On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

The New Software Package for Dynamic Hierarchical Clustering for Circles Types of Shapes

In data mining, efforts have focused on finding methods for efficient and effective cluster analysis in large databases. Active themes of research focus on the scalability of clustering methods, the effectiveness of methods for clustering complex shapes and types of data, high-dimensional clustering techniques, and methods for clustering mixed numerical and categorical data in large databases. One of the most accuracy approach based on dynamic modeling of cluster similarity is called Chameleon. In this paper we present a modified hierarchical clustering algorithm that used the main idea of Chameleon and the effectiveness of suggested approach will be demonstrated by the experimental results.

Modeling Optical Response of Thin Films: Choice of the Refractive Index Dispersion Law

Determination of the so-called optical constants (complex refractive index N, which is usually a function of the wavelength, and physical thickness D) of thin films from experimental data is a typical inverse non-linear problem. It is still a challenge to the scientific community because of the complexity of the problem and its basic and technological significance in optics. Usually, solutions are looked for models with 3-10 parameters. Best estimates of these parameters are obtained by minimization procedures. Herein, we discuss the choice of orthogonal polynomials for the dispersion law of the thin film refractive index. We show the advantage of their use, compared to the Selmeier, Lorentz or Cauchy models.

Training a Linear Neural Network with a Stable LSP Solution for Jamming Cancellation

Two jamming cancellation algorithms are developed based on a stable solution of least squares problem (LSP) provided by regularization. They are based on filtered singular value decomposition (SVD) and modifications of the Greville formula. Both algorithms allow an efficient hardware implementation. Testing results on artificial data modeling difficult real-world situations are also provided.

Applied Aspects of Mathematical Modeling and Optimization of Dynamics of Charged Beams

The complex of questions connected with the analysis, estimation and structural-parametrical optimization of dynamic system is considered in this article. Connection of such problems with tasks of control by beams of trajectories is emphasized. The special attention is concentrated on the review and analysis of spent scientific researches, the attention is stressed to their constructability and applied directedness. Efficiency of the developed algorithmic and software is demonstrated on the tasks of modeling and optimization of output beam characteristics in linear resonance accelerators.

Method of Linear Programming as an Idea for High School Curriculum

2010 Mathematics Subject Classification: 97D40, 97M10, 97M40, 97N60, 97N80, 97R80

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Mathematical Modeling, Music Literacy and Their Transmission in Fine Arts Education

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014