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  • This book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics. Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fréchet and Hilbert, with new developments on Neumann spaces, but also on extractable spaces. The author presents the main properties of these spaces, which are useful for the construction of Lebesgue and Sobolev distributions with real or vector values and for solving partial differential equations. Differential calculus is also extended to semi-normed spaces. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers without restricting or generalizing the results.
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  • A ground-breaking and enlightening exploration of the structures which elevate architecture to spirituality. Sacred Spaces showcases 30 of the most breath-taking,...
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  • This title concerns the use of a particle filter framework to track objects defined in high-dimensional state-spaces using high-dimensional observation spaces. Current tracking applications require us to consider complex models for objects (articulated objects, multiple objects, multiple fragments, etc.) as well as multiple kinds of information (multiple cameras, multiple modalities, etc.). This book presents some recent research that considers the main bottleneck of particle filtering frameworks (high dimensional state spaces) for tracking in such difficult conditions.
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  • The main objective to the study of theory of Partial Differential Equations (PDEs) is to insure or find out properties of solutions of PDE that are not directly attainable by direct analytical means. Certain function spaces have certain known properties for which solutions of PDEs can be classified. As a result, this work critically looked into some function spaces and their properties. We consider extensively, Lp-spaces, distribution theory and sobolev spaces. The emphasis is made on sobolev spaces, which permit a modern approach to the study of differential equations. Looking at the linear elliptic partial differential equations considered in this work, we see that the key is Lax-Milgram theorem and the full understanding of Sobolev spaces and its properties. We are able to remove the rigor associated with second order partial differential equations and present it in the form that we can easily handle through the function spaces discussed. The book is based on variational formulation of some Boundary Value Problems (PDEs) using some known theorem (Lax-Milgram Theorem) to ascertain the existence and uniqueness of weak solution to such linear Elliptic PDEs.
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  • This book deals with a concise study of convergence in intuitionistic fuzzy n-normed linear spaces. This book mainly contains the author's own research work in the area of lacunary ideal convergence. Fuzzy normed spaces have been an increasingly popular area of mathematical research in recent times, both in terms of theory and applications. But the availability of books in the area of fuzzy normed spaces is very rare. This book provides a good discussion on the development of both fuzzy and intuitionistic fuzzy set theory. The transition from fuzzy normed linear spaces to intuitionistic fuzzy n-normed linear spaces has been presented systematically. Anybody interested in the theory or application of fuzzy or intuitionistic fuzzy normed spaces will find this book more than useful. The book is written in such a way that mathematical prerequisites are minimum. Since the main subject of study in this book is a generalisaton of the concept of usual convergence, so all the related results in convergence have been incorporated in the book. This book may be used as a ready reference for an up to date account of results in the theory of fuzzy/intuitionistic fuzzy normed linear spaces.
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  • Places and Spaces I've Been, this volume documents the continuing adventures in art and design of one of the most influential figures in contemporary music and popular...
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  • Fibonacci sequence is one of the most rapidly growing areas of mathematics which has a wide variety of applications in science and mathematics. This sequence is constructed by choosing the first two numbers (The "seeds" of the sequence) then assigning the rest by the rule that each number be the sum of the two preceding numbers. The Fibonacci sequence is defined as 1 1 2 3 5 8 13 21 34 55 89 144 .... The terms are called Fibonacci numbers. Fibonacci numbers are studied as part of number theory and have many applications in the counting of mathematical objects such as sets, permutations and sequences and to computer science. This sequence is a very intriguing and interesting subject. This book is centered on generalization of Fibonacci sequences. Fibonacci sequence has been generalized in a number of ways. The author simply presented the subject matter in his own style and makes the subject easier by giving concepts and number of results related to each chapter. Emphasis has been made on methods of generalization for Fibonacci sequence in various patterns. Identities of coupled Fibonacci sequences are presented in additive and multiplicative forms.
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  • I stand before you without fear, for I have fully realized the limitless potential of a beneficial existence. I speak of peace as I have personally experienced it. A voice of reason that is free of ego, and rings true in the vacant spaces where the empty promises of state sponsored propaganda, scientific hypothesis, and religious rhetoric, have left you with more questions than answers, more hype than hope, and more prayers than prosperity.
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  • The study of instanton moduli spaces has led to striking results in the geometry of four-manifolds, for they constitute the groundwork for the construction of Donaldson's polynomial invariants, which are capable of distinguishing non-diffeomorphic smooth structures. This construction fails when the base manifold has a negative definite intersection form, since in this case the moduli spaces contain reducible solutions and these are usually singular points. This book is therefore concerned with the study of the geometry of instanton moduli spaces for those manifolds which have negative definite intersection form. In the first part, the topology and the Riemannian geometry near the reducible locus are described. This yields a purely topological condition for one construction of differential topological invariants. In the second part, explicit examples of instanton moduli spaces are computed for all minimal complex surfaces of class VII with second Betti number one and with respect to any Gauduchon metric. This monograph contains the author's PhD thesis, which was written at the Université de Provence Aix-Marseille I (France) under the supervision of Professor Andrei Teleman.
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  • The book investigates graph groupoids and the path spaces associated with their unit spaces. Three main questions are solved. For the first, a natural question that was asked by A.Kumjian in the case of the Cuntz graph was how the topological space X relates to an earlier topological space investigated by J. Renault (Orleans). I show that the two topological spaces are homeomorphic and so can be identified. I then discuss the graph groupoid in the general case. For this investigation, it is important to be able to use the axiomatic approach to groupoids, and I show that this is equivalent to the usual definition of a groupoid as a "small category with inverses". This proof of this equivalence answers the second main question. The last is to construct the graph groupoid and prove that it is a second countable, locally compact, Hausdorff groupoid.
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  • Master's Thesis from the year 2014 in the subject Computer Science - Bioinformatics, grade: N, , language: English, abstract: The data from next generation sequencing technologies has led to an explosion in genome sequence data available in public databases. This data provides unique opportunities to study the molecular mechanisms of gene evolution: how new genes and proteins originate and how they diversify. A major challenge is retracing origin of extant genes or proteins, by searching existing databases for related sequences and identifying evolutionary similarities. Therefore, enhanced and faster search algorithms are being developed, e.g. on accelerators such as GPU, in order to cope with the huge size of today's DNA or protein sequence databases. Gene-Tracer is a tool was developed to localize the common sub-sequences between two ancestors and its offspring. Besides, compute percentages of ancestors' contributions in offspring. Gene-Tracer was developed to find the origin of unknown shuffling/offspring sequence. A database is scanned and the similarity between offspring sequence and each one in the database is computed using pairwise local sequence alignment algorithm. Based on similarity score, 100 sequences that have the highest score is re-aligned with shuffling sequence to determine length of common sub-sequences between them using local alignment algorithm. The two sequences that have longest sub-sequences with shuffling are the nearest origin to offspr...
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  • The work contained in this book goes along way into extending the boundary of topological concepts. The author uses very simple language to explain notions of topology and therefore provide an elaborate explanation of the hitherto difficult mathematical ideas. It is now clear that isotonic spaces can easily substitute topological spaces in the study of most concepts in topology. This book gives preliminary understanding of Topos theory.
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  • Industrial Spaces features designs derived from the need of various industries to provide efficient, safe and workable spaces for both operations and administration, while at the same time complying with rigorous industry standards and incorporating the latest technology. The setting of the industry itself also influences such space, whether it be on an industrial estate, on the city fringe, in a rural precinct, or an inner urban area. This book with its 400 color images will depict how these industrial space designs are a far cry from the utilitarian constructions of the past. These industrial spaces are award-winning architectural masterpieces. Издание на английском языке.
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  • Master's Thesis from the year 2016 in the subject Art - Architecture / History of Construction, grade: Excellent, Addis Ababa University (Ethiopian Institute of Architecture, Building Construction and City Development), course: Housing and Sustainable Development, language: English, abstract: The main objective of this research is to understand the age long experiences of people living around shared residential open spaces in the old neighborhoods of Addis Ababa. And the manner is focused on the comprehension of the shared open spaces in the neighborhoods as a social and cultural products or phenomena.Case study research is employed to do this research because it is an auspicious method to study such contemporary phenomenological processes. Particularly four shared open spaces are systematically chosen from the inner-city old neighborhoods and studied. The research tries to understand the shared open spaces through their physical and spatial character: spatial configurations and transformations and their relationship with the dwellers; covering such aspects as: activities, meanings, behaviors, communications and perception. And both quantitative and qualitative data are collected through in-depth interviews, mapping, time diaries, observations and photography. The collected data is analyzed through comparative pattern matching, statistical computations, semantic differentials and cross-compound analysis.The study revealed that the open spaces have from four up to five lay...
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  • The main purpose of this book is to introduce the generalized composition operators and the generalized multiplication operators on weighted Hardy spaces . Composition operators have been the subject matter of intensive study over past several decades and they find applications in ergodic theory ,quantum mechanics and other branches of mathematical and physical sciences . The 1st chapter of the book contains introductory material . The compact, Fredholm generalized composition operators are characterized in the second chapter. The Hermitian,Normal ,Quasi normal ,Isometric and co isometric generalized composition operators are presented in the third chapter. It is shown that most of the properties of the generalized multiplication operators differ from the multiplication operators acting on other function spaces .eg:- On most of the function spaces multiplication operators are normal .But this result is not valid incase of generalized multiplication operators on weighted Hardy spaces . In this book some light is thrown on differential and anti-differential operators acting on weighted Hardy spaces .
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