The characterization of the local ill-posedness and the local degree of nonlinearity are of particular importance for the stable solution of nonlinear ill-posed problems. We present assertions concerning the interdependence between the ill-posedness of the nonlinear problem and its linearization. Moreover, we show that the concept of the degree of nonlinearity com bined with source conditions can be used to characterize the local ill-posedness and to derive a posteriori estimates for nonlinear ill-posed problems. A posteriori estimates are widely used in finite element and multigrid methods for the solution of nonlinear partial differential equations, but these techniques are in general not applicable to inverse an ill-posed problems. Additionally we show for the well-known Landweber method and the iteratively regularized Gauss-Newton method that they satisfy a posteriori estimates under source conditions; this can be used to prove convergence rates results.

This paper is concerned with the anisotropic singular behaviour of the solution of elliptic boundary value problems near edges. The paper deals first with the description of the analytic properties of the solution in newly defined, anisotropically weighted Sobolev spaces. The finite element method with anisotropic, graded meshes and piecewise linear shape functions is then investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates in anisotropically weighted spaces are derived. Moreover, it is shown that the condition number of the stiffness matrix is not affected by the mesh grading. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones.

In this paper introduce new approach for unified theory for continuous and discrete time (optimal) control problems based on the generalized Cayley transformation. We also relate the associated discrete and continuous generalized algebraic Riccati equations. We demonstrate the potential of this new approach proving new result for discrete algebraic Riccati equations. But we also discuss where this new approach as well as all other approaches still is non-satisfactory. We explain a discrepancy observed between the discrete and continuous cse and show that this discrepancy is partly due to the consideration of the wrong analogues. We also present an idea for a metatheorem that relates general theorems for discrete and continuous control problems.

Two efficient methods for solving generalized Lyapunov equations and their implementations in FORTRAN 77 are presented. The first one is a generalization of the Bartels--Stewart method and the second is an extension of Hammarling's method to generalized Lyapunov equations. Our LAPACK based subroutines are implemented in a quite flexible way. They can handle the transposed equations and provide scaling to avoid overflow in the solution. Moreover, the Bartels--Stewart subroutine offers the optional estimation of the separation and the reciprocal condition number. A brief description of both algorithms is given. The performance of the software is demonstrated by numerical experiments.

We study the regularization problem for linear, constant coefficient descriptor systems $E x^. = AX + Bu, y_1 = Cx, y_2=\Gamma x^.$ by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and $E +BG\Gamma$ has a desired rank, i.e. there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedbacks gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang (Math. Comp. 54(1990)190, 483--493) are discussed. The modified operators are defined for non-smooth functions and are suited for the application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges.

Multiple sclerosis (MS) is an autoimmune disease that affects the central nervous system (CNS) and leads to demyelination and loss of CNS neurons. MS usually occurs in young people, and it is mostly women between the ages of 20 and 40 who are affected by the disease. The disease can lead to impairments in motor functions such as walking ability, coordination, reduced balance, and strength. Until now, there is no treatment that can cure the disease, but there is complementary medicine that can suppress the symptoms of the disease or prevent the development of the disease. Nowadays there are studies that show that there may be alternative treatments that can be an ultimate treatment for MS disease that can be effective and beneficial. A novel treatment that researchers have developed is transplantation of autologous mesenchymal multipotent stem cells (MSC), which appear to be the most promising of the emerging treatments of MS. There is research in the field that shows that the treatment is progressive and beneficial. However, there are some study results that show that the treatment can cause side effects. The four chosen articles are reviewed on how effective and safe the treatment with MSC transplantation is in patients with MS. The studies show promising results bur have some shortcomings such as low study population, uneven gender distribution and ethnic considerations. To confirm these results, larger studies with high quality and quantity are needed. The results showed that the treatment gave indications of beneficial effects, including improvements in neurological functions. The Expanded Disability Status Scale (EDSS) value improved during the MSC transplantation in the patients with severe disease which indicate a beneficial effect of this novel treatment.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Trotz intensiver Forschung im Rahmen der Bänder- und Sehnenerkrankungen gelten bestimmte Fragestellungen hinsichtlich Erkrankungs- sowie Heilungsmechanismen als unbeantwortet. Verschiedenste Konzepte des Tissue Engineerings sollen helfen entsprechende Fragen zu beantworten und moderne Therapiekonzepte zu etablieren. Für grundlegende Untersuchungen zur Biologie der Tenogenese sowie zum Wirkmechanismus applizierter mesenchymaler Stromazellen (MSC), gewinnt die Anwendung von dezellularisiertem Sehnengewebe immer mehr an Bedeutung. Zudem erscheint der Einsatz dezellularisierter Sehnen- und Bandkonstrukte zur Wiederherstellung der betreffenden erkrankten Organe sehr vielversprechend. In der vorliegenden Arbeit sollte der Grundstein zur Entwicklung eines in vitro-Modells auf Grundlage equiner Beugesehnen gelegt werden. Primäres Ziel war es, ein optimales Dezellularisierungsprotokoll für intakte equine Beugesehnen (oberflächliche und tiefe Beugesehne) zu etablieren. Um die Zytokompatibilität der dezellularisierten Sehnen zu überprüfen, erfolgte nach Präparation von Sehnenstreifen die Besiedlung mit equinen MSC mit Kontrolle des Besiedlungserfolges. Materialien und Methoden: Oberflächliche und tiefe Beugesehnen (OBS und TBS) des Pferdes (n = 6) wurden nach vier verschiedenen Protokollen dezellularisiert. In zwei Protokollen (Protokolle A und B) erfolgte zunächst die Anwendung von Gefrier-Auftau- Zyklen mit anschließender Lagerung in hypertoner Lösung. Protokoll A sah danach eine Inkubation in 1 % Triton X 100 und Protokoll B eine Inkubation in 1 % Sodium-Dodecyl-Sulfat (SDS) enthaltender Lösung vor. Die beiden anderen Protokolle (Protokolle C und D) sahen ein Verbringen in hypertone Lösung ohne vorherige Gefrierzyklen vor. Anschließend erfolgte bei Protokoll C die Inkubation in Triton X 100 und bei Protokoll D die Inkubation in SDS enthaltender Lösung. Die Effektivität der angewandten Dezellularisierungsprotokolle wurde durch histologischer Färbung, Zellzählung nach Kollagenaseverdau, DNA-Quantifizierung und transmissionselektronenmikroskopischer Untersuchung ermittelt. Nach Evaluierung der Effektivität der Protokolle wurden oberflächliche Beugesehnen nach den Protokollen A und B dezellularisiert (n=3). Nach Präparation von Sehnenstreifen in definierter Größe erfolgte die Besiedelung mit Eisenoxid-markierten equinen MSC. Der Besiedlungserfolg wurde mit verschiedenen histologischen und Fluoreszenzfärbungen (Fluoreszenzmikroskopie) und MRT-Untersuchung kontrolliert. Die Prüfung auf statistische Unterschiede zwischen den Protokollen erfolgte mit dem Friedman-Test und im Falle eines statistisch signifikanten Unterschieds mit dem Wilcoxon-Rang-Test. Das Signifikanzniveau wurde mit p < 0,05 festgelegt. Die Auswertung des Besiedlungserfolges erfolgte deskriptiv. Ergebnisse: Für alle angewandten Protokolle konnte ein signifikanter Dezellularisie-rungseffekt in beiden Sehnenstrukturen (OBS und TBS) gezeigt werden. Die Anzahl der vitalen Zellen nach Kollagenaseverdau sowie die histologisch ermittelte Zellzahl der dezellularisierten Sehnen belief sich in Abhängigkeit des jeweiligen Dezellularisie-rungsprotokolls und der Sehne (OBS und TBS) auf 1 bis 21 % (Median) des nativen Gewebes. Der ermittelte DNA-Gehalt nach Anwendung der mit Gefrier-Auftau-Zyklen kombinierten Protokollen A und B entsprach < 24 % (Median) des nativen Gewebes. Die Anwendung der Protokolle C und D führte zu einem DNA-Gehalt von < 47 % (Median). Die Auswertung der transmissionselektronenmikroskopischen Untersuchung zeigte ebenfalls eine effektive Dezellularisierung des Sehnengewebes bei Erhalt der Struktur der extra-zellulären Matrix. Nach Anwendung der Protokolle A und B konnte wiederum tendenziell eine bessere Effektivität der Dezellularisierung festgestellt werden. Eine gelungene Besiedlung der Sehnenstreifen mit equinen MSC konnte anhand der mikroskopischen Untersuchung und MRT-Untersuchung gezeigt werden. Das beobachtete Zellwachstum bei beibehaltender Vitalität der Zellen sprechen für eine gute Zytokompatibilität. Die nach Protokoll A dezellularisierten und besiedelten Sehnenstreifen ließen ein besseres Zellwachstum über eine Kulturdauer von 14 Tagen erkennen. In der vorliegenden Arbeit konnte eine effektive Dezellularisierung von intakten equinen Beugesehnen gezeigt werden. Anhand der Ergebnisse der Besiedlung erwies sich die Dezellularisierung nach Protokoll A (Gefrier-Auftau-Zyklen und Triton X 100) als vielversprechende Grundlage zur Entwicklung eins in vitro Modells auf Grundlage dezellularisierter equiner Beugesehnen.

As células de pluripotência induzida (iPS) foram reportadas pela primeira vez em 2006 por Takahashi e Yamanaka e desde então vem sendo extensivamente estudadas. Por meio da técnica, células somáticas adultas adquirem comportamento muito semelhante às células tronco embrionárias, reduzindo as questões éticas relacionadas ao uso destas em pesquisas. Entretanto, os mecanismos biológicos das células iPS ainda não estão completamente elucidados. Ainda são necessárias pesquisas mais aprofundadas para garantir a segurança e eficácia de sua possível utilização em futuras terapias. Os coelhos, como modelos experimentais, são vantajosos tanto pelo seu tamanho ideal para procedimentos cirúrgicos quanto por sua manutenção fácil e econômica. As células tronco derivadas do tecido adiposo (ADSC) consistem em um tipo de célula tronco mesenquimal multipotente que se destaca pela facilidade, rapidez e segurança de coleta e processamento. As ADSC foram coletadas e caracterizadas por meio de análises de curva de crescimento celular, doubling time, viabilidade após criopreservação, capacidade de formação de colônias fibroblastoides, diferenciação osteogênica, condrogênica e adipogênica, imunocitoquímica e citometria de fluxo. Elas demonstraram possuir as características básicas de células tronco mesenquimais, destacando-se por uma alta e rápida capacidade proliferativa. A indução de pluripotência foi realizada nas ADSC de coelhos pela introdução de quatro fatores de transcrição (OCT4, SOX2, cMYC, e KLF4), pelo vetor lentiviral STEMCCA (Milipore). Cinco protocolos de indução foram testados. Células resultantes da indução foram caracterizadas quanto à atividade da fosfatase alcalina e perfil fenotípico por citometria de fluxo. A proliferação acentuada das ADSC parece ser um fator limitante para a eficácia da reprogramação. A partir destes dados, espera-se contribuir para o desenvolvimento de uma tecnologia brasileira ainda inédita em coelhos e adicionar informações importantes à literatura, acerca das propriedades das células iPS, visando sua utilização como modelo experimental para futuras terapias. / Induced Pluripotent Stem (iPS) cells were first reported in 2006 by Takahashi e Yamanaka and has been intensively studied since then. Through the technique, adult somatic cells acquire behavior very similar to embryonic stem cells, reducing the ethical issues related to the use of such research. However, biological mechanisms of iPS cells are not yet fully elucidated. Thus, further research is needed to ensure the safety and efficacy for their possible use in future therapies. Rabbits, as experimental models, are advantageous by their ideal size for surgical procedures and easy and economic maintenance. Adipose Derived Stem Cells (ADSC) consists of multipotent mesenchymal stem cells that stand for ease, speed and safety of collection and processing. The ADSC were collected and characterized by analysis of cell growth curve, doubling time, viability after cryopreservation, ability of fibroblast colony formation, osteogenic, adipogenic and chondrogenic differentiation, immunocytochemistry and flow cytometry. They showed to have the basic characteristics of mesenchymal stem cells, standing out by a high and fast proliferative capacity. Induction of pluripotency was performed in rabbits ADSC by the introduction of four transcription factors (OCT4, SOX2, cMYC, and KLF4) by lentiviral vector STEMCCA (Millipore). Five protocols were tested and analyzed. The resulting cells after induction were characterized by alkaline phosphatase activity and phenotypic profile by flow cytometry. The great proliferation of ADSC seems to be detrimental for the reprogramming efficiency. From these data, it is expected to contribute to the development of a Brazilian technology still unpublished in rabbits, and to add important information to the literature about the properties of iPS cells, aiming their use as an experimental model for future therapies.