Problema di Cauchy-Dirichlet per l'equazione del calore di una sbarra omogenea

In questa tesi vengono forniti risultati sulle serie di Fourier e successivamente sulle serie di Fejér, utili per poter analizzare il cosiddetto problema di Cauchy-Dirichlet per l'equazione del calore di una sbarra omogenea. Lo scopo è trovare soluzioni classiche del problema che presenta come dato iniziale dapprima una funzione di classe C^1 e successivamente una funzione solamente continua.

An isolated, surface-expressed I domain of the integrin αLβ2 is sufficient for strong adhesive function when locked in the open conformation with a disulfide bond

We introduced disulfide bonds to lock the integrin αLβ2 I domain in predicted open, ligand binding or closed, nonbinding conformations. Transfectants expressing αLβ2 heterodimers containing locked-open but not locked-closed or wild-type I domains constitutively adhered to intercellular adhesion molecule-1 (ICAM-1) substrates. Locking the I domain closed abolished constitutive and activatable adhesion. The isolated locked-open I domain bound as well as the activated αLβ2 heterodimer, and binding was abolished by reduction of the disulfide. Lovastatin, which binds under the conformationally mobile C-terminal α-helix of the I domain, inhibited binding to ICAM-1 by αLβ2 with wild-type, but not locked-open I domains. These data establish the importance of conformational change in the αL I domain for adhesive function and show that this domain is sufficient for full adhesive activity.

Antioxidative function of L-FABP in L-FABP stably transfected Chang liver cells

Liver fatty acid binding protein (L-FABP) contains amino acids that are known to possess antioxidant function. In this study, we tested the hypothesis that L-FABP may serve as an effective endogenous cytoprotectant against oxidative stress. Chang liver cells were selected as the experimental model because of their undetectable L-FABP mRNA level. Full-length L-FABP cDNA was subcloned into the mammalian expression vector pcDNA3.1 (pcDNA-FABP). Chang cells were stably transfected with pc-DNA-FABP or vector (pcDNA3.1) alone. Oxidative stress was induced by incubating cells with 400 mu mol/L H2O2 or by subjecting cells to hypoxia/reoxygenation. Total cellular reactive oxygen species (ROS) was determined using the fluorescent probe DCF. Cellular damage induced by hypoxia/reoxygenation was assayed by lactate dehydrogenase (LDH) release. Expression of L-FABP was documented by regular reverse transcription polyrnerase chain reaction (RT-PCR), real-time RT-PCR, and Western blot. The pcDNA-FABP-transfected cells expressed full-length L-FABP mRNA, which was absent from vector-transfected control cells. Western blot showed expression of 14-kd L-FABP protein in pcDNA-FABP-transfected cells, but not in vector-transfected cells. Transfected cells showed decreased DCF fluorescence intensity under oxidative stress (H2O2 and hypoxia/reoxygenation) conditions versus control in inverse proportion to the level of L-FABP expression. Lower LDH release was observed in the higher L-FABP-expressed cells in hypoxia/reoxygenation experiments. In conclusion, we successfully transfected and cloned a Chang liver cell line that expressed the L-FABP gene. The L-FABP-expressing cell line had a reduced intracellular ROS level versus control. This finding implies that L-FABP has a significant role in oxidative stress.

Functional-structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function

This paper presents a new method for producing a functional-structural plant model that simulates response to different growth conditions, yet does not require detailed knowledge of underlying physiology. The example used to present this method is the modelling of the mountain birch tree. This new functional-structural modelling approach is based on linking an L-system representation of the dynamic structure of the plant with a canonical mathematical model of plant function. Growth indicated by the canonical model is allocated to the structural model according to probabilistic growth rules, such as rules for the placement and length of new shoots, which were derived from an analysis of architectural data. The main advantage of the approach is that it is relatively simple compared to the prevalent process-based functional-structural plant models and does not require a detailed understanding of underlying physiological processes, yet it is able to capture important aspects of plant function and adaptability, unlike simple empirical models. This approach, combining canonical modelling, architectural analysis and L-systems, thus fills the important role of providing an intermediate level of abstraction between the two extremes of deeply mechanistic process-based modelling and purely empirical modelling. We also investigated the relative importance of various aspects of this integrated modelling approach by analysing the sensitivity of the standard birch model to a number of variations in its parameters, functions and algorithms. The results show that using light as the sole factor determining the structural location of new growth gives satisfactory results. Including the influence of additional regulating factors made little difference to global characteristics of the emergent architecture. Changing the form of the probability functions and using alternative methods for choosing the sites of new growth also had little effect. (c) 2004 Elsevier B.V. All rights reserved.

Solvability of singular second order m-point boundary value problems of Dirichlet type

Let f : [0, 1] x R2 -> R be a function satisfying the Caxatheodory conditions and t(1 - t)e(t) epsilon L-1 (0, 1). Let a(i) epsilon R and xi(i) (0, 1) for i = 1,..., m - 2 where 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1 - In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem [GRAPHICS] The proof of our main result is based on the Leray-Schauder continuation theorem.

L-arginine improves cardiovascular function in DOCA-salt hypertensive rats

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Problema di Cauchy-Dirichlet per l'equazione del calore

In quest'elaborato si risolve il problema di Cauchy-Dirichlet per l'equazione del calore, prendendo come oggetto d'esame una sbarra omogenea. Nel primo capitolo si studiano le serie di Fourier reali a partire dalle serie trigonometriche; vengono dati, poi, i principali risultati di convergenza puntuale, uniforme ed in L^2 e si discute l'integrabilità termine a termine di una serie di Fourier. Il secondo capitolo tratta la convergenza secondo Cesàro, le serie di Fejèr ed i principali risultati di convergenza di queste ultime. Nel terzo, ed ultimo, capitolo si risolve il Problema di Cauchy-Dirichlet, distinguendo i casi in cui il dato iniziale sia di classe C^1 o solo continuo; nel secondo caso si propone una risoluzione basata sulle serie di Fejér e sul concetto di barriera ed una utilizzando il nucleo di Green per l'equazione del calore.

Mathematical modelling of muscle recruitment and function in the lumbar spine

Low back pain is an increasing problem in industrialised countries and although it is a major socio-economic problem in terms of medical costs and lost productivity, relatively little is known about the processes underlying the development of the condition. This is in part due to the complex interactions between bone, muscle, nerves and other soft tissues of the spine, and the fact that direct observation and/or measurement of the human spine is not possible using non-invasive techniques. Biomechanical models have been used extensively to estimate the forces and moments experienced by the spine. These models provide a means of estimating the internal parameters which can not be measured directly. However, application of most of the models currently available is restricted to tasks resembling those for which the model was designed due to the simplified representation of the anatomy. The aim of this research was to develop a biomechanical model to investigate the changes in forces and moments which are induced by muscle injury. In order to accurately simulate muscle injuries a detailed quasi-static three dimensional model representing the anatomy of the lumbar spine was developed. This model includes the nine major force generating muscles of the region (erector spinae, comprising the longissimus thoracis and iliocostalis lumborum; multifidus; quadratus lumborum; latissimus dorsi; transverse abdominis; internal oblique and external oblique), as well as the thoracolumbar fascia through which the transverse abdominis and parts of the internal oblique and latissimus dorsi muscles attach to the spine. The muscles included in the model have been represented using 170 muscle fascicles each having their own force generating characteristics and lines of action. Particular attention has been paid to ensuring the muscle lines of action are anatomically realistic, particularly for muscles which have broad attachments (e.g. internal and external obliques), muscles which attach to the spine via the thoracolumbar fascia (e.g. transverse abdominis), and muscles whose paths are altered by bony constraints such as the rib cage (e.g. iliocostalis lumborum pars thoracis and parts of the longissimus thoracis pars thoracis). In this endeavour, a separate sub-model which accounts for the shape of the torso by modelling it as a series of ellipses has been developed to model the lines of action of the oblique muscles. Likewise, a separate sub-model of the thoracolumbar fascia has also been developed which accounts for the middle and posterior layers of the fascia, and ensures that the line of action of the posterior layer is related to the size and shape of the erector spinae muscle. Published muscle activation data are used to enable the model to predict the maximum forces and moments that may be generated by the muscles. These predictions are validated against published experimental studies reporting maximum isometric moments for a variety of exertions. The model performs well for fiexion, extension and lateral bend exertions, but underpredicts the axial twist moments that may be developed. This discrepancy is most likely the result of differences between the experimental methodology and the modelled task. The application of the model is illustrated using examples of muscle injuries created by surgical procedures. The three examples used represent a posterior surgical approach to the spine, an anterior approach to the spine and uni-lateral total hip replacement surgery. Although the three examples simulate different muscle injuries, all demonstrate the production of significant asymmetrical moments and/or reduced joint compression following surgical intervention. This result has implications for patient rehabilitation and the potential for further injury to the spine. The development and application of the model has highlighted a number of areas where current knowledge is deficient. These include muscle activation levels for tasks in postures other than upright standing, changes in spinal kinematics following surgical procedures such as spinal fusion or fixation, and a general lack of understanding of how the body adjusts to muscle injuries with respect to muscle activation patterns and levels, rate of recovery from temporary injuries and compensatory actions by other muscles. Thus the comprehensive and innovative anatomical model which has been developed not only provides a tool to predict the forces and moments experienced by the intervertebral joints of the spine, but also highlights areas where further clinical research is required.

Androgen-regulated genes differentially modulated by the androgen receptor coactivator L-dopa decarboxylase in human prostate cancer cells

Background The androgen receptor is a ligand-induced transcriptional factor, which plays an important role in normal development of the prostate as well as in the progression of prostate cancer to a hormone refractory state. We previously reported the identification of a novel AR coactivator protein, L-dopa decarboxylase (DDC), which can act at the cytoplasmic level to enhance AR activity. We have also shown that DDC is a neuroendocrine (NE) marker of prostate cancer and that its expression is increased after hormone-ablation therapy and progression to androgen independence. In the present study, we generated tetracycline-inducible LNCaP-DDC prostate cancer stable cells to identify DDC downstream target genes by oligonucleotide microarray analysis. Results Comparison of induced DDC overexpressing cells versus non-induced control cell lines revealed a number of changes in the expression of androgen-regulated transcripts encoding proteins with a variety of molecular functions, including signal transduction, binding and catalytic activities. There were a total of 35 differentially expressed genes, 25 up-regulated and 10 down-regulated, in the DDC overexpressing cell line. In particular, we found a well-known androgen induced gene, TMEPAI, which wasup-regulated in DDC overexpressing cells, supporting its known co-activation function. In addition, DDC also further augmented the transcriptional repression function of AR for a subset of androgen-repressed genes. Changes in cellular gene transcription detected by microarray analysis were confirmed for selected genes by quantitative real-time RT-PCR. Conclusion Taken together, our results provide evidence for linking DDC action with AR signaling, which may be important for orchestrating molecular changes responsible for prostate cancer progression.