48 resultados para Interval analysis (Mathematics)

em Bulgarian Digital Mathematics Library at IMI-BAS


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An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

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2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.

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The reasonable choice is a critical success factor for decision- making in the field of software engineering (SE). A case-driven comparative analysis has been introduced and a procedure for its systematic application has been suggested. The paper describes how the proposed method can be built in a general framework for SE activities. Some examples of experimental versions of the framework are brie y presented.

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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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In this paper we study some of the characteristics of the art painting image color semantics. We analyze the color features of differ- ent artists and art movements. The analysis includes exploration of hue, saturation and luminance. We also use quartile’s analysis to obtain the dis- tribution of the dispersion of defined groups of paintings and measure the degree of purity for these groups. A special software system “Art Paint- ing Image Color Semantics” (APICSS) for image analysis and retrieval was created. The obtained result can be used for automatic classification of art paintings in image retrieval systems, where the indexing is based on color characteristics.

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An embedding X ⊂ G of a topological space X into a topological group G is called functorial if every homeomorphism of X extends to a continuous group homomorphism of G. It is shown that the interval [0, 1] admits no functorial embedding into a finite-dimensional or metrizable topological group.

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∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).

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The polyparametric intelligence information system for diagnostics human functional state in medicine and public health is developed. The essence of the system consists in polyparametric describing of human functional state with the unified set of physiological parameters and using the polyparametric cognitive model developed as the tool for a system analysis of multitude data and diagnostics of a human functional state. The model is developed on the basis of general principles geometry and symmetry by algorithms of artificial intelligence systems. The architecture of the system is represented. The model allows analyzing traditional signs - absolute values of electrophysiological parameters and new signs generated by the model – relationships of ones. The classification of physiological multidimensional data is made with a transformer of the model. The results are presented to a physician in a form of visual graph – a pattern individual functional state. This graph allows performing clinical syndrome analysis. A level of human functional state is defined in the case of the developed standard (“ideal”) functional state. The complete formalization of results makes it possible to accumulate physiological data and to analyze them by mathematics methods.

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The paper introduces a method for dependencies discovery during human-machine interaction. It is based on an analysis of numerical data sets in knowledge-poor environments. The driven procedures are independent and they interact on a competitive principle. The research focuses on seven of them. The application is in Number Theory.

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2000 Mathematics Subject Classification: 26A33, 42B20

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Mathematics Subject Classification: 74D05, 26A33

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Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

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Mathematics Subject Classification: 45G10, 45M99, 47H09

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This paper considers the use of the computer algebra system Mathematica for teaching university-level mathematics subjects. Outlined are basic Mathematica concepts, connected with different mathematics areas: algebra, linear algebra, geometry, calculus and analysis, complex functions, numerical analysis and scientific computing, probability and statistics. The course “Information technologies in mathematics”, which involves the use of Mathematica, is also presented - discussed are the syllabus, aims, approaches and outcomes.

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The paper presents a computational analysis of Bulgarian dialect variation, concentrating on pronunciation differences. It describes the phonetic data set compiled during the project* ‘Measuring Linguistic Unity and Diversity in Europe’ that consists of the pronunciations of 157 words collected at 197 sites from all over Bulgaria. We also present the results of analyzing this data set using various quantitative methods and compare them to the traditional scholarship on Bulgarian dialects. The results have shown that various dialectometrical techniques clearly identify east-west division of the country along the ‘jat’ border, as well as the third group of varieties in the Rodopi area. The rest of the groups specified in the traditional atlases either were not confirmed or were confirmed with a low confidence.