The counting of fuzzy subsets of a finite set is of great interest in both practical and theoretical contexts in Mathematics. We have used some counting techniques such as the principle of Inclusion-Exclusion and the Mõbius Inversion to enumerate the fuzzy subsets of a finite set satisfying different conditions. These two techniques are interdependent with the M¨obius inversion generalizing the principle of Inclusion-Exclusion. The enumeration is carried out each time we redefine new conditions on the set. In this study one of our aims is the recognition and identification of fuzzy subsets with same features, characteristics or conditions. To facilitate such a study, we use some ideas such as the Hamming distance, mid-point between two fuzzy subsets and cardinality of fuzzy subsets. Finally we introduce the fuzzy scanner of elements of a finite set. This is used to identify elements and fuzzy subsets of a set. The scanning process of identification and recognition facilitates the choice of entities with specified properties. We develop a procedure of selection under the fuzzy environment. This allows us a framework to resolve conflicting issues in the market place.

From Introduction: The research concentrates primarily on a feasibility study involving the setting up of an image processing workstation. As broad as this statement concerning the workstation may seem, there are several factors limiting the extent of the research. This project is not concerned with the design and implementation of a fully-fledged image processing workstation. Rather, it concerns an initial feasibility study of such a workstation, centered on the theme image processing aided by the parallel processing paradigm. In looking at the hardware available for the project, in the context of an image processing environment, a large amount of initial investigation was required prior to that concerned with the transputer and parallel processing. Work was done on the capturing and displaying of images. This formed a vital part of the project. Furthermore, considering that a new architecture was being used as the work horse within a conventional host architecture, the INTEL 80286, several aspects of the host architecture had also to be investigated. These included the actual processing capabilities of the host, the capturing and storing of the images on the host, and most importantly, the interface between the host and the transputer [C0089]. Benchmarking was important in order for good conclusions to be drawn about the viability of the two types of hardware used, both individually and together. On the subject of the transputer as the workhorse, there were several areas whlch required investigation. Initial work had to cover the choice of network topology on whlch the benchmarking of some of the image processing applications were performed. Research into this was based on the previous work of several authors, whlch introduced features relevant to this investigation. The network used for this investigation was chosen to be generally applicable to a broad spectrum of applications in image processing. It was not chosen for its applicability for a single dedicated application, as has been the case for much of the past research performed in image processing [SAN88] [SCH89]. The concept of image processing techniques being implemented on the transputer required careful consideration in respect of what should be implemented. Image processing is not a new subject, and it encompasses a large spectrum of applications. The transputer, with image processing being hlghly suited to it, has attracted a good deal of research. It would not be rash to say that the easy research was covered first. The more trivial operations in image processing, requiring matrix type operations on the pixels attracted, the most coverage. Several researchers in the field of image processing on the transputer have broken the back of this set of problems. Conclusions regarding these operations on the transputer returned a fairly standard answer. An area of image processing which has not produced the same volume of return as that concerning the more trivial operations, is the subject of Fourier Analysis, that is, the Fourier Transform. Thus a major part of this project concerns an investigation into the Fourier Transform in image processing, in particular the Fast Fourier Transform. The network chosen for thls research has placed some constraint upon the degree of parallelism that can be achleved. It should be emphasized that this project is not concerned with the most efficient implementation of a specific image processing algorithm on a dedicated topology. Rather, it looks at the feasibility of a general system in the domain of image processing, concerned with a hlghly computationally intensive operation. This has had the effect of testing the processing power of the hardware used, and contributing a widely applicable parallel algorithm for use in Fourier Analysis. 3 These are discussed more fully in Chapter 2, which covers the work related to tbis project. The results of the investigation are presented along with a discussion of the methods throughout the thesis. The final chapter summarizes the findings of the research, assesses the value of the investigation, and points out areas for future investigation.

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Les alliages de titane sont actuellement très utilisés comme implants orthopédiques de part leurs bonnes propriétés mécaniques, leur bonne résistance à la corrosion ainsi que leur excellente biocompatibilité. Cependant, l’alliage Ti-6Al-4V qui est le plus utilisé présente un module d'élasticité élevé (110GPa), ce qui peut provoquer le phénomène de « stress shielding » et finalement causer l’échec de l’implantation. De plus, l’utilisation à long terme de ce type d’alliage est remise en question à cause de la présence de certains éléments (Al et V) considérés comme cytotoxiques et/ou allergènes. Les alliages -métastables à base de titane peuvent être des candidats de remplacement intéressants grâce à l’addition d'éléments biocompatibles tel que Nb, Zr et Sn.L'alliage superélastique biocompatible de composition Ti-24Nb-4Zr-8Sn (% massique) a été étudié dans le cadre de cette thèse. Cet alliage montre des propriétés intéressantes telles qu’un bas module d’élasticité, une résistance mécanique élevée et une ductilité relativement importante.Dans ce travail de thèse, différents traitements thermomécaniques ont été réalisés afin d’obtenir des textures cristallographiques différentes. Les influences de changement de texture sur les propriétés mécaniques et la superélasticité ont été ainsi préalablement étudiées. La transformation martensitique a été caractérisée par des essais in situ de diffraction des rayons X sous rayonnement synchrotron (SXRD) pendant une sollicitation mécanique et par analyse mécanique dynamique (DMA) sous différentes contraintes statiques. De plus, les microstructures de déformation ont été observées par EBSD et MET pour caractériser précisément les mécanismes de déformation plastique, en particulier le maclage. / Titanium alloys have already been extensively used as orthopedic implants due to the good mechanical properties, corrosion resistance and excellent biocompability. However, the most widely used Ti-6Al-4V alloy exhibits high elastic modulus (110GPa) which would cause the stress shield effect and eventually lead to the implantation failure. Furthermore, elements of Al and V are proved to be toxic for long-term application. Low modulus metastable  titanium alloy can be a suitable candidate through proper addition of non-toxic alloying element such as Nb, Zr and Sn.The present investigated Ti-24Nb-4Zr-8Sn alloy is a new -type metastable alloy potentially interesting for biomedical applications. This alloy displays high strength, low elastic modulus, high ductility, superelastic property and good biocompatibility according to previous investigations.In this work, the as-cold rolled Ti-24Nb-4Zr-8Sn alloy was subjected to different thermo-mechanical treatments in order to introduce different crystallographic texture. Influences of texture change on mechanical properties and superelasticity have been preliminarily studied. Martensitic transformation which is responsible for the superelasticity has been characterized by both in situ synchrotron X-ray diffraction and dynamic mechanical analysis. Moreover, deformed microstructures have been observed by EBSD and TEM to characterize precisely the plastic deformation mechanisms, and particularly the twinning.

The purpose of this paper is to present the results of a study of linear spaces with special emphasis of linear transformations, norms, and inner products.

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This study of the Euclidean N-space looks at some definitions and their characteristics, some comparisons, boundedness and compactness, and transformations and mappings.

Polymer gels undergo the volume phase transition in response to an infinitesimal environmental change. This remarkable phenomenon results in many potential applications of polymer gels. This dissertation systematically investigates the chemical and physical properties of polymer gels. It is found that infrared radiation laser not only induces a volume phase transition in N-isopropylacrylamide (NIPA) gel, but also causes the gel to bend toward the laser beam. The transmission of visible laser light through a NIPA gel can also be controlled by adjusting the infrared laser power. A new class of environmentally responsive materials based on spatial modulation of the chemical nature of gels has been proposed and demonstrated. Three simple applications based on the modulated gels are presented: a bi-gel strip, a shape memory gel, and a gel hand. The bending of bi-gels has been studied as a function of temperature, acetone aqueous solution, and salt solution. As the polymer network concentration increases, the behavior of shear modulus of acrylamide (PAAM) gels deviates significantlyfromthe classical theory. The ionic NIPA gels undergo two sequential volume phase transitions: one occurs in dilute NaCl solution, the other occurs in concentrated NaCl solution. An interpenetrating polymer network (IPN) of PAAM--NIPA has also been synthesized using free radical polymerization. It is found that the IPN gels preserve the essential properties of individual components. The volume phase transition of the IPN gels can be triggered by multiple external stimuli including temperature, acetone concentration, and salt concentration.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21788号 / 工博第4605号 / 新制||工||1717(附属図書館) / 京都大学大学院工学研究科物質エネルギー化学専攻 / (主査)教授 近藤 輝幸, 教授 辻 康之, 教授 大江 浩一 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

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