We analyze a possible minimal counterexample to theJacobian Conjecture P;Q with gcd(deg(P); deg(Q)) = 16 and show that its existence depends only on the existence of solutions for a certain Abel dierential equation of the second kind. / Analizamos un posible contraejemplo P;Q a la conjetura del jacobiano con gcd(deg(P); deg(Q)) = 16 y mostramos que su existencia depende exclusivamente de la existencia de soluciones de una cierta ecuacion diferencial de Abel de segundo tipo.

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.

As características das células estromais mesenquimais multipotentes (MSC) podem ser influenciadas em microambientes inflamatórios. No entanto, o comportamento das MSC frente às infecções virais e a exata contribuição da infecção para disfunção das MSC continuam a ser elucidadas. Neste trabalho, avaliamos o efeito imunossupressor de MSC em linfócitos T infectados pelo HTLV-1 e a susceptibilidade da MSC à infecção por este retrovírus. Os ensaios de co-cultivo utilizando MSC e linhagens de linfócitos infectados pelo HTLV-1 resultaram em diminuição na expressão do gene viral tax e do antígeno p19 do HTLV-1. A redução na expressão do gene tax e da proteína p19 foi relacionada com a maior secreção de IL-6 e aumento na expressão dos genes PGE2, IDO e VCAM-1. Para confirmar a influência da imunorregulação das MSC sobre linfócitos T infectados, comparamos a proliferação de linfócitos T isolados de indivíduos infectados pelo HTLV-1 e indivíduos controles cultivados na presença de MSC. Foi observado que as MSC inibem a linfoproliferação de forma similar em amostras controle e na infecção pelo HTLV-1; e este efeito foi mediado pela expressão de PGE2 e IDO. Além disso, a expressão do gene pol e da proteína p19 do HTLV-1 foi menor após o co-cultivo com MSC, indicando que a imunorregulação pelas MSC também atua nas células infectadas pelo HTLV-1. Em seguida, para investigar as alterações provocadas pelo HTLV-1 nas MSC, realizamos análises morfológicas e ultraestruturais em MSC expostas ao HTLV-1 in vitro. Os resultados revelaram que o HTLV-1 induziu o aparecimento de vesículas intracelulares e a expressão das moléculas de superfície VCAM-1, ICAM-1 e HLA-DR. Os níveis de VCAM-1 e HLA-DR também foram mais expressos em MSC cultivadas na presença de PBMC isoladas de indivíduos HAM/TSP. O HTLV-1 não alterou o processo de diferenciação das MSC em osteócitos e adipócitos. No entanto, o contato direto in vitro das MSC com células infectadas pelo HTLV-1 proporcionou uma eficiente infecção das MSC. As partículas virais isentas de células não foram capazes de causar a infecção em MSC. Por fim, para certificar a existência biológica de MSC infectadas pelo HTLV-1, avaliamos a medula óssea de seis indivíduos acometidos por esta infecção. Foi observado um infiltrado de linfócitos T CD4+ na medula óssea de indivíduos HTLV-1+ e a análise do DNA proviral revelou a presença do provírus integrado nessas células T CD4+. O número de unidades formadoras de colônia fibroblastóide (CFU-F) foi menor em indivíduos infectados pelo HTLV-1 quando comparado com o grupo controle. A expressão dos marcadores de superfície e o potencial de diferenciação in vitro em adipócitos e osteócitos foram similares nas MSC obtidas de indivíduos HTLV-1 e indivíduos controle. Foi demonstrada a presença do DNA proviral e da proteína p19 do HTLV-1 nas MSC isoladas de pacientes HTLV-1+. A comparação do perfil de expressão gênica global entre MSC isoladas de HAM/TSP e indivíduos assintomáticos para o HTLV-1 revelou que os genes da catepsina B e da proteína ribossomal L10 foram diferencialmente expressos. Em conclusão, este trabalho demonstra a importância das MSC na imunomodulação de linfócitos infectados pelo HTLV-1 e que a infecção pelo HTLV-1 altera características biológicas das MSC. / The characteristics of human multipotent mesenchymal stromal cells (MSC) can be influenced by the inflammatory microenvironment. However, the activity of the MSC against viral infections and the exact contribution of the infection to MSC dysfunction remain to be elucidated. We evaluated the immunosuppressive effect of MSC on HTLV-1 infected T lymphocytes and the susceptibility of MSC for this retroviral infection. Assays using co-culture of MSC and HTLV-1+ T lymphocyte lineages resulted in a decrease of tax gene expression and HTLV-1 p19 antigen. The reduction of the tax gene expression and the HTLV-1 p19 were associated with increased IL-6 secretion and higher PGE2, IDO and VCAM-1 gene expression. To confirm if MSC immunoregulation can influence the proliferation of HTLV-1 infected T lymphocytes, we compared the proliferation of HTLV-1+ individuals and healthy individuals cultured in the presence of MSC. It was observed that the lymphoproliferative inhibition by MSC in infected lymphocytes was similar to the control cells, and this effect was mediated by the expression of IDO and PGE2 genes. Furthermore, the pol gene and the HTLV-1 p19 protein were less expressed after co-culture assay with MSC, suggesting that the immunoregulation by MSC is effective in HTLV-1 infected T cells. In order to investigate the changes caused by HTLV-1 in MSC, we performed morphological and ultrastructural analysis of MSC exposed to HTLV-1 in vitro. The contact with HTLV-1 induced an increase of the intracellular vesicles, in addition the MSC cell surface molecules VCAM-1, ICAM-1 and HLA-DR were upregulated. The expression levels of VCAM-1 and HLA-DR molecules were increased in MSC cultured in the presence of PBMC isolated from HTLV-1 associated myelopathy/tropical spastic paraparesis (HAM/TSP) individuals. The MSC differentiation process into osteocytes and adipocytes was not impaired by HTLV-1. In addition, MSCs were efficiently infected by HTLV-1 in vitro due to the direct contact with the HTLV-1-infected cells. However, cell-free virus particles were not capable of causing productive infection. Finally, to ensure the biological function of MSC in HTLV-1 infected patients, we investigated bone marrow (BM) cells from HTLV-1 asymptomatic carriers (HAC) and HAM/TSP individuals. Initially, we observed an infiltration of CD4+ T-cell lymphocytes in BM from HTLV-1 infected individuals and the detection of provirus revealed HTLV-1 integration. The number of colonies of fibroblast progenitor cells (CFU-F) was lower in HTLV-1 infected individuals compared to control. HTLV-1 MSC isolated showed surface molecules expression and differentiation into adipogenic and osteogenic cells similar to control MSC. Proviral DNA and HTLV-1 p19 protein were detected in MSC from HTLV-1 patients. The comparison of global gene expression profiles between MSC isolated from HAM/TSP and HAC individuals revealed that cathepsin B and ribosomal protein L10 were differentially expressed. In conclusion, this study suggests the importance of MSC immunomodulation on HTLV-1 infected T lymphocytes and describe that HTLV-1 infects and alters the biological characteristics of MSC.

The paper describes a storage scheme for sparse symmetric or nonsymmetric matrices which has been developed and used for many years at the Technical University of Chemnitz. An overview of existing library subroutines using such matrices is included.

A perturbation analysis shows that if a numerically stable procedure is used to compute the matrix sign function, then it is competitive with conventional methods for computing invariant subspaces. Stability analysis of the Newton iteration improves an earlier result of Byers and confirms that ill-conditioned iterates may cause numerical instability. Numerical examples demonstrate the theoretical results.

A parallel realisation of the Conjugate Gradient Method with Schur-Complement preconditioning, based on a domain decomposition approach, is described in detail. Special kinds of solvers for the resulting interiour and coupling systems are presented. A large range of numerical results is used to demonstrate the properties and behaviour of this solvers in practical situations.

Adaptive finite element methods for the solution of partial differential equations require effective methods of mesh refinement and coarsening, fast multilevel solvers for the systems of FE equations need a hierarchical structure of the grid. In the paper a technology is presented for the application of irregular hierarchical triangular meshes arising from refinement by only dividing elements into four congruent triangles. The paper describes the necessary data structures and data structure management, the principles and algorithms of refining and coarsening the mesh, and also a specific assembly technique for the FE equations system. Aspects of the parallel implementation on MIMD computers with a message passing communication are included.

The purpose of this paper is to supply a summary of library subroutines and functions for parallel MIMD computers. The subroutines have been developed at the University of Chemnitz during a period of the last five years. In detail, they are concerned with vector operations, inter-processor communication and simple graphic output to workstations. One of the most valuable features is the machine-independence of the communication subroutines proposed in this paper for a hypercube topology of the parallel processors (excepting a kernel of only two primitive system-dependend operations). They were implemented and tested for different hardware and operating systems including transputer, nCube, KSR, PVM. The vector subroutines are optimized by the use of C language and enrolled loops (BLAS1-like). The paper includes hints for using the libraries with both Fortran and C programs.

Three-dimensional basic problems of statics, pseudo-oscillations, general dynamics and steady state oscillations of the thermoelasticity of isotropic bodies have been completely investigated by many authors. In particular, exterior steady state oscillation problems have been studied on the basis of Sommerfeld-Kupradze radiation conditions in the thermoelasticity, and the uniqueness theorems were proved with the help of the well-known Rellich's lemma, since the components of the displacement vector and the temperature in the isotropic case can be represented as a sum of metaharmonic functions . Unfortunately, the methods of investigation of thermoelastic steady state oscillation problems developed for the isotropic case are not applicable in the case of general anisotropy. This is stipulated by a very complicated form of the corresponding characteristic equation which plays a significant role in the study of far field behaviour of solutions to the oscillation equa- tions. We note that the basic and crack type boundary value problems (BVPs) for the pseudo-oscillation equations of the thermoelasticity theory in the anisotropic case are considered in [3,14]. To the best of the authors' knowledge the problems of thermoelastic steady oscillations for anisotropic bodies have not been treated in the scientific literature. In the present paper we will consider a wide class of basic and mixed type BVPs for the equations of thermoelastic steady state oscillations. We will formulate thermoelastic radiation conditions for an anisotropic medium (the generalized Sommerfeld-Kupradze type radiation conditions) and prove the uniqueness theorems in corresponding spaces. To derive these conditions we have essentially applied results of Vainberg. Further, using the potential method and the theory of pseudodifferential equations on manifolds we will prove existence theorems in various functional spaces and establish the smoothness properties of solutions.

Parmi les différents isotopes du Scandium qui peuvent être utilisés en médecine nucléaire, on peut citer le ⁴⁷Sc et le ⁴⁴Sc. Le premier se désintègre en émettant un électron associé à un gamma de 159 keV et peut donc être utilisé soit pour faire de la radiothérapie, soit de l’imagerie TEMP. Le ⁴⁴Sc (3.97 h) se désintègre dans 94.27 % des cas en émettant un positron, accompagné d’un photon γ d’énergie égale à 1.157 MeV. Cet isotope est alors un candidat idéal pour des applications en imagerie TEP. Actuellement, le Cyclotron de haute énergie et haute intensité Arronax produit le ⁴⁴Sc et coproduit son état isomérique le ⁴⁴mSc (2.44 j). Le ⁴⁴mSc a des propriétés (Eᵧ=270 keV, 98.8 %) qui permet d’envisager son utilisation comme potentiel générateur in vivo. Les travaux précédents ont permis de montrer que le ligand DOTA est le plus adapté et le plus stable pour le Sc. Ce travail de thèse a pour but de mettre en évidence la faisabilité du générateur in vivo ⁴⁴m/⁴⁴Sc. Dans un premier temps une procédure a été optimisée et validée pour la production du ⁴⁴m/⁴⁴Sc avec une haute activité spécifique et pureté chimique. Le radiomarquage sur des peptides contenant du DOTA a été ensuite développé et optimisé. Des études théoriques et expérimentales ont été réalisées dans le but de démontrer la faisabilité du ⁴⁴m/⁴⁴Sc comme potentiel générateur in vivo. En fin des études de stabilité in vitro sur des complexes radiomarqués du ⁴⁴m/⁴⁴Sc suivi d’études de biodistribution et d’imagerie TEP ont été réalisées. / Among the different isotopes of Scandium that can be used in nuclear medicine may be mentioned the ⁴⁷Sc and ⁴⁴Sc. The first decays by emitting an electron associated with a 159 keV gamma can thus be used either for radiotherapy or TEMP imaging. The ⁴⁴Sc (3.97 h) decays in 94.27% in case by emitting a positron, with a γ photon energy equal to 1.157 MeV. This isotope is then an ideal candidate for applications in PET imaging. Currently, the Cyclotron of high energy and high intensity ARRONAX produce ⁴⁴Sc and co-produces the isomeric state the ⁴⁴mSc(2.44 d). The ⁴⁴mSc has properties (Eᵧ = 270 keV, 98.8%), which allows to consider its use as a potential in vivo generator. Previous work had demonstrated that the DOTA ligand is most suitable and stable for Sc. This thesis aims; make in evidence the feasibility of the in vivo ⁴⁴m/⁴⁴Sc generator. Initially a procedure was optimized and validated for the production of ⁴⁴m/⁴⁴Sc with a high specific activity and chemical purity. Radiolabeling of DOTA conjugated peptides was then developed and optimized. Theoretical and experimental studies have been performed in order to demonstrate the feasibility of ⁴⁴m/⁴⁴Sc as a potential in vivo generator. Finally, in vitro stability studies on radiolabeled ⁴⁴m / ⁴⁴Sc complexes were performed, followed by biodistribution studies and PET imaging.