Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons

We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area triangulations of convex polygons in two dimensions and their algorithmic implications. We improve the algorithm’s running time to quadratic for large classes of convex polygons. We also present experimental results on MaxMin area triangulation.

Application of Salagean and Ruscheweyh Operators on Univalent Holomorphic Functions with Finitely many Coefficients

MSC 2010: 30C45, 30C50

Digital Repository of Information and Knowledge - Fund “BellKnow”

The aim was to develop an archive containing detailed description of church bells. As an object of cultural heritage the bell has general properties such as geometric dimensions, weight, sound of each of the bells, the pitch of the tone as well as acoustical diagrams obtained using contemporary equipment. The audio, photo and video archive is developed by using advanced technologies for analysis, reservation and data protection.

Digitization of Cultural and Historical Heritage of Armenians in Bulgaria - Priorities and Perspectives

The paper deals with digitization as a method of protecting and preserving cultural and historical heritage of Armenians in Bulgaria. It attempts to establish the level of development of this process in the country, to identify the good examples and information gaps in order to outline the priorities and perspectives.

Discover the Thracians - An Approach for Use of 2D and 3D Technologies for Digitization of Cultural Heritage in the Field of E-learning

Information and communication technologies (ICT) offer an easier access to and a multi-perspective view of cultural heritage artifacts and may also enrich and improve cultural heritage education through the adoption of innovative learning/teaching methods. This paper examines the different practices and opportunities for digitization of cultural artifacts with historical significance and describes the work on a pilot project concerning the development of e-learning materials in the Thracian cultural and historical heritage. The proposed method presents an approach based on a combination of 2D and 3D technologies to facilitate the overall process of digitization of individual objects. This approach not only provides greater opportunities for presenting the Thracian heritage but also new perspectives for studying it - students, scientists, PhD students will have the opportunity to work with the materials without having access to them.

Partner Projects of “Ivan Vazov” Public Library – Plovdiv on Digitization of Cultural and Historical Heritage

Digitization offers excellent opportunities for the preservation and safe-keeping of valuable library collections. The article recounts the first coordinated attempts of “Ivan Vazov” Public Library – Plovdiv at digitizing some of its treasured collections such as manuscripts, early printed books and archives through partner projects and revealing them to the world community.

Digital Humanities: Challenges of the Transformation of Tools and Objects of Knowledge in Contemporary Humanities

This paper aims to sketch some bases for the problematization of digital tools as objects of knowledge for Social Sciences and Humanities (SSH). Our purpose is to raise some relevant questions about the Digital Humanities (DH) and how SSH and Computer Sciences (CS) can work together to face new challenges. We discuss some tension points and propose a model for SSH and CS collaboration for joint projects in cultural digitization.

Principles of Extremum and Application to some Problems of Analysis

AMS subject classification: 41A17, 41A50, 49Kxx, 90C25.

Estimation of the Offspring and Immigration Mean Vectors for Bisexual Branching Processes with Immigration of Females and Males

2000 Mathematics Subject Classification: 60J80, 62M05.

Combination of Global and Local Attributional Similarities for Synonym Detection

2000 Mathematics Subject Classification: 68T50.

Comparison of Multivariate and Univariate Models for Genetic Evaluation of Milk Yield based on Test Day Data

2000 Mathematics Subject Classification: 62H12, 62P99

On the Equality of Sharp and Germ - Fields for Gaussian Processes and Fields

2000 Mathematics Subject Classification: 60G15, 60G60; secondary 31B15, 31B25, 60H15

Hausdorff Measures of Noncompactness and Interpolation Spaces

2000 Mathematics Subject Classification: 46B50, 46B70, 46G12.

Some generalization of Desargues and Veronese configurations

2000 Mathematics Subject Classification: 51E14, 51E30.

Smale's Conjecture on Mean Values of Polynomials and Electrostatics

2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.