We establish the theory of normal families of meromorphic functions taking values in the extended complex plane, which can be regarded as a metric space equipped with the spherical metric. Using the notion of spherical derivatives, we state and prove Marty's theorem on normal families of meromorphic functions. As a result, we deduce the classical Montel's theorem on relatively compact fami

Neural networks can be utilized for an ever widening selection of tasks. In this thesis the most common optimization algorithms underlying neural networks are investigated: classical momentum, Nesterov momentum, AdaGrad, AdaDelta, RMSprop, Adam, AdaMax, and Nadam. The underlying mathematics that these algorithms are based on is described. There is a summary of key components of a neural network—ac

In this thesis, entropy conservative and entropy stable finite volume methods for one-dimensional scalar conservation laws are studied. The need for weak solutions is shown and entropy is explored to obtain uniqueness. Using discrete analogues of properties of entropy solutions, entropy stable finite volume methods are constructed and implemented to solve a number of scalar conservation laws, in p

In this thesis we introduce the mathematical fields of representation theory and character theory, providing a broad outline of the main concepts of each from the background of a general knowledge of abstract algebra. We cover a broad introduction to the representations of groups viewed as group and algebra homomorphisms and as modules over the group algebra, then proceed to consider key results o

In this thesis we will attempt to classify groups and rings based on whether the associated group rings are Noetherian or not. As this is still an open problem, we present the current state of research. While there are several classes of groups proven not to have Noetherian group rings, such as non-amenable and non-Noetherian groups, so far, virtually polycyclic groups are the only class for which

Fully implicit Runge-Kutta methods play an important role in the numerical integration of stiff differential equations. Radau IIA is the most commonly used fully implicit method due to its good theoretical performance. However, Radau IA and Lobatto IIIC might also be suitable for different problems. These three methods are constructed using simplified order conditions that ensures specific integra

Let (G, g) be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation with minimal leaves. Let J be an almost Hermitian structure on G adapted to the foliation. The corresponding Lie algebra must then belong to one of 20 families according to S. Gudmundsson and M. Svensson. We classify such structures J which are almost Kähler, integrable or Kähler. Hereby, we

In this thesis, we examine the Arnoldi iteration - an iterative algorithm used for finding a Hessenberg form of a matrix as well as approximating its eigenvalues by forming an orthonormal basis of a Krylov subspace. We explore the mechanism behind the work of the algorithm and how the values it finds approximate the eigenvalues. In the process of answering these questions we consider the concepts

In this paper a parallel implementation of three methods, Jacobi, Gauss-Seidel and Successive over relaxation (SOR), for solving large and sparse linear systems derived from Poisson type PDEs are investigated in order to find the faster solver method. Workload which is decoupled can be done faster in parallel than sequentially. We use a grid to discretize the PDE and the order of the grid cells yi

In this thesis we will explore methods to generate random numbers from any distribution. The basic idea behind generating random numbers is to use a mathematical sequence for which it should be impossible to guess what the next number is without knowing exactly how the sequence is generated. Although any hard to guess sequence would work, this thesis focuses on the linear congruential sequence, $

OBJECTIVE: Niemann-Pick Type C (NPC) is a genetic neurodegenerative lysosomal storage disorder commonly associated with psychiatric symptoms and delays to accurate diagnosis and treatment. This study investigated biomarker levels and diagnostic utility of plasma neurofilament light chain (NfL) and glial fibrillary acidic protein (GFAP) in NPC compared to healthy controls. METHODS: Patients with NP

BackgroundSocial and geographical inequity in access to primary healthcare is an ongoing concern in Sweden. Digital care can potentially decrease geographical inequity. This study aimed to evaluate how urbanicity affects the utilization of a public digital primary healthcare service - PHC Online.MethodsWe performed an ecological cross-sectional study of 4,482 PHC Online visits grouped by 83 public

Similar to systematic reviews (SRs) in clinical fields, preclinical SRs address a specific research area, furnishing information on current knowledge, possible gaps, and potential methodological flaws of study design, conduct, and report. One of the main goals of preclinical SRs is to identify aspiring treatment strategies and evaluate if currently available data is solid enough to translate to cl

Introduction: Neurofilament light chain (NfL), a blood biomarker of neuronal injury, shows promise in distinguishing neurodegenerative disorders from psychiatric conditions. This is especially relevant in psychosis, given neurological conditions such as autoimmune encephalitis and Niemann Pick Type C disease (NPC) may initially present with psychotic symptoms. Whilst NfL levels have been studied i

The ability of machine learning (ML) techniques to forecast the shear strength of corroded reinforced concrete beams (CRCBs) is examined in the present study. These ML techniques include artificial neural networks (ANN), adaptive-neuro fuzzy inference systems (ANFIS), decision tree (DT) and extreme gradient boosting (XGBoost). A thorough databank with 140 data points about the shear capacity of CR

OBJECTIVE: The antineutrophil cytoplasmic antibody (ANCA)-associated vasculitides (AAV) are inflammatory disorders with ANCA autoantibodies recognising either proteinase 3 (PR3-AAV) or myeloperoxidase (MPO-AAV). PR3-AAV and MPO-AAV have been associated with distinct loci in the human leucocyte antigen (HLA) region. While the association between MPO-AAV and HLA has been well characterised in East A

Due to the COVID-19 outbreak, industries have gained a thrust on contactless processing for computing technologies and industrial automation. Cloud of Things (CoT) is one of the emerging computing technologies for such applications. CoT combines the most emerging cloud computing and the Internet of Things. The development in industrial automation made them highly interdependent because the cloud c

In this chapter, I address the “containment” of meaning in relation to questions of authorship (or lack of authorship) in biblical studies. By revisiting Roland Barthes’ and Michel Foucault’s critiques of the author figure, I suggest that the implication for biblical studies is the opening of meaning-making beyond the figure of the author in his or her original context. Engaging with Brennan Breed