On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin

Mathematics Subject Classification: 44A05, 46F12, 28A78

Fractal Analysis for Cancer Research: Case Study and Simulation of Fractals

2010 Mathematics Subject Classification: 65D18.

Algebraic Computations with Hausdorff Continuous Functions

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

Hausdorff Distances for Searching in Binary Text Images

This work has been partially supported by Grant No. DO 02-275, 16.12.2008, Bulgarian NSF, Ministry of Education and Science.

Application of the Artificial Intelligence Algorithms for System Analysis of Multi Dimension Physiological Data for Developing Polyparametric Information System of Public Health Diagnostics

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.

A Super-Dimension Approach in ROLAP Environments

Often the designer of ROLAP applications follows up with the question “can I create a little joiner table with just the two dimension keys and then connect that table to the fact table?” In a classic dimensional model there are two options - (a) both dimensions are modeled independently or (b) two dimensions are combined into a super-dimension with a single key. The second approach is not widely used in ROLAP environments but it is an important sparsity handling method in MOLAP systems. In ROLAP this design technique can also bring storage and performance benefits, although the model becomes more complicated. The dependency between dimensions is a key factor that the designers have to consider when choosing between the two options. In this paper we present the results of our storage and performance experiments over a real life data cubes in reference to these design approaches. Some conclusions are drawn.

Dimension Reduction of the Explanatory Variables in Multiple Linear Regression

2002 Mathematics Subject Classification: 62J05, 62G35.

Hausdorff Approximation of Functions Different from Zero at One Point - Implementation in Programming Environment Mathematica

ACM Computing Classification System (1998): G.1.2.

Diagonalizable Complex Systems, Reduced Dimension and Hermitian Systems II

2002 Mathematics Subject Classification: 35L40

Hausdorff Measures of Noncompactness and Interpolation Spaces

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

Denoising Manifolds for Dimension

2000 Mathematics Subject Classification: 68T01, 62H30, 32C09.

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

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