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I denna avhandling diskuterar vi två kraftfulla verktyg inom matematiken – SAGBI-baser och Gröbner-baser – samt deras samspel med invariantteori. Dessa baser används främst för att effektivt hantera system av polynom. För att illustrera deras tillämpningar inom invariantteori och närliggande områden presenterar vi olika algoritmer genom hela avhandlingen. Invariantteori är studiet av matematiska This thesis investigates the computation of SAGBI-Gröbner bases for ideals in invariant polynomial rings under non-modular permutation group actions. We extend Buchberger's Algorithm for ideals in polynomial rings to ideals in invariant polynomial rings. By introducing a suitable degree bound, we construct a partial invariant Gröbner basis for an ideal in an invariant ring, from which minimal

The room impulse response (RIR) is an important function describing how sound reflects and propagates in a room. The inverse problem of estimating the impulse response from source and measurement signals is often of interest in various audio applications, but can become ill-posed if there is not enough information. Using regularization, one can impose prior physicality assumptions to the estimator

An introductory analysis of complex conjugation operators and complex structures is presented. We show that complex structures can be constructed on a real vector space V if V is the direct sum of two isomorphic subspaces, and relate this to the existence of a well-defined conjugation operator. Additionally, it is shown that all complex structures on a vector space V are similar operators. Some ap

Variationskalkyl handlar om problemet att bestämma det minsta värdet av en funktion som har en funktion som input, nämligen en så kallad funktional. Det vill säga, man minimerar $f(x)$ där $x$ själv är en funktion. Funktionalen brukar vara i form av en integral och $x$ är ett element av ett funktionsrum, till exempel rummet av alla kontinuerliga funktioner. Först och främst kommer frågan om existeIn this Bachelor thesis we will provide a light treatment to the topic of optimality gaps and regularity for integral functionals. First we will establish the classical existence result by Tonelli, via the so calleddirect method. Proceedingly we discuss examples of gaps between the infima over different classes of functions. We start with the classical Lavrentiev phenomenon (gap between AC and Lip

We investigate the vanishing conditions for harmonic functions in planar domains. We first prove that if a complex-valued harmonic function $u$ in an open set $\Omega \subseteq \mathbb{C}$ vanishes at a point $a \in \Omega \cap \mathbb{R}$ and satisfies $(\partial+\bar{\partial})^k u(a)=0$ for all $k \geq 0$, then $u$ vanishes identically on the connected component of $\Omega \cap \mathbb{R}$ cont

In many fields of science, solving large sparse systems of linear equations is a critical task. Direct solvers often fall out favour due to their high computational costs and memory requirements. Iterative solvers alleviate this issue but run the risk of converging slower than satisfactory when the associated matrix is ill-conditioned and has poorly distributed eigenvalues. This work will focus on

Syftet med studien var att undersöka om det finns en relation mellan upplevelsen av destruktivt ledarskap från närmsta chef och upplevelsen av stress respektive utbrändhet hos anställda. Studien undersökte även om det finns en relation mellan aktivt respektive passivt destruktivt ledarskap och stress respektive utbrändhet. Slutligen syftade studien till att undersöka om det finns en relation mellaThe purpose of the study was to investigate whether there was a relationship between the experience of destructive leadership by the immediate manager and the experience of stress and burnout among employees. The study also investigated whether there was a relationship between active and passive destructive leadership and stress and burnout. Finally, the study aimed to investigate whether there wa

Alpha-synuclein (aSyn) post-translational modifications (PTM), especially phosphorylation at serine 129 and C-terminal truncations, are highly enriched in Lewy bodies (LB), Lewy neurites, and other pathological aggregates in Parkinson’s disease and synucleinopathies. However, the precise role of these PTM in pathology formation, neurodegeneration, and pathology spreading remains unclear. Here, we

Dust storms are meteorological phenomena that occur in arid and semi-arid regions, causing harm to the environment and human health. The frequency and intensity of dust storms have increased in recent years due to climate change and human activities. In response, various dust storm mitigation strategies were introduced, including land use management, afforestation, and mulching. The existing resea

This article examines how the U.S. ‘inclusion-and-difference paradigm’translates to the Swedish context. According to Steven Epstein (2007), thisparadigm combines health equity arguments for racialised minorities andwomen with a biological understanding of racial and gender differences inmedicine. Drawing on interviews with experts, policymakers, and clini-cians involved in international clinical

Jaboticaba (Plinia jaboticaba) is an underutilized Brazilian berry and a source of dietary fiber, cyanidin-3-O-glucoside, and ellagic acid derivatives. Non-clinical studies have shown the potential of jaboticaba to alleviate insulin resistance, low-grade inflammation, and obesity-related cognitive decline, although clinical evidence remains limited. A clinical study was conducted to investigate wh

Comprehensive epigenomic studies in multiple myeloma (MM) that unravel the connections between major epigenetic regulators, their intertwined collaboration and the potential of combinatorial targeting remain limited. Utilizing ChIP-seq, ATAC-seq, RNA-seq, and DNA methylation (DNAme) data, we generated whole-genome chromatin annotations from normal plasma cells and MM patients, revealing epigenomic

This article exposes the invisible sand that underpins Copenhagen’s transformation from fishing village to global city. By “following sand,” we trace how planetary material flows sustain urban expansion while entangling the city in processes of capital accumulation, class restructuring, and ecological degradation. Drawing on Science and Technology Studies (STS) approaches, yet situating them firml

Background and purpose: Angiosarcoma (AS), a rare and highly malignant tumour, can manifest spontaneously (primary AS, pAS) or secondary to previous radiation, exposure to chemical agents or Stewart-Treves syndrome (secondary AS, sAS). The aim of this study was to characterise the clinical presentation, management, treatment and outcome—including local recurrence, metastasis and overall survival—a

When it comes to random walk on the integers Z, the arguably first step of generalization beyond simple random walk is the class of one-sidedly continuous random walk, where the stepsize in only one direction is bounded by 1. Moreover, the time until state 0 is hit by left-continuous random walk on Z started at 1 has a direct connection to the total progeny in branching processes. In the analysis

Försök att beskriva och rekonstruera omständigheterna kring Carl Johan Tornbergs (1807-1877) utnämning till och installation som professor i österländska språk 1850.