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.

Linear Stochastic State Space Theory In The White Noise Space Setting, 2010 Chapman University

#### Linear Stochastic State Space Theory In The White Noise Space Setting, Daniel Alpay, David Levanony, Ariel Pinhas

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

We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring, and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant, stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system, namely its average behavior.

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.

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.

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.

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.

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 ...

Rank Distance Bicodes And Their Generalization, 2010 University of New Mexico

#### Rank Distance Bicodes And Their Generalization, Florentin Smarandache, W.B. Vasantha Kandasamy, N. Suresh Babu, R.S. Selvaraj

*Mathematics and Statistics Faculty and Staff Publications*

In this book the authors introduce the new notion of rank distance bicodes and generalize this concept to Rank Distance n-codes (RD n-codes), n, greater than or equal to three. This definition leads to several classes of new RD bicodes like semi circulant rank bicodes of type I and II, semicyclic circulant rank bicode, circulant rank bicodes, bidivisible bicode and so on. It is important to mention that these new classes of codes will not only multitask simultaneously but also they will be best suited to the present computerised era. Apart from this, these codes are best suited in cryptography ...

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.

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 ...

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.

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 ...

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.

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.

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.

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 ...