Τα τελευταία χρόνια, γίνεται πολύς λόγος για τους καρκινικούς όγκους, καθώς η νόσος αυτή προσβάλλει ολοένα και περισσότερα άτομα κάθε χρόνο. Ιδιαίτερη βαρύτητα έχει δοθεί τόσο ερευνητικά όσο και ιατρικά στην αντιμετώπιση του καρκίνου μέσω θεραπευτικών τεχνικών (χημειοθεραπείες, χειρουργικές επεμβάσεις κλπ) καθώς και στην βελτίωση των συνθηκών διαβίωσης των καρκινοπαθών. Επίσης, αρκετή έμφαση στην έρευνα σχετικά με την ανάπτυξη του καρκίνου σε βιοχημικό επίπεδο και για την βαθύτερη κατανόηση της νόσου. Η έρευνα αφορά ερευνητές πολλών διαφορετικών ειδικοτήτων μεταξύ των οποίων και των μαθηματικών. Από το 1954 με την πρόταση των Armitage και Doll σχετικά με την μαθηματική μοντελοποίηση της γένεσης των καρκινικών όγκων, αρκετοί έχουν ασχοληθεί με την μαθηματική προτυποποίηση των διαφόρων φάσεων του καρκίνου, από την δημιουργία του μέχρι και την αντίσταση του σε φαρμακευτική αγωγή. Η εργασία αυτή πραγματεύεται την μαθηματική θεμελίωση και προτυποποίηση των καρκινικών όγκων όσον αφορά την γεωμετρική τους ανάπτυξη. Με βάση το θεμελιώδες μαθηματικό μοντέλο που προτάθηκε το 1976 από τον H. P. Greenspan, μελετάται η επίπτωση επιφανειακών διαταραχών στην ανάπτυξη σφαιρικών καθώς και ελλειψοειδών όγκων. Στην πρωτότυπη εργασία, η μελέτη περιορίστηκε στην ανάλυση των διαταραχών με μεταβλητή την πολική γωνία των σφαιρικών συντεταγμένων. Στην εργασία αυτή αρχικά μελετάται η γενίκευση του μοντέλου διαταραχών και στις δυο γωνίες του σφαιρικού συστήματος συντεταγμένων (πολική θ και αζιμουθιακή φ). Στην συνέχεια επεκτείνεται η μέθοδος σε τρία μοντέλα που γενικεύουν τις παραδοχές του αρχικού μοντέλου διατηρώντας την παραδοχή της σφαιρικής γεωμετρίας και μελετάται η ευστάθεια των αντίστοιχων επιφανειακών διαταραχών. Τέλος, μελετάται και η ευστάθεια του ίδιου προβλήματος στην ελλειψοειδή γεωμετρία επειδή η ανισοτροπία του ελλειψοειδούς σχήματος καθιστά πιο ρεαλιστική την προσέγγιση του πραγματικού σχήματος του καρκινικού όγκου. / The mathematical analysis of the tumour growth attracted a lot of interest in the last two decades. However, as of today no generally accepted model for tumour growth exists. This is due partially to the incomplete understanding of the related pathology as well as the extremely complicated procedure that guides the evolution of a tumour. Moreover, the growth of a tumour does depend on the available tissue surrounding the tumour and therefore it represents a physical case that is realistically modelled by ellipsoidal geometry. The remarkable aspect of the ellipsoidal shape is that it represents the sphere of the anisotropic space. It provides the appropriate geometrical model for any direction dependent physical quantity. In the present work we analyze the stability of a spherical tumour for four continuous models of an avascular tumour and the stability study of an ellipsoidal tumour. For all five models, conditions for the stability are stated and the results are implemented numerically. For the spherical cases, it is observed that the steady state radii that secure the stability of the tumour are different for each of the four models, and that results to differences in the stable and unstable modes. As for the ellipsoidal model, it is shown that, in contrast to the highly symmetric spherical case, where stability is possible to be achieved, there are no conditions that secure the stability of an ellipsoidal tumour. Hence, as in many physical cases, the observed instability is a consequence of the lack of symmetry.

Σκοπός της παρούσας Διατριβής Ειδίκευσης είναι η παρακολούθηση του κατολισθητικού φαινομένου του οικισμού Καρυάς του Δήμου Πατρέων, με μετρήσεις αποκλισιομέτρων ώστε να προσδιοριστεί ποσοτικά ο ρυθμός μετακίνησης της περιοχής μελέτης και να εξαχθούν συμπεράσματα για την μελλοντική του εξέλιξη, όπως καθορίζεται μέσω αναλύσεων ευστάθειας πρανών. Η εν λόγω περιοχή παρουσιάζει αξιόλογο ενδιαφέρον, λόγω των ιδιαίτερων και σύνθετων γεωλογικών συνθηκών, των συχνών και σημαντικών κατολισθητικών φαινομένων των τελευταίων ετών που προκάλεσαν σημαντικές καταστροφές σε τεχνικά έργα και ανθρώπινες περιουσίες. Στα πλαίσια της Διατριβής και της παράλληλης Έρευνας του Εργαστηρίου Τεχνικής Γεωλογίας στην περιοχή ενδιαφέροντος πραγματοποιήθηκε λεπτομερής γεωτεχνική έρευνα που περιελάμβανε ανόρυξη δειγματοληπτικών γεωτρήσεων σε επιλεγμένες θέσεις με ταυτόχρονη τοποθέτηση αποκλισιομέτρων, συστηματική λήψη αποκλισιομετρικών μετρήσεων, σειρά εργαστηριακών και επί τόπου δοκιμών σε κατάλληλα διαμορφωμένα δείγματα, λεπτομερή καταγραφή των τεχνικογεωλογικών συνθηκών της περιοχής με βάση κυρίως τη σύσταση, τη δομή των γεωλογικών σχηματισμών. Έγινε διάκριση των σχηματισμών της περιοχής έρευνας σε επιμέρους Γεωτεχνικές Ενότητες και σχεδιάστηκαν αντιπροσωπευτικές γεωτεχνικές – τεχνικογεωλογικές διατομές με σκοπό τη σύνθεση και ερμηνεία του γεωτεχνικού περιβάλλοντος της περιοχής. Παράλληλα πραγματοποιήθηκαν αναλύσεις ευστάθειας πρανών με χρήση εξειδικευμένου λογισμικού σε επιλεγμένες διατομές κατά μήκος των γεωτρήσεων στην κατολισθαίνουσα ζώνη Καρυάς. Σκοπός των αναλύσεων ευστάθειας πρανών ήταν να γίνει εκτίμηση πιθανών μετακινήσεων σε επιλεγμένα σημεία της περιοχής έρευνας και να παρατηρηθεί εάν το είδος ολίσθησης εξακολουθεί να είναι το ίδιο με αυτό που είχε διαπιστωθεί κατά την τελευταία εκδήλωση του κατολισθητικού φαινομένου. / The Aim of this ΜSc. Project is the exploration of the landslide phenomeno in the region of Karya, Patras, Western Greece by inclinometer measurements in order to define quantitatively the movement rate of the study area and export conclusions on its future development, as it specified via slope stability analysis. The study area is an area with complex geological conditions and is well known especially for the important and large-scale landslide phenomena which have taken place during the last years near Karya village and caused important destructions in engineering works and human fortunes. This project was done along with survey of the Laboratory of Engineering Geology, Geology Department, University of Patras. The full survey program included geological mapping focused on the engineering properties of the soil and rock formations, fifteen (15) sampling boreholes, inclinometer installation and measurement and laboratory tests. Through laboratory testing and detailed description of soil and rock samples the formations were classified in several units and several geotechnical cross-sections were constructed to make a general geological-geotechnical model of the study area. The geological and geotechnical data were used to perform Limit Equilibrium Slope Stability analysis. The survey results were used to define probable movements of the study area and to establish the slipping type.

No description available.

The purpose of this thesis is to contribute to the methodology at the intersection of relational and evaluative bibliometrics. Experimental investigations are presented that address the question of how we can most successfully produce estimates of the subject similarity between documents. The results from these investigations are then explored in the context of citation-based research evaluations in an effort to enhance existing citation normalization methods that are used to enable comparisons of subject-disparate documents with respect to their relative impact or perceived utility. This thesis also suggests and explores an approach for revealing the uncertainty and stability (or lack thereof) coupled with different kinds of citation indicators.This suggestion is motivated by the specific nature of the bibliographic data and the data collection process utilized in citation-based evaluation studies. The results of these investigations suggest that similarity-detection methods that take a global view of the problem of identifying similar documents are more successful in solving the problem than conventional methods that are more local in scope. These results are important for all applications that require subject similarity estimates between documents. Here these insights are specifically adopted in an effort to create a novel citation normalization approach that – compared to current best practice – is more in tune with the idea of controlling for subject matter when thematically different documents are assessed with respect to impact or perceived utility. The normalization approach is flexible with respect to the size of the normalization baseline and enables a fuzzy partition of the scientific literature. It is shown that this approach is more successful than currently applied normalization approaches in reducing the variability in the observed citation distribution that stems from the variability in the articles’ addressed subject matter. In addition, the suggested approach can enhance the interpretability of normalized citation counts. Finally, the proposed method for assessing the stability of citation indicators stresses that small alterations that could be artifacts from the data collection and preparation steps can have a significant influence on the picture that is painted by the citationindicator. Therefore, providing stability intervals around derived indicators prevents unfounded conclusions that otherwise could have unwanted policy implications. Together, the new normalization approach and the method for assessing the stability of citation indicators have the potential to enable fairer bibliometric evaluative exercises and more cautious interpretations of citation indicators.

Superplastic forming (SPF) is a valuable near net shape fabrication method, used to produce very complex, contoured and monolithic structures that are often lighter, stronger and safer than the assemblies they replace. However, the widespread industrial use of Superplastic (SP) alloys is hindered by a number of issues including low production rate and limited predictive capabilities of stability during deformation and failure. Failure during SPD may result from geometrical macroscopic instabilities and/or microstructural aspects. However, the available failure criteria are either based on geometrical instabilities or microstructural features and do not account for both failure modes. The present study presents a generalized multi-scale stability criterion for SP materials, accounting for both aspects of failure under various loading conditions. A combined model accounting for cavity nucleation and plasticity controlled cavity growth along with a grain growth model and a modified microstructure based constitutive equation for SP materials is incorporated into Harts stability analysis to develop the proposed stability criterion for different loading conditions. Effects of initial grain size, initial levels of cavitation, nucleation strain, strain-rate sensitivity, and grain-growth exponent on the optimum forming curves of different SP alloys are investigated, for different loading conditions.

In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics of the instability as the perturbation growth rate omega and the cut-off wave number are studied as functions of key physical parameters.

Impulsive differential equations are useful for modelling certain biological events. We present three biological applications showing the use of impulsive differential equations in real-world problems. We also look at the effects of stability on a reduced two-dimensional impulsive HIV system. The first application is a system describing HIV induction-maintenance therapy, which shows how the solution to an impulsive system is used in order to find biological results (adherence, etc). A second application is an HIV system describing the interaction between T-cells, virus and drugs. Stability of the system is determined for a fixed drug level in three specific regions: low, intermediate and high drug levels. Numerical simulations show the effects of varying drug levels on the stability of a system by including an impulse. We reduce these two models to a two-dimensional impulsive model. We show analytically the existence and uniqueness of T-periodic solutions, and show how stability changes when varying the immune response rate, the impulses and a certain nonlinear infection term. The third application shows how seasonal changes can be incorporated into an impulsive differential system of Rift Valley Fever, and looks at how stability may differ when impulses are included. The analysis of impulsive differential systems is crucial in developing more realistic mathematical models for infectious diseases.

abstract: The primary focus of this dissertation lies in extremal combinatorics, in particular intersection theorems in finite set theory. A seminal result in the area is the theorem of Erdos, Ko and Rado which finds the upper bound on the size of an intersecting family of subsets of an n-element set and characterizes the structure of families which attain this upper bound. A major portion of this dissertation focuses on a recent generalization of the Erdos--Ko--Rado theorem which considers intersecting families of independent sets in graphs. An intersection theorem is proved for a large class of graphs, namely chordal graphs which satisfy an additional condition and similar problems are considered for trees, bipartite graphs and other special classes. A similar extension is also formulated for cross-intersecting families and results are proved for chordal graphs and cycles. A well-known generalization of the EKR theorem for k-wise intersecting families due to Frankl is also considered. A stability version of Frankl's theorem is proved, which provides additional structural information about k-wise intersecting families which have size close to the maximum upper bound. A graph-theoretic generalization of Frankl's theorem is also formulated and proved for perfect matching graphs. Finally, a long-standing conjecture of Chvatal regarding structure of maximum intersecting families in hereditary systems is considered. An intersection theorem is proved for hereditary families which have rank 3 using a powerful tool of Erdos and Rado which is called the Sunflower Lemma. / Dissertation/Thesis / Ph.D. Mathematics 2011

[pt] Em países de clima tropical, como o Brasil, é comum a formação de solos residuais, que, por estarem expostos a períodos de seca após as chuvas, costumam encontrar-se não saturados em campo. Portanto, uma análise de estabilidade de um talude considerando o solo saturado não seria a mais condizente com a realidade em um caso destes, devendo ser considerado o acréscimo na resistência ao cisalhamento por conta da sucção na determinação do fator de segurança. Este trabalho teve como objetivo analisar a estabilidade de um talude composto por solo residual de granulito localizado no bairro do Santo Antônio Além do Carmo, Salvador, BA. O programa experimental contou com a coleta de material em campo para realização de ensaios de caracterização química, física e mineralógica, resistência e permeabilidade. A envoltória não saturada, de onde se obteve a relação entre o fluxo magnético e sucção mártrica, foi determinada através da função hiperbólica proposta por Vilar (2006). Com os parâmetros obtidos, foram realizadas as análises de infiltração e estabilidade. Os resultados mostraram que o mecanismo de ruptura provável associou-se à elevação do nivel de água provocado pela infiltração das águas provenientes das fortes chuvas dos dias 8 e 9 de novembro, bem como das águas servidas lançadas no talude pela população. A ação antrópica também se fez presente através de sobrecarga no talude provocada pelo peso das edificações. Conclui-se, então, que seria necessária a ação conjunta da chuva e fatores humanos para que haja uma situação de instabilidade no local estudado. / [en] In countries with a tropical climate, such as Brazil, the formation of residual soils is common, and because they are exposed to periods of drought after rainfall, they are often found unsaturated. Therefore, a stability analysis of a slope considering saturated soil would not be the most consistent in these case, and the increase in shear strength due to suction should be considered on the determination of the the safety factor. The objective of this work was to analyze the stability of a slope composed of residual granulite soil located in the district of Santo Antônio Além do Carmo, Salvador, BA. The experimental program included the collection of material in the field to perform chemical, physical and mineralogical characterization, resistance and permeability tests. The unsaturated envelope from which the relationship between magnetic flow and matric suction was determined by the hyperbolic function proposed by Vilar (2006). With the obtained parameters, infiltration and stability analyzes were performed. The results showed that the probable failure mechanism was associated to the elevation of the water level caused by the infiltration of the water from the heavy rains of November 8 and 9, as well as the wastewater thrown into the slope by the population. The anthropic action was also present through overloading the slope, caused by the weight of the houses. It can be concluded that it would be necessary the rainfall to work together with the human factors so it will happen an instabilization situation in the study site.

This thesis proposes novel methods for identification and control of multivariable systems including multiple delays and describes their application to control of general anesthesia administration. First, an identification method for multivariable systems whose input and output paths have different time delays is presented. Second, a state predictor for multivariable systems whose input and output paths have different time delays is proposed. Third, the state predictor is used for constructing a state-predictive servo control system for controlled processes whose output paths have different time delays. A robust stability analysis method of the state-predictive servo control system is also examined. Furthermore, based on results of these theoretical studies, control systems for use in general anesthesia administration are developed. First, an identification method for multivariable systems whose input and output paths have different time delays is proposed. This method comprises two steps. In the first step, the delay lengths are estimated from the impulse response matrix identified from input and output (I/O) sequences using a subspace identification algorithm. In the second step, I/O sequences of a delay-free part are constructed from the original sequences and the delay estimates, and the system matrices of the delay-free part are identified. The proposed method is numerically stable and efficient. Moreover, it requires no complex optimization to obtain the delay estimates, nor does it require an assumption about the structure of the system matrices. Second, a state predictor is proposed for multivariable systems whose input and output paths have different time delays. The predictor consists of a full-order observer and a prediction mechanism. The former estimates a vector consisting of past states from the output. The latter predicts the current state from the estimated vector. The prediction error converges to zero at an arbitrary rate, which can be determined using pole assignment method, etc. In the proposed predictor, the interval length of the finite interval integration fed to the observer is shorter than that of an existing delay-compensating observer. Consequently, the proposed predictor is more numerically accurate than the delay-compensating observer. Using the proposed state predictor, a design method of a state-predictive servo controller is described for multivariable systems whose output paths have different time delays. Furthermore, a sufficient stability condition of the state-predictive servo control system against parameter mismatches is derived. Using a characteristic equation of the perturbed closed-loop system, a stability margin can be given on a plane whose axes correspond to the magnitudes of the mismatches on system matrices and on delay lengths. In the remainder of this thesis, development of anesthesia control systems is described to illustrate an application of the theoretical results described above. First, a hypnosis control system is presented. This system administers an intravenous hypnotic drug to regulate an electroencephalogram-derived index reflecting the patient’s hypnosis. The system comprises three functions: i) a model predictive controller that can take into account effects of time delay adequately, ii) an estimation function of individual parameters, and iii) a risk-control function for preventing undesirable states such as drug over-infusion or intra-operative arousal. Results of 79 clinical trials show that the system can reduce the total amount of drug infusion and maintain hypnosis more accurately than an anesthesiologist’s manual adjustment. Second, a simultaneous control system of hypnosis and muscle relaxation is described. For development of this system, a multivariable model of hypnosis and muscle relaxation is identified using the method proposed in this thesis. Then a state-predictive servo control system is designed for controlling hypnosis and muscle relaxation. Finally, the control system’s performance is evaluated through simulation. The resultant simultaneous control system satisfies the performance specifications of settling time, disturbance rejection ability, and a robust stability range. Although this system is not fully developed, the procedure of constructing this control system demonstrates the effectiveness of the proposed methods: the identification method for systems whose input and output paths have different time delays and the design and stability analysis methods of the state-predictive servo control system. / Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第13820号 / 工博第2924号 / 新制||工||1432(附属図書館) / 26036 / UT51-2008-C736 / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 小林 哲生, 教授 萩原 朋道, 准教授 古谷 栄光 / 学位規則第4条第1項該当