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.

Local Fractional Fourier’S Transform Based On The Local Fractional Calculus, 2010 Zongxin Kang, Changhe Liu

#### Local Fractional Fourier’S Transform Based On The Local Fractional Calculus, Yang Xiao-Jun

*Xiao-Jun Yang*

A new modeling for the local fractional Fourier’s transform containing the local fractional calculus is investigated in fractional space. The properties of the local fractional Fourier’s transform are obtained and two examples for the local fractional systems are investigated in detail.

Grafika Inżynierska Ćw., 2010 Wroclaw University of Technology

#### Grafika Inżynierska Ćw., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Projektowanie Procesów Biotechnologicznych Proj., 2010 Wroclaw University of Technology

#### Projektowanie Procesów Biotechnologicznych Proj., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Projektowanie I Optymalizacja Procesów Proj., 2010 Wroclaw University of Technology

#### Projektowanie I Optymalizacja Procesów Proj., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Metody Numeryczne Lab., 2010 Consulting Services

#### Metody Numeryczne Lab., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Odnawialne Źródła Energii W., 2010 Wroclaw University of Technology

#### Odnawialne Źródła Energii W., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

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.

Financial Risk Management In Restructured Wholesale Power Markets: Concepts And Tools, 2010 Iowa State University

#### Financial Risk Management In Restructured Wholesale Power Markets: Concepts And Tools, Nanpeng Yu, Abhishek Somani, Leigh Tesfatsion

*Economics Presentations, Posters and Proceedings*

The goal of this tutorial is three-fold: to facilitate cross-disciplinary communication among power engineers and economists by explaining and illustrating basic financial risk management concepts relevant for wholesale power markets (WPMs); to illustrate the complicated and risky strategic decision making required of power traders and risk managers operating in multiple interrelated submarkets comprising modern WPMs; and to briefly discuss the potential of agent-based modeling for the study of this decision making.

On The Characteristics Of A Class Of Gaussian Processes Within The White Noise Space Setting, 2010 Chapman University

#### On The Characteristics Of A Class Of Gaussian Processes Within The White Noise Space Setting, Daniel Alpay, Haim Attia, David Levanony

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

Using the white noise space framework, we define a class of stochastic processes which include as a particular case the fractional Brownian motion and its derivative. The covariance functions of these processes are of a special form, studied by Schoenberg, von Neumann and Krein.

Linear Stochastic Systems: A White Noise Approach, 2010 Chapman University

#### Linear Stochastic Systems: A White Noise Approach, Daniel Alpay, David Levanony

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

Using the white noise setting, in particular the Wick product, the Hermite transform, and the Kondratiev space, we present a new approach to study linear stochastic systems, where randomness is also included in the transfer function. We prove BIBO type stability theorems for these systems, both in the discrete and continuous time cases. We also consider the case of dissipative systems for both discrete and continuous time systems. We further study ℓ1-ℓ2 stability in the discrete time case, and L2-L∞ stability in the continuous time case.

Krein Systems And Canonical Systems On A Finite Interval: Accelerants With A Jump Discontinuity At The Origin And Continuous Potentials, 2010 Chapman University

#### Krein Systems And Canonical Systems On A Finite Interval: Accelerants With A Jump Discontinuity At The Origin And Continuous Potentials, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

This paper is devoted to connections between accelerants and potentials of Krein systems and of canonical systems of Dirac type, both on a finite interval. It is shown that a continuous potential is always generated by an accelerant, provided the latter is continuous with a possible jump discontinuity at the origin. Moreover, the generating accelerant is uniquely determined by the potential. The results are illustrated on pseudo-exponential potentials. The paper is a continuation of the earlier paper of the authors [1] dealing with the direct problem for Krein systems.

Discrete-Time Multi-Scale Systems, 2010 Chapman University

#### Discrete-Time Multi-Scale Systems, Daniel Alpay, Mamadou Mboup

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the poly-disc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.

EΠi + 1=0: The History & Development, 2010 Bridgewater State University

#### EΠi + 1=0: The History & Development, Dawne Charters-Nelson

*Undergraduate Review*

I have on occasion run across the equation in books, articles and in conversation with other mathematicians. In each of these encounters the person alluded to a fascination with this equation which links the five most important constants in the whole of analysis:

- 0 = The additive identity
- 1 = The multiplicative identity
- π = The circular constant
- e = The base of the natural logarithms
- i = The imaginary unit

Being a novice mathematician, I wondered how all these fundamental constants could end up in one equation and what it meant. Along with this thought came the realization that there was some fun investigating ...

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.

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.