The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Kuormituksen vaikutus kromatografiseen erotukseen alikriittisellä vedellä

Teollisessa kromatografiassa kolonnia pyritään kuormittamaan mahdollisimman paljon, jotta saataisiin maksimoitua erotetun komponentin määrä aikayksikköä kohden. Tässä työssä kuormitusta tutkittiin nostamalla syöttöliuoksen, synteettisen melassin, näyteväkevyyttä 80-125 ºC:ssa. Eluenttina oli paineistettu kuumaa vesi ja hartsina vahva Na-muotoinen PS-DVB pohjainen vahva kationinvaihtohartsi. Lämpötilaa nostamalla piikit kapenivat ja tulivat symmetrisemmiksi, erotus nopeutui sekä suola erottui usein paremmin sokereista. Syöttöliuoksen kuiva-ainetta lisättiin asteittain 55 p-% saakka, jolloin ei vielä havaittu ongelmia erotuksessa. Lämpötilassa 125 ºC havaittiin erotuksen aikana kuormituksesta riippumatonta sakkaroosin invertoitumista. Vertailtaessa eri stationäärifaaseja havaittiin Na-muotoisen PS-DVB pohjaisen kationinvaihtohartsin erottavan yleensä sokereita, sokerialkoholeja, oligosakkarideja ja betaiinia lähes poikkeuksetta paremmin alhaisilla pitoisuuksilla kuin neutraalihartsi ja Na-muotoinen zeoliitti. Erottuminen ei yleensä parantunut lämpötilaa nostamalla, mutta piikit kapenivat ja erotus nopeutui. Monosakkaridien erotus huononi 125 ºC:ssa kationinvaihtohartsilla. Tutkittaessa terveysvaikutteisten ksylo-oligosakkaridien soveltuvuutta alikriittiseen erotukseen, niiden havaittiin huomattavasti hydrolysoituvan happamissa olosuhteissa koeputkessa 100 ºC:ssa kahdessa tunnissa. Näytteessä olevien epäpuhtauksien havaittiin katalysoineen hydrolyysiä. Hydrolysoituminen oli hitaampaa neutraaleissa olosuhteissa korotetussa lämpötilassa. Tästä voitiin tehdä johtopäätös, että alikriittiset olosuhteet eivät sovi ksylo-oligosakkaridien erotukseen.

On Innovative Search: the use of internal and external sources of innovation among Finnish innovators

This dissertation explores the use of internal and external sources of knowledge in modern innovation processes. It builds on a framework that combines theories such as a behavioural theory of the firm, the evolutionary theory of economic change, and modern approaches to strategic management. It follows the recent increase in innovation research focusing on the firm-level examination of innovative activities instead of traditional industry-level determinants. The innovation process is seen as a problem- and slack- driven search process, which can take several directions in terms of organizational boundaries in the pursuit of new knowledge and other resources. It thus draws on recent models of technological change, according to which firms nowadays should build their innovative activities on both internal and external sources of innovation rather than relying solely on internal resources. Four different research questions are addressed, all of which are empirically investigated via a rich dataset covering Finnish innovators collected by Statistics Finland. Firstly, the study examines how the nature of problems shapes the direction of any search for new knowledge. In general it demonstrates that the nature of the problem does affect the direction of the search, although under resource constraints firms tend to use external rather than internal sources of knowledge. At the same time, it shows that those firms that are constrained in terms of finance seem to search both internally and externally. Secondly, the dissertation investigates the relationships between different kinds of internal and external sources of knowledge in an attempt to find out where firms should direct their search in order to exploit the potential of a distributed innovation process. The concept of complementarities is applied in this context. The third research question concerns how the use of external knowledge sources – openness to external knowledge – influences the financial performance of firms. Given the many advantages of openness presented in the current literature, the focus is on how it shapes profitability. The results reveal a curvilinear relationship between profitability and openness (taking an inverted U-shape), the implication being that it pays to be open up to a certain point, but being too open to external sources may be detrimental to financial performance. Finally, the dissertation addresses some challenges in CISbased innovation research that have received relatively little attention in prior studies. The general aim is to underline the fact that comprehensive understanding of the complex process of technological change requires the constant development of methodological approaches (in terms of data and measures, for example). All the empirical analyses included in the dissertation are based on the Finnish CIS (Finnish Innovation Survey 1998-2000).

Entrepreneurship, Service Innovation, International Expansion and Performance in SMEs: Empirical Evidence from Finnish ICT Industry

The thesis aims to clarify the mixed results of prior literature regarding the performance impacts of entrepreneurship and human capital through service innovation and international expansion. The thesis examines the factors affecting degree of internationalization (DOI) and performance in ICT SMEs. These factors are entrepreneurial orientation (EO), human capital and service innovation (SI). The data was collected via questionnaire from Finnish ICT SMEs. The results suggest that EO consist of three dimensions that have different impact in DOI and SI. Also DOI has inverted U-shaped relationship with international performance, whereas DOI-profitability relationship is linear. The results of the study suggest that SMEs should not blindly increase their DOI, and that strategic focus is important.

Unraveling the functional divergence of membrane-bound pyrophosphatases

Inorganic pyrophosphatases (PPases) are enzymes that hydrolyze pyrophosphate (PPi)which is produced as a byproduct in many important growth related processes e.g. in the biosynthesis of DNA, proteins and lipids. PPases can be either soluble or membranebound. Membrane-bound PPases (mPPases) are ion transporters that couple the energy released during PPi hydrolysis to Na+ or H+ transport. When I started the project, only three Na+-transporting mPPases were known to exist. In this study, I aimed to confirm if Na+-transport is a common function of mPPases. Furthermore, the amino acid residues responsible for determining the transporter specificity were unknown. I constructed a phylogenetic tree for mPPases and selected the representative bacterial and archaeal mPPases to be investigated. I expressed different prokaryotic mPPases in Escherichia coli, isolated these as inverted membrane vesicles and characterized their functions. In the first project I identified four new Na+-PPases, two K+-dependent H+-PPases and one K+-independent mPPase. The residues determining the transporter specificity were identified by site-directed mutagenesis. I showed that the conserved glutamate residues are important for specificity, though are not the only residues that influence it. This research clarified the ion transport specificities throughout the mPPase phylogenetic tree, and revealed that Na+ transport is a widespread function of mPPases. In addition, it became clear that the transporter specificity can be predicted from the amino acid sequence in combination with a phylogenetic analysis. In the second project, I identified a novel class of mPPases, which is capable of transporting both Na+ and H+ ions and is mainly found in bacteria of the human gastrointestinal tract. The physiological role of these novel enzymes may be to help the bacteria survive in the demanding conditions of the host. In the third project, I characterized the Chlorobium limicola Na+-PPase and found that this and related mPPases are able to transport H+ ions at subphysiological Na+ concentrations. In addition, the H+-transport activity was shown to be a common function of all studied Na+-PPases at low Na+ concentrations. I observed that mutating gate-lysine to asparagine eliminated the H+ but not the Na+ ion transport function, indicating the important role of the residue in the transport of H+. In the fourth project, I characterized the unknown and evolutionary divergent mPPase clade of the phylogenetic tree. The enzymes belonging to this clade are able to transport H+ ions and, based on their sequence, were expected to be K+- and Na+-independent. The sequences of membrane-bound PPase are usually highly conserved, but the enzymes belonging to this clade are more divergent and usually contain 100−150 extra amino acid residues compared to other known mPPases. Despite the vast sequence differences, these mPPases have the full set of important residues and, surprisingly, are regulated by Na+ and K+ ions. These enzymes are mainly of bacterial origin.

Development of 3D super-resolution tomographic STED microscopy and its application to studies on bone resorption

In this doctoral thesis, a tomographic STED microscopy technique for 3D super-resolution imaging was developed and utilized to observebone remodeling processes. To improve upon existing methods, wehave used a tomographic approach using a commercially available stimulated emission depletion (STED) microscope. A certain region of interest (ROI) was observed at two oblique angles: one at a standard inverted configuration from below (bottom view) and another from the side (side view) via a micro-mirror positioned close to the ROI. The two viewing angles were reconstructed into a final tomogram. The technique, named as tomographic STED microscopy, was able to achieve an axial resolution of approximately 70 nm on microtubule structures in a fixed biological specimen. High resolution imaging of osteoclasts (OCs) that are actively resorbing bone was achieved by creating an optically transparent coating on a microscope coverglass that imitates a fractured bone surface. 2D super-resolution STED microscopy on the bone layer showed approximately 60 nm of lateral resolution on a resorption associated organelle allowing these structures to be imaged with super-resolution microscopy for the first time. The developed tomographic STED microscopy technique was further applied to study resorption mechanisms of OCs cultured on the bone coating. The technique revealed actin cytoskeleton with specific structures, comet-tails, some of which were facing upwards and some others were facing downwards. This, in our opinion, indicated that during bone resorption, an involvement of the actin cytoskeleton in vesicular exocytosis and endocytosis is present. The application of tomographic STED microscopy in bone biology demonstrated that 3D super-resolution techniques can provide new insights into biological 3D nano-structures that are beyond the diffraction-limit when the optical constraints of super-resolution imaging are carefully taken into account.