Historia critica demonstrationis existentiae Dei a priori

Arkit: 1 arkintunnukseton lehti, A-B4 C2.

Index fossilium analysibus chemicis examinatorum

Arkit: 1 arkintunnukseton lehti, G4 H2.

De commodis et incommodis philosophiae liberae

Invocatio: Q.F.F.Q.E.J.D.T.O.M.

De epistola Eliae ad Joramum, ex 2. Paral. XXI: 12. &c

Mennanderin gratulaatio painettu uudelleen: Das Inland (Dorpat) 1856 pg. 562-563

De silica ex solutione alkalina per calcem praecipitata

Dedicatio: Pierre Jean Bladh [ransk. pr.], Israël Holstius.

De natura acidi nitrici

Dedicatio: Carl Lundström [ruots. pr.], Henric Ståhlström [ruots. pr.].

De methodis quibusdam trigonometricis

Dedicatio: Magnus Jacobus Alopaeus.

Historia doctrinae de affinitatibus chemicis

Painovuosi nimekkeestä.

De laceratione vestium apud Hebraeos

Invocatio: [hepreaa].

De vitiis literatorum in excolendis linguis

Invocatio: Q.B.V.

De sensibus externis

Arkit: A-B4 C2.

Historia doctrinae de affinitatibus chemicis

Painovuosi nimekkeestä.

Suffragio ampliss: facult. philosoph. Regiae ad Auram Academiae

Invocatio: Ope altissimi.

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.

Estudo fitossociológico de uma comunidade vegetal sobre canga como subsídio para a reabilitação de áreas mineradas no quadrilátero ferrífero, MG

O objetivo deste trabalho foi caracterizar a estrutura e composição de um campo rupestre sobre canga para servir de base a estudos sobre reabilitação de áreas degradadas pela mineração de ferro. Estudou-se uma canga no Parque Estadual da Serra do Rola-Moça, MG. Em 30 parcelas de 2 m², foram amostrados 2.151 indivíduos pertencentes a 32 espécies e 16 famílias, com diversidade de 2,45 nats/ind. A altura média foi de 15,8 ± 16,3 cm, com 80% dos indivíduos menores do que 25 cm. As famílias mais importantes foram Orchidaceae, Poaceae e Cyperaceae, e as espécies com maior valor de importância foram Andropogon ingratus (Poaceae), Lychnophora pinaster (Asteraceae), Bulbostylis fimbriata (Cyperaceae), Sophronitis caulescens (Orchidaceae) e Sebastiania glandulosa (Euphorbiaceae). Sugere-se que essas espécies mais importantes, aquelas com crescimento clonal como gramíneas, ciperáceas e orquídeas epilíticas, as facilitadoras como Stachytarpheta glabra e Mimosa calodendron e espécies tolerantes a metais pesados como Vellozia spp. sejam candidatas prioritárias em programas de recuperação de áreas degradadas por mineração de ferro.