163 resultados para isomorphism


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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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What would be the ""terrible loneliness"" and what would be the ""wonderful agreement"" in the present paper? The ""terrible loneliness"" is the only reality that a person perceives and/or thinks during the now going on. For the person, an enormous quantity of occurrences is in the present moment absent. A very small quantity of occurrences is present. The person is the only being in having this. And, this is only during a little moment. The person never thinks about his loneliness in this moment. On the contrary, he thinks he is plenty of people and full of occurrences. But, if he were thinking about reality, he would live in a terrible loneliness. How does he escape himself from this loneliness? He thinks that the probable occurrences are real occurrences. He may be right in a plenty of times. Going through what I call opening hypotheses-basic hypotheses and non-basic but important hypotheses-and going through what I call simply hypotheses he is able to sanction a wonderful agreement of human beings about the known parts of the Universe. However, they are hypotheses, not absolute realities.

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A loop is said to be automorphic if its inner mappings are automorphisms. For a prime p, denote by A(p) the class of all 2-generated commutative automorphic loops Q possessing a central subloop Z congruent to Z(p) such that Q/Z congruent to Z(p) x Z(p). Upon describing the free 2-generated nilpotent class two commutative automorphic loop and the free 2-generated nilpotent class two commutative automorphic p-loop F-p in the variety of loops whose elements have order dividing p(2) and whose associators have order dividing p, we show that every loop of A(p) is a quotient of F-p by a central subloop of order p(3). The automorphism group of F-p induces an action of GL(2)(p) on the three-dimensional subspaces of Z(F-p) congruent to (Z(p))(4). The orbits of this action are in one-to-one correspondence with the isomorphism classes of loops from A(p). We describe the orbits, and hence we classify the loops of A(p) up to isomorphism. It is known that every commutative automorphic p-loop is nilpotent when p is odd, and that there is a unique commutative automorphic loop of order 8 with trivial center. Knowing A(p) up to isomorphism, we easily obtain a classification of commutative automorphic loops of order p(3). There are precisely seven commutative automorphic loops of order p(3) for every prime p, including the three abelian groups of order p(3).

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We introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordan's simple localization of the multiparameter quantized Weyl algebra and Hayashi's q-analog of the Weyl algebra are special cases of this construction. We classify all simple weight modules over any multiparameter twisted Weyl algebra. Extending results by Benkart and Ondrus, we also describe all Whittaker pairs up to isomorphism over a class of twisted generalized Weyl algebras which includes the multiparameter twisted Weyl algebras. (C) 2011 Elsevier Inc. All rights reserved.

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Interactive theorem provers (ITP for short) are tools whose final aim is to certify proofs written by human beings. To reach that objective they have to fill the gap between the high level language used by humans for communicating and reasoning about mathematics and the lower level language that a machine is able to “understand” and process. The user perceives this gap in terms of missing features or inefficiencies. The developer tries to accommodate the user requests without increasing the already high complexity of these applications. We believe that satisfactory solutions can only come from a strong synergy between users and developers. We devoted most part of our PHD designing and developing the Matita interactive theorem prover. The software was born in the computer science department of the University of Bologna as the result of composing together all the technologies developed by the HELM team (to which we belong) for the MoWGLI project. The MoWGLI project aimed at giving accessibility through the web to the libraries of formalised mathematics of various interactive theorem provers, taking Coq as the main test case. The motivations for giving life to a new ITP are: • study the architecture of these tools, with the aim of understanding the source of their complexity • exploit such a knowledge to experiment new solutions that, for backward compatibility reasons, would be hard (if not impossible) to test on a widely used system like Coq. Matita is based on the Curry-Howard isomorphism, adopting the Calculus of Inductive Constructions (CIC) as its logical foundation. Proof objects are thus, at some extent, compatible with the ones produced with the Coq ITP, that is itself able to import and process the ones generated using Matita. Although the systems have a lot in common, they share no code at all, and even most of the algorithmic solutions are different. The thesis is composed of two parts where we respectively describe our experience as a user and a developer of interactive provers. In particular, the first part is based on two different formalisation experiences: • our internship in the Mathematical Components team (INRIA), that is formalising the finite group theory required to attack the Feit Thompson Theorem. To tackle this result, giving an effective classification of finite groups of odd order, the team adopts the SSReflect Coq extension, developed by Georges Gonthier for the proof of the four colours theorem. • our collaboration at the D.A.M.A. Project, whose goal is the formalisation of abstract measure theory in Matita leading to a constructive proof of Lebesgue’s Dominated Convergence Theorem. The most notable issues we faced, analysed in this part of the thesis, are the following: the difficulties arising when using “black box” automation in large formalisations; the impossibility for a user (especially a newcomer) to master the context of a library of already formalised results; the uncomfortable big step execution of proof commands historically adopted in ITPs; the difficult encoding of mathematical structures with a notion of inheritance in a type theory without subtyping like CIC. In the second part of the manuscript many of these issues will be analysed with the looking glasses of an ITP developer, describing the solutions we adopted in the implementation of Matita to solve these problems: integrated searching facilities to assist the user in handling large libraries of formalised results; a small step execution semantic for proof commands; a flexible implementation of coercive subtyping allowing multiple inheritance with shared substructures; automatic tactics, integrated with the searching facilities, that generates proof commands (and not only proof objects, usually kept hidden to the user) one of which specifically designed to be user driven.

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The purpose of this thesis is to establish a direct relationship between literature and fields of knowledge such as science and technology, by focusing on some concepts that were fundamental for both science and the humanities at the beginning of the 20th century. The concepts are those of simultaneity, multiple points of view, map, relativity and acausality. In the spirit of several recent ideas, for example Katherine Hayles’ isomorphism notion, the dissertation shows how writers such as James Joyce, Virginia Woolf, Thomas Mann and Robert Musil developed the mentioned concepts within their narratives. The working hypothesis is that those concepts were at a crossroad of human activities, and that those authors used them extensively within their narratives. It is further argued that those same concepts – as developed by Joyce in Ulysses, Woolf’s shorts stories and novels from the end of the 1910’s until the end of the1920’s, Mann’s Der Zauberberg (The Magic Mountain), and Musil’s Der Mann ohne Eigenschaften (The Man Without Qualities) — are still fundamental for our conception of time and space today. The thesis is divided into two parts. The first two chapters will analyse the concepts of simultaneity and multiple points of view and their relationship to cartography as developed within English literature and culture. The next two chapters will address the concepts of relativity and acausality, as developed within German literature and culture.

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This work of thesis involves various aspects of crystal engineering. Chapter 1 focuses on crystals containing crown ether complexes. Aspects such as the possibility of preparing these materials by non-solution methods, i.e. by direct reaction of the solid components, thermal behavior and also isomorphism and interconversion between hydrates are taken into account. In chapter 2 a study is presented aimed to understanding the relationship between hydrogen bonding capability and shape of the building blocks chosen to construct crystals. The focus is on the control exerted by shape on the organization of sandwich cations such as cobalticinium, decamethylcobalticinium and bisbenzenchromium(I) and on the aggregation of monoanions all containing carboxylic and carboxylate groups, into 0-D, 1-D, 2-D and 3-D networks. Reactions conducted in multi-component molecular assemblies or co-crystals have been recognized as a way to control reactivity in the solid state. The [2+2] photodimerization of olefins is a successful demonstration of how templated solid state synthesis can efficiently synthesize unique materials with remarkable stereoselectivity and under environment-friendly conditions. A demonstration of this synthetic strategy is given in chapter 3. The combination of various types of intermolecular linkages, leading to formation of high order aggregation and crystalline materials or to a random aggregation resulting in an amorphous precipitate, may not go to completeness. In such rare cases an aggregation process intermediate between crystalline and amorphous materials is observed, resulting in the formation of a gel, i.e. a viscoelastic solid-like or liquid-like material. In chapter 4 design of new Low Molecular Weight Gelators is presented. Aspects such as the relationships between molecular structure, crystal packing and gelation properties and the application of this kind of gels as a medium for crystal growth of organic molecules, such as APIs, are also discussed.

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The Curry-Howard isomorphism is the idea that proofs in natural deduction can be put in correspondence with lambda terms in such a way that this correspondence is preserved by normalization. The concept can be extended from Intuitionistic Logic to other systems, such as Linear Logic. One of the nice conseguences of this isomorphism is that we can reason about functional programs with formal tools which are typical of proof systems: such analysis can also include quantitative qualities of programs, such as the number of steps it takes to terminate. Another is the possiblity to describe the execution of these programs in terms of abstract machines. In 1990 Griffin proved that the correspondence can be extended to Classical Logic and control operators. That is, Classical Logic adds the possiblity to manipulate continuations. In this thesis we see how the things we described above work in this larger context.

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La trattazione è volta all'esposizione dell'algoritmo di Lindell per determinare in logspazio se due alberi sono isomorfi. Un'ampia parte introduttiva richiama i prerequisiti teorici necessari alla comprensione della parte di esposizione dell'algoritmo.

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This book will serve as a foundation for a variety of useful applications of graph theory to computer vision, pattern recognition, and related areas. It covers a representative set of novel graph-theoretic methods for complex computer vision and pattern recognition tasks. The first part of the book presents the application of graph theory to low-level processing of digital images such as a new method for partitioning a given image into a hierarchy of homogeneous areas using graph pyramids, or a study of the relationship between graph theory and digital topology. Part II presents graph-theoretic learning algorithms for high-level computer vision and pattern recognition applications, including a survey of graph based methodologies for pattern recognition and computer vision, a presentation of a series of computationally efficient algorithms for testing graph isomorphism and related graph matching tasks in pattern recognition and a new graph distance measure to be used for solving graph matching problems. Finally, Part III provides detailed descriptions of several applications of graph-based methods to real-world pattern recognition tasks. It includes a critical review of the main graph-based and structural methods for fingerprint classification, a new method to visualize time series of graphs, and potential applications in computer network monitoring and abnormal event detection.

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In this paper, concepts from the emerging family-centered paradigm in child welfare and mental health are applied to evaluative research in family preservation: the ecological perspective, enhancement of competence, a consumer orientation, and collaborative relationships. The experience of family preservation research collaborators from the School of Social Work at the University of Nevada, Reno and the Nevada Division of Child and Family Services illustrate these concepts. The researchers apply the theory of isomorphism to the research endeavor to produce eight principles of effective research partnerships derived from family-centered concepts and their own experiences.

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he simulation of complex LoC (Lab-on-a-Chip) devices is a process that requires solving computationally expensive partial differential equations. An interesting alternative uses artificial neural networks for creating computationally feasible models based on MOR techniques. This paper proposes an approach that uses artificial neural networks for designing LoC components considering the artificial neural network topology as an isomorphism of the LoC device topology. The parameters of the trained neural networks are based on equations for modeling microfluidic circuits, analogous to electronic circuits. The neural networks have been trained to behave like AND, OR, Inverter gates. The parameters of the trained neural networks represent the features of LoC devices that behave as the aforementioned gates. This would mean that LoC devices universally compute.

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Este estudio se centra en examinar la evolución en los niveles de éxito en la resolución de problemas de estructura multiplicativa por estudiantes de Educación Primaria (desde 1º a 6º curso, alumnos de 6 a 12 años). Los resultados indican que, en función de las categorías, los problemas de producto de medida fueron los más difíciles en todos los cursos y los problemas de isomorfismos de medida los más fáciles, mientras que los de comparación multiplicativa se mantuvieron entre ambos. Por el contrario, la evolución de los niveles de éxito en función de la clase de problema, no fue uniforme a lo largo de la educación primaria para los problemas de isomorfismo de medida pero sí en las otras dos categorías.

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Thesis (Ph.D.)--University of Washington, 2016-06