Study on Fuzzy Ordered FuzzyTopological Spaces

In this study we combine the notions of fuzzy order and fuzzy topology of Chang and define fuzzy ordered fuzzy topological space. Its various properties are analysed. Product, quotient, union and intersection of fuzzy orders are introduced. Besides, fuzzy order preserving maps and various fuzzy completeness are investigated. Finally an attempt is made to study the notion of generalized fuzzy ordered fuzzy topological space by considering fuzzy order defined on a fuzzy subset.

ON APPROXIMATION METHODS FOR UNBOUNDED OPERATORS

Department of Mathematics, Cochin University of Science and Technology

A Study of Closure and Fuzzy Closure Spaces with Reference to H-Closedness and Convexity

Department of Mathematics, Cochin University of Science and Technology.

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. Even mathematicians like H. Poincare worried about this. He observed that mathematical models are over idealizations, for instance, he said that only in Mathematics, equality is a transitive relation. A first attempt to save this situation was perhaps given by K. Menger in 1951 by introducing the concept of statistical metric space in which the distance between points is a probability distribution on the set of nonnegative real numbers rather than a mere nonnegative real number. Other attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A. Sklar and others. An aspect in common to all these approaches is that they model impreciseness in a probabilistic manner. They are not able to deal with situations in which impreciseness is not apparently of a probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces.

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. The 1st chapter give a brief summary of the arithmetic of fuzzy real numbers and the fuzzy normed algebra M(I). Also we explain a few preliminary definitions and results required in the later chapters. Fuzzy real numbers are introduced by Hutton,B [HU] and Rodabaugh, S.E[ROD]. Our definition slightly differs from this with an additional minor restriction. The definition of Clementina Felbin [CL1] is entirely different. The notations of [HU]and [M;Y] are retained inspite of the slight difference in the concept.the 3rd chapter In this chapter using the completion M'(I) of M(I) we give a fuzzy extension of real Hahn-Banch theorem. Some consequences of this extension are obtained. The idea of real fuzzy linear functional on fuzzy normed linear space is introduced. Some of its properties are studied. In the complex case we get only a slightly weaker analogue for the Hahn-Banch theorem, than the one [B;N] in the crisp case

Finding Spaces for Urban Food Production – Matching Spatial and Stakeholder Analysis with Urban Agriculture Approaches in the Urban Renewal Area of Dortmund-Hörde, Germany

Using the case of an economically declined neighbourhood in the post-industrial German Ruhr Area (sometimes characterized as Germany’s “Rust Belt”), we analyse, describe and conclude how urban agriculture can be used as a catalyst to stimulate and support urban renewal and regeneration, especially from a socio-cultural perspective. Using the methodological framework of participatory action research, and linking bottom-up and top-down planning approaches, a project path was developed to include the population affected and foster individual responsibility for their district, as well as to strengthen inhabitants and stakeholder groups in a permanent collective stewardship for the individual forms of urban agriculture developed and implemented. On a more abstract level, the research carried out can be characterized as a form of action research with an intended transgression of the boundaries between research, planning, design, and implementation. We conclude that by synchronously combining those four domains with intense feedback loops, synergies for the academic knowledge on the potential performance of urban agriculture in terms of sustainable development, as well as the benefits for the case-study area and the interests of individual urban gardeners can be achieved.

On the V(subscript gamma) Dimension for Regression in Reproducing Kernel Hilbert Spaces

This paper presents a computation of the $V_gamma$ dimension for regression in bounded subspaces of Reproducing Kernel Hilbert Spaces (RKHS) for the Support Vector Machine (SVM) regression $epsilon$-insensitive loss function, and general $L_p$ loss functions. Finiteness of the RV_gamma$ dimension is shown, which also proves uniform convergence in probability for regression machines in RKHS subspaces that use the $L_epsilon$ or general $L_p$ loss functions. This paper presenta a novel proof of this result also for the case that a bias is added to the functions in the RKHS.

Using zappers in Common Learning Spaces (Windows XP)

This resource is now obsolete and has been replaced by http://www.edshare.soton.ac.uk/5920/ This PowerPoint is an animated step-by-step guide that shows tutors how to use zappers in a teaching session. It covers starting the PC, distributing the zappers, plugging in the receiver, starting the software, running the presentation and managing voting, saving data at the end and collecting the handsets. It takes around 5 minutes to view.

Lecture notes pdf

Lecture notes in PDF

Lecture notes

Lecture notes in LaTex

Large Scale Structure of Metric Spaces

How the mathematical concept of Coarse Geometries is useful to analysing the Web

The cultural magazines as spaces of resistence in the lasta argentinian militar dictatorship. From the “El Expreso Imaginario” to “El Porteño”, 1976 – 1983

Although they were a few, there were places during the military dictatorship, which produced innovative cultural goods, in continuity with experiences of the artistic avant-garde in the sixties. Alongside the political and military repression  they could articulate in their environment groups identified with alternative aesthetic  codes, in opposition to the dominant culture in the period. The first one of the aces  we examine in the article, El Expreso Imaginario is a privileged place where we may regard the origins of the traits of that social space. Towards the end of  the dictatorship, another one like El Porteño, marks a new era, even if we can  establish various continuities with the first one. The circulation places of these ideas and practices were often taking place in cellars and other hiding places. Is  that because they take the literal sense of underground in the eighties to groups  who having been part of that story or not, were willing to receive his inspiring legacy. Between both magazines we   fer identifies the transition from one state of the field to another, identifying the evolution of these zone of the culture field.

Delineating difference and spaces of resistance : reading the Nana’s Silence in Rosario Castellanos’ ''Balún Canán''

A escritora mexicana Rosario Castellanos incorpora silêncios em suas obras de uma forma que permite ao leitor a questionar o próprio significado da agência e da natureza da subjetividade de uma protagonista feminina. Silêncios tendem a criar brechas no texto, iluminando as diferenças sociais e raciais que a narração em primeira pessoa foge. Além disso, é revelado que o sujeito se imagina em oposição ao silêncio de mulheres menos privilegiadas, e que realmente não existe um local em que o subalterno pode falar. Este projecto se centra em seu romance Balún Canan (1957), em que a babá Indígena de uma menina complica o desejo de ascender dentro da estrutura patriarcal da sua família mais privilegiada, como a menina descobre que o que faria sua vida confortável é a causa da subjugação de sua “outra mãe.” O texto é desenvolvido em torno de um desejo de falar a partir das margens, e há um esforço claro para dar voz aos subalternos. No entanto, a relação entre a menina e sua babá não é nem romântica nem idealizada; a presença da mulher colonizada resiste a marginalização e ressalta que está sendo coberto no processo de desenvolvimento individual. Ansiedadesurge dentro da narração da menina como ela percebe seu privilégio como membro da classe latifundiária, e a escrita navega entre diferentes manifestações de silêncio: o silenciamento da babá em uma replicação de violência colonial, e a manutenção do silêncio como uma barreira respeitosa.

Dunford-Pettis properties, Hilbert spaces and projective tensor products

We study complete continuity properties of operators onto ℓ2 and prove several results in the Dunford–Pettis theory of JB∗-triples and their projective tensor products, culminating in characterisations of the alternative Dunford–Pettis property for where E and F are JB∗-triples.