Subject of presented master thesis are two 7-meter objects of crystalline structure located in production hall in Brno former factory Zbrojovka

A thirsty young actor's desperate journey for fame leads him, unknowingly, into a love triangle with the two people he thought he could trust the most.

The purpose of this study was to describe how manipulatives facilitated the growth of one group of high school students' mathematical understanding of combinatorics and Pascal's Triangle. The role of manipulatives in mathematics education has been extensively studied, but much of the interest in manipulatives is focused on the general uses of manipulatives to support student learning. Unfortunately, there is a lack of research that explicitly defines how manipulatives can help students develop mathematical understanding. I have chosen to examine mathematical understanding through the lens of the Pirie-Kieren Theory for Growth of Mathematical Understanding. Through analysis of the students' explorations of the Towers Task, I identified ways in which manipulatives facilitated students' understanding of combinatorics and Pascal's Triangle. It was found that the properties and arrangements of the manipulatives were significant in prompting students' progression through levels of understanding and helped students to reason abstractly and develop mathematical generalizations and theories. From this study we can gain insights into explicit ways in which manipulatives facilitate mathematical understanding. These results have implications for research, teaching and teacher education.

Between the years 1998 and 2002, the United States suffered a time in which several large companies engaged in fraudulent behavior which eroded investor confidence in the stock market and to some extent destabilized the economy. Audits, which were conducted to assess the validity and reliability of a company's financial statements, were not detecting the material misstatements in the statements. As a result, both the US Government and the accounting profession needed to come up with a way to prevent these immense frauds from occurring in the future. As a response to these large frauds, in 2002, the US Government passed the Sarbanes-Oxley Act of 2002 (SOX) and the American Institute of Certified Public Accountants (AICPA) issued Statement on Auditing Standards No. 99(SAS No. 99) to improve investor confidence and the auditing function's ability to detect material frauds. The intent of this thesis was to look at the fraudulent factors associated with several recent corporate frauds and compare them to the standards set by SAS No. 99. Through the analysis conducted, this thesis looks at the relationships between pressures, opportunities, and rationalizations made during the act of fraud.

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A network (graph) is a powerful abstraction for interactions among entities in a system. Examples include various social, biological, collaboration, citation, and co-purchase networks. Real-world networks are often characterized by an abundance of triangles and the existence of well-structured communities. Thus, counting triangles and detecting communities in networks have become important algorithmic problems in network mining and analysis. In the era of big data, the network data emerged from numerous scientific disciplines are very large. Online social networks such as Twitter and Facebook have millions to billions of users. Such massive networks often do not fit in the main memory of a single machine, and the existing sequential methods might take a prohibitively large runtime. This motivates the need for scalable parallel algorithms for mining and analysis. We design MPI-based distributed-memory parallel algorithms for counting triangles and detecting communities in big networks and present related analysis. The dissertation consists of four parts. In Part I, we devise parallel algorithms for counting and enumerating triangles. The first algorithm employs an overlapping partitioning scheme and novel load-balancing schemes leading to a fast algorithm. We also design a space-efficient algorithm using non-overlapping partitioning and an efficient communication scheme. This space efficiency allows the algorithm to work on even larger networks. We then present our third parallel algorithm based on dynamic load balancing. All these algorithms work on big networks, scale to a large number of processors, and demonstrate very good speedups. An important property, very related to triangles, of many real-world networks is high transitivity, which states that two nodes having common neighbors tend to become neighbors themselves. In Part II, we characterize networks by quantifying the number of common neighbors and demonstrate its relationship to community structure of networks. In Part III, we design parallel algorithms for detecting communities in big networks. We propose efficient load balancing and communication approaches, which lead to fast and scalable algorithms. Finally, in Part IV, we present scalable parallel algorithms for a useful graph preprocessing problem-- converting edge list to adjacency list. We present non-trivial parallelization with efficient HPC-based techniques leading to fast and space-efficient algorithms. / Ph. D.

In this thesis we consider the maximum number of points in $mathbb{R}^d$ which form exactly $t$ distinct triangles, which we denote by $F_d(t)$. We determine the values of $F_d(1)$ for all $dgeq3$, as well as determining $F_3(2)$. It was known from the work of Epstein et al. cite{Epstein} that $F_2(1) = 4$. Here we show somewhat surprisingly that $F_3(1) = 4$ and $F_d(1) = d + 1$, whenever $d geq 3$, and characterize the optimal point configurations. We also show that $F_3(2) = 6$ and give one such optimal point configuration. This is a higher dimensional extension of a variant of the distinct distance problem put forward by ErdH{o}s and Fishburn cite{ErdosFishburn}. / Master of Science / In this thesis we consider the following question: Given a number of triangles, t, where each of these triangles are different, we ask what is the maximum number of points that can be placed in d-dimensional space, such that every triplets of these points form the vertices of only the t allowable triangles. We answer this for every dimension, d when the number of triangles is t = 1, as well as show that when t = 2 triangle are in d = 3-dimensional space. This set of questions rises from considering the work of Erd˝os and Fishburn in higher dimensional space [EF].

Yes / Effective communication can aid in improving oral healthcare measures such as treatment outcomes and satisfaction of edentulous patients (EDPs) toward the treatment process. The triangle of communication (ToC) involves communication between the dentist, dental technician (DTech), and EDPs. This research aimed to explore the ToC between dental professionals (DPs) and patients undergoing complete denture prostheses (CDP) treatment in Fiji. Materials and Methods: A descriptive qualitative study was conducted among DPs under purposive sampling where focus group discussions were conducted at the four dental prosthetic clinics in Fiji. A semi-structured questionnaire with open-ended questions was applied to participants virtually via Zoom. The collected data were collated and analyzed manually using thematic analysis. Results: A total of 28 DPs participated in the study. Three themes were identified while exploring the ToC from DPs’ perspectives on CDP treatment and care in Fiji: staff communication—dentist and DTech, ToC and information sharing (dentist–DTech and EDPs), and stage-by-stage procedural checks for CDP between DPs. Effective collaboration between dentists and DTechs is an essence of a successful CDP treatment outcome. Most DPs agreed to undergo continuous communication throughout the treatment to keep EDPs engaged throughout the treatment process. In addition, stage-by-stage procedural checks in dental clinics as well as in dental laboratories improved the quality of CDPs. Conclusion: DPs highlighted predominantly the ToC between DPs and EDPs when receiving CDP treatment in Fiji as an essential tool for effective DP and patient engagement. Discussions should be complemented with the use of verbal, nonverbal, and written modes together with the utilization of interpreters to improve CDP treatment and care in Fiji.