This thesis consists of six scientific papers, an introduction and a summary. All six papers concern the boundary behavior of non-negative solutions to partial differential equations. Paper I concerns solutions to certain p-Laplace type operators with variable coefficients. Suppose that u is a non-negative solution that vanishes on a part Γ of an Ahlfors regular NTA-domain. We prove among other things that the gradient Du of u has non-tangential limits almost everywhere on the boundary piece Γ, and that log|Du| is a BMO function on the boundary.  Furthermore, for Ahlfors regular NTA-domains that are uniformly (N,δ,r0)-approximable by Lipschitz graph domains we prove a boundary Harnack inequality provided that δ is small enough.  Paper II concerns solutions to a p-Laplace type operator with lower order terms in δ-Reifenberg flat domains. We prove that the ratio of two non-negative solutions vanishing on a part of the boundary is Hölder continuous provided that δ is small enough. Furthermore we solve the Martin boundary problem provided δ is small enough. In Paper III we prove that the boundary type Riesz measure associated to an A-capacitary function in a Reifenberg flat domain with vanishing constant is asymptotically optimal doubling. Paper IV concerns the boundary behavior of solutions to certain parabolic equations of p-Laplace type in Lipschitz cylinders. Among other things, we prove an intrinsic Carleson type estimate for the degenerate case and a weak intrinsic Carleson type estimate in the singular supercritical case. In Paper V we are concerned with equations of p-Laplace type structured on Hörmander vector fields. We prove that the boundary type Riesz measure associated to a non-negative solution that vanishes on a part Γ of an X-NTA-domain, is doubling on Γ. Paper VI concerns a one-phase free boundary problem for linear elliptic equations of non-divergence type. Assume that we know that the positivity set is an NTA-domain and that the free boundary is a graph. Furthermore assume that our solution is monotone in the graph direction and that the coefficients of the equation are constant in the graph direction. We prove that the graph giving the free boundary is Lipschitz continuous.

Die Arbeit Synthese dendritischer Redoxverbindungen und deren Einsatz in der Bioanalytik beschreibt die Synthese von Dendrimeren und Dendronen mit benzylisch N-quarternisierten 4,4 -Bipyridinium-Verbindungen (Viologenen) im dendritischen Gerüst. Weiterhin werden Synthesen neuer Nitrilotriessigsäure (NTA)-Verbindungen synthetisiert, die eine disulfidische Gruppe oder einen Pyrrolrest besitzen.Sensorik: Es gelang, in Zusammenarbeit mit der Arbeitsgruppe von Prof. Wieczorek, mittels eines massenspezifischen Sensorsystems (QCM) die Analyse zweier Proteine (G-Aktin und C-Untereinheit) bezüglich ihrer Interaktion und Stöchometrie nachzuweisen.NTA modifizierte Elektroden: Es wurden verschiedene NTA-Verbindungen auf Goldelektroden immobilisiert und mittels elektrochemischen Methoden und XPS beschrieben. Darüber hinaus gelang eine NTA Modifizierung einer GC-Elektrode. Eine Polypyrrolfilm-Elektrode, welche aktivierte Propansäureesterseitenkette besitzt, wurde mit Aminobutyl-NTA (AB-NTA) verknüpft. Diese modifizierte Elektrode zeigt reversible Nickelionen Aufnahme bzw. Abgabe.Im Bereich der Multielektronen- bzw. hoch geladenen Labels für Proteine wurden kegelförmige, dendritische Viologenderivaten mit funktionalisierten Fokalpunkt hergestellt und diese mit Proteinen derivatisiert (u.a. Cytochrome C). Der Nachweis der nunmehr pH-unabhängigen Oberflächenladungen des Proteins wurde nachgewiesen. (P. Schön et. al., JACS 2005, 127, 11486).

A rational long-horizon stock investment decision is a complex process due to uncertainty in supply and demand, competitive advantage, macroeconomic parameters and various perspectives of investors. Today, the '€˜non-tangible assets'€™ (NTA) that include goodwill and intangible assets are a significant part of corporate assets, but their role in stock performance has not well studied. The purpose of this research is to empirically analyze the implications of NTA and of gross domestic product (GDP) of the United States on the stock price. According to the efficient market hypothesis, stock price reflects all relevant information. The research question focused on the extent to which NTA and the GDP reflected in the stock price. To determine the extent to which NTA and GDP reflected on the stock price, regression analysis and other statistical tests were used. The sample for the empirical study was 56 corporations listed on the New York Stock Exchange (NYSE) and National Association of Securities Dealers Automated Quotation (NASDAQ). The required data from October 2007 to September 2018 were collected from the United States Securities and Exchange Commission (SEC) and the United States Bureau of Economics (BEA). The key findings of the study are: the NTA and stock price of 45 corporations have a statistically significant correlation as opposed to 11 corporations. The combined NTA of these 11 corporations for the third quarter of 2018 was $531.64 billion. Furthermore, the GDP and stock price of 53 corporations have a statistically significant correlation, but no evidence for three corporations was found. The significance for positive social change is knowledge from this research about the implications of NTA and GDP on stock performance that the investors, policymakers, and other stakeholders could use for preserving the limited resources and creating wealth.

Předkládaná diplomová práce se zabývá extrakcí nanočástic oxidu titaničitého z produktů osobní péče, konkrétně opalovacích krémů a následnou charakterizací těchto částic. Počet komerčně dostupných produktů s obsahem nanočástic TiO2 se neustále zvyšuje a to se sebou přináší potřebu vyhodnotit potenciální osud a nepřímou expozici TiO2 nanošástic o různých velikostí a tvarů a zkoumat jejich celý životní cyklus. Bylo zkoumáno použití ultrafiltrace a ultracentrifugace jako extrakční metody. Dvě metody pro extrakci TiO2 nanočástic byly vyvinuty a aplikovány na vzorky opalovacích krémů. Extrahované částice mohou být použity pro ekotoxikologické studie, případně experimenty v mesokosmu. Velikost částic byla stanovena pomocí metody dynamického rozptylu světla a transmisní elektronové mikroskopie.

Nanopartiklar är partiklar med storlekar i området 1 till 100 nm, och som uppvisar nanospecifika egenskaper. Egenskaperna kan variera helt mellan olika typer av nanopartiklar, även bland partiklarna och deras respektive material i bulk format på grund av deras unika storlekar, former och strukturer. I denna studie har vi analyserat storlekarna och den kolloidal stabiliteten på tre nanopartiklar, Co, Y2O3, CeO2 i färskvatten och färskvatten med naturligt organiskt material med hjälp av sonifikation, NTA, AAS och ICP analys. Nanopartiklarna lät vara utsatta i lösningarna i upp till six timmar, där analys med hand av NTA skedde efter den nollte, första och sjätte timmen. Partiklarna uppvisade olika egenskaper, och alla tre partiklar varierade i storlek under experimentet. Kobalt hade tendensen att minska i storlek i bägge lösningar, medan storlekarna på yttrium- och cerium oxid tenderade att variera. För att främja vår förståelse av nanopartiklar, behövs fler studier för att få en full förståelse för de unika egenskaperna hos dessa partiklar. / Nanoparticles are particles with sizes in the range of 1 to 100 nm, which also have nanospecific properties. Their properties vary wildly between different types of nanoparticles, even among nanoparticles and their respective particles in bulk format heeding to their highly individual shapes, sizes and structures. In this study we analyzed the sizes and colloidal stability of three different nanoparticles, Co, Y2O3 and CeO2 in freshwater and freshwater with natural organic matter solutions using sonication, NTA-, AAS-, and ICP analysis. The nanoparticles were exposed to the solutions for up to six hours, with analysis being performed at the zero, first and sixth hour. The particles indeed showed different properties, as all three particles varied in size throughout the experiment. Cobalt had the tendency to decrease in size as time progressed in both solutions, while the mean size of yttrium- and cerium oxide varied. To further our understanding of nanoparticles, more studies need to be performed to properly understand the individual properties of these nanoparticles.

This thesis concerns the boundary behavior of solutions to parabolic equations. It consists of a comprehensive summary and four scientific papers. The equations concerned are different generalizations of the heat equation. Paper I concerns the solutions to non-linear parabolic equations with linear growth. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the Riesz measure associated with such solutions, and the Hölder continuityof the quotient of two such solutions up to the boundary. Paper 2 concerns the solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a Muckenhoupt weight of class 1+2/n. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the parabolic measure, and the Hölder continuity of the quotient of two such solutions up to the boundary. Paper 3 concerns a fractional heat equation. The first main result is that a solution to the fractional heat equation in Euclidean space of dimension n can be extended as a solution to a certain linear degenerate parabolic equation in the upper half space of dimension n+1. The second main result is the Hölder continuity of quotients of two non-negative solutions that vanish continuously on the latteral boundary of a Lipschitz domain. Paper 4 concerns the solutions to uniformly parabolic linear equations with complex coefficients. The first main result is that under certain assumptions on the opperator the bounds for the single layer potentials associated to the opperator are bounded. The second main result is that these bounds always hold if the opperator is realvalued and symmetric.

Background: The focus of this study was to investigate how producing human bone marrow (hBM) derived mesenchymal stromal cell (MSC) extracellular vehicles (EVs) in a high purity isolation system would affect their established characterization criteria and address the validity of these methods of EV production. Additionally, we set out to functionally characterize the hBM-MSC-EVs for their identified immunomodulatory ability while also assessing the presence of novel MSC-EV marker NRP1 identified by our group to further affirm its validity as a functional MSC-EV identity marker. Methods: Each hBM-MSC-EV donor was cultured in a hollow-fiber bioreactor system in non-stimulating serum/xeno-free conditions for 25 days to produce EVs persistently under quiescent conditions to characterize the hBM-MSC-EVs in their native form. EVs were isolated by traditional PEG-based precipitation for preliminary characterization to monitor bioreactor production wherein they were characterized using multimodal tangential flow filtration coupled with fast protein liquid chromatograph (FPLC) size exclusion/high-affinity purifications to obtain the final highly purified EV sample. Additionally, functional analysis of their immunomodulatory ability, EVs and MSCs were incubated with activated peripheral blood mononuclear cells (PBMCs) as an in-vitro model to evaluate their potency. Results: The hBM-MSC-EVs produced from the bioreactor system showed consistent characterization in accordance with the MISEV2018 establish criteria. We were also able to demonstrate their functional ability by observing statistically significantly immunomodulatory ability of activated PBMCs equivalent to native MSC ability. We were also able to validate the present of NRP1 on all hBM-MSC-EV samples produced confirming its validity as a MSC-EV marker. Conclusion: The significance of the results obtained from this study confirms the production of MSC-EV using a bioreactor and high purity isolation for obtaining consistent MSC-EVs for downstream investigation. Additionally, we were able to demonstrate the significance of MSC-EVs on MSC signaling for immunomodulation by showing equivalent functional potency when tested in-vitro. These results contribute to further understanding the biological attributes of MSC-EVs and contribute to the validation of currently established characterization guidelines.

This thesis consists of a comprehensive summary and six scientific papers dealing with the boundary behaviour of functions related to parabolic partial differential equations and several complex variables. Paper I concerns solutions to non-linear parabolic equations of linear growth. The main results include a backward Harnack inequality, and the Hölder continuity up to the boundary of quotients of non-negative solutions vanishing on the lateral boundary of an NTA cylinder. It is also shown that the Riesz measure associated with such solutions has the doubling property. Paper II is concerned with solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a weight in the Muckenhoupt class 1+2/n. Two main results are that non-negative solutions which vanish continuously on the lateral boundary of an NTA cylinder satisfy a backward Harnack inequality and that the quotient of two such functions is Hölder continuous up to the boundary. Another result is that the parabolic measure associated to such equations has the doubling property. In Paper III, it is shown that a bounded pseudoconvex domain whose boundary is α-Hölder for each 0<α<1, is hyperconvex. Global estimates of the exhaustion function are given. In Paper IV, it is shown that on the closure of a domain whose boundary locally is the graph of a continuous function, all plurisubharmonic functions with continuous boundary values can be uniformly approximated by smooth plurisubharmonic functions defined in neighbourhoods of the closure of the domain. Paper V studies  Poletsky’s notion of plurisubharmonicity on compact sets. It is shown that a function is plurisubharmonic on a given compact set if, and only if, it can be pointwise approximated by a decreasing sequence of smooth plurisubharmonic functions defined in neighbourhoods of the set. Paper VI introduces the notion of a P-hyperconvex domain. It is shown that in such a domain, both the Dirichlet problem with respect to functions plurisubharmonic on the closure of the domain, and the problem of approximation by smooth plurisubharmoinc functions in neighbourhoods of the closure of the domain have satisfactory answers in terms of plurisubharmonicity on the boundary.