Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

On the fast approximation of Green's functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integralequation formulation is examined and is found to be limited to low values of k(0) rho (in this context k(0) rho = 2 pirho/ lambda(0), where rho is the distance between the source and the field points of the Green's function and lambda(0) is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large k(0) rho is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media.

Phylogeny of the Sporobolus indicus complex, based on internal transcribed spacer (ITS) sequences

The entire internal transcribed spacer ( ITS) region, including the 5.8S subunit of the nuclear ribosomal DNA ( rDNA), was sequenced by direct double-stranded sequencing of polymerase chain reaction (PCR) amplified fragments. The study included 40 Sporobolus ( Family Poaceae, subfamily Chloridoideae) seed collections from 14 putative species ( all 11 species from the S. indicus complex and three Australian native species). These sequences, along with those from two out-group species [ Pennisetum alopecuroides ( L.) Spreng. and Heteropogon contortus ( L.) P. Beauv. ex Roemer & Schultes, Poaceae, subfamily Panicoideae], were analysed by the parsimony method (PAUP; version 4.0b4a) to infer phylogenetic relationships among these species. The length of the ITS1, 5.8S subunit and ITS2 region were 222, 164 and 218 base pairs ( bp), respectively, in all species of the S. indicus complex, except for the ITS2 region of S. diandrus P. Beauv. individuals, which was 217 bp long. Of the 624 characters included in the analysis, 245 ( 39.3%) of the 330 variable sites contained potential phylogenetic information. Differences in sequences among the members of the S. pyramidalis P. Beauv., S. natalensis (Steud.) Dur & Schinz and S. jacquemontii Kunth. collections were 0%, while differences ranged from 0 to 2% between these and other species of the complex. Similarly, differences in sequences among collections of S. laxus B. K. Simon, S. sessilis B. K. Simon, S. elongatus R. Br. and S. creber De Nardi were 0%, compared with differences of 1-2% between these four species and the rest of the complex. When comparing S. fertilis ( Steud.) Clayton and S. africanus (Poir.) Robyns & Tourney, differences between collections ranged from 0 to 1%. Parsimony analysis grouped all 11 species of the S. indicus complex together, indicating a monophyletic origin. For the entire data set, pair-wise distances among members of the S. indicus complex varied from 0.00 to 1.58%, compared with a range of 20.08-21.44% among species in the complex and the Australian native species studied. A strict consensus phylogenetic tree separated 11 species of the S. indicus complex into five major clades. The phylogeny, based on ITS sequences, was found to be congruent with an earlier study on the taxonomic relationship of the weedy Sporobolus grasses revealed from random amplified polymorphic DNA ( RAPD). However, this cladistic analysis of the complex was not in agreement with that created on past morphological analyses and therefore gives a new insight into the phylogeny of the S. indicus complex.

On differentiability and analyticity of positive definite functions

We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.

Gene expression regulation and lineage evolution: the North and South tale of the hybrid polyploid Squalius alburnoides complex

The evolution of hybrid polyploid vertebrates, their viability and their perpetuation over evolutionary time have always been questions of great interest. However, little is known about the impact of hybridization and polyploidization on the regulatory networks that guarantee the appropriate quantitative and qualitative gene expression programme. The Squalius alburnoides complex of hybrid fish is an attractive system to address these questions, as it includes a wide variety of diploid and polyploid forms, and intricate systems of genetic exchange. Through the study of genome-specific allele expression of seven housekeeping and tissue-specific genes, we found that a gene copy silencing mechanism of dosage compensation exists throughout the distribution range of the complex. Here we show that the allele-specific patterns of silencing vary within the complex, according to the geographical origin and the type of genome involved in the hybridization process. In southern populations, triploids of S. alburnoides show an overall tendency for silencing the allele from the minority genome, while northern population polyploids exhibit preferential biallelic gene expression patterns, irrespective of genomic composition. The present findings further suggest that gene copy silencing and variable expression of specific allele combinations may be important processes in vertebrate polyploid evolution.

Reducing the number of membership functions in linguistic variables

Dissertation presented at Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia in fulfilment of the requirements for the Masters degree in Mathematics and Applications, specialization in Actuarial Sciences, Statistics and Operations Research

Contrasting magma types and timing of intrusion in the Permian layered mafic complex of Mont Collon (Western Alps, Valais, Switzerland): evidence from U/Pb zircon and 40Ar/39Ar amphibole dating

We have selected and dated three contrasting rock-types representative of the magmatic activity within the Permian layered mafic complex of Mont Collon, Austroalpine Dent Blanche nappe, Western Alps. A pegmatitic gabbro associated to the main cumulus sequence yields a concordant U/Pb zircon age of 284.2 +/- 0.6 Ma, whereas a pegmatitic granite dike crosscutting the latter yields a concordant age of 282.9 +/- 0.6 Ma. A Fe-Ti-rich ultrabasic lamprophyre, crosscutting all other lithologies of the complex, yields an 40Ar/39Ar plateau age of 260.2 +/- 0.7 Ma on a kaersutite concentrate. All ages are interpreted as magmatic. Sub-contemporaneous felsic dikes within the Mont Collon complex are ascribed to anatectic back-veining from the country-rock, related to the emplacement of the main gabbroic body in the continental crust, which is in accordance with new isotopic data. The lamprophyres have isotopic compositions typical of a depleted mantle, in contrast to those of the cumulate gabbros, close to values of the Bulk Silicate Earth. This indicates either contrasting sources for the two magma pulses - the subcontinental lithospheric mantle for the gabbros and the underlying asthenosphere for the lamprophyres - or a single depleted lithospheric source with variable degrees of crustal contamination of the gabbroic melts during their emplacement in the continental crust. The Mont Collon complex belongs to a series of Early Permian mafic massifs, which emplaced in a short time span about 285-280 Ma ago, in a limited sector of the post-Variscan continental crust now corresponding to the Austroalpine/ Southern Alpine domains and Corsica. This magmatic activity was controlled in space and time by crustal-scale transtensional shear zones.

Geometry, petrology and growth of a shallow crustal laccolith : the Torres del Paine Mafic Complex (Patagonia)

1. ABSTRACTS - RÉSUMÉSSCIENTIFIC ABSTRACT - ENGLISH VERSIONGeometry, petrology and growth of a shallow crustal laccolith: the Torres del Paine Mafi c Complex (Patagonia)The Torres del Paine intrusive complex (TPIC) is a composite mafic-granitic intrusion, ~70km2, belonging to a chain of isolated Miocene plutons in southern Patagonia. Their position is intermediate between the Mesozoic-Cenozoic calc-alkaline subduction related Patagonian batholith in the West and the late Cenozoic alkaline basaltic back-arc related plateau lavas in the East. The Torres del Paine complex formed during an important reconfiguration of the Patagonian geodynamic setting, with a migration of magmatism from the arc to the back-arc, possibly related to the Chile ridge subductionThe complex intruded the flysch of the Cretaceous Cerro Toro and Punta Barrosa Formations during the Miocene, creating a well-defined narrow contact aureole of 200-400 m width.In its eastern part, the Torres del Paine intrusive complex is a laccolith, composed of a succession of hornblende-gabbro to diorite sills at its base, with a total thickness of ~250m, showing brittle contacts with the overlying granitic sills, that form spectacular cliffs of more than 1000m. This laccolith is connected, in the western part, to its feeding system, with vertical alternating sheets of layered gabbronorite and Hbl-gabbro, surrounded and percolated by diorites. ID-TIMS U-Pb on zircons on feeder zone (FZ) gab- bros yield 12.593±0.009Ma and 12.587±0.009Ma, which is identifcal within error to the oldest granite dated so far by Michel et al. (2008). In contrast, the laccolith mafic complex is younger than than the youngest granite (12.50±0.02Ma), and has been emplaced from 12.472±0.009Ma to 12.431 ±0.006Ma, by under-accretion beneath the youngest granite at the interface with previously emplaced mafic sills.The gabbronorite crystallization sequence in the feeder zone is dominated by olivine, plagioclase, clinopyroxene and orthopyroxene, while amphibole forms late interstitial crystals. The crystallization sequence is identical in Hornblende-gabbro from the feeder zone, with higher modal hornblende. Gabbronorite and Hornblende-gabbro both display distinct Eu and Sr positive anomalies. In the laccolith, a lower Hornblende-gabbro crystallized in sills and evolved to a high alkali shoshonitic series. The Al203, Ti02, Na20, K20, Ba and Sr composition of these gabbros is highly variable and increases up to ~50wt% Si02. The lower hornblende-gabbro is characterized by kaersutite anhedral cores with inclusions of olivine, clino- and orthopyroxene and rare apatite and An70 plagioclase. Trace element modelling indicates that hornblende and clinopyroxene are in equilibrium with a liquid whose composition is similar to late basaltic trachyandesitic dikes that cut the complex. The matrix in the lower hornblende gabbro is composed of normally zoned oligoclase, Magnesio-hornblende, biotite, ilmenite and rare quartz and potassium feldspar. This assemblage crystallized in-situ from a Ba and Sr-depleted melts. In contrast, the upper Hbl-gabbro is high-K calc-alkaline. Poikilitic pargasite cores have inclusions of euhedral An70 plagioclase inclusions, and contain occasionally clinopyroxene, olivine and orthopyroxene. The matrix composition is identical to the lower hornblende-gabbro and similar to the diorite. Diorite bulk rock compositions show the same mineralogy but different modal proportions relative to hornblende-gabbrosThe Torres del Paine Intrusive Complex isotopic composition is 87Sr/86Sr=0.704, 143Nd/144Nd=0.5127, 206Pb/204Pb=18.70 and 207Pb/204Pb=15.65. Differentiated dioritic and granitic units may be linked to the gabbroic cumulates series, with 20-50% trapped interstitial melt, through fractionation of olivine-bearing gabbronorite or hornblende-gabbro fractionation The relative homogeneity of the isotopic compositions indicate that only small amounts of assimilation occurred. Two-pyroxenes thermometry, clinopyroxene barometry and amphibole-plagioclase thermometry was used to estimate pressure and temperature conditions. The early fractionation of ultramafic cumulates occurs at mid to lower crustal conditions, at temperatures exceeding 900°C. In contrast, the TPIC emplacement conditions have been estimated to ~0.7±0.5kbar and 790±60°C.Based on field and microtextural observations and geochemical modelling, fractionation of basaltic-trachyandesitic liquids at intermediate to lower crustal levels, has led to the formation of the Torres del Paine granites. Repetitive replenishment of basaltic trachy- andesitic liquid in crustal reservoirs led to mixed magmas that will ascend via the feeder zone, and crystallize into a laccolith, in the form of successive dioritic and gabbroic sills. Dynamic fractionation during emplacement concentrated hornblende rich cumulates in the center of individual sills. Variable degrees.of post-emplacement compaction led to the expulsion of felsic liquids that preferentially concentrated at the top of the sills. Incremental sills amalgamation of the entire Torres del Paine Intrusive Complex has lasted for ~160ka.RESUME SCIENTIFIQUE - VERSION FRANÇAISEGéométrie, pétrologie et croissance d'un laccolite peu profond : Le complexe ma- fique du Torres del Paine (Patagonie)Le Complexe Intrusif du Torres del Paine (CITP) est une intrusion bimodale, d'environ 70km2, appartenant à une chaîne de plutons Miocènes isolés, dans le sud de la Patago-nie. Leur position est intermédiaire entre le batholite patagonien calco-alcalin, à l'Ouest, mis en place au Mesozoïque-Cenozoïque dans un contexte de subduction, et les basal-tes andésitiques et trachybasaltes alcalins de plateau, plus jeune, à l'Est, lié à l'ouverture d'un arrière-arc.A son extrémité Est, le CITP est une succession de sills de gabbro à Hbl et de diorite, sur une épaisseur de ~250m, avec des évidences de mélange. Les contacts avec les sills de granite au-dessus, formant des parois de plus de 1000m, sont cassants. Ce laccolite est connecté, dans sa partie Ouest, à une zone d'alimentation, avec des intrusions sub-ver- ticales de gabbronorite litée et de gabbro à Hbl, en alternance. Celles-ci sont traversées et entourées par des diorites. Les zircons des gabbros de la zone d'alimentation, datés par ID-TIMS, ont cristallisés à 12.593±0.009Ma et 12.587±0.009Ma, ce qui correspond au plus vieux granite daté à ce jour par Michel et al. (2008). A l'inverse, les roches manques du laccolite se sont mises en place entre 12.472±0.009Ma et 12.431 ±0.006Ma, par sous-plaquage successifs à l'interface avec le granite le plus jeune daté à ce jour (12.50±0.02Ma).La séquence de cristallisation des gabbronorites est dominée par Ol, Plg, Cpx et Opx, alors que la Hbl est un cristal interstitiel. Elle est identique dans les gabbros à Hbl de la zone d'alimentation, avec ~30%vol de Hbl. Les gabbros de la zone d'alimentation montrent des anomalies positives en Eu et Sr distinctes. Dans le laccolite, le gabbro à Hbl inférieur évolue le long d'une série shoshonitique, riche en éléments incompatibles. Sa concentration en Al203, Ti02, Na20, K20, Ba et Sr est très variable et augmente rapide-ment jusqu'à ~50wt% Si02. Il est caractérisé par la présence de coeurs résorbés de kaer- sutite, entourés de Bt, et contenant des inclusions d'OI, Cpx et Opx, ou alors d'Ap et de rares Plg (An70). Hbl et Cpx ont cristallisés à partir d'un liquide de composition similaire aux dykes trachy-andesite basaltique du CITP. La matrice, cristallisée in-situ à partir d'un liquide pauvre en Ba et Sr, est composée d'oligoclase zoné de façon simple, de Mg-Hbl, Bt, llm ainsi que de rares Qtz et KF. Le gabbro à Hbl supérieur, quant à lui, appartient à une suite chimique calco-alcaline riche en K. Des coeurs poecilitiques de pargasite con-tiennent de nombreuses inclusions de Plg (An70) automorphe, ainsi que des Ol, Cpx et Opx. La composition de la matrice est identique à celle des gabbros à Hbl inférieurs et toutes deux sont similaires à la minéralogie des diorites. Les analyses sur roches totales de diorites montrent la même variabilité que celles de gabbros à Hbl, mais avec une ten-eur en Si02 plus élevée.La composition isotopique des liquides primitifs du CITP a été mesurée à 87Sr/86Sr=0.704, 143Nd/144Nd=0.5127, 206Pb/204Pb=18.70 et 207Pb/204Pb=15.65. Les granites et diorites différenciés peuvent être reliés à des cumulais gabbronoritiques (F=0.74 pour les granites et F=1-0.5 pour les diorites) et gabbroïques à Hbl (fractionnement supplémentaire pour les granites, avec F=0.3). La cristallisation de 20 à 50%vol de liquide interstitiel piégé dans les gabbros du CITP explique leur signature géochimique. Seules de faibles quantités de croûte continentale ont été assimilées. La température et la pression de fractionnement ont été estimées, sur la base des thermobaromètres Opx-Cpx, Hbl-Plg et Cpx, à plus de 900°C et une profondeur correspondant à la croûte inférieure-moyenne. A l'inverse, les conditions de cristallisation de la matrice des gabbros et diorites du laccolite ont été estimées à 790±60°C et ~0.7±0.5kbar.Je propose que les liquides felsiques du CITP se soient formés par cristallisation frac-tionnée en profondeur des assemblages minéralogiques observés dans les gabbros du CITP, à partir d'un liquide trachy-andesite basaltique. La percolation de magma dans les cristaux accumulés permet la remontée du mélange à travers la zone d'alimentation, vers le laccolite, où des sills se mettent en place successivement. L'amalgamation de sills dans le CITP a duré ~160ka.Le CITP s'est formé durant une reconfiguration importante du contexte géodynamique en Patagonie, avec un changement du magmatisme d'arc vers un volcanisme d'arrière- arc. Ce changement est certainement lié à la subduction de la ride du Chili.RESUME GRAND PUBLIC - VERSION FRANÇAISEGéométrie, pétrologie et croissance d'une chambre magmatique peu profonde : Le complexe mafique du Torres del Paine (Patagonie)Le pourtour de l'Océan Pacifique est caractérisé par une zone de convergence de plaques tectoniques, appelée zone de subduction, avec le plongement de croûte océa-nique sous les Andes dans le cas de la Patagonie. De nombreux volcans y sont associés, formant la ceinture de feu. Mais seuls quelques pourcents de tout le magma traversant la croûte terrestre parviennent à la surface et la majeure partie cristallise en profondeur, dans des chambres magmatiques. Quelles est leur forme, croissance, cristallisation et durée de vie ? Le complexe magmatique du Torres del Paine représente l'un des meilleurs endroits au monde pour répondre à ces questions. Il se situe au sud de la Patagonie, formant un massif de 70km2. Des réponses peuvent être trouvées à différentes échelles, variant de la montagne à des minéraux de quelques 1000ème de millimètres.Il est possible de distinguer trois types de roches : des gabbros et des diorites sur une épaisseur de 250m, surmontées par des parois de granite de plus de 1000m. Les contacts entre ces roches sont tous horizontaux. Entre granites et gabbro-diorite, le contact est net, indiquant que le second magma s'est mis en place au contact avec un magma plus ancien, totalement solidifié. Entre gabbros et diorites, les contacts sont diffus, souvent non-linéaires, indiquant à l'inverse la mise en contact de magmas encore partiellement liquides. Dans la partie Ouest de cette chambre magmatique, les contacts entre roches sont verticaux. Il s'agit certainement du lieu de remplissage de la chambre magmatique.Lors du refroidissement d'un magma, différents cristaux vont se former. Leur stabilité et leur composition varient en fonction de la pression, de la température ou de la chimie du magma. La séquence de cristallisation peut être définie sur la base d'observations microscopiques et de la composition chimique des minéraux. Différents gabbros sont ainsi distingués : le gabbro à la base est riche en hornblende, d'une taille de ~5mm, sans inclusion de plagioclase mais avec des cristaux d'olivine, clinopyroxene et orthopyroxene inclus ; le gabbro supérieur est lui-aussi riche en hornblende (~5mm), avec les mêmes inclusions additionnées de plagioclase. Ces cristaux se sont formés à une température supérieure à 900°C et une profondeur correspondant à la croûte moyenne ou inférieure. Les minéraux plus fin, se trouvant hors des cristaux de hornblende des deux gabbros, sont similaires à ceux des diorites : plagioclase, biotite, hornblende, apatite, quartz et feldspath alcalin. Ces minéraux sont caractéristiques des granites. Ils ont cristallisé à ~790°C et ~2km de profondeur.La cristallisation des minéraux et leur extraction du magma par gravité provoque un changement progressif de la composition de ce dernier. Ainsi, après extraction d'olivine et d'orthopyroxene riches en Mg, de clinopyroxene riche en Ca, de plagioclase riche en Ca et Al et d'hornblende riche en Ca, Al et Mg, le liquide final sera appauvri en ces élé-ments. Un lien peut ainsi être proposé entre les diorites dont la composition est proche du liquide de départ, les granites dont la composition est similaire au liquide final, et les gabbros dont la minéralogie correspond aux minéraux extraits.L'utilisation de zircons, un minéral riche en U dont les atomes se transforment en Pb par décomposition radioactive au cours de millions d'années, permet de dater le refroidissement des roches qui les contiennent. Ainsi, il a été observé que les roches de la zone d'alimentation, à l'Ouest du complexe magmatique, ont cristallisés il y a 12.59±0.01 Ma, en même temps que les granites les plus vieux, se trouvant au sommet de la chambre magmatique, datés par Michel et al. (2008). Les deux roches pourraient donc avoir la même origine. A l'inverse, les gabbros et diorites de la chambre magmatique ont cristallisé entre 12.47±0.01Ma et 12.43±0.01Ma, les roches les plus vieilles étant à la base.En comparant la composition des roches du Torres del Paine avec celles d'autres en-tités géologiques de Patagonie, les causes du magmatisme peuvent être recherchées. A l'Ouest, on trouve en effet des intrusions granitiques, plus anciennes, caractéristiques de zones de convergence de plaque tectonique, alors qu'à l'Est, des laves basaltiques plus jeunes sont caractéristiques d'une dynamique d'extension. Sur la base des compositions chimiques des roches de ces différentes entités, l'évolution progressive de l'une à l'autre a pu être démontrée. Elle est certainement due à l'arrivée d'une dorsale océanique (zone d'extension crustale et de création de croûte océanique par la remontée de magma) dans la zone de subduction, le long des Andes.Je propose que, dans un premier temps, des magmas granitiques sont remontés dans la chambre magmatique, laissant d'importants volumes de cristaux dans la croûte pro-fonde. Dans un second épisode, les cristaux formés en profondeur ont été transportés à travers la croûte continentale, suite au mélange avec un nouveau magma injecté. Ces magmas chargés de cristaux ont traversé la zone d'alimentation avant de s'injecter dans la chambre magmatique. Différents puises ont été distingués, injectés dans la chambre magmatique du sommet à la base concernant les granites, puis à la base du granite le plus jeune pour les gabbros et diorites. Le complexe magmatique du Torres del Paine s'est construit sur une période totale de 160'000±20'000 ans.

On the configuration of Herman rings of meromorphic functions

We prove some results concerning the possible configuration s of Herman rings for transcendental meromorphic functions. We show that one pole is enough to obtain cycles of Herman rings of arbitrary period a nd give a sufficient condition for a configuration to be realizable.

Role of major histocompatibility complex class II expression by non-hematopoietic cells in autoimmune and inflammatory disorders: facts and fiction.

It is well established that interactions between CD4(+) T cells and major histocompatibility complex class II (MHCII) positive antigen-presenting cells (APCs) of hematopoietic origin play key roles in both the maintenance of tolerance and the initiation and development of autoimmune and inflammatory disorders. In sharp contrast, despite nearly three decades of intensive research, the functional relevance of MHCII expression by non-hematopoietic tissue-resident cells has remained obscure. The widespread assumption that MHCII expression by non-hematopoietic APCs has an impact on autoimmune and inflammatory diseases has in most instances neither been confirmed nor excluded by indisputable in vivo data. Here we review and put into perspective conflicting in vitro and in vivo results on the putative impact of MHCII expression by non-hematopoietic APCs-in both target organs and secondary lymphoid tissues-on the initiation and development of representative autoimmune and inflammatory disorders. Emphasis will be placed on the lacunar status of our knowledge in this field. We also discuss new mouse models-developed on the basis of our understanding of the molecular mechanisms that regulate MHCII expression-that constitute valuable tools for filling the severe gaps in our knowledge on the functions of non-hematopoietic APCs in inflammatory conditions.

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Bandlimited Lipschitz functions

We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of interpolating and sampling sequences for this space. We also give a description of the trace of such functions to sequences of critical density in terms of a cancellation condition.

The Mont Collon mafic complex (Austroalpine Dent Blanche nappe) : permian evolution of the Western European mantle

Résumé: Le complexe du Mont Collon (nappe de la Dent Blanche, Austroalpin) est l'un des exemples les mieux préservés du magmatisme mafique permien des Alpes occidentales. Il est composé d'affleurements discontinus et d'une stratification magmatique en son centre (Dents de Bertol) et est composé à 95% de roches mafiques cumulatives (gabbros à olivine et/ou cpx, anorthositiques, troctolites, wehrlites et wehrlites à plagioclase) et localement de quelques gabbros pegmatitiques. Ces faciès sont recoupés par de nombreux filons acides (aphtes, pegmatites quartziques, microgranodiorites et filons anorthositiques) et mafiques tardifs (dikes mélanocrates riches en Fe et Ti). Les calculs thermométriques (équilibre olivine-augite) montrent des températures de 1070-1120 ± 6°C, tandis que le thermomètre amphibole-plagioclase indique une température de 740 ± 40°C à 0.5 GPa pour les amphiboles magmatiques tardives. La geobarométrie sur pyroxène donne des pressions moyennes de 0.3-0.6 GPa, indiquant un emplacement dans la croûte moyenne. De plus, les températures obtenues sur des amphiboles coronitiques indiquent des températures de l'ordre de 700 ± 40°C confirmant que les réactions coronitiques apparaissent dans des conditions subsolidus. Les âges concordants U/Pb sur zircons de 284.2 ± 0.6 et 282.9 ± 0.6 Ma obtenus sur un gabbro pegmatitique et une pegmatitique quartzique, sont interprétés comme des âges de cristallisation. Les datations 40Ar/39Ar sur amphiboles des filons mélanocrates donnent un âge plateau de 260.2 ± 0.7 Ma, qui est probablement très proche de l'âge de cristallisation. Ainsi, cet age 40Ar/39Ar indique un second évènement magmatique au sein du complexe. Les compositions des roches totales en éléments majeurs et traces montrent peu de variations, ainsi que le Mg# (75-80). Les éléments traces enregistrent le caractère cumulatif des roches (anomalie positive en Eu) et révèlent des anomalies négatives systématiques en Nb, Ta, Zr, Hf et Ti dans les faciès basiques. Le manque de corrélation entre éléments majeurs et traces est caractéristique d'un processus de cristallisation in situ impliquant une quantité variable de liquide interstitiel (L) entre les phases cumulus. Les distributions des éléments traces dans les minéraux sont homogènes, indiquant une rééquilibration .subsolidus entre cristaux et liquide interstitiel. Un modèle quantitatif basé sur les équations de cristallisation in situ de Langmuir reproduisent correctement les concentrations en terres rares légères des minéraux cumulatifs montrant la présence de 0 à 35% de liquide interstitiel L pour des degrés de différenciation F de 0 à 45%, par rapport au faciès les moins évolués du complexe. En outre, les valeurs de L sont bien corrélées avec les proportions modales d'amphibole interstitielle et les concentrations en éléments incompatibles des roches (Zr, Nb). Le liquide parental calculé des cumulats du Mont Collon est caractérisé par un enrichissement relatif en terres rares légères et Th, un appauvrissement en terres rares lourdes typique d'une affinité transitionnelle (T-MORB) et une forte anomalie négative en Nb-Ta. Les roches cumulatives montrent des compositions isotopiques en Nd-Sr proches de la terre globale silicatée (BSE), soit 0.6<εNdi<+3.2, 0.7045<87Sr/86Sri<0.7056. Les rapports initiaux en Pb indiquent une source dans le manteau enrichi subcontinental lithosphérique, préalablement contaminé par des sédiments océaniques. Les dikes mélanocrates Fe-Ti sont représentatifs de liquides et ont des spectres de terres rares enrichis, une anomalie positive en Nb-Ta et des εNdi de +7, des 87Sr/86Sri de 0.703 et des rapports initiaux en Pb, similaires à ceux des basaltes d'île océanique, indiquant une source asthénosphérique modérément appauvrie. Ainsi, la fusion partielle du manteau lithosphérique subcontinental est induite par l'amincissement post-orogénique et la remontée de l'asthénosphère. Les filons mélanocrates proviennent, après délamination du manteau lithosphérique, de la fusion de l'asthénosphère. Abstract The early Permian Mont Collon mafic complex (Dent Blanche nappe, Austroalpine nappe system) is one of the best preserved examples of the Permian mafic magmatism in the Western Alps. It is composed of discontinuous exposures and a well-preserved magmatic layering (the Dents de Bertol cliff) crops out in the center part of the complex. It mainly consists of cumulative mafic rocks, which represent 95 vol-% of the mafic complex (ol- and cpx-bearing gabbros and rare anorthositic layers, troctolites, wehrlites and plagioclase-wehrlites) and locally pegmatitic gabbros. All these facies are crosscut by widespread acidic (aplites, quartz-rich pegmatites, microgranodiorites) and late mafic Fe-Ti melanocratic dikes. Olivine-augite thermometric calculations yield a range of 1070-1120 ± 6°C, while amphibole-plagioclase thermometer yields a temperature of 740 ± 40°C at 0.5 GPa. Pyroxene geobarometry points to a pressure of 0.3-0.6 GPa, indicating a middle crustal level of emplacement. Moreover, temperature calculations on the Mont Conon coronitic amphiboles indicate temperatures of 700 ± 40°C, close to those calculated for magmatic amphiboles. These temperatures confirm that coronitic reactions occurred at subsolidus conditions. ID-TIMS U/Pb zircon ages of 284.2 ± 0.6 and 282.9 ± 0.6 Ma obtained on a pegmatitic gabbro and a quartz-pegmatitic dike, respectively, were interpreted as the crystallization ages of these rocks. 40Ar/39Ar dating on amphiboles from Fe-Ti melanocratic dikes yields a plateau age of 260.2 ± 0.7 Ma, which is probably very close to the crystallization age. Consequently, this 40Ar/P39Ar age indicates a second magmatic event. Whole-rock major- and trace-element compositions show little variation across the whole intrusion and Mg-number stays within a narrow range (75-80). Trace-element concentrations record the cumulative nature of the rocks (e.g. positive Eu anomaly) and reveal systematic Nb, Ta, Zr, Hf and Ti negative anomalies for all basic facies. The lack of correlation between major and trace elements is characteristic of an in situ crystallization process involving variable amounts of interstitial liquid (L) trapped between the cumulus mineral phases. LA-ICPMS measurements show that trace-element distributions in minerals are homogeneous, pointing to subsolidus re-equilibration between crystals and interstitial melts. A quantitative modeling based on Langmuir's in situ crystallization equation successfully reproduced the Rare Earth Element (REE) concentrations in cumulitic minerals. The calculated amounts of interstitial liquid L vary between 0 and 35% for degrees of differentiation F of 0 to 45%, relative to the least evolved facies of the intrusion. Furthermore, L values are well correlated with the modal proportions of interstitial amphibole and whole-rock incompatible trace-element concentrations (e.g. Zr, Nb) of the tested samples. The calculated parental melt of the Mont Collon cumulates is characterized by a relative enrichment in Light REE and Th, a depletion in Heavy REE, typical of a transitional affinity (T-MORB), and strong negative Nb-Ta anomaly. Cumulative rocks display Nd-Sr isotopic compositions close to the BSE (-0.6 < εNdi < +3.2, 0.7045 < 87Sr/86Sri < 0.7056). Initial Pb ratios point to an origin from the melting of an enriched subcontinental lithospheric mantle source, previously contaminated at the source by oceanic sediments. The contrasted alkaline Fe-Ti melanocratic dikes are representative of liquids. They display enriched fractionated REE patterns, a positive Nb-Ta anomaly and εNdi of +7, 87Sr/86Sri of 0.703 and initial Pb ratios, all reminiscent of Ocean Island Basalt-type rocks, pointing to a moderately

Development of rotating drum under mechanical and thermal load

A variable temperature field sets exacting demands to the structure under mechanical load. Most of all the lifetime of the rotating drum structure depends on temperature differences between parts inside the drum. The temperature difference was known because of the measurements made before. The list of demands was created based on customers’ needs. The limits of this paper were set to the inner structure of the drum. Creation of ideas for the inner structure was started open minded. The main principle in the creation process was to create new ideas for the function of the product with the help of sub-functions. The sub-functions were created as independent as possible. The best sub-functions were combined together and the new working principles were created based on them. Every working principle was calculated separately and criticized at the end of the calculation process. The main objective was to create the new kind of structure, which is not based too much to the old, inoperative structure. The affect of own weight of the inner structure to the stress values was quite small but it was also taken into consideration when calculating the maximum stress value of the structure. Because of very complex structures all of the calculations were made with the help of the ProE – Mechanica software. The fatigue analyze was made also for the best structure solution.

Phylogeography and population genetics of north European Atlantic salmon (Salmo salar L.)

Although abundant in the number of individuals, the Atlantic salmon may be considered as a threatened species in many areas of its native distribution range. Human activities such as building of power plant dams, offshore overfishing, pollution, clearing of riverbeds for timber floating and badly designed stocking regimes have diminished the distribution of Atlantic salmon. As a result of this, many of the historical populations both in Europe and northern America have gone extinct or are severely depressed. In fact, only 1% of Atlantic salmon existing today are of natural origin, the rest being farmed salmon. All of this has lead to a vast amount of research and many restoration programmes aiming to bring Atlantic salmon back to rivers from where it has vanished. However, many of the restoration programmes conducted thus far have been unsuccessful due to inadequate scientific research or lack of its implementation, highlighting the fact that more research is needed to fully understand the biology of this complex species. The White and Barents Seas in northwest Russia are among the last regions in Europe where Atlantic salmon populations are still stable, thus forming an important source of biodiversity for the entire European region. Salmon stocks from this area are also of immense economic and social importance for the local people in the form of fishing tourism. The main aim of this thesis was to elucidate the post-glacial history and population genetic structure of north European and particularly northwest Russian Atlantic salmon, both of which are aspects of great importance for the management and conservation of the species. Throughout the whole thesis, these populations were studied by utilizing microsatellites as the main molecular tool. One of the most important discoveries of the thesis was the division of Atlantic salmon from the White and Barents Seas into four separate clusters, which has not been observed in previous studies employing nuclear markers although is supported by mtDNA studies. Populations from the western Barents Sea clustered together with the northeast Atlantic populations into a clearly distinguishable group while populations from the White Sea and eastern Barents Sea were separated into three additional groups. This has important conservation implications as this thesis clearly indicates that conservation of populations from all of the observed clusters is warranted in order to conserve as much of the genetic diversity as possible in this area. The thesis also demonstrates how differences in population life histories within a species, migratory behaviour in this case, and in their phylogeographic origin affect the genetic characteristics of populations, namely diversity and divergence levels. The anadromous populations from the Atlantic Ocean, White Sea and Barents Sea possessed higher levels of genetic diversity than the anadromous populations form the Baltic Sea basin. Among the non-anadromous populations the result was the opposite: the Baltic freshwater populations were more variable. This emphasises the importance of taking the life history of a population into consideration when developing conservation strategies: due to the limited possibilities for new genetic diversity to be generated via gene flow, it is expected that freshwater Atlantic salmon populations would be more vulnerable to extinction following a population crash and thus deserve a high conservation status. In the last chapter of this thesis immune relevant marker loci were developed and screened for signatures of natural selection along with loci linked to genes with other functions or no function at all. Also, a novel landscape genomics method, which combines environmental information with molecular data, was employed to investigate whether immune relevant markers displayed significant correlations to various environmental variables more frequently than other loci. Indications of stronger selection pressure among immune-relevant loci compared to non-immune relevant EST-linked loci was found but further studies are needed to evaluate whether it is a common phenomenon in Atlantic salmon.