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- White noise space (3)
- Wick product (3)
- Random systems (2)
- Algebras over a monad (1)
- Bitopologies (1)
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- Coalgebra (1)
- Coalgebras (1)
- Discrete-scale transformation (1)
- Distributive lattices (1)
- Duality theory (1)
- Families (1)
- Fractional Brownian motion (1)
- Fuzzy rank distance codes (1)
- Heyting algebras (1)
- History-dependent Automata (1)
- Interval arithmetics (1)
- Interval groupoids (1)
- Interval linear algebra (1)
- Interval mathematics (1)
- Linear systems (1)
- Matrix groupoids (1)
- Named Sets (1)
- Partition Refinement (1)
- Polynomial groupoids (1)
- Presheaves (1)
- Rank distance bicodes (1)
- Rank distance codes (1)
- Reproducing kernels (1)
- Scale invariance (1)
- Self-similarity (1)
Articles 1 - 13 of 13
Full-Text Articles in Algebra
Bitopological Duality For Distributive Lattices And Heyting Algebras, Guram Bezhanishvili, Nick Bezhanishvili, David Gabelaia, Alexander Kurz
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 the study …
On Coalgebras Over Algebras, Adriana Balan, Alexander Kurz
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.
On Universal Algebra Over Nominal Sets, Alexander Kurz, Daniela Petrişan
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.
Families Of Symmetries As Efficient Models Of Resource Binding, Vincenzo Ciancia, Alexander Kurz, Ugo Montanari
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 good …
Algebraic Theories Over Nominal Sets, Alexander Kurz, Daniela Petrişan, Jiří Velebil
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.
On The Characteristics Of A Class Of Gaussian Processes Within The White Noise Space Setting, Daniel Alpay, Haim Attia, David Levanony
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.
Interval Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy
Interval Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch 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 interval vector …
Rank Distance Bicodes And Their Generalization, Florentin Smarandache, W.B. Vasantha Kandasamy, N. Suresh Babu, R.S. Selvaraj
Rank Distance Bicodes And Their Generalization, Florentin Smarandache, W.B. Vasantha Kandasamy, N. Suresh Babu, R.S. Selvaraj
Branch 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. …
Interval Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy, Moon Kumar Chetry
Interval Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy, Moon Kumar Chetry
Branch 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.
Linear Stochastic State Space Theory In The White Noise Space Setting, Daniel Alpay, David Levanony, Ariel Pinhas
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.
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
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.
Linear Stochastic Systems: A White Noise Approach, Daniel Alpay, David Levanony
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, Daniel Alpay, Mamadou Mboup
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.