Compared to binary switching functions, the multiple-valued functions (MV) offer more compact representations of the information content of signals modeled by logic functions and, therefore, their use fits very well in the general settings of data compression attempts and approaches. The first task in dealing with such signals is to provide mathematical methods for their representation in a way that will make their application in practice feasible. Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for application of related implementation methods and tools. This book presents in a uniform way different representations of multiple-valued logic functions, including functional expressions, spectral representations on finite Abelian groups, and their graphical counterparts (various related decision diagrams). Three-valued, or ternary functions, are traditionally used as the first extension from the binary case. They have a good feature that the ratio between the number of bits and the number of different values that can be encoded with the specified number of bits is favourable for ternary functions. Four-valued functions, also called quaternary functions, are particularly attractive, since in practical realization within today prevalent binary circuits environment, they may be easy coded by binary values and realized with two-stable state circuits. At the same time, there is much more considerable advent in design of four-valued logic circuits than for other $p$-valued functions. Therefore, this book is written using a hands-on approach such that after introducing the general and necessarily abstract background theory, the presentation is based on a large number of examples for ternary and quaternary functions that should provide an intuitive understanding of various representation methods and the interconnections among them. Table of Contents: Multiple-Valued Logic Functions / Functional Expressions for Multiple-Valued Functions / Spectral Representations of Multiple-Valued Functions / Decision Diagrams for Multiple-Valued Functions / Fast Calculation Algorithms
Discover applications of Fourier analysis on finite non-Abeliangroups The majority of publications in spectral techniques considerFourier transform on Abelian groups. However, non-Abelian groupsprovide notable advantages in efficient implementations of spectralmethods. Fourier Analysis on Finite Groups with Applications in SignalProcessing and System Design examines aspects of Fourieranalysis on finite non-Abelian groups and discusses differentmethods used to determine compact representations for discretefunctions providing for their efficient realizations and relatedapplications. Switching functions are included as an example ofdiscrete functions in engineering practice. Additionally,consideration is given to the polynomial expressions and decisiondiagrams defined in terms of Fourier transform on finitenon-Abelian groups. A solid foundation of this complex topic is provided bybeginning with a review of signals and their mathematical modelsand Fourier analysis. Next, the book examines recent achievementsand discoveries in: Matrix interpretation of the fast Fourier transform Optimization of decision diagrams Functional expressions on quaternion groups Gibbs derivatives on finite groups Linear systems on finite non-Abelian groups Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications ofabstract harmonic analysis on finite non-Abelian groups in compactrepresentations of discrete functions and related tasks in signalprocessing and system design, including logic design. All chaptersare self-contained, each with a list of references to facilitatethe development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this isan excellent textbook for graduate-level students and researchersin signal processing, logic design, and system theory-as well asthe more general topics of computer science and appliedmathematics.
This book is about the formation and development of Latin America as name, idea and concept, as well as the wider concepts of location, knowledge and the relationship between them. Latin America is not only a subject or an academic construct, it is also a perspective from which subjectivities are established, knowledge is developed and narratives are produced. This study argues that epistemology cannot exist in abstract terms, despite traditional academic arguments to the contrary. Therefore the author uses 'Latin America' to anchor his more general arguments in a particular location and calls this approach 'geo-epistemology'. The author discusses how the specificity of a particular location can contribute to the establishment of both a method of formulating human knowledge and the boundaries of what can be known. The text explores the relationship between philosophy, geography and geometry, and analyses the notions of science, empire and colonialism. In response to the contemporary debate on 'space of thinking', the author proposes a new concept of 'reversal thinking', which leads to an examination of the roles of language and writing from an epistemic point of view.
In this literary, co-constructed narrative, two Brazilian scholars explore the spaces “in-between”—between their own biographies, one raised privileged, the other poor; between the experience of being raised in Brazil and finding acceptance in United States universities; between their lives in the academic establishment and their studies of poverty in Latin America; between the constraints of apolitical scholarship and the need to promote social justice; between contrasting styles of researching, theorizing, and writing. Their dialogue seeks to decolonize the world of American scholarship and promote the use of research toward inclusive social justice.
This panoramic account of 1776 chronicles the other revolutions unfolding that year across North America, far beyond the British colonies. In this unique history of 1776, Claudio Saunt looks beyond the familiar story of the thirteen colonies to explore the many other revolutions roiling the turbulent American continent. In that fateful year, the Spanish landed in San Francisco, the Russians pushed into Alaska to hunt valuable sea otters, and the Sioux discovered the Black Hills. Hailed by critics for challenging our conventional view of the birth of America, West of the Revolution “[coaxes] our vision away from the Atlantic seaboard” and “exposes a continent seething with peoples and purposes beyond Minutemen and Redcoats” (Wall Street Journal).
This book presents the most thorough analysis to date on the jurisprudence of the Inter-American Court of Human Rights (IACtHR) concerning full reparations. This jurisprudence interprets Article 63 of the American Convention on Human Rights. In its interpretation of the Convention, the IACtHR is guided by the important notion that human rights instruments should be interpreted in light of its object and purpose, in accordance with the State members of the Organization of the American States. The Court’s jurisprudence ensures that victims of human rights violations are awarded not only monetary compensation in cases, but also a full array of reparations designed to restore their dignity and reaffirm the value of the rule of law. Accordingly, reparation also includes moral compensation, guarantees of non repetition, and truth as a measure of satisfaction. More specifically, the book explores the notions of “fair remedy,” “injured party,” and the possibility of achieving “restitutio in integrum” for human rights violations through an analysis of decisions issued by the Inter-American Court. The book urges its reader to consider not only the current status of the law, but also the role played by victims, lawyers, Commissioners, and Judges in its jurisprudential development. As a living instrument, the value of the American Convention depends in great part on their actions and decisions. This book, by presenting the role of the different actors through concrete cases that shaped the system, encourages everyone to think how the System should continue to satisfy the aspirations of justice in cases of human rights violations.
How do we persuade people that we all have common experiences and hopes? That we are ever more dependent on each other in times of globalization via technology, commerce, climate change, and overpopulation? How do we move from an "Us and Them" mentality to simply "Us"? In this book, a follow-up to their first book Betweener Talk, the authors share autoethnographies about being and doing scholarship as betweeners searching for inclusivity. The authors have witnessed an escalation of division in their native Brazil and in the USA, as well as in South America more broadly and Europe – places that had been making steady, albeit slow, progress toward greater inclusion. The book explores identity, interactions, existence, and possibilities in the spaces between "Us" and "Them" to help current and future generations imagine a more inclusive way of living – as Us. It is about how two Third World scholars think the Postcolonial/Decolonizing discourse – with a performance studies lens – can further notions of inclusive social justice through scholarship borne out of lived oppression and the struggle for humanization. It is a union of two authors who, in their own words "have been close friends since our youth, both captivated by Paulo Freire’s notion of education and social transformation through a praxis of conscientização (conscientization), but who experienced life growing up at opposite ends of the social class spectrum. Early through love and later through theory, we have come to viscerally inhabit and embrace our betweener identities in scholarship and daily lives, breaking the distance between us and the paradigms that attempt to separate political, personal, and professional life." The authors’ hope is that their own and other betweener autoethnographies can contribute to the larger qualitative inquiry global movement and its central goal: marching together toward ever greater social justice.
Compared to binary switching functions, the multiple-valued functions (MV) offer more compact representations of the information content of signals modeled by logic functions and, therefore, their use fits very well in the general settings of data compression attempts and approaches. The first task in dealing with such signals is to provide mathematical methods for their representation in a way that will make their application in practice feasible. Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for application of related implementation methods and tools. This book presents in a uniform way different representations of multiple-valued logic functions, including functional expressions, spectral representations on finite Abelian groups, and their graphical counterparts (various related decision diagrams). Three-valued, or ternary functions, are traditionally used as the first extension from the binary case. They have a good feature that the ratio between the number of bits and the number of different values that can be encoded with the specified number of bits is favourable for ternary functions. Four-valued functions, also called quaternary functions, are particularly attractive, since in practical realization within today prevalent binary circuits environment, they may be easy coded by binary values and realized with two-stable state circuits. At the same time, there is much more considerable advent in design of four-valued logic circuits than for other $p$-valued functions. Therefore, this book is written using a hands-on approach such that after introducing the general and necessarily abstract background theory, the presentation is based on a large number of examples for ternary and quaternary functions that should provide an intuitive understanding of various representation methods and the interconnections among them.
Discover applications of Fourier analysis on finite non-Abeliangroups The majority of publications in spectral techniques considerFourier transform on Abelian groups. However, non-Abelian groupsprovide notable advantages in efficient implementations of spectralmethods. Fourier Analysis on Finite Groups with Applications in SignalProcessing and System Design examines aspects of Fourieranalysis on finite non-Abelian groups and discusses differentmethods used to determine compact representations for discretefunctions providing for their efficient realizations and relatedapplications. Switching functions are included as an example ofdiscrete functions in engineering practice. Additionally,consideration is given to the polynomial expressions and decisiondiagrams defined in terms of Fourier transform on finitenon-Abelian groups. A solid foundation of this complex topic is provided bybeginning with a review of signals and their mathematical modelsand Fourier analysis. Next, the book examines recent achievementsand discoveries in: Matrix interpretation of the fast Fourier transform Optimization of decision diagrams Functional expressions on quaternion groups Gibbs derivatives on finite groups Linear systems on finite non-Abelian groups Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications ofabstract harmonic analysis on finite non-Abelian groups in compactrepresentations of discrete functions and related tasks in signalprocessing and system design, including logic design. All chaptersare self-contained, each with a list of references to facilitatethe development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this isan excellent textbook for graduate-level students and researchersin signal processing, logic design, and system theory-as well asthe more general topics of computer science and appliedmathematics.
Compared to binary switching functions, the multiple-valued functions (MV) offer more compact representations of the information content of signals modeled by logic functions and, therefore, their use fits very well in the general settings of data compression attempts and approaches. The first task in dealing with such signals is to provide mathematical methods for their representation in a way that will make their application in practice feasible. Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for application of related implementation methods and tools. This book presents in a uniform way different representations of multiple-valued logic functions, including functional expressions, spectral representations on finite Abelian groups, and their graphical counterparts (various related decision diagrams). Three-valued, or ternary functions, are traditionally used as the first extension from the binary case. They have a good feature that the ratio between the number of bits and the number of different values that can be encoded with the specified number of bits is favourable for ternary functions. Four-valued functions, also called quaternary functions, are particularly attractive, since in practical realization within today prevalent binary circuits environment, they may be easy coded by binary values and realized with two-stable state circuits. At the same time, there is much more considerable advent in design of four-valued logic circuits than for other $p$-valued functions. Therefore, this book is written using a hands-on approach such that after introducing the general and necessarily abstract background theory, the presentation is based on a large number of examples for ternary and quaternary functions that should provide an intuitive understanding of various representation methods and the interconnections among them. Table of Contents: Multiple-Valued Logic Functions / Functional Expressions for Multiple-Valued Functions / Spectral Representations of Multiple-Valued Functions / Decision Diagrams for Multiple-Valued Functions / Fast Calculation Algorithms
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