Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Algebras for rough sets (1)
- Formal Concept Analysis (1)
- Grassmann algebra (1)
- Half space (1)
- Kalman–Yakubovich–Popov lemma (1)
-
- Lattice-based logics (1)
- Modal logic (1)
- Negative squares (1)
- Positive real functions (1)
- Proper display calculi (1)
- Residuated binars (1)
- Residuated lattices (1)
- Residuation (1)
- Rough set theory (1)
- Schur analysis (1)
- Slice hyperholomorphic functions (1)
- Subvariety lattices (1)
- Toeplitz matrices (1)
- Unit ball (1)
- Wiener algebra (1)
- Publication
- Publication Type
Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Distributive Laws In Residuated Binars, Wesley Fussner, Peter Jipsen
Distributive Laws In Residuated Binars, Wesley Fussner, Peter Jipsen
Mathematics, Physics, and Computer Science Faculty Articles and Research
In residuated binars there are six non-obvious distributivity identities of ⋅,/,∖ over ∧,∨. We show that in residuated binars with distributive lattice reducts there are some dependencies among these identities; specifically, there are six pairs of identities that imply another one of these identities, and we provide counterexamples to show that no other dependencies exist among these.
Positivity, Rational Schur Functions, Blaschke Factors, And Other Related Results In The Grassmann Algebra, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
Positivity, Rational Schur Functions, Blaschke Factors, And Other Related Results In The Grassmann Algebra, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
We begin a study of Schur analysis in the setting of the Grassmann algebra when the latter is completed with respect to the 1-norm. We focus on the rational case. We start with a theorem on invertibility in the completed algebra, and define a notion of positivity in this setting. We present a series of applications pertaining to Schur analysis, including a counterpart of the Schur algorithm, extension of matrices and rational functions. Other topics considered include Wiener algebra, reproducing kernels Banach modules, and Blaschke factors.
Logics For Rough Concept Analysis, Giuseppe Greco, Peter Jipsen, Krishna Manoorkar, Alessandra Palmigiano, Apostolos Tzimoulis
Logics For Rough Concept Analysis, Giuseppe Greco, Peter Jipsen, Krishna Manoorkar, Alessandra Palmigiano, Apostolos Tzimoulis
Mathematics, Physics, and Computer Science Faculty Books and Book Chapters
Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough algebra counterparts of certain subclasses of rough formal contexts, and introduce proper display calculi for the logics associated with these varieties which are sound, complete, conservative and with uniform cut elimination and subformula property. These calculi modularly extend the multi-type calculi for rough algebras to a ‘nondistributive’ (i.e. general lattice-based) setting.
Positive And Generalized Positive Real Lemma For Slice Hyperholomorphic Functions, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini
Positive And Generalized Positive Real Lemma For Slice Hyperholomorphic Functions, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the half space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball.
Distribution Spaces And A New Construction Of Stochastic Processes Associated With The Grassmann Algebra, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
Distribution Spaces And A New Construction Of Stochastic Processes Associated With The Grassmann Algebra, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
We associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives.
A (Co)Algebraic Approach To Hennessy-Milner Theorems For Weakly Expressive Logics, Zeinab Bakhtiari, Helle Hvid Hansen, Alexander Kurz
A (Co)Algebraic Approach To Hennessy-Milner Theorems For Weakly Expressive Logics, Zeinab Bakhtiari, Helle Hvid Hansen, Alexander Kurz
Engineering Faculty Articles and Research
"Coalgebraic modal logic, as in [9, 6], is a framework in which modal logics for specifying coalgebras can be developed parametric in the signature of the modal language and the coalgebra type functor T. Given a base logic (usually classical propositional logic), modalities are interpreted via so-called predicate liftings for the functor T. These are natural transformations that turn a predicate over the state space X into a predicate over TX. Given that T-coalgebras come with general notions of T-bisimilarity [11] and behavioral equivalence [7], coalgebraic modal logics are designed to respect those. In particular, if two states are behaviourally …
Positive Subreducts In Finitely Generated Varieties Of Mv-Algebras, Leonardo M. Cabrer, Peter Jipsen, Tomáš Kroupa
Positive Subreducts In Finitely Generated Varieties Of Mv-Algebras, Leonardo M. Cabrer, Peter Jipsen, Tomáš Kroupa
Mathematics, Physics, and Computer Science Faculty Articles and Research
Positive MV-algebras are negation-free and implication-free subreducts of MV-algebras. In this contribution we show that a finite axiomatic basis exists for the quasivariety of positive MV-algebras coming from any finitely generated variety of MV-algebras.