On some implication type results involving generalized bounded Mocanu variations

This paper is the study of certain implication type results involving functions related to generalized bounded Mocanu variations. Basic properties involving generalized Bernardi integral transform, inclusion results and a sharp radius problem are investigated for such classes. Many interesting implications are observed as special cases of our results.     

On the bounded real lemma

In this paper we deal with special generalizations of the well-known bounded real lemma. We develop general statements for comparison of rational transfer functions in the sense of quadratic forms on the imaginary axis. The main results can be expressed by means of Hamiltonian matrices.     

On multipliers for bounded and monotone nonlinearities

Recent results in equivalence between classes of multipliers for slope-restricted nonlinearities are extended to multipliers for bounded and monotone nonlinearities. This extension requires a slightly modified version of the Zames–Falb theorem and a more general definition of phase-substitution. The results in this paper resolve apparent contradictions in the literature on classes of multipliers for bounded and monotone nonlinearities.     

On bounded real matrix inequality dilation

We discuss a variation of dilated matrix inequalities for the conventional Bounded Real matrix inequality and other similarly structured inequalities. Here, system matrices are separated from Lyapunov matrix to allow the use of different Lyapunov matrices in multi-objective and robust problems. The search involves a bounded scalar parameter that enters the problem nonlinearly and is dealt with a line search. To demonstrate the benefits of the new dilated matrix inequalities over the conventional ones, an example of controller synthesis with ?₂-gain performance measure (?_∞ control) for a system with polytopic uncertainty (robust problem) has been studied. It is shown that for the resulting robust problem the performance obtained via the dilated form is at least equal to that of the conventional one. Also, the connection between the proposed dilated form and the Full Block S-procedure is discussed.     

On internal and locally internal uninorms on bounded lattices

In this paper, we introduce the definition of an internal uninorm on an arbitrary bounded lattice L. We investigate some properties of these operators and the relationship with locally internal uninorms. We show that an internal uninorm need not always exist on an arbitrary bounded lattice. Furthermore, based on the Zermelo's well-ordering theorem, we propose two construction methods to obtain internal uninorms on a bounded lattice L with some additional constraints.     

On bounded input–bounded output stability of a class of nonlinear retarded systems

Nonlinear retarded systems are considered. Explicit bounded input–bounded output stability conditions are derived. Copyright © 2000 John Wiley & Sons, Ltd.     

On the hilbert transform of bounded bandlimited signals

In this paper we analyze the Hilbert transform and existence of the analytical signal for the space B _?? ^?? of bandlimited signals that are bounded on the real axis. Originally, the theory was developed for signals in L ²(?) and then extended to larger signal spaces. While it is well known that the common integral representation of the Hilbert transform may diverge for some signals in B _?? ^?? and that the Hilbert transform is not a bounded operator on B _?? ^?? , it is nevertheless possible to define the Hilbert transform for the space B _?? ^?? . We use a definition that is based on the H ¹-BMO(?) duality. This abstract definition, which can be used for general bounded signals, gives no constructive procedure to compute the Hilbert transform. However, for the practically important special case of bounded bandlimited signals, we can provide such an explicit procedure by giving a closed-form expression for the Hilbert transform. Further, it is shown that the Hilbert transform of a signal in B _?? ^?? is still bandlimited but not necessarily bounded. With these results we continue the work of [1, 2].     

满层L-收敛空间的局部有界与局部紧性

对满层[L]-收敛空间引入了有界集（紧集）和局部有界（紧）空间的概念,它们可以看作J?ger相应概念的推广。证明了：（1）广义Lowen函子（收敛空间范畴可以通过广义Lowen函子余反射嵌入到满层[L]-收敛空间范畴）保持并且反射有界（紧）性和局部有界（紧）性;（2）局部有界（紧）的满层[L]-收敛空间是满层[L]-收敛空间的余反射子范畴。     

Indecomposability of free algebras in some subvarieties of residuated lattices and their bounded subreducts

In this paper, we show that free algebras in the variety of residuated lattices and some of its subvarieties are directly indecomposable and show, as a consequence, the direct indecomposability of free algebras for some classes of their bounded implicative subreducts.     

On bounded lattices satisfying Elkan’s law

In this short paper we shall prove that every bounded lattice L with the conditions: (c1) 1′ =  0 and (EL): (a · b′)′ =  b +  a′ · b′ for all a, b ∈ L is a Boolean algebra. This is a more general result than that of Renedo et al. (Proceedings NAFIPS’04, 2004), in which it is proved that every orthocomplemented lattice with (EL) is a Boolean algebra.     

On improving the performance with bounded continuous feedback laws

We present controller design methods to smooth the discontinuity resulting from a piecewise linear control law which was proposed to improve the convergence performance for systems with input constraints. The continuous control laws designed in this paper are explicit functions of the state and are easily implementable. We also show that the convergence performance can be further improved by using a saturated high-gain feedback law. The efficiency of the proposed methods is illustrated with the PUMA 560 robot model.     

On minimum-time paths of bounded curvature with position-dependent constraints

We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with constraints on the minimum turning radius of the particle over multiple regions of the state space. Necessary conditions for optimality of these paths are derived to characterize the nature of optimal paths, both when the particle is inside a region and when it crosses boundaries between neighboring regions. These conditions are used to characterize families of optimal and nonoptimal paths. Among the optimality conditions, we derive a “refraction” law at the boundary of the regions that generalizes the so-called Snell’s law of refraction in optics to the case of paths with bounded curvature. Tools employed to deduce our results include recent principles of optimality for hybrid systems. A numerical example is given to demonstrate the derived results.     

On characterizing boundedness of database schemes with bounded dependencies

We investigate the effect of bounded dependencies on the boundedness of database schemes. The following results are proved. A database scheme with only bounded equality-generating dependencies is always bounded with respect to dependencies; a lossless database scheme with bounded full implicational dependencies is bounded w.r.t. dependencies if and only if the implicational dependencies are equivalent to a single join dependency and some equality-generating dependencies. By a known method, this condition can be tested effectively. These results are relevant in database theory in that they determine in a rather general case whether queries under the representative instance approach can be expressed in relational algebra.     

On generating database schemes bounded or constant-time-maintainable by extensibility

Summary Under the weak instance model, determining whether a class of database schemes is bounded (with respect to dependencies or with respect to consistency) is fundamental for the analysis of the behavior of the class of database schemes with respect to query processing and updates. However, proving that a class of database schemes is bounded seems to be very difficult even for restricted cases. To resolve this problem, we need to develop techniques or to explore other ideas for characterizing bounded database schemes. In particular, the idea of generating bounded database schemes is completely unexplored. In this paper, we give a formal methodology for the generation of bounded database schemes using a new technique called extensibility. This methodology can also be used to generate constant-time-maintainable database schemes.An extended abstract of a preliminary version of this paper appears as On Designing Database Schemes Bounded or Constant-time-maintainable with respect to Functional Dependencies in Proc. Sixth ACM SIGACT-S1GMOD-SIGART Symposium on Principles of Database Systems, 1987, pp. 48–57. Part of the work was done while the authors were at the University of Alberta     

On closure properties of bounded two-sided error complexity classes

We show that if a complexity classC is closed downward under polynomial-time majority truth-table reductions ( _mtt ^p ), then practically every other polynomial closure property it enjoys is inherited by the corresponding bounded two-sided error class BP[C]. For instance, the Arthur-Merlin game class AM [B1] enjoys practically every closure property of NP. Our main lemma shows that, for any relativizable classD which meets two fairly transparent technical conditions, we haveC ^BP[C] BP[D ^C]. Among our applications, we simplify the proof by Toda [Tol], [To2] that the polynomial hierarchy PH is contained in BP[P]. We also show that relative to a random oracleR, PH ^R is properly contained in P ^R .The first author was supported in part by NSF Grant CCR-9011248 and the second author was supported in part by NSF Grant CCR-89011154.