775 resultados para Borel-Leroy summability


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This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

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Das Studium der Auflösungs- und Wachstumsprozesse an Feststoff-Flüssigkeits-Grenzflächen unter nicht-hydrostatischen Beanspruchungen ist wesentlich für das Verständnis von Defor-mationsprozessen, die in der Erde ablaufen. Unter diesen genannten Prozessen gehört die Drucklösung zu den wichtigsten duktilen Deformationsprozessen, von der Diagenese bishin zur niedrig- bis mittelgradigen metamorphen Bedingungen. Bisher ist allerdings wenig darüber bekannt, welche mechanischen, physikalischen oder chemischen Potentialenergie-Gradienten die Drucklösung steuern. I.a. wird angenommen, daß die Drucklösung durch Un-terschiede kristallplastischer Verformungsenergien oder aber durch Unterschiede der Normal-beanspruchung an Korngrenzen gesteuert wird. Unterschiede der elastischen Verformungs-energien werden dabei allerdings als zu gering erachtet, um einen signifikanten Beitrag zu leisten. Aus diesem Grund werden sie als mögliche treibende Kräfte für die Drucklösung vernachlässigt. Andererseits haben neue experimentelle und theoretische Untersuchungen gezeigt, daß die elastische Verformung in der Tat einen starken Einfluß auf Lösungs- und Wachstumsmechanismen von Kristallen in einer Lösung haben kann. Da die in der Erdkruste vorherrschenden Deformationsmechanismen überwiegend im elastischen Verformungsbereich der Gesteine ablaufen, ist es sehr wichtig, das Verständnis für die Effekte, die die elastische Verformung verursacht, zu erweitern, und ihre Rolle während der Deformation durch Drucklösung zu definieren. Die vorliegende Arbeit beschäftigt sich mit Experimenten, bei denen der Effekt der mechanisch kompressiven Beanspruchung auf Lösungs- und Wachstumsprozesse von Einzelkristallen unterschiedlicher, sehr gut löslicher, elastisch/spröder Salze untersucht wurde. Diese Salze wurden als Analoga gesteinsbildender Minerale wie Quarz und Calcit ausgewählt. Der Einfluß von Stress auf die Ausbildung der Oberflächenmikrostrukturen in einer untersättigten Lösung wurde an Kaliumalaun untersucht.Lösungsrillen (20 – 40 µm breit, 10 – 40 µm tief und 20 – 80 µm Abstand) entwickelten sich in den Bereichen, in denen die Beanspruchung im Kristall am größten war. Sie verschwanden wieder, sobald der Kristall entlastet wurde. Diese Rillen entwickelten sich parallel zu niedrig indizierten kristallographischen Richtungen und sub-perpendikular zu den Trajektorien, die der maximalen, lokalen kompressiven Beanspruchung entsprachen. Die Größe der Lösungsrillen hing von der lokalen Oberflächenbeanspruchung, der Oberflächenenergie und dem Untersättigungsgrad der wässrigen Lösung ab. Die mikrostrukturelle Entwicklung der Kristalloberflächen stimmte gut mit den theoretischen Vorhersagen überein, die auf den Modellen von Heidug & Leroy (1994) und Leroy & Heidug (1994) basieren. Der Einfluß der Beanspruchung auf die Auflösungsrate wurde an Natriumchlorat-Einzelkristallen untersucht. Dabei wurde herausgefunden, daß sich gestresste Kristalle schneller lösen als Kristalle, auf die keine Beanspruchung einwirkt. Der experimentell beobachtete Anstieg der Auflösungsrate der gestressten Kristalle war ein bis zwei Größenordnungen höher als theoretisch erwartet. Die Auflösungsrate stieg linear mit dem Stress an, und der Anstieg war um so größer, je stärker die Lösung untersättigt war. Außerdem wurde der Effekt der Bean-spruchung auf das Kristallwachstum an Kaliumalaun- und Kaliumdihydrogenphosphat-Ein-zelkristallen untersucht. Die Wachstumsrate der Flächen {100} und {110} von Kalium-alaun war bei Beanspruchung stark reduziert. Für all diese Ergebnisse spielte die Oberflächenrauhigkeit der Kristalle eine Schlüsselrolle, indem sie eine nicht-homogene Stressverteilung auf der Kristalloberfläche verursachte. Die Resultate zeigen, daß die elastische Verformung eine signifikante Rolle während der Drucklösung spielen kann, und eine signifikante Deformation in der oberen Kruste verursachen kann, bei Beanspruchungen, die geringer sind, als gemeinhin angenommen wird. Somit folgt, daß die elastische Bean-spruchung berücksichtigt werden muß, wenn mikrophysikalische Deformationsmodelle entwickelt werden sollen.

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The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

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Partiamo dal lavoro di Kolmogorov per definire una misura della quantità di informazione contenuta in una stringa tramite un approccio computazionale: la complessità di una stringa è la lunghezza del più corto programma capace di produrla. Vediamo poi gli sviluppi moderni di questa teoria, in particolare i contributi di Chaitin, e notiamo subito i forti legami con la teoria della probabilità e con l'entropia di Shannon. Successivamente proponiamo di identificare le stringhe casuali (nel senso intuitivo) con quelle algoritmicamente incomprimibili, seguendo l'idea che minore comprimibilità significhi minore regolarità e dunque maggiore casualità. Infine vediamo che, in effetti, le stringhe incomprimibili soddisfano tutte le proprietà stocastiche effettivamente verificabili, cioè le proprietà che la teoria della probabilità attribuisce a successioni di variabili aleatorie indipendenti e identicamente distribuite. Facciamo ciò in maniera generale utilizzando la notevole teoria di Martin-Löf e poi vediamo in dettaglio l'aspetto della normalità di Borel.

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Injecting drug use (IDU) before and after liver transplantation (LT) is poorly described. The aim of this study was to quantify relapse and survival in this population and to describe the causes of mortality after LT.

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We propose an innovative, integrated, cost-effective health system to combat major non-communicable diseases (NCDs), including cardiovascular, chronic respiratory, metabolic, rheumatologic and neurologic disorders and cancers, which together are the predominant health problem of the 21st century. This proposed holistic strategy involves comprehensive patient-centered integrated care and multi-scale, multi-modal and multi-level systems approaches to tackle NCDs as a common group of diseases. Rather than studying each disease individually, it will take into account their intertwined gene-environment, socio-economic interactions and co-morbidities that lead to individual-specific complex phenotypes. It will implement a road map for predictive, preventive, personalized and participatory (P4) medicine based on a robust and extensive knowledge management infrastructure that contains individual patient information. It will be supported by strategic partnerships involving all stakeholders, including general practitioners associated with patient-centered care. This systems medicine strategy, which will take a holistic approach to disease, is designed to allow the results to be used globally, taking into account the needs and specificities of local economies and health systems.

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Breast cancer is the most common cancer among women, and tamoxifen is the preferred drug for estrogen receptor-positive breast cancer treatment. Many of these cancers are intrinsically resistant to tamoxifen or acquire resistance during treatment. Consequently, there is an ongoing need for breast cancer drugs that have different molecular targets. Previous work has shown that 8-mer and cyclic 9-mer peptides inhibit breast cancer in mouse and rat models, interacting with an unsolved receptor, while peptides smaller than eight amino acids did not. We show that the use of replica exchange molecular dynamics predicts the structure and dynamics of active peptides, leading to the discovery of smaller peptides with full biological activity. Simulations identified smaller peptide analogues with the same conserved reverse turn demonstrated in the larger peptides. These analogues were synthesized and shown to inhibit estrogen-dependent cell growth in a mouse uterine growth assay, a test showing reliable correlation with human breast cancer inhibition.

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Cyclo[EKTOVNOGN] (AFPep), a cyclic 9-amino acid peptide derived from the active site of alpha-fetoprotein, has been shown to prevent carcinogen-induced mammary cancer in rats and inhibit the growth of ER+ human breast cancer xenografts in mice. Recently, studies using replica exchange molecular dynamics predicted that the TOVN region of AFPep might form a dynamically stable putative Type I beta-turn, and thus be biologically active without additional amino acids. The studies presented in this paper were performed to determine whether TOVN and other small analogs of AFPep would inhibit estrogen-stimulated cancer growth and exhibit a broad effective-dose range. These peptides contained nine or fewer amino acids, and were designed to bracket or include the putative pharmacophoric region (TOVN) of AFPep. Biological activities of these peptides were evaluated using an immature mouse uterine growth inhibition assay, a T47D breast cancer cell proliferation assay, and an MCF-7 breast cancer xenograft assay. TOVN had very weak antiestrogenic activity in comparison to AFPep's activity, whereas TOVNO had antiestrogenic and anticancer activities similar to AFPep. OVNO, which does not form a putative Type I beta-turn, had virtually no antiestrogenic and anticancer activities. A putative proteolytic cleavage product of AFPep, TOVNOGNEK, significantly inhibited E2-stimulated growth in vivo and in vitro over a wider dose range than AFPep or TOVNO. We conclude that TOVNO has anticancer potential, that TOVNOGNEK is as effective as AFPep in suppressing growth of human breast cancer cells, and that it does so over a broader effective-dose range.

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The management of expanding melanonychia in childhood is controversial. Here, we present three cases and discuss their operating indications and reconstruction. Between January 1, 1995 and December 31, 2007, one boy and two girls, were operated for expanding melanonychia, involving the thumb, index finger or the middle finger. They were 2, 4, and 7 years at the time of surgery. A complete resection of the nail plate was performed followed by a direct finger reconstruction using a free short-pedicle vascularized nail flap of the toe. Histology showed a junctional nevus in all cases. The follow-ups were after 2, 3, and 5 years and without any complications or recurrence. Regarding reconstruction, the mean Foucher and Leclère score were, respectively, 17 and 16 points. It is concluded that for expanding melanonychia, in case of doubt, an examination of the entire lesion is necessary. Reconstruction of the nail unit after wide excision with nail plate ablation can be performed using microsurgery as discussed below. However, new guidelines on shave biopsy can make this microsurgical procedure obsolete.

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Chlamydophila (C.) abortus is the most common infectious abortigenic agent in small domestic ruminants in Switzerland. In contrast, the knowledge about chlamydiae in wild ruminants is scarce. As interactions between livestock and Alpine ibex (Capra i. ibex) occur on alpine pastures, the question raises if wild ruminants could play a role as carriers of chlamydiae. Thus, we investigated the prevalence of chlamydiae in Alpine ibex in Switzerland. In total, 624 sera, 676 eye swabs, 84 organ samples and 51 faecal samples from 664 ibex were investigated. Serum samples were tested by two commercial ELISA kits specific for C. abortus. Eye swabs, organs and faecal samples were examined by a Chlamydiaceae-specific real-time polymerase chain reaction (PCR). Positive cases were further investigated by the ArrayTube (AT) microarray method for chlamydial species determination. Of 624 serum samples investigated, 612 animals were negative, whereas nine sera (1.5%) reacted positively in one of the two tests and three sera showed an inconclusive result. Eye swabs of seven out of 412 ibex (1.7%) were tested positive for Chlamydiaceae by real-time PCR. By AT microarray, Chlamydophila (C.) pecorum was identified in two animals, Chlamydophila (C.) pneumoniae was detected in one animal and a mixed infection with C. abortus and C. pecorum was found in four animals. Organs and faecal samples were all negative by real-time PCR analysis. In summary, we conclude that C. abortus is not a common infectious agent in the Swiss ibex population. To our knowledge, this is the first description of C. pneumoniae in ibex. Further studies are necessary to elucidate the situation in other species of wild ruminants as chamois (Rupicapra r. rupicapra), red deer (Cervus elaphus) and roe deer (Capreolus c. capreolus) in Switzerland.

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Because interactions between livestock and chamois occur on Alpine pastures, transmission of infectious diseases is considered possible. Thus, the occurrence of Chlamydiaceae, Mycoplasma conjunctivae, and pestiviruses in Alpine chamois (Rupicapra r. rupicapra) of the Surselva region (eastern Swiss Alps) was investigated. In total, 71 sera, 158 eye swabs, 135 tissue samples, and 23 fecal samples from 85 chamois were analyzed. The sera were tested by 2 enzyme-linked immunosorbent assay (ELISA) kits specific for Chlamydophila abortus. Eye swabs, tissue, and fecal samples were examined by a Chlamydiaceae-specific real-time polymerase chain reaction (PCR). Positive cases were further investigated by microarray method. One serum sample (1.4%) was positive in 1 of the ELISAs. Eye swabs of 3 chamois (3.8%) were positive for Chlamydiaceae. The microarray method revealed the presence of Chlamydophila abortus, C pecorum, and C pneumoniae. All tissue and fecal samples were negative. With real-time PCR, 3.9% of the chamois tested positive for Mycoplasma conjunctivae. One chamois had a simultaneous infection with Al. conjunctivae and 2 chlamydial species (C abortus, C. pecorum). Skin and tongue tissue samples of 35 chamois were negative for pestivirus antigen by immunohistochemistry. It was concluded that in contrast to the findings in Pyrenean chamois (Capra p. pyrenaica) of Spain, the occurrence of Chlamydiaceae in Alpine chamois of the Surselva region is low, and the transmission between domestic and wild Caprinae seems not to be frequent. Comparably, persistent pestiviral infections do not seem to be common in chamois of the Surselva region.

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In the early 2000s, several colonies of Alpine ibex (Capra ibex ibex) in Switzerland ceased growing or began to decrease. Reproductive problems clue to infections with abortive agents might have negatively affected recruitment. We assessed the presence of selected agents of abortion in Alpine ibex by serologic, molecular, and culture techniques and evaluated whether infection with these agents might have affected population densities. Blood and fecal samples were collected from 651 ibex in 14 colonies throughout the Swiss Alps between 2006 and 2008. All samples were negative for Salmonella. spp., Neospora caninum, and Bovine Herpesvirus-1. Antibodies to Coxiella burnetii, Leptospira spp., Chlamydophila abortus, Toxoplasma gondii, and Bovine Viral Diarrhea virus were detected in at least one ibex. Positive serologic results for Brucella spp. likely were false. Overall, 73 samples (11.2%) were antibody-positive for at least one abortive agent. Prevalence was highest for Leptospira spp. (7.9%, 95% CI=5.0-11.7). The low prevalences and the absence of significant differences between colonies with opposite population trends suggest these pathogens do not play a significant role in the population dynamics of Swiss ibex. Alpine ibex do not seem to be a reservoir for these abortive agents or an important source of infection for domestic livestock in Switzerland. Finally, although interactions on summer pastures occur frequently, spillover from infected livestock to free-ranging ibex apparently is uncommon.