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Semilinear stochastic evolution equations
Kršek, Daniel ; Maslowski, Bohdan (advisor) ; Čoupek, Petr (referee)
Stochastic partial differential equations have proven useful in many applied areas of mathematics, such as physics or mathematical finance. A major part of such equations consists of linear equations with additive noise. In certain cases, however, the drift part of the differential equation additionally contains a possibly problematic non-linear term, which makes it unsolvable by the standard methods and even a solution in the mild sense may be out of reach. In such situations, we may still find a solution in the weak sense by employing a suitable transformation of the probability space. This thesis deals with semilinear stochastic evolution equations in a separable Hilbert space, where the driving process is an element of a large class of processes - so called Volterra processes, which can be understood as a generalisation of the Wiener process and may be of use to model a wide range of phenomena. The weak solutions, however, have been studied so far only for equations with the cylindrical fractional Brownian motion as the driving process. In this thesis, we introduce a generalisation of the Girsanov theorem for cylindrical Gaussian Volterra processes and give, in full generality, sufficient conditions for the existence of a weak solution and the uniqueness of the equation in law. Further, we introduce...
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Abiotic stress resposes in apple (Malus domestica Borkh.) tissue cultures
Krsek, Daniel
Abiotic stress factors, primarily those which disturb plant water balance, cause extensive crop losses. With regard to sessile lifestyle, many mechanisms how to cope with these unfavourable conditions were developed during evolution of plants. As common impact of many of these stresses like drought, salinity or low temperatures is of osmotic nature, the osmotic adjustment represents important part of plant stress response. Mostly, this component of stress reaction is provided by organic compounds, which are referred to as compatible solutes, including polyhydroxyl compounds (sucrose, sugar alcohols, cyclitols, and oligosacharides) and nitrogen-containing compounds (mainly proline). The effect of these solutes is not only osmotic, but also osmoprotective as they are able to preserve integrity of membranes and macromolecules by mimicking their water envelope. The compatible solutes also contribute to quenching of reactive oxygen species overproduced under these stress conditions. This study is focused on apple (Malus domestica) producing, beside sucrose, sugar alcohol sorbitol as primary photosynthetic product and transporting these carbohydrates along with raffinose family oligosaccharides (RFO) for a long distance. In vitro tissue cultures derived from leaves of two apple cultivars differing in...
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Riemann-Liouville integral, fractional derivative and their applications in probability theory
Kršek, Daniel ; Maslowski, Bohdan (advisor) ; Čoupek, Petr (referee)
Fractional integrals and derivatives in a sense generalize common integrals and derivatives. They can be used to define the integral b a f(x) dg(x) on a bounded interval for large set of integrands f and integrators g, in ge- neral, of unbounded variation. This concept may be utilized in theory of stochastic differential equations, where the standard random processes are not of bounded variation, yet they admit a version with Hölder continuous sample paths. This thesis deals with a particular type of multidimensional differential equations, where subject to certain conditions an existence of a unique solution may be proved. It presents the proof of continuous depen- dence of solutions on initial condition. Furthermore, this thesis analyzes the situation in which coefficients in equations continuously depend on a para- meter from certain metric space. For such a situation, the thesis introduces a proof of continuous dependence of solutions on these parameters. 1
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Abiotic stress resposes in apple (Malus domestica Borkh.) tissue cultures
Krsek, Daniel ; Pospíšilová, Jana (referee) ; Lipavská, Helena (advisor)
Abiotic stress factors, primarily those which disturb plant water balance, cause extensive crop losses. With regard to sessile lifestyle, many mechanisms how to cope with these unfavourable conditions were developed during evolution of plants. As common impact of many of these stresses like drought, salinity or low temperatures is of osmotic nature, the osmotic adjustment represents important part of plant stress response. Mostly, this component of stress reaction is provided by organic compounds, which are referred to as compatible solutes, including polyhydroxyl compounds (sucrose, sugar alcohols, cyclitols, and oligosacharides) and nitrogen-containing compounds (mainly proline). The effect of these solutes is not only osmotic, but also osmoprotective as they are able to preserve integrity of membranes and macromolecules by mimicking their water envelope. The compatible solutes also contribute to quenching of reactive oxygen species overproduced under these stress conditions. This study is focused on apple (Malus domestica) producing, beside sucrose, sugar alcohol sorbitol as primary photosynthetic product and transporting these carbohydrates along with raffinose family oligosaccharides (RFO) for a long distance. In vitro tissue cultures derived from leaves of two apple cultivars differing in...
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Abiotic stress resposes in apple (Malus domestica Borkh.) tissue cultures
Krsek, Daniel
Abiotic stress factors, primarily those which disturb plant water balance, cause extensive crop losses. With regard to sessile lifestyle, many mechanisms how to cope with these unfavourable conditions were developed during evolution of plants. As common impact of many of these stresses like drought, salinity or low temperatures is of osmotic nature, the osmotic adjustment represents important part of plant stress response. Mostly, this component of stress reaction is provided by organic compounds, which are referred to as compatible solutes, including polyhydroxyl compounds (sucrose, sugar alcohols, cyclitols, and oligosacharides) and nitrogen-containing compounds (mainly proline). The effect of these solutes is not only osmotic, but also osmoprotective as they are able to preserve integrity of membranes and macromolecules by mimicking their water envelope. The compatible solutes also contribute to quenching of reactive oxygen species overproduced under these stress conditions. This study is focused on apple (Malus domestica) producing, beside sucrose, sugar alcohol sorbitol as primary photosynthetic product and transporting these carbohydrates along with raffinose family oligosaccharides (RFO) for a long distance. In vitro tissue cultures derived from leaves of two apple cultivars differing in...
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