A conspectus on estimating function theory and its applicability to recurrent modeling issues in forest biometry

Summary

Molecular modeling of asymmetric induction in heterogeneously catalyzed hydrogenation of the C=O bond

Modifiering av metallytor med starkt adsorberade kirala organiska molekyler är eventuellt den mest relevanta teknik man vet i dag för att skapa kirala ytor. Den kan utnyttjas i katalytisk produktion av enantiomeriskt rena kirala föreningar som behövs t.ex. som läkemedel och aromkemikalier. Trots många fördelar av asymmetrisk heterogen katalys jämfört med andra sätt för att få kirala föreningar, har den ändå inte blivit ett allmänt verktyg för storskaliga tillämpningar. Detta beror t.ex. på brist på djupare kunskaper i katalytiska reaktionsmekanismer och ursprunget för asymmetrisk induktion. I denna studie användes molekylmodelleringstekniker för att studera asymmetriska, heterogena katalytiska system, speciellt hydrering av prokirala karbonylföreningar till motsvarande kirala alkoholer på cinchona-alkaloidmodifierade Pt-katalysatorer. 1-Fenyl-1,2-propandion (PPD) och några andra föreningar, som innehåller en prokiral C=O-grupp, användes som reaktanter. Konformationer av reaktanter och cinchona-alkaloider (som kallas modifierare) samt vätebundna 1:1-komplex mellan dem studerades i gas- och lösningsfas med metoder som baserar sig på vågfunktionsteori och täthetsfunktionalteori (DFT). För beräkningen av protonaffiniteter användes också högst noggranna kombinationsmetoder såsom G2(MP2). Den relativa populationen av modifierarnas konformationer varierade som funktion av modifieraren, dess protonering och lösningsmedlet. Flera reaktant–modifierareinteraktionsgeometrier beaktades. Slutsatserna på riktning av stereoselektivitet baserade sig på den relativa termodynamiska stabiliteten av de diastereomeriska reaktant–modifierare-komplexen samt energierna hos π- och π*-orbitalerna i den reaktiva karbonylgruppen. Adsorption och reaktioner på Pt(111)-ytan betraktades med DFT. Regioselektivitet i hydreringen av PPD och 2,3-hexandion kunde förklaras med molekyl–yta-interaktioner. Storleken och formen av klustret använt för att beskriva Pt-ytan inverkade inte bara på adsorptionsenergierna utan också på de relativa stabiliteterna av olika adsorptionsstrukturer av en molekyl. Populationerna av modifierarnas konformationer i gas- och lösningsfas korrelerade inte med populationerna på Pt-ytan eller med enantioselektiviteten i hydreringen av PPD på Pt–cinchona-katalysatorer. Vissa modifierares konformationer och reaktant–modifierare-interaktionsgeometrier var stabila bara på metallytan. Teoretiskt beräknade potentialenergiprofiler för hydrering av kirala α-hydroxiketoner på Pt implicerade preferens för parvis additionsmekanism för väte och selektiviteter i harmoni med experimenten. De uppnådda resultaten ökar uppfattningen om kirala heterogena katalytiska system och kunde därför utnyttjas i utvecklingen av nya, mera aktiva och selektiva kirala katalysatorer.

Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.

Hyperbolic type metrics and distortion of quasiconformal map pings

This Ph.D. thesis consists of four original papers. The papers cover several topics from geometric function theory, more specifically, hyperbolic type metrics, conformal invariants, and the distortion properties of quasiconformal mappings. The first paper deals mostly with the quasihyperbolic metric. The main result gives the optimal bilipschitz constant with respect to the quasihyperbolic metric for the M¨obius self-mappings of the unit ball. A quasiinvariance property, sharp in a local sense, of the quasihyperbolic metric under quasiconformal mappings is also proved. The second paper studies some distortion estimates for the class of quasiconformal self-mappings fixing the boundary values of the unit ball or convex domains. The distortion is measured by the hyperbolic metric or hyperbolic type metrics. The results provide explicit, asymptotically sharp inequalities when the maximal dilatation of quasiconformal mappings tends to 1. These explicit estimates involve special functions which have a crucial role in this study. In the third paper, we investigate the notion of the quasihyperbolic volume and find the growth estimates for the quasihyperbolic volume of balls in a domain in terms of the radius. It turns out that in the case of domains with Ahlfors regular boundaries, the rate of growth depends not merely on the radius but also on the metric structure of the boundary. The topic of the fourth paper is complete elliptic integrals and inequalities. We derive some functional inequalities and elementary estimates for these special functions. As applications, some functional inequalities and the growth of the exterior modulus of a rectangle are studied.

Threat Simulation- The Function of Dreaming?

Dreaming is a pure form of phenomenality, created by the brain untouched by external stimulation or behavioral activity, yet including a full range of phenomenal contents. Thus, it has been suggested that the dreaming brain could be used as a model system in a biological research program on consciousness (Revonsuo, 2006). In the present thesis, the philosophical view of biological realism is accepted, and thus, dreaming is considered as a natural biological phenomenon, explainable in naturalistic terms. The major theoretical contribution of the present thesis is that it explores dreaming from a multidisciplinary perspective, integrating information from various fields of science, such as dream research, consciousness research, evolutionary psychology, and cognitive neuroscience. Further, it places dreaming into a multilevel framework, and investigates the constitutive, etiological, and contextual explanations for dreaming. Currently, the only theory offering a full multilevel explanation for dreaming, that is, a theory including constitutive, etiological, and contextual level explanations, is the Threat Simulation Theory (TST) (Revonsuo, 2000a; 2000b). The empirical significance of the present thesis lies in the tests conducted to test this specific theory put forth to explain the form, content, and biological function of dreaming. The first step in the empirical testing of the TST was to define exact criteria for what is a ‘threatening event’ in dreams, and then to develop a detailed and reliable content analysis scale with which it is possible to empirically explore and quantify threatening events in dreams. The second step was to seek answers to the following questions derived from the TST: How frequent threatening events are in dreams? What kind of qualities these events have? How threatening events in dreams relate to the most recently encoded or the most salient memory traces of threatening events experienced in waking life? What are the effects of exposure to severe waking life threat on dreams? The results reveal that threatening events are relatively frequent in dreams, and that the simulated threats are realistic. The most common threats include aggression, are targeted mainly against the dream self, and include simulations of relevant and appropriate defensive actions. Further, real threat experiences activate the threat simulation system in a unique manner, and dream content is modulated by the activation of long term episodic memory traces with highest negative saliency. To sum up, most of the predictions of the TST tested in this thesis received considerable support. The TST presents a strong argument that explains the specific design of dreams as threat simulations. The TST also offers a plausible explanation for why dreaming would have been selected for: because dreaming interacted with the environment in such a way that enhanced fitness of ancestral humans. By referring to a single threat simulation mechanism it furthermore manages to explain a wide variety of dream content data that already exists in the literature, and to predict the overall statistical patterns of threat content in different samples of dreams. The TST and the empirical tests conducted to test the theory are a prime example of what a multidisciplinary approach to mental phenomena can accomplish. Thus far, dreaming seems to have always resided in the periphery of science, never regarded worth to be studied by the mainstream. Nevertheless, when brought to the spotlight, the study of dreaming can greatly benefit from ideas in diverse branches of science. Vice versa, knowledge learned from the study of dreaming can be applied in various disciplines. The main contribution of the present thesis lies in putting dreaming back where it belongs, that is, into the spotlight in the cross-road of various disciplines.