Bilingual Corpus - Digital Repository for Preservation of Language Heritage

The article briefly reviews bilingual Slovak-Bulgarian/Bulgarian-Slovak parallel and aligned corpus. The corpus is collected and developed as results of the collaboration in the frameworks of the joint research project between Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, and Ľ. Štúr Institute of Linguistics, Slovak Academy of Sciences. The multilingual corpora are large repositories of language data with an important role in preserving and supporting the world's cultural heritage, because the natural language is an outstanding part of the human cultural values and collective memory, and a bridge between cultures. This bilingual corpus will be widely applicable to the contrastive studies of the both Slavic languages, will also be useful resource for language engineering research and development, especially in machine translation.

Online Dictionary - Tool for Preservation of Language Heritage

The paper aims to represent a bilingual online dictionary as a useful tool helping preservation of the natural languages. The author focuses on the approach that was taken to develop compatible bilingual lexical database for the Bulgarian-Polish online dictionary. A formal model for the dictionary encoding is developed in accordance with the complex structures of the dictionary entries. These structures vary depending on the grammatical characteristics of Bulgarian headwords. The Web-application for presentation of the bilingual dictionary is also describred.

3D Laser Scanning for Digital Preservation and Dissemination of Cultural Heritage Main scanned objects - Four Temples of Different Religions in Sofia

The project demonstrates the use of modern technologies for preservation and presentation of the cultural and historical heritage. The idea is a database of cultural and historical heritage sites to be created applying three dimensional laser scanning technology and a combination of geodetic and photogrammetric methods and shooting techniques. For the purposes of carrying out this project, we have focused on some heritage sites in the central part of Sofia. We decided to include these particular buildings because of the fact that there is hardly another city in the world where within a radius of 400 m are located four temples of different religions - Jewish, Muslim, Orthodox and Catholic. In the recent years, preservation of cultural heritage has been increasingly linked to objectives of sustainable development. Today, it has become clear that cultural heritage is also an economic resource that should be used for further economic development (through compulsory preservation of its authentic cultural values). There has been a more active public debate on the role of cultural heritage, regarding the following topics: improving the quality of life through development of cultural tourism, leading to an increase of the employment rate, constantly improving the business climate, etc. Cultural heritage preservation is becoming one of the priority objectives of the urban development policy. The focus has been shifted to new ways of preservation, mainly combinations of sophisticated technological solutions and their application for the purposes of preservation and dissemination of the cultural heritage.

Digitization and Preservation of City Landmarks Using Limited and Free Web Services

This paper presents a practical approach for digitizing city landmarks based on free and limited Web resources. The digital replicas are then placed on the Web using popular services, like Google earth, and are accessible to a huge user base. The method is easily applicable and quite valuable to organizations with limited funding.

The Graves Theorem Revisited II: Robust Convergence of the Newton Method

AMS subject classification: 65J15, 47H04, 90C30.

A solution of the trigonometric moment problem via Tagamlitzki's "Theorem of the Cones"

In 1952 Y. Tagamlitzki gave an elegant proof of the classical Bochner’s theorem on the positively definite functions. Unfortunately, he never published his proof. In this paper we consider a related but simpler problem, the trigonometric moment problem, by using Tagamlitzki’s approach.

On a Theorem by Van Vleck Regarding Sturm Sequences

In 1900 E. B. Van Vleck proposed a very efficient method to compute the Sturm sequence of a polynomial p (x) ∈ Z[x] by triangularizing one of Sylvester’s matrices of p (x) and its derivative p′(x). That method works fine only for the case of complete sequences provided no pivots take place. In 1917, A. J. Pell and R. L. Gordon pointed out this “weakness” in Van Vleck’s theorem, rectified it but did not extend his method, so that it also works in the cases of: (a) complete Sturm sequences with pivot, and (b) incomplete Sturm sequences. Despite its importance, the Pell-Gordon Theorem for polynomials in Q[x] has been totally forgotten and, to our knowledge, it is referenced by us for the first time in the literature. In this paper we go over Van Vleck’s theorem and method, modify slightly the formula of the Pell-Gordon Theorem and present a general triangularization method, called the VanVleck-Pell-Gordon method, that correctly computes in Z[x] polynomial Sturm sequences, both complete and incomplete.

On the Critical Points of Kyurkchiev’s Method for Solving Algebraic Equations

This paper is dedicated to Prof. Nikolay Kyurkchiev on the occasion of his 70th anniversary This paper gives sufficient conditions for kth approximations of the zeros of polynomial f (x) under which Kyurkchiev’s method fails on the next step. The research is linked with an attack on the global convergence hypothesis of this commonly used in practice method (as correlate hypothesis for Weierstrass–Dochev’s method). Graphical examples are presented.

Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring

2000 Mathematics Subject Classification: 15A15, 15A24, 15A33, 16S50.

Another Generalization of Arhangel'skii's Theorem

MSC 2010: 54A25, 54A35.

Indice de Point Fixe pour les Morphismes de Chaînes

2000 Mathematics Subject Classification: 54H25, 55M20.

Growth Theorem and the Radius of Starlikeness of Close-to-Spirallike Functions

AMS Subj. Classification: 30C45