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Singular Initial Value Problem for Ordinary Differential and Integrodifferential Equations
Archalousová, Olga ; Beránek, Jaroslav (referee) ; Růžičková,, Miroslava (referee) ; Šmarda, Zdeněk (advisor)
The thesis deals with qualitative properties of solutions of singular initial value problems for ordinary differential and integrodifferential equations which occur in the theory of linear and nonlinear electrical circuits and the theory of therminionic currents. The research is concentrated especially on questions of existence and uniqueness of solutions, asymptotic estimates of solutions and modications of Adomian decomposition method for singular initial problems. Solution algoritms are derived for scalar differential equations of Lane-Emden type using Taylor series and modication of the Adomian decomposition method. For certain classes of nonlinear of integrodifferential equations asymptotic expansions of solutions are constructed in a neighbourhood of a singular point. By means of the combination of Wazewski's topological method and Schauder xed-point theorem there are proved asymptotic estimates of solutions in a region which is homeomorphic to a cone having vertex coinciding with the initial point. Using Banach xed-point theorem the uniqueness of a solution of the singular initial value problem is proved for systems of integrodifferential equations of Volterra and Fredholm type including implicit systems. Moreover, conditions of continuous dependence of a solution on a parameter are determined. Obtained results are presented in illustrative examples.
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Influence of harrowing of wheat on weeds rate, yield parameters and quality of spelt.
BERÁNEK, Jaroslav
The diploma thesis deals with harrowing of spelt wheat (Triticum spelta L.) by the weeding harrows and its influence on weed frequency, yield and quality parameters of wheat. In the literature review there are described general cultivation principles for the growing of spelt (Triticum spelta L.) used in current agricultural practice. There is overview of the general principles of spelt wheat cultivation in the organic farming, available varieties in the Czech Republic and brief description of agricultural technology suitable for its cultivation. We also describe the types of weeds, their brief description and the possibility of reducing their frequency in the organic farming growing system. The literature review provides also information about the technology of harrowing cereal crops as a measure to control weeds and other positive aspects of harrowing on grain crops. In the practical part, data from a field trial were collected, where the effect of harrowing on the weed frequency, the influence of harrowing on spelt wheat tillering and other parameters were statistically evaluated and compared with results in the literature. At the end of the thesis, given the results evaluated in the practical part, it was determined whether it is appropriate to use harrowing as protection of spelt wheat (Triticum spelta L.), its number, influence on weed infestation and its influence on both the quantitative and qualitative properties of spelt wheat (Triticum spelta L.).
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Agrotechnical aspects of spelt growing
BERÁNEK, Jaroslav
The bachelor thesis deals with agrotechnological aspects of spelt (Triticum spelta L.). The thesis is composed from general growing aspects of spelt in agricultural practice but also there are mentioned some new inovative growing methods. In the thesis there is also organic agrotechnology described. In the end of introduction there is also description other alternative crops and its characteristics. The practical part is composed from results of small plot field trials. The most important quality parameters were also analysed. All the results were compared to Triticum aestivum L. varieties. From the conclusions was possible to show which varieties are suitable for organic farming in our soil and climatic conditions. The differences between Triticum spelta L. and Triticum aestivum L. were also compared and evaluated in relation to yield parameters and grain quality.
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Singular Initial Value Problem for Ordinary Differential and Integrodifferential Equations
Archalousová, Olga ; Beránek, Jaroslav (referee) ; Růžičková,, Miroslava (referee) ; Šmarda, Zdeněk (advisor)
The thesis deals with qualitative properties of solutions of singular initial value problems for ordinary differential and integrodifferential equations which occur in the theory of linear and nonlinear electrical circuits and the theory of therminionic currents. The research is concentrated especially on questions of existence and uniqueness of solutions, asymptotic estimates of solutions and modications of Adomian decomposition method for singular initial problems. Solution algoritms are derived for scalar differential equations of Lane-Emden type using Taylor series and modication of the Adomian decomposition method. For certain classes of nonlinear of integrodifferential equations asymptotic expansions of solutions are constructed in a neighbourhood of a singular point. By means of the combination of Wazewski's topological method and Schauder xed-point theorem there are proved asymptotic estimates of solutions in a region which is homeomorphic to a cone having vertex coinciding with the initial point. Using Banach xed-point theorem the uniqueness of a solution of the singular initial value problem is proved for systems of integrodifferential equations of Volterra and Fredholm type including implicit systems. Moreover, conditions of continuous dependence of a solution on a parameter are determined. Obtained results are presented in illustrative examples.
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