Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order

The transverse momentum dependent parton distribution/fragmentation functions (TMDs) are essential in the factorization of a number of processes like Drell-Yan scattering, vector boson production, semi-inclusive deep inelastic scattering, etc. We provide a comprehensive study of unpolarized TMDs at next-to-next-to-leading order, which includes an explicit calculation of these TMDs and an extraction of their matching coefficients onto their integrated analogues, for all flavor combinations. The obtained matching coefficients are important for any kind of phenomenology involving TMDs. In the present study each individual TMD is calculated without any reference to a specific process. We recover the known results for parton distribution functions and provide new results for the fragmentation functions. The results for the gluon transverse momentum dependent fragmentation functions are presented for the first time at one and two loops. We also discuss the structure of singularities of TMD operators and TMD matrix elements, crossing relations between TMD parton distribution functions and TMD fragmentation functions, and renormalization group equations. In addition, we consider the behavior of the matching coefficients at threshold and make a conjecture on their structure to all orders in perturbation theory.

IMPROVED SAMPLE INTRODUCTION SYSTEMS FOR INDUCTIVELY COUPLED PLASMA OPTICAL EMISSION SPECTROMETRY AND THEIR APPLICATION TO THE ANALYSIS OF SIMPLE AND COMPLEX MATRICES

The objective of this thesis is to explore new and improved methods for greater sample introduction efficiency and enhanced analytical performance with inductively coupled plasma optical emission spectrometry (ICP-OES). Three projects are discussed in which the capabilities and applications of ICP-OES are expanded: 1. In the first project, a conventional ultrasonic nebuliser was modified to replace the heater/condenser with an infrared heated pre-evaporation tube. In continuation from previous works with pre-evaporation, the current work investigated the effects of heating with infrared block and rope heaters on two different ICP-OES instruments. Comparisons were made between several methods and setups in which temperatures were varied. By monitoring changes to sensitivity, detection limit, precision, and robustness, and analyzing two certified reference materials, a method with improved sample introduction efficiency and comparable analytical performance to a previous method was established. 2. The second project involved improvements to a previous work in which a multimode sample introduction system (MSIS) was modified by inserting a pre-evaporation tube between the MSIS and torch. The new work focused on applying an infrared heated ceramic rope for pre-evaporation. This research was conducted in all three MSIS modes (nebulisation mode, hydride generation mode, and dual mode) and on two different ICP-OES instruments, and comparisons were made between conventional setups in terms of sensitivity, detection limit, precision, and robustness. By tracking both hydride-forming and non-hydride forming elements, the effects of heating in combination with hydride generation were probed. Finally, optimal methods were validated by analysis of two certified reference materials. 3. A final project was completed in collaboration with ZincNyx Energy Solutions. This project sought to develop a method for the overall analysis of a 12 M KOH zincate fuel, which is used in green energy backup systems. By employing various techniques including flow injection analysis and standard additions, a final procedure was formulated for the verification of K concentration, as well as the measurement of additives (Al, Fe, Mg, In, Si), corrosion products (such C from CO₃²¯), and Zn particles both in and filtered from solution. Furthermore, the effects of exposing the potassium zincate electrolyte fuel to air were assessed.

A Comparative Analysis Between Genetic Algorithms and Complex Nonlinear Least Squares on Electrical Impedance Characterization

This paper compares the performance of the complex nonlinear least squares algorithm implemented in the LEVM/LEVMW software with the performance of a genetic algorithm in the characterization of an electrical impedance of known topology. The effect of the number of measured frequency points and of measurement uncertainty on the estimation of circuit parameters is presented. The analysis is performed on the equivalent circuit impedance of a humidity sensor.

Improvement of The Driver Simulator Control and Comparison Between Driver-Road-Vehicle Interaction in Real and Simulated Environment

The present doctoral thesis discusses the ways to improve the performance of driving simulator, provide objective measures for the road safety evaluation methodology based on driver’s behavior and response and investigates the drivers' adaptation to the driving assistant systems. The activities are divided into two macro areas; the driving simulation studies and on-road experiments. During the driving simulation experimentation, the classical motion cueing algorithm with logarithmic scale was implemented in the 2DOF motion cueing simulator and the motion cues were found desirable by the participants. In addition, it found out that motion stimuli could change the behaviour of the drivers in terms of depth/distance perception. During the on-road experimentations, The driver gaze behaviour was investigated to find the objective measures on the visibility of the road signs and reaction time of the drivers. The sensor infusion and the vehicle monitoring instruments were found useful for an objective assessment of the pavement condition and the drivers’ performance. In the last chapter of the thesis, the safety assessment during the use of level 1 automated driving “ACC” is discussed with the simulator and on-road experiment. The drivers’ visual behaviour was investigated in both studies with innovative classification method to find the epochs of the distraction of the drivers. The behavioural adaptation to ACC showed that drivers may divert their attention away from the driving task to engage in secondary, non-driving-related tasks.

Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

Rotações no espaço tridimensional por meio de produtos quaterniônicos

Pós-graduação em Matemática Universitária - IGCE

Generalized convolution

The paper revisits the convolution operator and addresses its generalization in the perspective of fractional calculus. Two examples demonstrate the feasibility of the concept using analytical expressions and the inverse Fourier transform, for real and complex orders. Two approximate calculation schemes in the time domain are also tested.

Fat poetry: a kingdom for PPAR gamma.

Adipose tissue is not an inert cell mass contributing only to the storage of fat, but a sophisticated ensemble of cellular components with highly specialized and complex functions. In addition to managing the most important energy reserve of the body, it secretes a multitude of soluble proteins called adipokines, which have beneficial or, alternatively, deleterious effects on the homeostasis of the whole body. The expression of these adipokines is an integrated response to various signals received from many organs, which depends heavily on the integrity and physiological status of the adipose tissue. One of the main regulators of gene expression in fat is the transcription factor peroxisome proliferator-activated receptor gamma (PPARgamma), which is a fatty acid- and eicosanoid-dependent nuclear receptor that plays key roles in the development and maintenance of the adipose tissue. Furthermore, synthetic PPARgamma agonists are therapeutic agents used in the treatment of type 2 diabetes.This review discusses recent knowledge on the link between fat physiology and metabolic diseases, and the roles of PPARgamma in this interplay via the regulation of lipid and glucose metabolism. Finally, we assess the putative benefits of targeting this nuclear receptor with still-to-be-identified highly selective PPARgamma modulators.

L'éclatement en géométrie algébrique, différentielle et symplectique

L'éclatement est une transformation jouant un rôle important en géométrie, car il permet de résoudre des singularités, de relier des variétés birationnellement équivalentes, et de construire des variétés possédant des propriétés inédites. Ce mémoire présente d'abord l'éclatement tel que développé en géométrie algébrique classique. Nous l'étudierons pour le cas des variétés affines et (quasi-)projectives, en un point, et le long d'un idéal et d'une sous-variété. Nous poursuivrons en étudiant l'extension de cette construction à la catégorie différentiable, sur les corps réels et complexes, en un point et le long d'une sous-variété. Nous conclurons cette section en explorant un exemple de résolution de singularité. Ensuite nous passerons à la catégorie symplectique, où nous ferons la même chose que pour le cas différentiable complexe, en portant une attention particulière à la forme symplectique définie sur la variété. Nous terminerons en étudiant un théorème dû à François Lalonde, où l'éclatement joue un rôle clé dans la démonstration. Ce théorème affirme que toute 4-variété fibrée par des 2-sphères sur une surface de Riemann, et différente du produit cartésien de deux 2-sphères, peut être équipée d'une 2-forme qui lui confère une structure symplectique réglée par des courbes holomorphes par rapport à sa structure presque complexe, et telle que l'aire symplectique de la base est inférieure à la capacité de la variété. La preuve repose sur l'utilisation de l'éclatement symplectique. En effet, en éclatant symplectiquement une boule contenue dans la 4-variété, il est possible d'obtenir une fibration contenant deux sphères d'auto-intersection -1 distinctes: la pré-image du point où est fait l'éclatement complexe usuel, et la transformation propre de la fibre. Ces dernières sont dites exceptionnelles, et donc il est possible de procéder à l'inverse de l'éclatement - la contraction - sur chacune d'elles. En l'accomplissant sur la deuxième, nous obtenons une variété minimale, et en combinant les informations sur les aires symplectiques de ses classes d'homologies et de celles de la variété originale nous obtenons le résultat.

Optimization of inverse reflector design

Aquesta tesi presenta un nou mètode pel disseny invers de reflectors. Ens hem centrat en tres temes principals: l’ús de fonts de llum reals i complexes, la definició d’un algoritme ràpid pel càlcul de la il•luminació del reflector, i la definició d’un algoritme d’optimització per trobar més eficientment el reflector desitjat. Les fonts de llum estan representades per models near-field, que es comprimeixen amb un error molt petit, fins i tot per fonts de llum amb milions de raigs i objectes a il•luminar molt propers. Llavors proposem un mètode ràpid per obtenir la distribució de la il•luminació d’un reflector i la seva comparació amb la il•luminació desitjada, i que treballa completament en la GPU. Finalment, proposem un nou mètode d’optimització global que permet trobar la solució en menys passos que molts altres mètodes d’optimització clàssics, i alhora evitant mínims locals.

Climate change adaptation strategies in Sub-Saharan Africa: foundations for the future

Many institutions across sub-Saharan Africa (SSA) and many funding agencies that support them are currently engaged in initiatives that are targeted towards adapting rainfed agriculture to climate change. This does, however, present some very real and complex research and policy challenges. Given to date the generally low impact of agricultural research across SSA on improving the welfare of rainfed farmers under current climatic conditions, a comprehensive strategy is required if the considerably more complex challenge of adapting agriculture to future climate change is to bear fruit. In articulating such a strategy, it is useful to consider the criteria by which current successful initiatives should be judged.

Uma visita ao universo matemático de Lewis Carrol e o (re)encontro com sua lógica do nonsense

Notable mathematics teacher, Lewis Carroll, pseudonym of Charles Lutwidge Dodgson (1832-1898), made the mixture of mathematics with literature a ludic environment for learning that discipline. Author of Alice s Adventures In Wonderland and its sequel Alice Through The Looking Glass, he eventually created a real and complex universe which uses what we call the logic of the nonsense as an element to motivate the development of mathematical thinking of the reader, taking it as well, learn by establishing a link between the concrete (mathematics) and the imaginary (their universe). In order to investigate and discuss the educational potential of their works and state some elements that can contribute to a decentralized math education from the traditional method of following the models and decorate formulas, we visited his works based on the studies of archeology of knowledge (FOUCAULT, 2007), the rational thought and symbolic thinking (VERGANI, 2003) and about the importance of stories and narratives to the development of human cognition (FARIAS, 2006). Through a descriptive, analytical study, we used the literary construction and presented part of our study in form of a mathematical novel, to give the mathematical school a particular charm, without depriving it of its basics properties as discipline and content. Our study showed how the works of Carroll have a strong didactic element that can deploy in various activities of study and teaching for mathematics classes

Uma fundamentação para sinais e sistemas intervalares

In this work we use Interval Mathematics to establish interval counterparts for the main tools used in digital signal processing. More specifically, the approach developed here is oriented to signals, systems, sampling, quantization, coding and Fourier transforms. A detailed study for some interval arithmetics which handle with complex numbers is provided; they are: complex interval arithmetic (or rectangular), circular complex arithmetic, and interval arithmetic for polar sectors. This lead us to investigate some properties that are relevant for the development of a theory of interval digital signal processing. It is shown that the sets IR and R(C) endowed with any correct arithmetic is not an algebraic field, meaning that those sets do not behave like real and complex numbers. An alternative to the notion of interval complex width is also provided and the Kulisch- Miranker order is used in order to write complex numbers in the interval form enabling operations on endpoints. The use of interval signals and systems is possible thanks to the representation of complex values into floating point systems. That is, if a number x 2 R is not representable in a floating point system F then it is mapped to an interval [x;x], such that x is the largest number in F which is smaller than x and x is the smallest one in F which is greater than x. This interval representation is the starting point for definitions like interval signals and systems which take real or complex values. It provides the extension for notions like: causality, stability, time invariance, homogeneity, additivity and linearity to interval systems. The process of quantization is extended to its interval counterpart. Thereafter the interval versions for: quantization levels, quantization error and encoded signal are provided. It is shown that the interval levels of quantization represent complex quantization levels and the classical quantization error ranges over the interval quantization error. An estimation for the interval quantization error and an interval version for Z-transform (and hence Fourier transform) is provided. Finally, the results of an Matlab implementation is given

Fast-forward/fast-backward substitutions on vector computers

This paper deals with approaches for sparse matrix substitutions using vector processing. Many publications have used the W-matrix method to solve the forward/backward substitutions on vector computer. Recently a different approach has been presented using dependency-based substitution algorithm (DBSA). In this paper the focus is on new algorithms able to explore the sparsity of the vectors. The efficiency is tested using linear systems from power systems with 118, 320, 725 and 1729 buses. The tests were performed on a CRAY Y MP2E/232. The speedups for a fast-forward/fast-backward using a 1729-bus system are near 19 and 14 for real and complex arithmetic operations, respectively. When forward/backward is employed the speedups are about 8 and 6 to perform the same simulations.