In this work we study two random procedures in cubic graphs with large girth. The first procedure finds a probability distribution on edge-cuts such that each edge is in a randomly chosen cut with probability at least 0.88672. As corollaries, we derive lower bounds for the size of maximum cut in cubic graphs with large girth and in random cubic graphs, and also an upper bound for the fractional cut covering number in cubic graphs with large girth. The second procedure finds a probability distribution on independent sets such that each vertex is in an independent set with probability at least 0.4352. This implies lower bounds for the size of maximum independent set in cubic graphs with large girth and in random cubic graphs, as well as an upper bound for the fractional chromatic number in cubic graphs with large girth.

Title: The Collection of Exercises About Qaudrangles Author: Bc. Pavel Nohál Department: Department of Mathematics Education Supervisor: doc. RNDr. Jarmila Robová, CSc., Department of Mathematics Education Abstract: The master thesis is focused on exercises regarding qaudrangles. This gives a chance to pupils of primary schools and lower secondary schools to repeat and practice math curriculum with a view of further study, but also develop pupils' common sense and logical thinking. The quadrangles are being encountered by us every day and therefore the exercises in this area are largely connected with the practical life. As not many current Collections on the market are dealing exclusively with quadrangles, author would like to fill this vacancy by this thesis. Keywords: Quadrilaterals and their division Parallelograms and trapezoids Circumference and area Tops, sides and interior angles

For my dissertation, I have chosen to monitor and research growing children in Prague and in the Central Bohemian Region. Primarily, I am interested in the growth period of the younger school age (which corresponds to the first degree of compulsory school attendance). However, I also monitored and worked with the growth data of infant and pre-school aged children. The reason for this is that I needed the growth data from a longer period of time for a better assessment. I am really interested in the area of child anthropology because I belive the growth of every child is essential for their future. The final height and weight of the individual, specifically his/her total body proportions, can have a significant influence on their next life. I am convinced that this can have a major influence on the health, social application and self-confidence for each of us. Thanks to a very willing approach of a Prague pediatrician I managed to accumulate the growth data of children living in Prague. I would like to compare the obtained data with the data of children living in the Central Bohemian Region. I was able to gain the growth data of the children thanks to the friendly cooperation of my pupils'parents, my acquaintances and friends. Children were selected according to their health cards. On these cards...

The first part of this thesis is focused on the advantages of using the experiments during the physics education and their educational values. Furthermore, some types of experiments, their correct metodology of implementation and some other aspects which should be given an appropriate attention by the teacher are theoretically described. Then, some types of demonstrational sets and their brief history are described. The attention is aimed at the demonstrational set of DIDAKTIK, its content and composition. One chapter is devoted to the research of schools equipment for using the demonstrational experiments of electricity and magnetism and their evaluations. The last part deals with some experiments which can be made within this set, their documentation and evaluation. Further, there were worksheets created for some of these experiments. Two of these sheets were used among primary schools for didactic exploring and the reasults were evaluated.

The subject of this diploma thesis is the proposal of land consolidation in the cadastral area Všeradov. Part of the land consolidation is the evaluation and description of the area, with a focus on measures to access to the property, erosion control measures to protect the land fund, measures for the creation and protection of the environment and water management. An important part of the proposal is to establish the perimeter of land consolidation and last but not least, create the claims inventory owners and proposal a new land arrangement for selected owners. The results of this diploma thesis are presented in text and graphical form, processed using ArcGIS software.

This diploma thesis is devoted to the development of body measurements of children 0 to 6 months old being exclusively breastfed until the age of four months and then breastfed with appropriate complementary food. The anthropometrical parameters were the body length, the body weight and the head circumference. The results are shown separately for girls and boys in tables and graphs. The data were compared to the previous surveys of the Czech children. Student's t-test and Z- score were used for comparison. Selected somatic and other characteristics obtained by a questionnaire were taken into the study. The Life Satisfaction Questionnaire was used to evaluate the welfare of primiparas. The breastfed children do not reach lower average values of body length and weight than children of the reference survey CAV, 2001 (Vignerová et al., 2005) and Bláha a kol., 2001 (Bláha et al., 2010) in general. Body lenght, body weight and head circumference of boys and girls until the age of one month positively correlates with the gestation age of an infant. Life satisfaction of primiparas is mostly influenced by financial situation, marriage, partnership and sexuality. Life satisfaction of primiparas from our survey correlates statistically significantly with their health and satisfaction with marriage and partnership. The collected somatic data of infants could be used as a part of the standards for contemporary population of breastfed infants.

The topic of my thesis is the social and economic analysis of the administration district of municipality with extended competence Trhové Sviny. The social analysis focuses mostly on demographic characteristics and social infrastructure. The economic analysis focuses on regional labour market and structure of the economy. Next chapters focus on traffic and technical infrastructure, tourism, public administration and municipal co-operation.

The master thesis done within the master study programme Transport vehicles and handing machinery presents a design of a wood splitting machine. The first part of the thesis is a literary review focused on current state in the field of wood splitting machines and on the overview of the most common wood species including their technical parameters. In the second part of the thesis, suitable machine components were chosen for the conceptual design of the wood splitter, taking into account predefined parameters. Then a machine frame was designed and its strength was verified by analytical and FEM method. Finally, drawing documentation for the machine, machine frame and splitting tool was created.

This master thesis is concerned about the resynthesis of combinational circuits with the help of evolutional principles. The first part of this text describes logic synthesis and its weak spots, evolutional synthesis and its advantages, and also some of the existing synthesis programs. The second part shows usage of graph algorithms in logic synthesis and their possible usage in an extension for the chosen synthesis program. Suggested design and practical implementation of the extension is also described in this part. In the third part extension testing is mentioned. The fourth part is the last one and concludes gained knowledge and results.

The subject of this diploma thesis is the determination perimeter of the complex land consolidation in the cadastral area Dobronice. Documents for detection of borderlines are prepared on the basis of a defined perimeter. Borderlines of perimeter is examined with an officially appointed commission and with landowners. A geometric plan is made for the partition of the land, determination borderline of lands for land consolidation and running of specify borderlines from landowners. The results of detection borderlines are created in prescribed elaborate.