This research aimed to discuss the indigenous students’ learning effects of mathematics which was based on the self-designed localization and materialization of mathematics activities and had proceeded for one year. The quasi-experimental method was used in this research. There were 58 indigenous first grade students which were divided into three experimental groups (A, B, C) and one control group (D). Experimental instruments embodied written tests and manipulative tests which were designed by researchers according to the indicators proclaimed by Ministry of Education. The main findings were as followed: (1) The influence of localization and materialization of mathematics activities on the indigenous first grade students’ learning effects was limited. (2) According to the result of Paired T-test of the written and manipulative tests, most of scores of manipulative tests were higher written tests.

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Railway scheduling problems are quite popular scheduling and optimization problems which are treated in a large variety of papers and projects. Many special and even quite general situations have been investigated theoretically and also a variety of applied approaches tested on real-world instances has been developed.This thesis mainly deals with the problem of scheduling trains in railway networks with respect to given routings, fixed minimal travelling times, and other constraints like time-windows. It combines the theory of some well-known scheduling models with its applications in railway scheduling. The railway scheduling problems considered in this work are closely related to job-shop scheduling problems with blocking and some additional constraints. Therefore part of this research is related to these shop scheduling problems. Theoretical scheduling models are extended, complexity results are derived and solution methods are proposed. Most results are applied to the considered railway scheduling problems. In addition to approaches which treat railway problems as a whole also decomposition methods for these problems and corresponding solution methods are presented. These solution methods are tested and compared with simple greedy procedures.

For classical non-cyclic scheduling problems, we are given a set of operations,each of which has to be processed exactly once. The aim is to minimize or maximizea given objective function such as makespan or sum of all (weighted) completion times for a given set of constraints. The set of constraints is usually given by precedence constraints between the operations. In contrast to these problems, for cyclic scheduling problems we are given a set of operations, each of which has to be processed infinitely often. Such types of scheduling problems arise in different application areas like compiler design, manufacturing, digital signal processing, railway scheduling, timetabling, etc. The problem is to find a periodic schedule which minimizes a given objective function. There exist two objective functions which are important in this area of cyclic scheduling. The objective which is considered throughout this work is to minimize the time difference between two succeeding occurrences of one operation for a given set of constraints. This time difference is called cycle time. In this thesis, we develop a general framework to model and to describe cyclic scheduling problems with resource constraints. Furthermore, we extend the model to describe blocking constraints for cyclic scheduling problems. In order to solve the problem, we develop a local search approach.

The aim of this thesis is to define and study harvesting models of fish populations. These models are applied to particular fish species e.g., haddock and cod. The thesis is divided into five chapters: The first chapter is considered as an introductory one. In it, basics of fish biology and the recruitment process are defined. Two simple recruitment models known by the names Ricker and Beverton-Holt are used. In the second chapter the generalized Leslie model or Usher model is introduced. In section 2.2, some matrix theory is presented. For this matrix model, the net reproductive number is defined and studied in section 2.3. It turns out to be more useful than the spectral radius. In section 2.4, this study is extended to nonlinear matrix models. The nonlinearity, however, is defined only by the recruitment process. This allows to determine the equilibrium components. Finally section 2.5, the local stability of nonlinear matrix models is analyzed. Harvesting of such general matrix model is defined in chapter 3. We distinguish three different harvesting models (selective, net and semicontinuous harvesting models). In chapter 4, these harvesting models are then applied to concrete fish populations and analyzed with respect to its various parameters. In chapter 5, the stability is studied again along the lines of the paper of Levin, Goodyear [18]. The key results in this study are: 1) The maximum sustainable yields for selective harvesting and net harvesting are rather close. 2) Semicontinuous harvesting is more realistic harvesting models. 3) From a quantitative point of view, the choice of the recruitment function is important. 4) Harvesting process increases mortality and stability when we used Ricker recruitment model. 5) Stability of populations always holds if we use Beverton-Holt recruitment model.

The Chow/Van der Waerden approach to algebraic cycles via resultants is elaborated and used to give a purely algebraic proof for the algebraicity of the complex suspension over arbitrary fields. The algebraicity of the join pairing on Chow varieties then follows over the complex numbers. The approach implies a more algebraic proof of Lawson´s complex suspension theorem in characteristic 0. The continuity of the action of the linear isometries operad on the group completion of the stable Chow variety is a consequence. Further Hoyt´s proof of the independence of the algebraic-continuous homeomorphism type of Chow varieties on embeddings is rectified and worked out over arbitrary fields.

Diese Arbeit befasst sich mit der unimodularen Überdeckung und Triangulierung von Gitterpolytopen. Zentral ist in diesem Zusammenhang die Angabe einer möglichst guten oberen Schranke c0, so dass die Vielfachen cP eines Polytopes P für alle c>c0 eine unimodulare Überdeckung besitzen. Bruns und Gubeladze haben erstmals die Existenz einer solchen Schranke nachgewiesen und konnten sogar explizit eine solche in Abhängigkeit von der Dimension des Polytopes angeben. Allerdings war diese Schranke super-exponentiell. In dieser Arbeit wird nun u.a. eine polynomielle obere Schranke hergeleitet.

Das Skript zum Kurs Einführung in das symbolische Rechnen Sommersemester 2021 (Introduction to Symbolic Computing) gibt eine systematische Einführung in symbolische Methoden in der Mathematik, in die grundlegenden Algorithmen der Computeralgebra, die für Anwendungen in der Zahlentheorie, kommutativen Algebra und algebraischen Geometrie wichtig sind.:0 Einleitung 3 1 Computeralgebrasysteme im Einsatz 7 2 Aufbau und Arbeitsweise eines CAS der zweiten Generation 41 3 Das Simplifizieren von Ausdr ̈ucken 79 4 Algebraische Zahlen 114 5 Addendum: Die Stammfunktion einer rationalen Funktion 134 6 Addendum: Die Stellung des symbolischen Rechnens im Wissenschaftsgebäude 142