12 resultados para Radius of Convexity

em Bulgarian Digital Mathematics Library at IMI-BAS


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* Dedicated to the memory of Prof. N. Obreshkoff

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MSC 2010: 30C45, 30C50

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AMS Subj. Classification: 30C45

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2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.

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The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

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∗ Partially supported by grant No. 433/94 NSF of the Ministry of Education and Science of the Republic of Bulgaria 1991 Mathematics Subject Classification:30C45

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Николай М. Николов - Разгледани са характеризации на различни понятия за изпъкналост, като тези понятия са сравнени.

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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.

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2002 Mathematics Subject Classification: 65C05.

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We consider the question whether the assumption of convexity of the set involved in Clarke-Ledyaev inequality can be relaxed. In the case when the point is outside the convex hull of the set we show that Clarke-Ledyaev type inequality holds if and only if there is certain geometrical relation between the point and the set.

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MSC 2010: 34A08 (main), 34G20, 80A25

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MSC 2010: 30C45