On the basis of neutron diffraction data the Mn−O bond lengths and Mn−O−Mn bond angles for the poly- and nanocrystalline TbMnO3 samples are determined. All the samples crystallize in the orthorhombically distorted perovskite structure (space group Pnma) and exhibit antiferromagnetic ordering below 41 K. The Tb atoms and O1 atoms are in (4)c site, Mn atoms − in 4(b) site and O2 atoms − in 8(d) site. The Mn−O2−Mn bond angles for the polycrystalline and nanosize samples are similar, whereas the Mn−O1−Mn bond angles for the nanoparticle samples are larger. The temperature dependencies of the Mn−O bond lengths and the Mn−O−Mn bond angles, the Jahn-Teller distortion parameter (JT) and MnO6 − octahedron distortion parameter (delta) for polycrystalline sample exhibit anomalies at TN temperature for Mn sublattice.

In this paper a novel concept of adding structural responsibilities to meta-model classes for decreasing the meta-model complexity is introduced. This mechanism is supported by a combination of new Context Driven Meta-Modeling Paradigm (CDMM-P) and its implementation in the form of the Context-Driven Meta-Modeling Framework (CDMM-F) with aspect-oriented paradigm and its AspectJ implementation supporting functionality and structure enrichment. The concept presented in the paper confirms the openness of CDMM-P and CDMM-F on the applicability of the aspect-oriented approach. It is also crucial for the process of generalization of notions introduced into the meta-model when a new modeling language is designed. It also helps to restructure the metamodel from the perspective of reusability. The NamedElement, known from many Object Management Group’s (OMG) standards, was chosen.

The paper focuses on the problem of managing the scope understood as managing the multiplicity of elements that constitute the application context for Java Enterprise Edition (Java EE) frameworks. The subject of constructing graph modeling languages is the basis for scope management considerations. The problem can be demonstrated while the frameworks are superposed, which is necessary for meta- -modeling compliant to the Context-Driven Meta-Modeling (CDMM) approach. The realization of the approach is based on Spring and AspectJ frameworks, which offer incompatible concepts of scope management. As part of the analysis the scope management problem in Java EE frameworks application context was identified, formulated, its area was defined and the sketch of the generalized concept of scope management elaborated and implemented by the author in relation to Java EE frameworks was presented.

In this paper we study an integral modification of Szász-Mirakjan type operators. The modification will be called Szász-Mirakjan-Durrmeyer type operators as in many papers examining this type of operators. We give direct approximation theorems for these operators using the modulus of continuity and the modulus of smoothness for functions belonging to exponential weighted spaces.

Two point boundary value problems for fourth order, nonlinear, singular and non-singular ordinary differential equations occur in various areas of science and technology. A compact, three point finite difference scheme for solving such problems on nonuniform geometric meshes is presented. The scheme achieves a fifth or sixth order of accuracy on geometric and uniform meshes, respectively. The proposed scheme describes the generalization of Numerov-type method of Chawla (IMA J Appl Math 24:35-42, 1979) developed for second order differential equations. The convergence of the scheme is proven using the mean value theorem, irreducibility, and monotone property of the block tridiagonal matrix arising for the scheme. Numerical tests confirm the accuracy, and demonstrate the reliability and efficiency of the scheme. Geometric meshes prove superior to uniform meshes, in the presence of boundary and interior layers.

We give an elementary proof of the following theorem on definability of Hausdorff limits of one parameter families of definable sets: let A   R×Rⁿ be a bounded definable subset in o-minimal structure on (R,+,) such that for any y∈(0,c), c>0, the fibre Ay x y x A := { Rⁿ : (y , x) } is a Lipschitz cell with constant L independent of y. Then the Hausdorff limit lim y A_y →0 exists and is definable.

Abstract: We show that any compact subset K in the boundary of the unit disc D with a zero measure is a peak set for A(D).

In this paper we introduce some linear positive operators of the Baskakov-Durrmeyer type in the space of continuous functions of two variables. The theorems on convergence and the degree of approximation are established.

In this paper we introduce some linear positive operators of the Baskakov-Durrmeyer type in the space of uniformly continuous and bounded functions of several variables. The theorem on the degree of the convergence is established. Moreover, we give the Voronovskaya type formula for these operators.

We provide a self-contained discussion of the notions of δ-primeness and δ-semiprimeness for associative rings, possibly without identity. Some of the facts and properties presented in the article seem less known and quite difficult to find in standard reference sources.

In this paper we consider derivatives which are binary options of asset-or-nothing type with a payoff function depending on a parameter. The payoff is modelled on the payoff of catastrophe bonds. We examine the influence of the derivative on returns on shares. For this purpose two portfolios are compared: one consisting of stocks and a second additionally containing the derivative. Using the Black-Scholes model we derive an explicit formula for the standard deviation of the returns on the investment portfolios. Numerical examples show that the derivative reduces the volatility of returns on shares. For typical values of stock price volatility we indicate the value of the parameter appearing in the payoff for which the volatility of returns on shares reaches a minimum. All numerical calculations were made with MAPLE.

We give an example of a finite matrix with the property that expanding its language with a constant changes its finite axiomatization property: in the language with one binary operation the tautologies of the matrix are finitely axiomatizable while in the expanded language they are not. The constant we add is not definable in the original language.The deductive system generated by this matrix is not algebraizable.

For a metrizable space X, concepts of metric convergence in measure and of functional convergence in measure of sequences of measurable mappings taking their values in X are introduced and applied to a comparison of compactifications of X.

The main goal of the presented paper are numerical experiments of the convergence of the adaptation algorithm [4] developed by the author based on remeshing, which form the proof of the concept for the presented algorithm. The main feature of the considered algorithm is an application of the mesh generator to the adaptation with a mesh size function [5]. The proposed method uses a sequence of meshes obtained by successive modification of the mesh size function. The rate of the convergence is obtained numerically considering a known solution. The analysis of the unknown solution was restricted to the assessment of some properties of the strict solution.

This paper proposes a method of comparing the short texts using the Levenshtein distance algorithm and thesaurus for analysing terms enclosed in texts instead of popular methods exploiting the grammatical variations glossary. The tested texts contain a variety of nouns and verbs together with grammatical or orthographical mistakes. Based on the proposed new algorithm the similarity of such texts will be estimated. The described technique is compared with methods: Cosine distances, distance Dice and Jaccard distance constructed on the term frequency method. The proposition is competitive against well-known algorithms of stemming and lemmatization.

Straw tube detectors operating as drift detectors are commonly used in nuclear and particle physics experiments. The straw tubes are arranged in layers and placed in areas both with and without magnetic field. In order to resolve the 3D coordinates of a track, the straws are placed in multiple overlapping layers at varying angles of inclination. By measuring the drift time and then converting it to the drift distance, a position resolution per straw can be achieved. Knowing the geometry of the detector, the position of hit straws and the drift distances, it is possible to determine the tracks of the moving particles. In the paper we present the algorithm for the 3D track reconstruction in areas without magnetic field by using vertical and skewed straws. The algorithm has been prepared for the Forward Tracker in the PANDA experiment.

The following article presents the application of the Max-Plus Linear System (MPLS) method in the synthesis of different IT process control structures, taking place in the systems belonging to the class of Discrete Event Systems (DES). Modelling and analysis of these systems are based on the state equations, expressed in MPLS categories and classical principles of control theory, adapted for them. MPLS is based on max-plus algebra formalism and is supported with graphical representation in the form of Timed Event Graph (TEG), which is the special case of Timed Petri Nets (TPN). The article contains an overview of the theoretical work on discrete control processes, with a particular focus on the synthesis of control signals in the open control to obtain the desired output system. A practical example has been used for distributed computational process and data transmission for the system controlling selected technological process. Numerical results are presented.

This article presents a new concept of providing service quality with a level required by customers as outcome of an agent system decision making. Decisions are based on network state information and customer requirements concerning transmission quality with accepted costs of transmission. The proposed mechanism, which is called Pay&Require, combines features of decentralized routing systems in computer networks and the newly implemented concept of centralized control determined as SDN (Software-Defined Networking).