Search results for "Mertens"
showing 4 items of 4 documents
Complete nucleotide sequence of the mitochondrial genome of a salamander, Mertensiella luschani
2003
The complete nucleotide sequence (16,650 bp) of the mitochondrial genome of the salamander Mertensiella luschani (Caudata, Amphibia) was determined. This molecule conforms to the consensus vertebrate mitochondrial gene order. However, it is characterized by a long non-coding intervening sequence with two 124-bp repeats between the tRNA Thr and tRNA Pro genes. The new sequence data were used to reconstruct a phylogeny of jawed vertebrates. Phylogenetic analyses of all mitochondrial protein-coding genes at the amino acid level recovered a robust vertebrate tree in which lungfishes are the closest living relatives of tetrapods, salamanders and frogs are grouped together to the exclusion of cae…
Counting and equidistribution in Heisenberg groups
2014
We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension $2$. We prove a Mertens' formula for the integer points over a quadratic imaginary number fields $K$ in the light cone of Hermitian forms, as well as an equidistribution theorem of the set of rational points over $K$ in Heisenberg groups. We give a counting formula for the cubic points over $K$ in the complex projective plane whose Galois conjugates are orthogonal and isotropic for a given Hermitian form over $K$, and a counting and equidistribution result for …
A molecular phylogeny of ‘true’ salamanders (family Salamandridae) and the evolution of terrestriality of reproductive modes
2009
Key innovations enable species to conquer new habitats. Within the family Salamandridae, particular adaptations to terrestrial life, such as the anatomy and physiology of the feeding apparatus, courtship behaviour and in some cases viviparity, allowed the ‘true’salamanders (genera Chioglossa, Mertensiella, Salamandra) to shift from a semi-aquatic to a more terrestrial life cycle. We sequenced 423 base pairs of the 16S RNA gene of the mitochondrial DNA for all species of the ‘true’salamanders. Based on the resulting phylogeny we discuss the evolution of terrestrial reproductive modes within this species group. We especially tested two hypotheses of monophyletic origin of specific adaptations…
Reaalianalyyttistä lukuteoriaa
2016
Tämän tutkielman tarkoituksena on tutustuttaa lukija Bernoullin polynomeihin, Γ-funktioon ja lukuteoreettisiin Mertensin lauseisiin. Näiden lisäksi tutkitaan erästä lukuteoreettista tuloa, ja esitellään tähän tuloon liittyviä tiettävästi uusia tuloksia. Bernoullin polynomien avulla todistetaan erityisesti Euler-Maclaurinin lause, joka kertoo erilaisten summien ja integraalien välisestä yhteydestä. Γ-funktion avulla taas todistetaan Stirlingin kaava, joka antaa hyvän approksimaation kertoman n! kasvu- nopeudesta. Mertensin lauseista ensimmäinen kertoo, miten nopeasti lukua n pie- nempien alkulukujen käänteislukujen 1/p summa hajaantuu, kun kasvatetaan lukua n. Toinen Mertensin lause kertoo, …