q-Karamata functions and second order q-difference equations

In this paper we introduce and study $q$-rapidly varying functions on the lattice $q^{N_0}:=\{q^k:k\in N_0\}$, $q>1$, which naturally extend the recently established concept of $q$-regularly varying functions. These types of functions together form the class of the so-called $q$-Karamata functions. The theory of $q$-Karamata functions is then applied to half-linear $q$-difference equations to get information about asymptotic behavior of nonoscillatory solutions. The obtained results can be seen as $q$-versions of the existing ones in the linear and half-linear differential equation case. However two important aspects need to be emphasized. First, a new method of the proof is presented. This method is designed just for the $q$-calculus case and turns out to be an elegant and powerful tool also for the examination of the asymptotic behavior to many other $q$-difference equations, which then may serve to predict how their (trickily detectable) continuous counterparts look like. Second, our results show that $q^{N_0}$ is a very natural setting for the theory of $q$-rapidly and $q$-regularly varying functions and its applications, and reveal some interesting phenomena, which are not known from the continuous theory

Foster care and child with handicap

I divided my bachelor thesis named Foster care and child with handicap into three parts. The first three parts are focused on theoretical assessment of problem and the rest four on research and its conclusion. Chapters, which handling theory, are focused on general information about foster care defining it in system of substitute family care, following reasons for putting child into this system, couple´s motivation to offering their family as a safe place to upbringing a child, their financial cover and ending conditions. In the next chapter it comes with connection of foster care with upbringing of disabled child and it all makes combination of those two large themes. At first this part defines basic information about disabilities. Later it solves issue of upbringing, relationships between foster-parents, relations of siblings, adolescence and amount of information which are needy for parenting. In the last chapter of theoretical assessment is focused on relations of foster family and surroundings, thus with related or close people. I have concentrated on two objectives in research, which are in connection with two important elements of foster care. First one is targeting finding of foster-parent's satisfaction with provided services associated with their activity. In case of this objective I paid attention on relations of foster family to law changes related to foster care and also the services, which are used by foster children or family. The second objective of research was finding out foster-parent´s reasons for disabled child adoption. In the context of this objective, there is attention on reasons itself of decision and describing a fact of knowledge of disability before adoption and problems coming with. I used quantitative research, interrogation method, technic of non-structuralised dialog. This dialog I made with three couples situated in South Bohemia, who have disabled child in care. Due to achieving best results, I choose couples, who have more than five children and they are older than fifty years old. Couple's experiences were important criteria of choosing process. Many important facts came from the dialogs I made with respondents. At first, in case of finding out respondent´s satisfaction with provided services, I can tell that financial system is advantageous for single person compared to both parents dealing with foster care. I also found out that the most used provided service is specialist´s help, especially psychologist and doctors. Other important service, used by foster-parents, is meetings with other people participating in foster care program. It provides them chance to transfer experiences and information among other foster parents, which they consider usable. Except that they see special courses as a very important part, despite the fact it´s compulsory. It gives them opportunity to improve their care. In the context of second given objective I could determine for what important reason foster parents have decided to participate in foster care. The most important reason was impossibility of having own child and other was make a sibling to their own child. It comes from research that parents got lack of information about foster child´s disabilities before taking a child. Two cases had only partial information and in one case they didn´t know about child´s handicap at all. According to school, it was mainly explanations of children´s special needs. Foster parents emphasized need of services given to their children, which accomplished foster care, regardless disability or not. This bachelor service can serve as inspiration to make offer of services targeted to improve foster care. For example, foster parents implied to create controlling system above accompanying organizations to prevent some negative side effects

Self-Destructive Behavior and Actions of a Child

Diplomová práce se zabývá zkoumáním tématu autodestruktivní chování a jednání dětí. K tomu v první části práce využívá teoretické zkoumání dokumentů, přičemž se zaměřuje na suicidium a sebepoškozování. Pro vymezení problematiky tak definuje základní pojmy, popisuje konkrétní rizikové chování a jednání, zaměřuje se na příčiny jeho vzniku, rizikové faktory a projevy. Pozornost věnuje také statistikám souvisejícím s tématem a reakcím okolí. Poslední kapitoly této části se pak zabývají prevencí, pomocí a léčbou. V druhé části se diplomová práce zaměřuje na zkoumání dvou konkrétních případů autodestruktivního chování a jednání, konkrétně sebepoškozování. K tomu využívá kvalitativní výzkum, metodu zkoumání dokumentů. Snaží se z případových studií zjistit, v jakém rodinném prostředí děti s tímto chováním a jednáním vyrůstají a jaké jsou příčiny u konkrétních případů. V poslední kapitole druhé části nazvané Diskuse, se práce zaměřuje na interpretaci získaných informací a jejich zhodnocení v kontextu teoretického vymezení problematiky a předkládá návrhy na další směřování výzkumu.The diploma thesis focuses on self-destructive behavior and actions of a child research. In the first part there is theoretical examination of documents aiming on suicidium and self-harm. It defines basic terminology, describes specific dangerous behaviour and acts focused on causes of origins, risk factors and manifestations. Thesis follows with statistics of people´s reactions connected with cases. Last chapters of this part explore prevention and treatment. The second part of the diploma thesis analyses two specific cases of self-destructive behavior and actions, especially self-harm. It uses qualitative research, a method of examining documents. It's trying to discover family background of these children and its connections with causes. In the last chapter there is an interpretation of gained information and their evaluation in the context of theoretical problem determination. It continues with suggestions of future research development

Theory of rapid variation on time scales with applications to dynamic equations

summary:In the first part of this paper we establish the theory of rapid variation on time scales, which corresponds to existing theory from continuous and discrete cases. We introduce two definitions of rapid variation on time scales. We will study their properties and then show the relation between them. In the second part of this paper, we establish necessary and sufficient conditions for all positive solutions of the second order half-linear dynamic equations on time scales to be rapidly varying. Note that these results are new even for the linear (dynamic) case and for the half-linear discrete case. In the third part of this paper we give a complete characterization of all positive solutions of linear dynamic equations and of all positive decreasing solutions of half-linear dynamic equations with respect to their regularly or rapidly varying behavior. The paper is finished by concluding comments and open problems of these themes

Progress and organization of fire protection and the Fire Brigade of Czech republic

Bakalářská práce se snaží zachytit klíčové momenty v historickém vývoji požární ochrany a Hasičského záchranného sboru ČR a to od prvních zmínek v jednotlivých etapách dějin, až po současnou dobu. Věnuje se stěžejním právním předpisům, které výrazným způsobem ovlivnily další vývoj, jak v dobrovolných, tak profesionálních organizacích. Jsou zde popsána vznikající práva a povinnosti jednotlivých subjektů v této oblasti. Zároveň jsou nastíněny vazby mezi vznikající požární ochranou a státním či samosprávným zřízením v jednotlivých časových úsecích.Katedra veřejné správyObhájenoThe target of this bachelor thesis is to highlight the most important moments and progress in the history of Fire and Rescue Service of Czech Republic, starting deep in the history and also covering present situation.The most important law regulations influencing progress in both volunteer and professional organizations, are stated in the thesis. Rights and duties of every subject and relationship between Fire Rescue Service and government are described in each particular period of time

Lower and upper estimates of solutions to systems of delay dynamic equations on time scales

In this paper we study a system of delay dynamic equations on the time scale \T of the form $$y^{\Delta}(t)=f(t,y_{\tau}(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$, $y_\tau(t)=(y_1(\tau_1(t)),\ldots,y_n(\tau_n(t)))$ and \tau_i\colon\T\rightarrow \T, $i=1,\ldots,n$ are the delay functions. We are interested about the asymptotic behavior of solutions of mentioned system.In this paper we study a system of delay dynamic equations on the time scale \T of the form $$y^{\Delta}(t)=f(t,y_{\tau}(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$, $y_\tau(t)=(y_1(\tau_1(t)),\ldots,y_n(\tau_n(t)))$ and \tau_i\colon\T\rightarrow \T, $i=1,\ldots,n$ are the delay functions. We are interested about the asymptotic behavior of solutions of mentioned system. More precisely, we formulate conditions on a function $f$, which guarantee that the graph of at least one solution of above mentioned system stays in the prescribed domain. This result generalizes some previous results concerning the asymptotic behavior of solutions of non-delay systems of dynamic equations or of delay dynamic equations. A relevant example is considered

Podmíněná oscilace pololineární dynamické rovnice Eulerova typu na časových škálách

We investigate second-order half-linear Euler-type dynamic equations on time scales with positive periodic coefficients. We show that these equations are conditionally oscillatory, i.e., there exists a sharp borderline (a constant given by the coefficients of the given equation) between oscillation and non-oscillation of these equations. In addition, we explicitly find this so-called critical constant. In the cases that the time scale is reals or integers, our result corresponds to the classical results as well as in the case that the coefficients are replaced by constants and we take into account the linear equations. An example and corollaries are provided as well.Zkoumáme pololineární Eulerovy dynamické rovnice druhého řádu na časových škálách s kladnými periodickými koeficienty. Ukážeme, že tyto rovnice jsou podmíněně oscilatorické, tj., existuje přesná hranice (konstanta zadaná pomocí koeficientů dané rovnice) mezi oscilací a neoscilací těchto rovnic. Navíc, tuto takzvanou kritickou konstantu explicitně určíme. V případě, že časová škála jsou reálná čísla nebo celá čísla, naše výsledky odpovídají klasickým výsledkům, stejně jako případ, že koeficienty zkoumané rovnice jsou nahrazeny konstantami a uvažujeme lineární rovnici. Příklad a další důsledky jsou též uvedeny