We investigate the number of periodic points of certain discrete quadratic maps modulo prime numbers. We do so by first exploring previously known results for two particular quadratic maps, after which we explain why the methods used in these two cases are hard to adapt to a more general case. We then perform experiments and find striking patterns in the behaviour of these general cases which suggest that, apart from the two special cases, the number of periodic points of all quadratic maps of this type behave the same. Finally we formulate a conjecture to this effect.

In this thesis we study the number of periodic points of congruential monomial dynamical system. By concept of index calculus we are able to calculate the number of solutions for congruential equations. We give formula for the number of r-periodic points over prime power. Then we discuss about calculating the total number of periodic points and cycles of length r for prime power.

In the masters work „The supervision and durability of railway points and their parts” I analyst the constructions of the existent railway points and their types, viewer the technical state of the railway points that „Vilniaus geležinkelių infrastruktūra”, a branch of „Lietuvos geležinkeliai” changed last year. The interaction of the railway points and the wheels of the railing – stock when a train rolls through the parts of the railway point is analysed. The ways and possibilities to enlarge the durability of the railway points and their parts is viewed. The rules and norms of the railway point service are examined. In order to explore the influence of the deflection of the railway point geometrical parameters to the wane of their parts, the works of levelling and measuring the geometrical parameters of 17 railway points and their parts fitted in 2003 has been done. The received measurement result data has been analysed. The economic affect of the railway point durability enlargement tentatively counted. At the end of the work, on the ground of the measurement results and their analysis, the conclusions are formulated and there are also proposals how to prolong the durability of railway points and their parts.

No description available.

No description available.

The Clovis style point was used by Paleoindians to hunt and kill the proboscidean mammoths and mastodons of the era in the New World. How the Paleoindians specifically used Clovis technology and their hunting strategies are ambiguous. Middle range theory is used in a comparison of ethnographic, archaeological, paleontological, and experimental archaeological evidence. Deductive and inductive reasoning are used in conjunction with this data to develop an interpretive model. This type of study can help to reconstruct a part of the past lifeways of the Clovis Paleoindians. A general model taken from the evidence is presented of Paleoindian proboscidean hunting strategy and the possible design and use of weaponry. However, the majority of the data comes from western Clovis sites associated with Columbian mammoths. A universal or regional based model for Paleoindian proboscidean hunting tactics and weapon design and employment cannot be fully dictated. Creating a model of this type requires an intensively thorough survey of all Clovis archaeological and ancient proboscidean sites. / Department of Anthropology

The objective of my thesis is to find optimal points and the quantization error for a probability measure defined on a Cantor set. The Cantor set, we have considered in this work, is generated by two self-similar contraction mappings on the real line with distinct similarity ratios. Then we have defined a nonhomogeneous probability measure, the support of which lies on the Cantor set. For such a probability measure first we have determined the n-optimal points and the nth quantization error for n = 2 and n = 3. Then by some other lemmas and propositions we have proved a theorem which gives all the n-optimal points and the nth quantization error for all positive integers n. In addition, we have given some properties of the optimal points and the quantization error for the probability measure. In the end, we have also given a list of n-optimal points and error for some positive integers n. The result in this thesis is a nonhomogeneous extension of a similar result of Graf and Luschgy in 1997. The techniques in my thesis could be extended to discretise any continuous random variable with another random variable with finite range.

Leaves play a vital role in the development of a plant, as they are major resource collectors. Adequate models of leaves are therefore required for the modelling of plants. Such models may be used for visualisation purposes only, or they may incorporate leaf function such as photosynthesis. While the modelling of plant architecture has been researched extensively over the last decades, models of leaf surfaces have mostly not been generated with great accuracy or level of detail, and have often been handcrafted. This thesis aims to provide techniques for the creation of detailed, accurate models of leaf surfaces for the plant modelling community; models that may be used as parts of virtual plants for applications in fields as diverse as the arts, agriculture or computer games. These techniques are mathematical methods of surface fitting based on data that has been sampled from real leaves. First, leaf data needs to be collected. The digitising of leaf surfaces is described in detail in this thesis, and issues arising for three data collection techniques are discussed. The laser scanner is selected to sample data from leaf surfaces of four example leaf types. The two surface fitting methods which are applied to the data are finite element interpolation approaches. Since the size of a laser scanned data set can be enormous, an incremental algorithm is used to identify significant points that result in a surface fit that approximates all remaining data points to a specified accuracy. Interpretation of the positions of these points leads to the formulation of guidelines that describe the locations of significant points on a leaf surface. These are the points that should be digitised with a single-point device such as a sonic or magnetic digitiser, possibly the only digitising technique available to a plant scientist. Triangle-based finite element methods lead to surface models with piecewise linear viii boundaries in the triangulation reference plane. This may not be an issue for applications where the boundary of a model is not important. Leaf surfaces, however, possess a specific boundary. To generate a visually realistic model of a leaf surface the boundary needs to be captured; a method is introduced that improves the boundary of a triangle-based interpolant. A new boundary curve is specified that passes through all boundary points, and the surface is extended so that it matches the new curve. Visual criteria are listed for the acceptance or rejection of the boundary, and a preliminary discussion is made of numerical criteria. The research presented in this thesis is the first to model detailed and accurate leaf surfaces based on data points. It delivers a basis for further research both into the application of detailed models as well as into extensions of the presented model.

Thesis (Ph. D.)--University of Minnesota, 1924. / Biographical sketch. "Literature cited": leaves 85-88.

Thesis (Ph.D)--Physics, Georgia Institute of Technology, 2008. / Committee Chair: Chou, Mei-Yin; Committee Member: First,Phillip; Committee Member: Gao, Jianping; Committee Member: Landman, Uzi; Committee Member: wang, Xiao-Qian.