The work presented in this thesis was submitted to The University of Manchester for the degree of Doctor of Philosophy in June 2010 by Stuart K Stubbs and is entitled “Photo-physics and applications of colloidal quantum dots”. In this thesis the results of spectroscopic studies on various colloidal quantum dots, particularly related to the measurement and characterisation of multiple exciton generation are presented. Research conducted with Nanoco Technologies Ltd. that involved the design and development of hybrid quantum dot organic light emitting diodes for use in flat panel display technology is also presented. Cadmium selenide (CdSe), indium phosphide (InP), and lead sulphide (PbS) type I and cadmium selenide/cadmium telluride type II colloidal quantum dots were characterised using steady state photoluminescence and absorption spectroscopy. The fluorescence lifetimes of the decay of single excitons was measured in these quantum dots using time correlated single photon counting. An ultrafast transient absorption spectrometer was designed, built, and used to observe the picosecond dynamics of the decay of multiexcitons. These absorption transients were analysed in order to extract the quantum efficiency of producing multiple excitons per absorbed photon. The characteristic signature for multiple exciton generation was first found in CdSe using a time correlated single photon counting set-up. Results from the transient absorption spectrometer demonstrated efficient multiple exciton generation in InP for the first time as well as in PbS, where the efficiency was found to agree with values obtained by other research groups. The absorption transients taken for the type II CdSe/CdTe type II quantum dots demonstrated some novel decay dynamics that could not be attributed to the generation of multiple excitons. Quantum dot organic light emitting diodes were fabricated using Nanoco Technologies high quality cadmium based quantum dots and were shown to demonstrate bright, colour saturated emission originating from the quantum dot layer only. Using quantum dots of different sizes and structures red, green and blue devices were made and shown to be appropriate both in terms of brightness and chromaticity for the use as the red, green and blue pixels of a flat panel display. Because heavy metals like cadmium are restricted or banned from commercial products in many countries, Nanoco Technologies heavy metal free quantum dots, made from InP, were also incorporated in devices. Devices are demonstrated that emit from the quantum dot layer only, albeit at a lower luminance and efficiency than that found in the cadmium containing devices. This was the first demonstration of a heavy metal free, hybrid quantum dot organic light emitting diode.

This thesis is divided into two parts, each part exploring a different topic within the general area of nonlinear algebra. In the first part, we study several applications of tensors. First, we study tensor networks, and more specifically: uniform matrix product states. We use methods from nonlinear algebra and algebraic geometry to answer questions about topology, defining equations, and identifiability of uniform matrix product states. By an interplay of theorems from algebra, geometry, and quantum physics we answer several questions and conjectures posed by Critch, Morton and Hackbusch. In addition, we prove a tensor version of the so-called quantum Wielandt inequality, solving an open problem regarding the higher-dimensional version of matrix product states. Second, we present new contributions to the study of fast matrix multiplication. Motivated by the symmetric version of matrix multiplication we study the plethysm S^k(sl_n) of the adjoint representation sl_n of the Lie group SL_n . Moreover, we discuss two algebraic approaches for constructing new tensors which could potentially be used to prove new upper bounds on the complexity of matrix multiplication. One approach is based on the highest weight vectors of the aforementioned plethysm. The other approach uses smoothable finite-dimensional algebras. Finally, we study the Hessian discriminant of a cubic surface, a recently introduced invariant defined in terms of the Waring rank. We express the Hessian discriminant in terms of fundamental invariants. This answers Question 15 of the 27 questions on the cubic surface posed by Bernd Sturmfels. In the second part of this thesis, we apply algebro-geometric methods to study matroids and flag matroids. We review a geometric interpretation of the Tutte polynomial in terms of the equivariant K-theory of the Grassmannian. By generalizing Grassmannians to partial flag varieties, we obtain a new invariant of flag matroids: the flag-geometric Tutte polynomial. We study this invariant in detail, and prove several interesting combinatorial properties.

A large number and a variety of sensors and actuators, also known as edge devices of the Internet of Things, belonging to various industries - health care monitoring, home automation, industrial automation, have become prevalent in today's world. These edge devices need to communicate data collected to the central system occasionally and often in burst mode which is then used for monitoring and control purposes. To ensure secure connections, Asymmetric or Public Key Cryptography (PKC) schemes are used in combination with Symmetric Cryptography schemes. RSA (Rivest - Shamir- Adleman) is one of the most prevalent public key cryptosystems, and has computationally intensive operations which might have a high latency when implemented in resource constrained environments. The objective of this thesis is to design an accelerator capable of increasing the speed of execution of the RSA algorithm in such resource constrained environments. The bottleneck of the algorithm is determined by analyzing the performance of the algorithm in various platforms - Intel Linux Machine, Raspberry Pi, Nios soft core processor. In designing the accelerator to speedup bottleneck function, we realize that the accelerator architecture will need to be changed according to the resources available to the accelerator. We use high level synthesis tools to explore the design space of the accelerator by taking into consideration system level aspects like the number of ports available to transfer inputs to the accelerator, the word size of the processor, etc. We also propose a new accelerator architecture for the bottleneck function and the algorithm it implements and compare the area and latency requirements of it with other designs obtained from design space exploration. The functionality of the design proposed is verified and prototyped in Zynq SoC of Xilinx Zedboard.

This study is situated at the confluence of three calls for research within mathematics education: 1) work using novel approaches for studying students’ understanding of nonlinear meanings of multiplication; 2) work using discrete mathematics to explore social issues related to equity; and 3) work at the intersection of mathematical learning and critical race consciousness—specifically, social justice mathematics initiatives that explicitly address racism and the learners’ perspectives. The design research methodology of the study with 8th grade students provides practical curricular and pedagogical steps for doing work at the intersection of mathematical learning and race and racism; offers domain-specific learning insights; and merges theory and practice in conceptualizing the multiple complexities of learning and development in situ to create new possibilities for a more just mathematics education. Findings from this study offer insights at the intersection of the evolution of students’ establishment of nonlinear meanings of multiplication and critical race consciousness development. Specifically, this study identifies two schemes that students use to establish a nonlinear meaning of multiplication (SARC Scheme and RA Scheme), illustrates students’ growing racism awareness, and highlights how these initiatives can be mutually supportive in helping to normalize conversations about race and racism.

A boost converter is one of the most efficient techniques to step up DC input voltage to a higher needed DC output voltage. The boost converter has many possible applications, such as in a photovoltaic system, hybrid car and battery charger. The proposed prototype in this report is a proof of concept that a Two-Phase Boost Converter is a possible improvement topology to offer higher efficiency without compromising any advantages readily offered by a basic boost. The prototype is designed to be able to handle up to 200 watts of output power with an input of 36 volts and an output of 48 volts. This paper goes through step-by-step the calculation, design, build and test of a Two-Phase Boost Converter. Calculations found in this paper were done on Mathcad and the simulations were done on LTSpice and Pspice. These include converter’s efficiency and other measures of converter’s performance. Advantages, disadvantages as well as possible improvements of the proposed topology will be presented. Data collected and analyzed from the prototype were done on a bench test, not through an actual application.

This paper deals with the characterization of multiplication operators, especially with its behavior in the ill-posed case. We want to classify the different types and degrees of ill-posedness. We give some connections between this classification and regularization methods.

This thesis consists of two parts. In part I, a group of combinatorial problems pertaining to strings, boolean matrices and graphs is studied. For given two strings x and y, their edit distance is the minimum number of character insertions, deletions and substitutions required to convert x into y. In this thesis we provide an algorithm that computes a constant approximation of edit distance in truly sub-quadratic time. Based on the provided ideas, we construct a separate sub- quadratic time algorithm that can find an occurrence of a pattern P in a given text T while allowing a few edit errors. Afterwards we study the boolean matrix multiplication (BMM) problem where given two boolean matrices, the aim is to find their product over boolean semi-ring. For this problem, we present two combinatorial models and show in these models BMM requires Ω(n3 /2O( √ log n) ) and Ω(n7/3 /2O( √ log n) ) work respectively. Furthermore, we also give a construction of a sparse sub-graph that preserves the distance between a designated source and any other vertex as long as the total weight increment of all the edges is bounded by some constant. In part II, we study the efficient construction of quasi-Gray codes. We give a construction of space optimal quasi-Gray codes over odd sized alphabets with read complexity 4...

The purpose of the study is, through some aspects, to make it visible and compare the education in mathematics in classes 1-3 in Sweden and Turkey. I have also studied the mathematic lessons, textbook and teaching aids, examinations and the use of calculator, on the basis of steering documents in curriculum and syllabi. The method used in this study contains of qualitative interviews and have an unstructured character but also observations noted continuously. The result is a comparison between my own experiences and the observations connected to relevant theories and the questions.

Parallel sparse matrix-matrix multiplication algorithms (PSpGEMM) spend most of their running time on inter-process communication. In the case of distributed matrix-matrix multiplications, much of this time is spent on interchanging the partial results that are needed to calculate the final product matrix. This overhead can be reduced with a one-dimensional distributed algorithm for parallel sparse matrix-matrix multiplication that uses a novel accumulation pattern based on the logarithmic complexity of the number of processors (i.e., O (log (p)) where p is the number of processors). This algorithm's MPI communication overhead and execution time were evaluated on an HPC cluster, using randomly generated sparse matrices with dimensions up to one million by one million. The results showed a reduction of inter-process communication overhead for matrices with larger dimensions compared to another one dimensional parallel algorithm that takes O(p) run-time complexity for accumulating the results.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24389号 / 理博第4888号 / 新制||理||1699(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 玉川 安騎男, 教授 並河 良典, 教授 望月 新一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM