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Mathematical modeling of population problems in biology
Čampulová, Martina ; Opluštil, Zdeněk (referee) ; Čermák, Jan (advisor)
This bachelor´s thesis deals with the modeling of population problems in biology. The aim of this thesis is to mention some basic models describing dynamics of the evolution of one or two populations. Models mentioned in this thesis are described by first-order ordinary differential equations. Exploring the evolution of the population brings the main question - searching for singular points (and verifying their stability) of differential equations describing the evolution of the population. Therefore the thesis also deals with these problems.
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Biometric fingerprint identification
Ruttkay, Michal ; Smital, Lukáš (referee) ; Vítek, Martin (advisor)
This thesis describes the anatomical characteristics of fingerprints and their applications in identifying the person. The theoretical part describes the importance of papillary lines on fingerprints, statistical analysis and pre-processing of images in particular. The practical section provides the necessary operations to compare fingerprints. The implementation was done in Matlab.
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Singular Behavior of the Hartree-Fock Equations
Uhlířová, Tereza ; Zamastil, Jaroslav (advisor) ; Čížek, Martin (referee)
The non-linear Hartree-Fock (HF) equations are usually solved via the iterative self-consistent field method. However, there is no a priori guarantee of convergence, especially in systems with strong electron correlation where symmetry breaking occurs. This work focuses on closed- shell systems in the HF approximation and the (in)stability of the found solutions, and proposes new deterministic methods for the localization of both symmetry-adapted and broken symmetry solutions. We employ a perturbative method and show how one can always obtain a symmetry-adapted solution of the HF equations. We also determine the radius of convergence, related to the existence of at least one bound state, of the perturbative series. Next, we rederive the matrix of stability and adapt it to spin and orbital symmetry. Calculation of higher energy variations follows, first in terms of spin-orbitals and then orbitals. Motivated by the investigation of the structure of a broken-symmetry solution, we propose a new deterministic method for the localization of a broken-symmetry solution. The general expressions are verified by reformulating the stability conditions for simple cases. The proposed methods are successfully applied to helium-, beryllium- and neon-like systems.
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Biometric fingerprint identification
Ruttkay, Michal ; Smital, Lukáš (referee) ; Vítek, Martin (advisor)
This thesis describes the anatomical characteristics of fingerprints and their applications in identifying the person. The theoretical part describes the importance of papillary lines on fingerprints, statistical analysis and pre-processing of images in particular. The practical section provides the necessary operations to compare fingerprints. The implementation was done in Matlab.
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Mathematical modeling of population problems in biology
Čampulová, Martina ; Opluštil, Zdeněk (referee) ; Čermák, Jan (advisor)
This bachelor´s thesis deals with the modeling of population problems in biology. The aim of this thesis is to mention some basic models describing dynamics of the evolution of one or two populations. Models mentioned in this thesis are described by first-order ordinary differential equations. Exploring the evolution of the population brings the main question - searching for singular points (and verifying their stability) of differential equations describing the evolution of the population. Therefore the thesis also deals with these problems.
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