results of M. Stone and de Vries. An analogous problem is investigated for the homeomorphic embeddings, dense embeddings, LCA-embeddings etc., and a generalization of a theorem of Fedorchuk is obtained. Finally, in analogue to some well-known results of M. Stone, the dual objects of the open, regular open, clopen, closed, regular closed etc. subsets of a space $X\in\card{\HLC}$ or $X\in\card{\ZLC}$ are described by means of the dual objects of $X$; some of these results (e.g., for regular closed sets) are new even in the compact case.

Abstract:
A duality theorem for the category of locally compact Hausdorff spaces and continuous maps which generalizes the well-known Duality Theorem of de Vries is proved.

Abstract:
In this paper some applications of the methods and results of its first part and of the results of M. Stone, H. de Vries, P. Roeper are given. In particular: some generalizations of the Stone Duality Theorem are obtained; a completion theorem for local contact Boolean algebras is proved; a direct proof of the Ponomarev's solution of Birkhoff's Problem 72 is found, and the spaces which are co-absolute with the (zero-dimensional) Eberlein compacts are described.

Abstract:
Generalizing a theorem of Ph. Dwinger, we describe the partially ordered set of all (up to equivalence) zero-dimensional locally compact Hausdorff extensions of a zero-dimensional Hausdorff space. Using this description, we find the necessary and sufficient conditions which has to satisfy a map between two zero-dimensional Hausdorff spaces in order to have some kind of extension over arbitrary given in advance Hausdorff zero-dimensional local compactifications of these spaces; we regard the following kinds of extensions: continuous, open, quasi-open, skeletal, perfect, injective, surjective. In this way we generalize some classical results of B. Banaschewski about the maximal zero-dimensional Hausdorff compactification. Extending a recent theorem of G. Bezhanishvili, we describe the local proximities corresponding to the zero-dimensional Hausdorff local compactifications.

Abstract:
Generalizing de Vries Compactification Theorem and strengthening Leader Local Compactification Theorem, we describe the partially ordered set $(\LL(X),\le)$ of all (up to equivalence) locally compact Hausdorff extensions of a Tychonoff space $X$. Using this description, we find the necessary and sufficient conditions which has to satisfy a map between two Tychonoff spaces in order to have some kind of extension over arbitrary given in advance Hausdorff local compactifications of these spaces; we regard the following kinds of extensions: open, quasi-open, skeletal, perfect, injective, surjective. In this way we generalize some results of V. Z. Poljakov.

Abstract:
One of the important consequences of the climatic changes is the potential danger of increasing the concentrations of some pollutants, which may cause damages to humans, animals and plants. Therefore, it is worthwhile to study carefully the impact of future climate changes on the high pollution levels. The major topic of the discussion in this paper is the increase of some ozone levels in Bulgaria, but several related topics are also discussed. The particular mathematical tool applied in this study is a large-scale air pollution model, the Unified Danish Eulerian Model (UNI- DEM), which was successfully used in several investigations related to potentially dangerous pollution levels in several European countries. This model is described by a non-linear system of partial differential equations, which is solved numerically by using (a) advanced numerical algorithms and (b) modern computer architectures. Moreover, (c) the code is parallelized and (d) the cache memories of the available computers are efficiently utilized. It is shown that in Bulgaria, as in the other European countries, the climatic changes will result in permanent increases of some quantities related to the ozone pollution. The important issue is that in our study the changes of the dangerous pollution levels are followed year by year. In this way, an attempt is made both to capture the effect of the interannual variations of the meteorological conditions on the levels of the ozone concentrations and to follow directly the influence of the climatic changes on the pollution levels. Moreover, the sensitivity of the pollution levels to variations of the human made (anthropogenic) and natural (biogenic) emissions is also discussed.

Abstract:
The histochemical reaction for myofibrillar adenosine triphosphatase (mATPase) is widely used method in typing skeletal muscle fibers. The mATPase reaction allows a qualitative and quantitative evaluation of fiber types in normal, diseased, or experimentally altered muscles. The aim of this study was to investigate the reproducibility and validity of cationic dyes' use in the mATPase reaction for identifying fiber types in the rat soleus muscle by the method proposed by Doriguzzi et al. The soleus muscle was removed from 10 adult Wistar albino rats of both sexes under ether anesthesia. Serial frozen cross-sections 10 μm thick were prepared and reacted for mATPase after preincubation at pH 9.4, 4.5 and 4.3, and for modified mATPase with the use of Toluidine blue (TB) and Methylene blue (MB) in post-incubation treatment of sections. The mATPase reaction demonstrated by TB and MB displayed a clear cut differentiation of muscle fiber types corresponding to type I, IIA and IIC fibers, obtained by mATPase reaction with ammonium sulfide. The method based on the use of cationic dyes in mATPase reaction appears to be fast, reproducible and valid. However, in our experience, the intensity of coloration of muscle fibers decreased by time so that the distinction between fiber types become difficult, which stands for the main disadvantage when compared to the conventional mATPase method.