An operation of the coproduct of representations of a bialgebra is defined. The coproduct operation of representations for the Hopf algebra of functions on the quantum group SUq(2) is investigated. For this Hopf algeb...
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An operation of the coproduct of representations of a bialgebra is defined. The coproduct operation of representations for the Hopf algebra of functions on the quantum group SUq(2) is investigated. For this Hopf algebra a representation II called the stable representation is constructed. This representation is invariant with respect to the coproduct with an arbitrary representation. An expression for the trace in the representation II is derived. The invariant Voronovich integral in SUq(2) takes the form integral fd mu=tr(fcc*).
In this paper we provide a general method to prove that certain nonlinear families of continuous functions contain dense linear manifolds. An application is furnished.
In this paper we provide a general method to prove that certain nonlinear families of continuous functions contain dense linear manifolds. An application is furnished.
For a domain Omega in the complex plane C, let H(Omega) denote the space of functions holomorphic in Omega, and let P be a family of functions subharmonic in Omega. Denote by H-p (Omega) the class of f is an element o...
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For a domain Omega in the complex plane C, let H(Omega) denote the space of functions holomorphic in Omega, and let P be a family of functions subharmonic in Omega. Denote by H-p (Omega) the class of f is an element of H (Omega) satisfying vertical bar f (z)vertical bar <= C-f exp P-f (z), z is an element of Omega, where p(f) is an element of T and C-f is a constant. The paper is aimed at conditions for a set Lambda subset of Omega to be included in the zero set of some nonzero function in H-p(Omega). In the first part, certain preparatory theorems are established concerning "quenching" the growth of a subharmonic function by adding to it a function of the form log vertical bar h vertical bar, where h is a nonzero function in H(Omega). The method is based on the balayage of measures and subharmonic functions.
A general version of the Stone-Weierstrass theorem is presented - one which involves no structure on the domain set of the real valued functions. This theorem is similar to the 'Stone-Weierstrass theorem' whic...
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A general version of the Stone-Weierstrass theorem is presented - one which involves no structure on the domain set of the real valued functions. This theorem is similar to the 'Stone-Weierstrass theorem' which appears in the book by Gillman and Jerison, but instead of involving the concept of stationary sets the one presented here involves stationary filters. As a corollary to our results we obtain Nel's theorem of Stone-Weierstrass type for an arbitrary topological space. Finally, an application is made to the setting of Cauchy spaces.
Solution to the problem of fault accommodation in nonlinear and linear dynamic systems is related to constructing the control law which provides full decoupling with respect to fault effects. Special mathematical tech...
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Solution to the problem of fault accommodation in nonlinear and linear dynamic systems is related to constructing the control law which provides full decoupling with respect to fault effects. Special mathematical techniques called algebra of functions complemented by differential geometrical tools are considered to solve the fault decoupling problem. Existing conditions are formulated and calculating relations are given for the control law in nonlinear and linear cases.
The disturbance decoupling problem by dynamic measurement feedback (DDDPM) for discrete-time nonlinear control systems is considered in this paper. The mathematical approach known under the name the algebra of functio...
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The disturbance decoupling problem by dynamic measurement feedback (DDDPM) for discrete-time nonlinear control systems is considered in this paper. The mathematical approach known under the name the algebra of functions is used to derive an algorithm that finds, whenever possible, a measurement feedback which solves the DDDPM. Finally, the applicability of the DDDPM in fault tolerant control (FTC) is discussed.
Unified approach to the problem of full decoupling via output feedback is considered for the cases of continuous-time and discrete-time nonlinear system models as well as for discrete-event model. The feature of this ...
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Unified approach to the problem of full decoupling via output feedback is considered for the cases of continuous-time and discrete-time nonlinear system models as well as for discrete-event model. The feature of this approach is that it allows obtaining the unique solution of the problem on algorithmic level for all above kinds of the models. Conventional differential geometric and pair algebra of partitions tools are applied as auxiliary ones for providing the calculations in special model cases.
The connection between the concepts of the single-experiment and the multi-experiment unobservability of a nonlinear discrete-time control system is studied. The main result claims that if the system is single-experim...
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The connection between the concepts of the single-experiment and the multi-experiment unobservability of a nonlinear discrete-time control system is studied. The main result claims that if the system is single-experiment unobservable and the observable space is integrable, then the system is also multi-experiment unobservable. For the proof of the main result a novel mathematical technique, the so-called algebra of functions, is used.
We consider semigroups of transformations (partial mappings defined on a set ) closed under the set-theoretic intersection of mappings treated as subsets of . On such semigroups we define two relations: the relation o...
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We consider semigroups of transformations (partial mappings defined on a set ) closed under the set-theoretic intersection of mappings treated as subsets of . On such semigroups we define two relations: the relation of semicompatibility which identifies two transformations at the intersection of their domains and the relation of semiadjacency when the image of one transformation is contained in the domain of the second. Abstract characterizations of such semigroups are presented.
The abstract characterizations of relations of nonempty intersection, inclusion end equality of domains for partial n-place functions are presented. Representations of Menger (2, n)-semigroups by partial n-place funct...
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The abstract characterizations of relations of nonempty intersection, inclusion end equality of domains for partial n-place functions are presented. Representations of Menger (2, n)-semigroups by partial n-place functions closed with respect to these relations are investigated.
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