Abstract:
The article presents the results of sociological study carried out to obtain a general model of ideas, expectations and preferences of provincial students in their attitude to higher education. The received results are presented in the form of diagrams. Provides a general interpretation of the data and on their basis are proposed recommendations for development marketing strategy and campaign to attract university entrants to the provincial university.

Abstract:
We prove a non-linear version of a theorem of Grayson which is an analogue of the Fundamental Theorem of Algebraic $K$-theory and identify the $K$-theory of the endomorphism category over a space $X$ in terms of reduced $K$-theory of a certain localisation of the category of $\NN$-spaces over $X$. In particular we generalise the result of Klein and Williams describing the nil-terms of $A$-theory in terms of $K$-theory of nilpotent endomorphisms.

Abstract:
In this paper outer, or dual, billiards outside regular polygons are studied; in particular, periodic points for cases of strictly convex "tables" and for regular n-gons with n = 3,4,6,8,12 are discussed. The main result of the paper is existence of aperiodic points for outer billiards outside regular octagon and dodecagon.

Abstract:
We construct a functor from the category of $(\mathbb{Z},X)$-modules of Ranicki (cf. \cite{Ra92}) to the category of homotopy cosheaves of chain complexes of Ranicki-Weiss (cf. \cite{RaWei10}) inducing an equivalence on $L$-theory. The $L$-theory of $(\mathbb{Z},X)$-modules is central in the algebraic formulation of the surgery exact sequence and in the construction of the total surgery obstruction by Ranicki, as described in \cite{Ra79}. The symmetric $L$-theory of homotopy cosheaf complexes is used by Ranicki-Weiss in \cite{RaWei10}, to reprove the topological invariance of rational Pontryagin classes. The work presented here may be considered as an addendum to the latter article and suggests some translation of ideas of Ranicki into the language of homotopy chain complexes of cosheaves.

Abstract:
Bounds on the norm of quantum operators associated with classical Bell-type inequalities can be derived from their maximal eigenvalues. This quantitative method enables detailed predictions of the maximal violations of Bell-type inequalities.

Abstract:
Classical Pitowsky correlation polytopes are reviewed with particular emphasis on the Minkowski-Weyl representation theorem. The inequalities representing the faces of polytopes are Boole's ``conditions of possible experience.'' Many of these inequalities have been discussed in the context of Bell's inequalities. We introduce CddIF, a Mathematica package created as an interface between Mathematica and the cdd program by Komei Fukuda, which represents a highly efficient method to solve the hull problem for general classical correlation polytopes.

Abstract:
Bell-type inequalities and violations thereof reveal the fundamental differences between standard probability theory and its quantum counterpart. In the course of previous investigations ultimate bounds on quantum mechanical violations have been found. For example, Tsirelson's bound constitutes a global upper limit for quantum violations of the Clauser-Horne-Shimony-Holt (CHSH) and the Clauser-Horne (CH) inequalities. Here we investigate a method for calculating the precise quantum bounds on arbitrary Bell-type inequalities by solving the eigenvalue problem for the operator associated with each Bell-type inequality. Thereby, we use the min-max principle to calculate the norm of these self-adjoint operators from the maximal eigenvalue yielding the upper bound for a particular set of measurement parameters. The eigenvectors corresponding to the maximal eigenvalues provide the quantum state for which a Bell-type inequality is maximally violated.

Abstract:
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as criteria for the validity of quantum mechanics.

Abstract:
In this work, we investigate the problem of private statistical analysis in the distributed and semi-honest setting. In particular, we study properties of Private Stream Aggregation schemes, first introduced by Shi et al. \cite{2}. These are computationally secure protocols for the aggregation of data in a network and have a very small communication cost. We show that such schemes can be built upon any key-homomorphic \textit{weak} pseudo-random function. Thus, in contrast to the aforementioned work, our security definition can be achieved in the \textit{standard model}. In addition, we give a computationally efficient instantiation of this protocol based on the Decisional Diffie-Hellman problem. Moreover, we show that every mechanism which preserves $(\epsilon,\delta)$-differential privacy provides \textit{computational} $(\epsilon,\delta)$-differential privacy when it is executed through a Private Stream Aggregation scheme. Finally, we introduce a novel perturbation mechanism based on the \textit{Skellam distribution} that is suited for the distributed setting, and compare its performances with those of previous solutions.

Abstract:
The Differential Optical Absorption Spectroscopy (DOAS) technique is widely used to retrieve amounts of atmospheric species from measurements of the direct solar light transmitted through the Earth's atmosphere as well as of the solar light scattered in the atmosphere or reflected from the Earth's surface. For the transmitted direct solar light the theoretical basis of the DOAS technique represented by the Beer-Lambert law is well studied. In contrast, scarcely investigated is the theoretical basis and validity range of the DOAS method for those cases where the contribution of the multiple scattering processes is not negligible. Our study is intended to fill this gap by means of a theoretical investigation of the applicability of the DOAS technique for the retrieval of amounts of atmospheric species from observations of the scattered solar light with a non-negligible contribution of the multiple scattering. Starting from the expansion of the intensity logarithm in the functional Taylor series we formulate the general form of the DOAS equation. The thereby introduced variational derivative of the intensity logarithm with respect to the variation of the gaseous absorption coefficient, which is often referred to as the weighting function, is demonstrated to be closely related to the air mass factor. Employing some approximations we show that the general DOAS equation can be rewritten in the form of the weighting function (WFDOAS), the modified (MDOAS), and the standard DOAS equations. For each of these forms a specific equation for the air mass factor follows which, in general, is not suitable for other forms of the DOAS equation. Furthermore, the validity range of the standard DOAS equation is quantitatively investigated using a suggested criterion of a weak absorption. The results presented in this study are intended to provide a basis for a better understanding of the applicability range of different forms of the DOAS equation as well as of the relationship between the air mass factor and the weighting function. To facilitate the understanding of the paper content for unexperienced reader we start our discussion considering in detail the standard DOAS technique applied to the observations of the direct solar light transmitted through the Earth's atmosphere.