CoordenaÃÃo de AperfeiÃoamento de NÃvel Superior / Os mÃtodos tradicionais de tratamento do cÃncer, como a quimioterapia e a radioterapia, embora sejam eficazes em vÃrios tipos de tumores, encontram freqÃentemente populaÃÃes de cÃlulas neoplÃsicas resistentes, alÃm de apresentarem uma baixa margem de seguranÃa para os pacientes. A utilizaÃÃo da hipertermia associada à quimioterapia e/ou radioterapia jà se encontra fartamente relatada como vantajosa na literatura especializada, principalmente em pacientes portadores de cÃncer em estÃdio avanÃado, submetidos previamente aos mÃtodos clÃssicos de tratamento. A aplicaÃÃo de calor nos tecidos atravÃs de ultrassom contÃnuo torna mais Ãgil Ãste procedimento e com eficÃcia comprovada. O uso dos antiangiogÃnicos tambÃm vem sendo relatado como eficaz na literatura especializada e atualmente, a lista destas substÃncias vem aumentando consideravelmente. O estudo da aÃÃo da hipertermia associada a alguns agentes antiangiogÃnicos tem sido sugerida uma vez que os vasos tumorais ao encontrarem-se dilatados, nÃo promoverÃo a diminuiÃÃo da temperatura no tecido tumoral e, consequentemente, os efeitos desta associaÃÃo serÃo mais intensos do que no tecido normal devendo contribuir para a morte celular. Objetiva-se neste trabalho, avaliar o efeito antitumoral e antiangiogÃnico da hipertermia induzida por US isolada e combinada com etoricoxibe e pegaptanibe,no carcinossarcoma de Walker 256 implantado na tela subcutÃnea do dorso de ratos por meio de utilizaÃÃo do modelo experimental de hipertermoterapia por US assim como o estudo dos efeitos da hipertermia por US isolada e em combinaÃÃo com etoricoxibe e pegaptanibe,na angiogÃnese tumoral.O mÃtodo utilizado para o estudo teve inÃcio com o implante de cÃlulas de tumor de Walker 256 no dorso de ratos Wistar machos. Os animais foram tratados com hipertermia aplicada atravÃs de aparelho de ultrassom, mantida a nÃvel de 45o C durante cinco minutos no terceiro dia apÃs a inoculaÃÃo e tambÃm tratados com etoricoxibe e pegaptanibe por via oral e intraperitoneal respectivamente a partir do dia da inoculaÃÃo. Cada grupo de animais foi submetido a medidas do crescimento tumoral durante o perÃodo de 30 dias, assim como tambÃm à avaliaÃÃo da microdensidade vascular atravÃs de estudo mesoscÃpico fotogrÃfico, validado pelo estudo microscÃpico. A aplicaÃÃo do calor atravÃs de aparelho de ultrasom demonstrou eficiÃncia e agilidade A hipertermia, o etoricoxibe e o pegaptanibe, apresentaram capacidade antiangiogÃnica, expressada tanto pela curva de sobrevida, como pela avaliaÃÃo da microdensidade vascular. Particularmente, a hipertermia isoladamente apresentou um efeito antiangiogÃnico significativo tanto na curva de crescimento tumoral como na diminuiÃÃo da densidade microvascular. A associaÃÃo da hipertermia com o pegaptanibe, demonstrou uma eficiÃncia na diminuiÃÃo da densidade microvascular significativamente maior do que os demais grupos. O modelo de aplicaÃÃo de hipertermia gerada por um aparelho de ultrassom na modalidade contÃnua foi satisfatÃria, demonstrando ter sido efetiva tanto na diminuiÃÃo do crescimento tumoral, como na diminuiÃÃo da densidade microvascular. / The traditional methods of cancer treatment, like the chemotherapy and radiotherapy, even though they are effective in many types of tumours, they find frequently resistant neoplasic cellsâ population, beyond presenting a low security margin to the patients. The hyperthermia use associated to the chemotherapy and radiotherapy are plenty mentioned as profitable in the specialist literature, especially in patients with cancer in advanced stage, submitted previously to the classic methods of the treatment. The tissuesâ heat insertion through the continuous ultrasound becomes the procedure faster and with proved efficacy. The antiangiogenic use also is being related like effective in the specialist literature and, at this moment, the substancesâ list has grown vastly. The study of the hyperthermia action associated to antiangiogenic agents has been suggested, once the tumour vessels are dilated, would not promote the temperature reduction in the tumour vessels and, therefore, the effects of this association would be more intense than in the normal tissue, what might contribute to the death cell. The study objective is to evaluate the antitumor and antiangiogenic effect of the hyperthermia induced by isolated ultrasound and combined with etoricoxibe and pegaptanibe in the 256 Walker carcinossarcoma implanted in the subcutaneous back screen of mouse by using the hyperthermia experimental model by ultrasound, like the hyperthermia effects study by isolated ultrasound and linked with etoricoxibe and pegaptanibe, in the tumour angiogenesis. The method used describes the insertion of 256 Walker Tumour cells in the back of male Wistar mouse. The animals were treated with hyperthermia applied through the ultrasound equipment, kept to a 45 C level during five minutes in the third day after the inoculation and also treated with etoricoxibe and pegaptanibe by oral and intraperitoneal respectively since the inoculation day. Each animal group was submitted to a tumour growth measurement during a period of 30 days, as well as also a vascular microdensity evaluation through a photographic mesoscopic study, validated by the microscopic study. The heat application through the ultrasound equipment demonstrated efficiency and agility. The hyperthermia, the etoricoxibe and the pegaptanibe showed antiangiogenic capacity, expressed by the over life curve, and also by the vascular microdensity evaluation. Particularly, the isolated hyperthermia showed a significative antiangiogenic effect in the tumour growth curve and also in the decreasing of the micro vascular density. The association between the hyperthermia and the pegaptanibe demonstrated a greater efficiency in the reducing of the micro vascular density than the other groups. The hyperthermia application model generated by the ultrasound equipment in the continuous modality was satisfactory, demonstrating by being effective as much in the reducing of the tumour growth as in the decreasing of the micro vascular density.

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disorder characterized by loss of motor neurons and their supporting cells in the brain, brainstem and spinal cord, resulting in muscle paresis and paralysis including the bulbar (speech, chewing, swallowing) and respiratory muscles. The average age at onset is 55 years, and death due to respiratory failure occurs 2-5 years after symptom onset in ~ 85% of cases. Five to 10% of ALS is familial, and about 20% of familial cases are associated with mutations in the superoxide dismutase 1 (SOD1) gene. To date, 118 SOD1 mutations have been reported worldwide (www alsod.org). All are dominantly inherited, except for the D90A mutation, which is typically recessively inherited. D90A homozygous ALS is associated with long (~14 years) survival, and some atypical symptoms and signs. The reason for this is not known. In contrast, most other SOD1 mutations are associated with average survival, while some are associated with aggressive disease having lower motor neuron predominance and survival less than 12 months. The A4V mutation, which is the most frequently occurring SOD1 mutation in the United States, is an example of the latter. Understanding the pathogenic mechanisms of SOD1 mutants causing widely different disease forms like D90A and A4V is of paramount importance. Overwhelming scientific evidence indicates that mutations in the SOD1 gene are cytotoxic by a “gain of noxious” function, which although not fully understood results in protein aggregation and loss of cell function. This thesis explores different ALS-SOD1 gene mutations in British Columbia (BC), Canada. Two hundred and fifty-three ALS patients were screened for SOD1 mutations, and 12 (4.7%) unrelated patients were found to carry one of 5 different SOD1 mutations: A4V (n=2); G72C (n=1); D76Y (n=1); D90A (n=2); and 113T (n=6). Incomplete penetrance was observed in 3/12 families. Bulbar onset disease was not observed in the SOD1 mutation carriers in this study, but gender distribution was similar to previously reported studies. Age at symptom onset for all patients enrolled, with or without SOD1 mutations, was older than reported in previous studies. On average, patients with SOD1 mutations experience a longer diagnostic delay (22.6 months) compared to patients without mutations (12 months). Two SOD1 patients were originally misdiagnosed including the G72C patient who’s presenting features resembled a proximal myopathy. Neuropathological examination of this patient failed to reveal upper motor neuron disease. The I113T mutation was associated with variable age of onset and survival time, and was found in 2 apparently sporadic cases. The D76Y mutation was also found in an apparently sporadic case. I113T and D76Y are likely influenced by other genetic or environmental factors in some individuals. Two patients were homozygous for the D90A mutation, with clinical features comparable to patients originally described in Scandinavia. Clinical and electrophysiological motor neuron abnormalities were observed in heterozygous relatives of one D90A homozygous patient. The A4V patients were similar to those described in previous studies, although one had significant upper motor neuron disease both clinically and neuropathologically. Clinical neurophysiology is essential in the diagnosis of ALS, and helpful in monitoring disease progression. A number of transcranial magnetic stimulation (TMS) studies may detect early dysfunction of upper motor neurons when imaging techniques lack sensitivity. Peristimulus time histograms (PSTHs), which assess corticospinal function via recording of voluntarily activated single motor units during low intensity TMS of the motor cortex, were used to study 19 ALS patients having 5 different SOD1 mutations (including 8 of the 12 patients identified with SOD1 mutations from BC). Results were compared with idiopathic ALS cases, patients with multiple sclerosis (MS), and healthy controls. Significant differences were found in corticospinal pathophysiology between ALS patients with SOD1 mutations, idiopathic ALS, and MS patients. In addition, different SOD1 mutants were associated with significantly different neurophysiologic abnormalities. D90A homozygous patients show preserved if not exaggerated cortical inhibition and slow central conduction, which may reflect the more benign disease course associated with this mutant. In contrast, A4V patients show cortical hyper-excitability and only slightly delayed central conduction. I113T patients display a spectrum of abnormalities. This suggests mutant specific SOD1 pathology(s) of the corticospinal pathways in ALS.

This thesis provides an extensive study of the first molecular hyperpolarizability b of charge-transfer chromophores using hyper-Rayleigh scattering (HRS). The charge-transfer chromophores used in present work involve the tricyanohydrofuran¡]TCF¡^group as an electron acceptor, and/or thiophene in the pi-electron bridge. TCF is a very strong electron acceptor and thiophene greatly lowers the resonance energy. Their presence significantly increases the beta value of the chromophore, therefore enhancing potentials in applications. In hyper-Rayleigh scattering experiments, the laser radiation with tunable wavelengths is used as an excitation source for measuring the frequency dependence of beta. The experiment shows beta exhibiting a significant dispersion in the two-photon resonance region. Using the linear absorption spectrum in coordination with theory, we show that it is possible to use Kramers-Kronig (K-K) transform to reproduce the experimental beta value in the two-photon resonance region. The K-K approach provides an extension to the conventional Oudar-Chemla equation, which is invalid in the spectral region in which two-photon resonance occurs. Using the new approach, it is shown that reliable values of intrinsic hyperpolarizabilities beta_zero of charge-transfer chromophores can be extracted. The coordination of beta_zero with molecular structure provides one with an insight for the origin of the enhancement of the first molecular hyperpolarizability of charge-transfer chromophores. This thesis examines the variation of beta_zero with molecular structure. The same technique is also applied to a dendrimer that has charge-transfer nonlinear optical chromophores incorporated in the dendritic structure. The measured frequency dependent hyperpolarizability of the dendrimer is compared with that calculated from the linear absorption spectrum by the KK transform technique. The intrinsic hyperpolarizability beta_zero of the dendrimer obtained is compared with that of the single chromophore having a structure similar to that incorporated in the dendrimer. The comparison shows that the 3D dendritic structure is effective in reducing the interaction between chromophores by providing sufficient space between them, hence avoiding the possibility of aggregation formation due to attractive interactions between chromophores. The topic of two-photon fluorescence (TPF), which is related to HRS, is also investigated. The intensity of TPF is generally proportional to the square of the incident excitation intensity. Careful measurements of the TPF intensity of a nonlinear optical chromophore in conjunction with required auxiliary parameters have been used as a technique for determining the two-photon absorption cross-section. The TPF intensity measurement carried out in this thesis uses a variety of intensities. At low intensity excitation, the TPF intensity follows the usual quadratic intensity law (QIL), whereas deviations from the QIL are observed at higher incident intensities. The observation of similar lineshape associated with one- and two-photon fluorescence spectra suggests a 3-level model for the description of TPF excited by the incident intensity at various strengths. It is shown that by fitting the observed TPF intensity to an equation developed from the three-level model, it is possible to deduce the two-photon absorption cross section of the nonlinear optical chromophore in solution. The new technique developed using the three-level model is tested on a Rhodamine B/Chloroform solution. The two-photon absorption cross-section obtained by using the new technique is found in agreement with that reported in the literature. Having demonstrated the suitability of the new technique, it is used to determine the two-photon absorption cross-section of a novel nonlinear optical chromophore. The two-photon absorption cross-section using the new technique is then compared with that obtained by the nonlinear transmittance method. The two results are in good agreement, indicating the applicability of the new technique. The new technique is more convenient than the conventional low excitation TPF method as it does not require various auxiliary parameters, some of them are difficult to obtain. The second harmonic generation (SHG) of a chromophore/polymer film which is optically poled by using a coherent superposition of a fundamental and its second harmonic beams. The growth rate of the SHG intensity is found to be proportional to the fourth power of the incident intensity of the fundamental beam, and the plateau intensity SHG is proportional to the square of the incident intensity. These observations are not in agreement with the published theory. While the reason for disagreement is yet to be clarified, the information obtained is useful for the development of nonlinear optical devices.

Automatic Global Data Partitioning for Distributed Memory Machines (DMMs) is a difficult problem. Distributed memory machines are scalable, but since the memory is distributed across processors, the scheme of placement of data (arrays) onto local memories of different processors become crucial since any communication between processors for non-local data access is an order of magnitude costlier than access to local memory. Researchers have given varied solutions to this problem, most of which work for uniform dependences in loops and they suggest HPF-like distributions only. For non-uniform dependences the loop was made to run sequentially. In this work, we present a partitioning strategy called Hyperplane Partitioning which works well with loops with non-uniform dependences also. In this method of partitioning, the iteration space is partitioned into as many number of partitions as there are number of logical processors, in such a way that the overall inter-processor communication will be minimum. The idea is to localize as many as dependences as possible so that overall communication both beacuse of non-local data as well as inter-processor synchronizations are reduced. These partitions are then induced into data spaces of the arrays referenced in the loop. Each processor then runs its part of iteration space keeping the data partition that it owns locally. Any non-local data access is implemented by inter-processor communication at run-time.The Hyperplane Partitioning is also extended to a sequence of loops. This is done by first finding Best Local Distribution (BLD) for every loop first and then finding the best way of grouping different adjacent loops (just for finding the data partition) which gives best global data partition. This sequence of distributions/redistributions is found by constructing a data structure called Data Distribution Tree (DDT) and finding the least cost path from the source to any of the leaf nodes in the DDT. The costs for the edges come from the communication cost incurred while running a loop with a particular distribution and redistribution to suit the requirement at the next loop. For this a communication cost estimator is developed which works well for fewer dimensions. To handle complete programs we use some heuristic to find the best global distribution for the entire program.Some optimizations like message optimization to reduce the number of messages sent across processors, time optimization which is done by uniform scheduling across processors, and space optimization to keep only the part of array space that any processor owns onto its local memory, are studied. Hyperplane Partitioning is also implemented using an algorithm for synchronization to handle non-local memory access as well as obeying data dependence constraints. The algorithm is also proved to be correct. The target machine is IBM-SP2 using PVM for the message passing library. The performance of the tool on some standard benchmarks (ADI and RHS) and also on some programs designed by us to show the specific merits of the tool. The results show that the loops which have non-uniform dependences also can be run on DMM with good speed-ups.

This thesis deals with the investigation of the first hyperpolarizabilities (β) of a large number of molecules linked to other molecules either covalently or noncovalently. Chapter 1 gives a brief introduction to supramolecular chemistry and Nonlinear Optics (NLO). A survey of literature pertinent to noncovalently interacting supramolecular assembly and their NLO properties as well as NLO properties of oligomeric systems has been presented. The scope of the present investigation has been described at the end of the chapter. Chapter 2 discusses all the methods used in carrying out this thesis work. The first hyperpolarizabilities (β) of all the compounds have been measured by the hyper Rayleigh scattering (HRS) technique; the experimental details of which are written in this chapter. Various spectroscopic techniques such as NMR, IR, UV-Vis, etc. that were used in the investigation have been presented. The subsequent chapters 3-5 deal with the actual results obtained in this work. In chapter 3 first hyperpolarizabilities of o-, m-, and p-aminobenzoic acids and their oligomers viz., dimer, trimer and tetramer (covalently linked) have been studied. The compounds are synthesized and characterized by various spectroscopic methods and their β values have been measured by HRS. The hyperpolarizability increases in going from the monomer to the dimer but decreases subsequently from the dimer to the trimer to the tetramer. This unexpected trend in β has been attributed to the formation of molecular aggregates in the trimers and tetramers. Further evidences of aggregation come from the results of1H NMR spectroscopy and conductivity measurements. In chapter 4, synthesis, characterization and HRS investigation to probe the formation, dissociation and binding constants of hydrogen bonded supramolecular complexes (noncovalent interaction) formed in solution between 6-amino-2-(pivaloylamino)pyridine and ferrocene functionalized barbituric acid and 5-methoxy-N,N′-bis(6-amino-2-pyridinyl)-1,3-benzenedicarboxamide and ferrocenyl barbituric acid have been described. From the HRS data the stoichiometry of the supramolecular complexes has been determined and compared to that from the NMR data. Some of the complex stoichiometries that are measured by HRS have not been seen in the NMR data and vice versa. The results have been rationalized in terms of the strengths and weaknesses of various spectroscopic methods as applied to this problem. Many fold increase in the β value has been realized in the supramolecular complex formation process. Depolarized HRS experiments have been carried out to obtain structural information on the complexes. In the last chapter the synthesis, characterization and measurements on the first hyperpolarizabilities of unsubstituted tetraphenylporphyrin and its metallated complexes have been presented. Synthesis of supramolecular complexes of ferrocenyl barbituric acid with functionalized porphyrin compounds has been carried out although the amount of the final complex was insufficient for HRS measurements. This chapter ends with a perspective for the future work in the direction.

In recent years, coinage metal nanoparticles have emerged as materials with largest quadratic optical nonlinearity. Their first hyperpolarizabilities (β) are very high (105-106 x 10-30 esu) but such large values were quite unexpected because of their apparently centrosymmetric bulk structure. Only a small second harmonic generation (SHG) from coinage metal nanoparticles is expected through higher order multipolar (e.g., quadrupolar) polarization mechanisms. Various possible reasons have been attributed to the observation of large β values in coinage metal nanoparticles. They are: 1) Particles may not be overall centrosymmetric (as appears from the TEM pictures) which, in turn, can make SHG electric dipole allowed, 2) Several polarization mechanisms (dipolar, quadrupolar, retardation, etc.) may be operating simultaneously to render SHG very efficient, 3) SHG can be resonance enhanced if the incident or SH photons fall within the surface plasmon resonance (SPR) absorption bands or higher energy interband transitions in the metal particles, and 4) Surface capping agents used for stabilization of the nanoparticles in solution alter the SH response. It is, therefore, important to experimentally find out which of the above mentioned possibilities are dominant and under what conditions we can identify the contribution of various mechanisms to the overall SHG response of the coinage metal nanoparticles. In this thesis work, the origin of SHG from copper (one of the coinage metals) nanoparticles has been investigated using hyper-Rayleigh scattering (HRS). In chapter 1, an introduction to metal nanoparticles and their optical properties have been presented. A general introduction to second order nonlinear optics and various methods for the determination of first hyperpolarizability are provided. A literature survey on the second order NLO properties of metal nanoparticles is also done. At the end of the chapter, the motivation of the work done is outlined. In chapter 2, the experimental set-ups for unpolarized and polarization resolved hyper-Rayleigh scattering (HRS) measurements at different wavelengths are described. Generation of IR wavelength of 1543 and 1907 nm using stimulated Raman scattering in gases have been presented in this chapter. In chapter 3, synthesis and characterization of copper nanoparticles are described. Four different size copper nanoparticles (5, 9, 25, and 55 nm) were prepared by laser ablation. Size dependencies of first hyperpolarizability were investigated at different wavelengths and it was found that β increases with increasing size of the particle and that the SHG originates mainly from the surface of the particle. Dispersion in first hyperpolarizabilities of the copper nanoparticles has also been investigated and we find that at incident and SH wavelengths far from the SPR absorption band, the hyperpolarizability is large compared to molecular hyperpolarizabilities. In chapter 4, the results of polarization resolved HRS measurements on copper nanoparticles of five different sizes at four different wavelengths (738, 1064, 1543 and 1907 nm) are reported. Polarization analyses show that at small particle size to wavelength (d/λ) ratio the dipolar contribution to SHG is dominant whereas the quadrupolar and retardation effects become important at larger d/λ values. The “small particle limit” in the SHG from coinage metal nanoparticles has been assessed based on our results on copper and others’ results on silver and gold nanoparticles. In chapter 5, the effect of surface capping on the first hyperpolarizability of copper nanoparticles is investigated. Polyvinyl pyrrolidone (PVP) has been used as a capping agent. The results obtained for bare and capped copper nanoparticles show that capping enhances the hyperpolarizability by a factor of 2. In the last chapter 6, general conclusions drawn on SHG from coinage metal nanoparticles based on this work are presented along with future perspectives.

Le procédé de déroulage est un procédé de coupe orthogonale du bois vert dont l'arête de coupe est parallèle à la fibre et dont la valeur ajouté est apportée au copeau. L'enjeu actuel est de d'augmenter la déroulabilité du Douglas français ainsi que de déterminer celle des bois guyanais tout en évitant de trop lourdes expérimentations. Une modélisation de ce procédé est donc nécessaire. Le noeud scientifique est la loi de comportement du bois durant le déroulage, comme ce procédé est caractérisé par une grande vitesse de déformation et d'importantes et complexes déformations mêlant cisaillement et compression. Afin comprendre les phénomènes physiques mis en jeux, nous avons réalisé plus de 700 essais quasistatiques de traction, compression et torsion avec différents types de chargement. Nous avons aussi réalisé une centaine d'essais de déroulage sur une micro-dérouleuse instrumentée à laquelle nous avons ajouté des mesures de températures. Nous proposons une modélisation analytique adaptée à la description des régimes continus de coupe. La description de la zone de déformation est lagrangienne et la résolution se fait par les puissances mises en jeu. Nous proposons une loi de comportement hyper-élastique isotrope compressible de Rivlin généralisée d'ordre 4 dont nous avons déterminé la forme grâce aux essais quasi-statiques et les coefficients grâce à une résolution de problématique inverse de Levemberg-Marquardt afin de tenir compte de la vitesse de déformation. Pour la première fois, l'angle d'inclinaison de la zone de déformation prédit correspond aux observations expérimentales. De plus, au moins 75% des efforts calculés sont à moins de 15% des efforts expérimentaux.

Στόχος της παρούσας Διατριβής είναι να ερευνήσει τη διαμόρφωση των αντιλήψεων γύρω από τα απειροστά και τις σχετικές μ’ αυτά επ’ άπειρον διαδικασίες σε δύο κατευθύνσεις: 1. Την ιστορική εξέλιξη και ερμηνεία της έννοιας του απειροστού και 2. Την ανάλυση των σχετικών αντιλήψεων των φοιτητών-αυριανών καθηγητών των μαθηματικών. Στο πρώτο μέρος της διατριβής γίνεται ανάλυση και ερμηνεία των αντιλήψεων για τα απειροστά που εκφράστηκαν από την Αρχαία μέχρι τη σύγχρονη εποχή. Η μελέτη αυτή οδηγεί στην κατασκευή ενός ερμηνευτικού πλαισίου που διακρίνει τα ιστορικά ερμηνευτικά πρότυπα (μοντέλα) των απειροστών σε τρία αντιθετικά ζεύγη ως εξής: Ι. Εντασιακά-Εκτασιακά πρότυπα απειροστών. ΙΙ. Ομογενή-Μη ομογενή πρότυπα απειροστών. ΙΙΙ. Μηδενοδύναμα-μη μηδενοδύναμα πρότυπα απειροστών. Το παραπάνω πλαίσιο χρησιμοποιείται στο δεύτερο μέρος της διατριβής ως μεθοδολογικό εργαλείο για το σχεδιασμό διδακτικών πειραμάτων και την ανάλυση των εμπειρικών δεδομένων. Ειδικότερα, έγιναν τρία διδακτικά πειράματα με φοιτητές του Τμήματος των Μαθηματικών. Στο πρώτο πείραμα ερευνήθηκε η έννοια της ταχύτητας σύγκλισης ακολουθίας ως μια διαισθητική προσέγγιση στα απειροστά. Στο δεύτερο πείραμα, ερευνήθηκε η δυνατότητα προσέγγισης στα απειροστά μέσα από κλασσικά θέματα των διακριτών Μαθηματικών, όπως ο υπολογισμός του αθροίσματος των δυνάμεων φυσικών αριθμών. Στο τρίτο πείραμα έγινε διδασκαλία ενός συγκεκριμένου μοντέλου των υπερ-πραγματικών αριθμών και αναλύθηκαν τα αποτελέσματα. Τα κυριότερα συμπεράσματα της διατριβής είναι: 1. Η σημασία της κατασκευής μαθηματικών οντοτήτων που ικανοποιούν τα αξιώματα της Πραγματικής Ανάλυσης, 2. Η σημασία της διαισθητικής προσέγγισης και τα όριά της και 3. Η καταλληλότητα των προτεινόμενων μοντέλων και θεμάτων, ως διδακτικού υλικού. / The aim of this Ph.D thesis is the conceptions regarding infinitesimals and infinitesimal processes in two directions: 1. The historical evolution and interpretation of the concept of infinitesimal and 2. The analysis of the conception of the students–prospective teachers of Mathematics. The first part of the thesis contains a study and an analysis of infinitesimals that appeared in History from Antiquity to our era. This study leads to the construction of a framework of interpretation which distinguishes the interpretative models into three pairs of opposites: I. Homogenous-Nonhomogenous, models of infinitesimals II. Intensional-Extensional, models of infinitesimals III. Nilpotent-Non nilpotent, models of infinitesimals The above framework is applied in the second part of the thesis, as a methodological tool for the design of didactical experiments with students of Mathematics. The first experiment concerns a research study on the notion of the rate of convergence, as an intuitive approach to infinitesimals. The second experiment is referred to the emergence of infinitesimals through classical themes (issues) of discrete mathematics, such as the computation of sums of powers of integers. The third experiment concerns the teaching of a specific model of Hyper-Real numbers and the analysis of its empirical outcomes. The main conclusions of this thesis are: 1. The significance of the construction of mathematical entities, which satisfy the axioms of Real Analysis. 2. The significance of the intuitive approach, as well with a focus on its foreseen limitations. 3. The relevance of the proposed models and themes as potential didactical material.

No description available.

Under the electric dipole approximation, second harmonic of the incident light is scattered by a collection of randomly oriented molecular dipoles in solution due to instantaneous orientational fluctuation which is directional. If two such dipoles are correlated in space through intermolecular or other interactions, the intensity of the second harmonic scattered light (SHSL) will be related to the extent of such interactions. If two dipoles are arranged in a particular geometry by design, the geometry will determine the intensity of the SHSL. If a molecule has no dipole moment, the intensity of the SHSL will be less and is only allowed by higher order electric multipoles. If two such zero-dipole molecules interact with each other and transfer some amount of electronic charge from one to the other, the induced dipole moment will give rise to an enhanced SHSL. However, along with the direction of the dipole moment from the donor to the acceptor, the actual geometry of such molecular dimer/complex should also play an important role to determine the nature of the SHSL response. If all the isotropic nonzero components of first hyperpolarizability (β) are taken into account, from the measurement of β and related quantities such as depolarization ratios, in solution it should be possible to derive information about the geometry of the dimer/complex. This is precisely the motivation behind this thesis. Chapter 1 gives a brief introduction of 1:1 charge transfer (CT) complexes between a donor and an acceptor and their importance in chemistry. It also contains an introduction to nonlinear optics, various spectroscopic techniques to characterize CT complexes, etc. The motivation of extracting the geometry of such complexes from hyper-Rayleigh scattering (HRS) measurements in solution is presented in this chapter. In Chapter 2, all the experimental details of the unpolarized and polarization resolved HRS measurements at various excitation wavelengths have been described. Generation of infrared wavelengths (1543 nm and 1907 nm) using stimulated Raman scattering in gases have also been discussed. In Chapter 3, the first hyperpolarizability (βHRS) for two series of 1:1 molecular complexes between methyl substituted benzene donors with tetrachloro-p-benzoquinone (CHL) and dicyanodichloro-p-benzoquinone (DDQ) acceptors in solution at 1543 nm have been presented. Enhancement of βHRS due to charge transfer from the donor to the acceptor molecule which was predicted theoretically has been verified. Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, two macroscopic depolarization ratios D = I2ω,X,X/I2ω,Z,X and D' = I2ω,X,C/I2ω,Z,C in the laboratory fixed XYZ frame by detecting the SHSL in a polarization resolved fashion have been measured. The experimentally obtained first hyperpolarizability (βHRS), D and D' values, are then matched with the theoretically calculated values from single and double configuration interaction calculations using the Zerner’s intermediate neglect of differential overlap and the self-consistent reaction field (ZINDO–SDCI– SCRF) approach by adjusting the geometrical parameters. It has been found that in most of the CT complexes studied here, there exists a significant twist in the equilibrium geometry at room temperature which is not a simple slipped parallel geometry as was believed. In chapter 4, the βHRS, D and D' values of 1:1 pyridine (PY)-chloranil (CHL) complex at 1064 nm have been described. Previous theoretical studies have shown that there is a tilt angle of 77.9 degree in the gas phase PY-CHL complex. In this chapter, this prediction about the geometry of 1:1 PY-CHL complex has been probed. The experimentally found βHRS, D and D' are matched well with theoretically calculated values, using ZINDO–SDCI–SCRF, for a cofacial geometry of PY-CHL complex in solution indicating that the solution geometry is different from the gas phase geometry. In Chapter 5, the βHRS, D and D' for a series of 1:1 complexes of tropyliumtetrafluoroborate and methyl-substituted benzenes in solution at 1064 nm have been reported. The measured D and D' values vary from 1.36 to 1.46 and 1.62 to 1.72, respectively and are much lower than the values expected from a typical sandwich or a T-shaped geometry. The lowering in D and D' indicates that these complexes have higher symmetry than C2v. The value of D close to 1.5 indicates there is a significant octupolar contribution in such complexes. In order to probe it further, βHRS, D and D' were computed using the ZINDO-SDCI-SCRF technique in the presence of BF4-anion. By arranging the three BF4-ions in a C3 symmetry around the complex in such a way that electrical neutrality is maintained, the computed values are brought to agreement with experiments. This unprecedented influence of the anion on the HRS, D and D' values of these complexes are discussed in this chapter. In Chapter 6, the effect of dipolar interactions, within a multichromophoric system, on the second order nonlinear optical properties have been studied. It has been found that the βHRS response of the multichromophoric system is always larger than expected for uncorrelated chromophores demonstrating that the dipole moment of individual chromophores are not merely additive within the multichromophoric system but contribute cooperatively to the SHSL signal. Also the relative orientation and nature of the chromophores and the angle of interaction between them alter the HRS values. Chapter 7 is the concluding chapter in which all the work done in the thesis has been summarized and future direction has been proposed.