An Italian dominating function on a graph $G = (V,E)$ is a function such that $f : V \to \{0,1,2\}$, and for each vertex $v \in V$ for which $f(v) = 0$, we have $\sum_{u\in N(v)}f(u) \geq 2$. The weight of an Italian dominating function is $f(V) = \sum_{v\in V(G)}f(v)$. The minimum weight of all such functions on a graph $G$ is called the Italian domination number of $G$. In this thesis, we will consider Italian domination in various types of products of a graph $G$ with the complete graph $K_2$. We will find the value of the Italian domination number for ladders, specific families of prisms, mobius ladders and related products including categorical products $G\times K_2$ and lexicographic products $G\cdot K_2$. Finally, we will conclude with open problems.

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The current study evaluated the effects of discrete trial training versus the effects of relational training on the acquisition and retention of skills in four children with autism. Using a multiple baseline design across subjects, participants were trained on the skills sequencing from longest to shortest, discriminating full versus empty versus half empty, tacting “you” versus “I,” and responding to reasons why people cry. One of the four participants acquired and retained the skill. Many factors effected the results for the other three participants. Participant 2 never met mastery criteria with relational training procedures. Participant 3 learned PEAK programming four times faster than DTT, however, when using PEAK with the original target, 10 days were required to score all points opposed to the four days DTT required. Participant 4 displayed similar performance results using DTT and PEAK. Implications and limitations will be discussed.

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

The goal of this diploma thesis is to verify the practical applicability of the Raspberry Pi platform in control applications. The work consists of choosing a suitable operating system and implementing a discrete PID algorithm. An important part of the work was the Linux OS modification and compilation. Measurement has demonstrated the usability of the platform in control applications. The result of this work is a discreet PID controller implemented as a Linux kernel module. The solution also includes a web interface as a human-machine interface.

Discrete Differential Geometry (DDG) concerns discrete counterparts of notions and methods in differential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy different geometric or physical constraints. We study a combination of geometry and physics – the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences – a particular type of congruences defined by linear interpolation of vertex normals. The main results are a discussion of various definitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the practicability and accuracy of their applications in face recognition.

Automatic identification system is a prominent technology used in warehouses to give managers real time information of their products and assistance to warehouse employees in keeping an accurate inventory record. This kind of assistance is needed as an inaccurate inventory leads to profit loss due to misplacement or other mistakes. This project cooperated with an organization called Stora Enso specifically one of their forest nursery to find a solution to improve their inventory management system. Their current inventory system is a manual process which leads to mistakes occurring that affects the inventory accuracy. This thesis project evaluates automatic identification systems to observe if the technology is a possible solution and aims to answer the research question ”What are the significant impacts an automatic identification system has on an inventory management system?”. From the automatic identification evaluation one system is picked for further evaluation and due to its advantages radio frequency identification (RFID) is picked. To evaluate RFID in a warehouse setting a discrete-event simulation was created that simulates the forest nursery’s warehouse. The simulation is then used to evaluate the impact of different RFID implementations and their respective cost. The simulation results show that just a simple RFID implementation can improve inventory accuracy and remove some of the mistakes a manual system has with a relatively low direct cost. It also shows that a full RFID implementation that gives full visibility of a warehouse can almost remove inventory mistakes however the cost analysis shows that it requires a large investment.

In this rapidly changing product demand market, the pharmaceutical companies have adapted their production system to be more flexible and agile. In order to meet the demand, production lines need to be more efficient and effective. Even a small improvement is a great achievement as these production lines are designed to produce large volumes of medicines. To test the efficiency and effectiveness of the lines by analyzing production data would be time taking and needs the involvement of experts from different departments. When production lines are subjected to change, previous analysis done will no longer be valid and needs to be repeated again. Instead, this can be replaced with discrete even simulation analysis (DES).     DES is one of the key technology in developing a production system in this industry 4.0 era. As the production systems become more and more complicated it becomes difficult to understand and analyze the behavior of the system if there are any changes brought up in the system. Simulation is the right technology to analyze and understand the behavior of the real system when undergone small or big changes.  The purpose of this case study is to make use of DES using ExtenSim as a simulation tool at the case company in order to develop a virtual model of a production system containing five production lines to understand the behavior and analyze the production lines to identify possible improvement and evaluate the feasibility of production system to achieve the forecasted demand. Possible improvements are identified from the simulation results of the current state model and a future state simulation model is developed with the improvements. Furthermore, this future state simulation model is used to analyze the feasibility of production lines for forecasted demand. By developing the simulation model was identified that the production lines were not efficient and are underutilized as that the company assumed.

The onset of flowering time in a plant is extremely significant when evaluating population success. Floral growth, seed production, and dispersal are all dependent upon flowering time. Flowering early (and hence longer) increases the prospect of pollination but typically reduces vegetative growth and yields fewer/smaller flowers. Flowering late (and hence shorter) guarantees more/bigger flowers but carries the risk of insufficient pollination. This fundamental trade-off between growth and flowering time suggests that there may be an optimal time to initiate flowering. In this thesis, we consider a deterministic hybrid integrodifferential model where we represent the growing season in continuous time and the time between seasons as a discrete map. We track the evolution of flowering time, as a phenotype, by explicitly considering it as a variable in our model. The model is analyzed from two different viewpoints: (1) by mutual invasion analysis in the sense of adaptive dynamics; and (2) by deriving equations for the mean trait value and total population density when flowering time is considered to be Gamma-distributed. In both cases evolution to an intermediary flowering time was observed.

In this paper, new variations of some well-known permutation statistics are introduced and studied. Firstly, a double-descent of a permutation π is defined as a position i where πi ≥ 2πi+1. By proofs by induction and direct proofs, recursive and explicit expressions for the number of n-permutations with k double-descents are presented. Also, an expression for the total number of double-descents in all n-permutations is presented. Secondly, a double-inversion of a permutation π is defined as a pair (πi,πj) where i<j but πi ≥ 2πj. The total number of double-inversions in all n-permutations is presented.