Morphogrammatics Of Reflection, 2010 ThinkArt Lab Glasgow

#### Morphogrammatics Of Reflection, Rudolf Kaehr

*Rudolf Kaehr*

Turning back from the studies of morphogrammatics to some open questions of reflectional programming, the recountered problematics might be put into a different light and new methods of handling formal aspects of reflection and reflectionality shall be introduced. Albeit the use of light-metaphors, morphogrammatic reflection is not sketched along the paradigm of optical metaphors. Morphograms are presenting neither propositions nor perceptions able for mirroring (representation). Exercises in defining morphogrammatic retro-grade recursion and reflection schemata are continued from the paper “Sketches to Morphogrammatic Programming”.

The Life Of Evariste Galois And His Theory Of Field Extension, 2010 Liberty University

#### The Life Of Evariste Galois And His Theory Of Field Extension, Felicia N. Adams

*Senior Honors Theses*

Evariste Galois made many important mathematical discoveries in his short lifetime, yet perhaps the most important are his studies in the realm of field extensions. Through his discoveries in field extensions, Galois determined the solvability of polynomials. Namely, given a polynomial P with coefficients is in the field F and such that the equation P(x) = 0 has no solution, one can extend F into a field L with α in L, such that P(α) = 0. Whereas Galois Theory has numerous practical applications, this thesis will conclude with the examination and proof of the fact that it is impossible ...

Dancing With Heretics: Essays On Orthodoxy, Questioning And Faith, 2010 Utah State University

#### Dancing With Heretics: Essays On Orthodoxy, Questioning And Faith, Darren M. Edwards

*All Graduate Theses and Dissertations*

While much has been written about the conflicts, supposed or actual, between logic and faith, science and religion, few accounts of the personal turmoil these conflicts can cause exist. Likewise, many of these nonfiction accounts are written from a distinctly polarized place leaning either to science or faith. In this thesis, I mix research and history with memoir and a sense of poetry to explore my personal experience with this conflict. At its outset, I hoped for this project to capture my struggle as an orthodox member of The Church of Jesus Christ of Latter-day Saints (LDS) in dealing with ...

Memristics: Memristors, Again? – Part Ii, How To Transform Wired ‘Translations’ Between Crossbars Into Interactions?, 2010 ThinkArt Lab Glasgow

#### Memristics: Memristors, Again? – Part Ii, How To Transform Wired ‘Translations’ Between Crossbars Into Interactions?, Rudolf Kaehr

*Rudolf Kaehr*

The idea behind this patchwork of conceptual interventions is to show the possibility of a “buffer-free” modeling of the crossbar architecture for memristive systems on the base of a purely difference-theoretical approach. It is considered that on a nano-electronic level principles of interpretation appears as mechanisms of complementarity. The most basic conceptual approach to such a complementarity is introduced as an interchangeability of operators and operands of an operation. Therefore, the architecture of crossbars gets an interpretation as complementarity between crossbar functionality and “buffering” translation functionality. That is, the same matter functions as operator and at once, as operand – and ...

Memristics: Memristors, Again?, 2010 ThinkArt Lab Glasgow

#### Memristics: Memristors, Again?, Rudolf Kaehr

*Rudolf Kaehr*

This collection gives first and short critical reflections on the concepts of memristics, memristors and memristive systems and the history of similar movements with an own focus on a possible interplay between memory and computing functions, at once, at the same place and time, to achieve a new kind of complementarity between computation and memory on a single chip without retarding buffering conditions.

Sketch Of A Typology Of Abstract Memristic Machines, 2010 ThinkArt Lab Glasgow

#### Sketch Of A Typology Of Abstract Memristic Machines, Rudolf Kaehr

*Rudolf Kaehr*

A typology of memristic machines is sketched. This sketch gives an overview and orientation to the paper “Towards Abstract Memristic Machines”. It also intents to propose a concise systematization of the newly introduced terms and strategies to memristics and morphogrammatics. This sketch is introducing four types of sign-use for four types of machines of fundamentally different paradigms: 1. semiotic, 2. monomorphic, 3. polymorphic and 4. bisimilar abstract machines. Further definitions of abstract machines have to be based on those graphematic notational systems. A realization of such constructions of abstract machines, in contrast to existing abstract machines of the theory of ...

Towards Abstract Memristic Machines, 2010 ThinkArt Lab Glasgow

From Universe To Polyverses, 2010 ThinkArt Lab Glasgow

#### From Universe To Polyverses, Rudolf Kaehr

*Rudolf Kaehr*

Some thoughts about the power of speculation behind important discoveries in mathematics, physics and computer science. The exercise shows that there is no need for a compulsory ultimate unifying universe. It is speculated that just this paradigm of a single ultimate universe is unmasking itself today as the main obstacle for further development in Western science and technology.

Morphogrammatics For Dummies: The Domino Approach, 2010 ThinkArt Lab Glasgow

#### Morphogrammatics For Dummies: The Domino Approach, Rudolf Kaehr

*Rudolf Kaehr*

Dominoes, morphograms, cellular automata, memristics. Topics: possible continuation, coalitions, cooperations, substitution, morphic bisimilarity.

Mathematics In Motion: Linear Systems Of Differential Equations On The Differential Analyzer, 2010 Marshall University

#### Mathematics In Motion: Linear Systems Of Differential Equations On The Differential Analyzer, Devon A. Tivener

*Theses, Dissertations and Capstones*

In this work, I will provide an introduction to the dierential analyzer, a machine designed to solve dierential equations through a process called mechanical integration. I will give a brief historical account of dierential analyzers of the past, and discuss the Marshall University Dierential Analyzer Project. The goal of this work is to provide an analysis of solutions of systems of dierential equations using a dierential analyzer. In particular, we are interested in the points at which these systems are in equilibrium and the behavior of solutions that start away from equilibrium. After giving a description of linear systems of ...

New Classes Of Neutrosophic Linear Algebras, 2010 University of New Mexico

#### New Classes Of Neutrosophic Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

*Mathematics and Statistics Faculty and Staff Publications*

In this book we introduce mainly three new classes of linear algebras; neutrosophic group linear algebras, neutrosophic semigroup linear algebras and neutrosophic set linear algebras. The authors also define the fuzzy analogue of these three structures. This book is organized into seven chapters. Chapter one is introductory in content. The notion of neutrosophic set linear algebras and neutrosophic neutrosophic set linear algebras are introduced and their properties analysed in chapter two. Chapter three introduces the notion of neutrosophic semigroup linear algebras and neutrosophic group linear algebras. A study of their substructures are systematically carried out in this chapter. The fuzzy ...

Interval Linear Algebra, 2010 University of New Mexico

#### Interval Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy

*Mathematics and Statistics Faculty and Staff Publications*

This Interval arithmetic or interval mathematics developed in 1950’s and 1960’s by mathematicians as an approach to putting bounds on rounding errors and measurement error in mathematical computations. However no proper interval algebraic structures have been defined or studies. In this book we for the first time introduce several types of interval linear algebras and study them. This structure has become indispensable for these concepts will find applications in numerical optimization and validation of structural designs. In this book we use only special types of intervals and introduce the notion of different types of interval linear algebras and ...

Advances And Applications Of Dsmt For Information Fusion (In Chinese), 2010 University of New Mexico

#### Advances And Applications Of Dsmt For Information Fusion (In Chinese), Florentin Smarandache, Jean Dezert

*Mathematics and Statistics Faculty and Staff Publications*

No abstract provided.

Interval Groupoids, 2010 University of New Mexico

#### Interval Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy, Moon Kumar Chetry

*Mathematics and Statistics Faculty and Staff Publications*

This book introduces several new classes of groupoid, like polynomial groupoids, matrix groupoids, interval groupoids, polynomial interval groupoids, matrix interval groupoids and their neutrosophic analogues.

Super Special Codes Using Super Matrices, 2010 University of New Mexico

#### Super Special Codes Using Super Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

*Mathematics and Statistics Faculty and Staff Publications*

The new classes of super special codes are constructed in this book using the specially constructed super special vector spaces. These codes mainly use the super matrices. These codes can be realized as a special type of concatenated codes. This book has four chapters. In chapter one basic properties of codes and super matrices are given. A new type of super special vector space is constructed in chapter two of this book. Three new classes of super special codes namely, super special row code, super special column code and super special codes are introduced in chapter three. Applications of these ...

Bitopological Duality For Distributive Lattices And Heyting Algebras, 2010 New Mexico State University

#### Bitopological Duality For Distributive Lattices And Heyting Algebras, Guram Bezhanishvili, Nick Bezhanishvili, David Gabelaia, Alexander Kurz

*Engineering Faculty Articles and Research*

We introduce pairwise Stone spaces as a natural bitopological generalization of Stone spaces—the duals of Boolean algebras—and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important for ...

On Coalgebras Over Algebras, 2010 University Politehnica of Bucharest

#### On Coalgebras Over Algebras, Adriana Balan, Alexander Kurz

*Engineering Faculty Articles and Research*

We extend Barr’s well-known characterization of the final coalgebra of a Set-endofunctor as the completion of its initial algebra to the Eilenberg-Moore category of algebras for a Set-monad M for functors arising as liftings. As an application we introduce the notion of commuting pair of endofunctors with respect to the monad M and show that under reasonable assumptions, the final coalgebra of one of the endofunctors involved can be obtained as the free algebra generated by the initial algebra of the other endofunctor.

Families Of Symmetries As Efficient Models Of Resource Binding, 2010 Institute for Logic, Language and Computation - Amsterdam

#### Families Of Symmetries As Efficient Models Of Resource Binding, Vincenzo Ciancia, Alexander Kurz, Ugo Montanari

*Engineering Faculty Articles and Research*

Calculi that feature resource-allocating constructs (e.g. the pi-calculus or the fusion calculus) require special kinds of models. The best-known ones are presheaves and nominal sets. But named sets have the advantage of being finite in a wide range of cases where the other two are infinite. The three models are equivalent. Finiteness of named sets is strictly related to the notion of finite support in nominal sets and the corresponding presheaves. We show that named sets are generalisd by the categorical model of families, that is, free coproduct completions, indexed by symmetries, and explain how locality of interfaces gives ...

On Universal Algebra Over Nominal Sets, 2010 Chapman University

#### On Universal Algebra Over Nominal Sets, Alexander Kurz, Daniela Petrişan

*Engineering Faculty Articles and Research*

We investigate universal algebra over the category Nom of nominal sets. Using the fact that Nom is a full re ective subcategory of a monadic category, we obtain an HSP-like theorem for algebras over nominal sets. We isolate a `uniform' fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into `uniform' theories and systematically prove HSP theorems for models of these theories.

Algebraic Theories Over Nominal Sets, 2010 Chapman University

#### Algebraic Theories Over Nominal Sets, Alexander Kurz, Daniela Petrişan, Jiří Velebil

*Engineering Faculty Articles and Research*

We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to introduce new notions of finitary based monads and uniform monads. In a second part we spell out these notions in the language of universal algebra, show how to recover the logics of Gabbay-Mathijssen and Clouston-Pitts, and apply classical results from universal algebra.