arXiv subjects

M. Angelova

Publications and source records attributed to M. Angelova.

4 recordsLinked to original sources

arXiv2020

Global Stability and Periodicity in a Glucose-Insulin Regulation Model with a Single Delay

A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be globally asymptotically stable. They are given in terms of the global attractivity of the fixed point in a limiting interval map. The existence of slowly oscillating periodic solutions is shown in the case when the equilibrium is unstable. The mathematical results are supported by extensive numerical simulations. It is shown that typical behaviour in the system is the convergence to either a stable periodic solution or to the unique stable equilibrium. The coexistence of several periodic solutions together with the stable equilibrium is demonstrated as a possibility.

math.DS↗

arXiv2013

Squeezed coherent states and the one-dimensional Morse quantum system

The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of harmonic oscillator using ladder operators. Properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule.

math-ph↗

arXiv2010

Squeezed coherent states and the Morse quantum system

The Morse potential quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of harmonic oscillator using ladder operators. Properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule.

math-ph↗

arXiv2006

Targeted Projection Pursuit for Gene Expression Data Classification and Visualisation

We present a novel method for finding low dimensional views of high dimensional data: Targeted Projection Pursuit. The method proceeds by finding projections of the data that best approximate a target view. Two versions of the method are introduced; one version based on Procrustes analysis and one based on a single layer perceptron. These versions are capable of finding orthogonal or non-orthogonal projections respectively. The method is quantitatively and qualitatively compared with other dimension reduction techniques. It is shown to find two-dimensional views that display the classification of cancers from gene expression data with a visual separation equal to, or better than, existing dimension reduction techniques.

q-bio.QM↗