Showing papers on "Uniform boundedness published in 1993"

Rank one property for derivatives of functions with bounded variation

Abstract: In this paper we introduce a new tool in geometric measure theory and then we apply it to study the rank properties of the derivatives of vector functions with bounded variation.

The classical limit of a self-consistent quantum-vlasov equation in 3d

Abstract: Under natural assumptions on the initial density matrix of a mixed quantum state (Hermitian, non-negative definite, uniformly bounded trace, Hilbert-Schmidt norm and kinetic energy) we prove that accumulation points (as the scaled Planck constant tends to zero) of solutions of a corresponding slightly regularized Wigner-Poisson system are distributional solutions of the classical Vlasov-Poisson system. The result holds for the gravitational and repulsive cases. Also, for every phase-space density in (with bounded kinetic energy) we prepare a sequence of density matrices satisfying the above assumptions, such that the given density is the limit of the Wigner transforms of these density matrices.

Robust Model Selection and M-Estimation

Abstract: This paper studies the qualitative robustness properties of the Schwarz information criterion (SIC) based on objective functions defining M-estimators. A definition of qualitative robustness appropriate for model selection is provided and it is shown that the crucial restriction needed to achieve robustness in model selection is the uniform boundedness of the objective function. In the process, the asymptotic performance of the SIC for general M-estimators is also studied. The paper concludes with a Monte Carlo study of the finite sample behavior of the SIC for different specifications of the sample objective function.

On Morse's new adaptive controller: parameter convergence and transient performance

Abstract: Some transient and asymptotic performance properties are established for the model reference adaptive controller proposed by A.S. Morse (Proc. US-Italy Joint Seminar Syst., Models Feedback 1992). It is proved that the L/sub 2/ norm of the tracking error is uniformly bounded by the initial parameter estimation error. Further, if the initial conditions are sufficiently small, it is shown that the L/sub infinity / norm of the tracking error is uniformly bounded by the L/sub m2/ norm of the reference signal. These transient bounds are independent of the signals richness and the adaptation gain, making them arguably the strongest transient results available in the literature. Second, excitation conditions for exponential stability, a property which is well known to insure some local performance measures, are given. To this end, it is shown that, modulo a signal dependent time scale change, Morse's estimator is equivalent to a normalized gradient plus filtering identifier. >

Spectral Viscosity Approximations to Multidimensional Scalar Conservation Laws

Abstract: The authors study the spectral viscosity (SV) method in the context of multidimensional scalar conservation laws with periodic boundary conditions. They show that the spectral viscosity, which is sufficiently small to retain the formal spectral accuracy of the underlying Fourier approximation, is large enough to enforce the correct amount of entropy dissipation (which is otherwise missing in the standard Fourier method). Moreover, they prove that because of the presence of the spectral viscosity, the truncation error in this case becomes spectrally small, independent of whether the underlying solution is smooth or not. Consequently, the SV approximation remains uniformly bounded and converges to a measure-valued solution satisfying the entropy condition, that is, the unique entropy solution. They also show that the SV solution has a bounded total variation, provided that the total variation of the initial data is bounded, thus confirming its strong convergence to the entropy solution. They obtain an L[sup 1] convergence rate of the usual optimal order one-half. 22 refs.

Convergence Rates on Strong Laws of Large Numbers for Arrays of Rowwise Independent Elements

Abstract: Let be an array of rowwise independent random elements in a separable Banach spacer= 1 and 1 1 and .Let be uniformly bounded by a nonnegative real random variable X. Let It has been shown that if : 0 then for every e>0,

Market equilibrium with heterogeneous recursive-utility-maximizing agents

Abstract: The paper by C. Ma [1] contains several errors. First, statement and proof of Theorem 2.1 on the existence of intertemporal recursive utility function as a unique solution to the Koopmans equation must be amended. Several additional technical conditions concerning the consumption domain, measurability of certainty equivalent and utility process need to be assumed for the validity of the theorem. Second, the assumptions for Theorem 3.1 need to be amended to include the Feller's condition that, for any bounded continuous functionf e C(S × ℛn +), μ(f(St+1, θ)¦st =s) is bounded and continuous in (s, θ). In addition, for Theorem 3.1, the pricep, the endowmente and the dividend rateδ as functions of the state variables e S are assumed to be continuous. The Feller's condition for Theorem 3.1 is to ensure the value function to be well-defined. This condition needs to be assumed even for the expected additive utility functions (See Lucas [2]). It is noticed that, under this condition, the right hand side of equation (3.5) in [1] defines a bounded continuous function ins andφ. The proof of Theorem 3.1 remains valid with this remark in place. A correct version of Theorem 2.1 in [1] is stated and proved in this corrigendum. Ozaki and Streufert [3] is the first to cast doubt on the validity of this theorem. They point out correctly that additional conditions to ensure the measurability of the utility process need to be assumed. This condition is identified as conditionCE 4 below. In addition, I notice that, the consumption space is not suitably defined in [1], especially when a unbounded consumption set is assumed. In contrast to what claimed in [3], I show that the uniformly bounded consumption setX and stationary information structure are not necessary for the validity of Theorem 2.1.

Characterization of eigenfunctions of the Laplacian by boundedness conditions

Abstract: If {f k (x)} k ∈ Z is a doubly infinite sequence of functions on R n which are uniformly bounded and such that Δf k = f k+1 , then Δf 0 = − f 0 . This generalizes a therem of Roe (n = 1). The analogous statement is true on the Heisenberg group, but false in hyperbolic space

On the positive definiteness and uniform boundedness of the inertia matrix of robot manipulators

Abstract: In this paper we give a new alternative proof for the positive definiteness of the inertia matrix of robot manipulators and give an explicit uniform bound for its determinant. This in turn shows that the inertia matrix can not be arbitrarily singular and that its minimum eigenvalue is uniformly bounded if all its eigenvalues are bounded. Hence, we completely characterize the class of robot manipulators with bounded inertia matrix and show that it includes manipulators with nontrivial joint configurations. For manipulators of this class, we give easily computable uniform bounds for the minimum and maximum eigenvalues of the inertia matrix. >

Convergence in lotka-volterra type diffusive delay systems without dominating instantaneous negative feedbacks

Abstract: This paper deals with the convergence aspect of diffusive delay Lotka-Volterra systems with infinite delays. It is well known that such a system has a globally asymptotically stable steady state if the negative feedbacks of the intraspecific competitions are dominant and instantaneous. It is shown here that such a globally asymptotically stable steady state continues to exist even if the instantaneous assumption is removed, provided that solutions of the system are eventually uniformly bounded and the delays involved in the intraspecific competitions are small. This work generalises several recent related ones.

Entire Functions of Bounded Type on Fréchet Spaces

Abstract: We show that holomorphic mappings of bounded type defined on Frechet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

Abstract: The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z e W then I − Kz is invertible for each z e W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

General lemmas for stability analysis of linear continuous-time systems with slowly time-varying parameters

Abstract: This note investigates stability conditions for some dynamic systems with slowly time-varying parameters or with unknown internal or external disturbances. The models and conditions are motivated by adaptive control problems. The results presented here provide some sufficient conditions for the exponential convergence of the state sequence of systems without system disturbance, and for the uniform boundedness of the state sequence of such systems when they are subject to uniformly bounded system disturbances.

Space‐time extensions I

Abstract: The local extendibility of causal geodesically incomplete space‐times is examined. It is shown that for a space‐time including an incomplete inextendible causal geodesic curve γ there exists a particular Ck (resp. Ck−) local extension provided that the curvature and its covariant derivatives are uniformly bounded up to order k+1 (resp. k) in a synchronized frame field along a family of causal geodesics in some neighborhood of a final segment of γ and the strong causality condition is satisfied locally.

A delay-independent robust stability condition for linear discrete-time systems

Abstract: In this note, we point out that a result on the stability of so-called asynchronous iterative processes can be interpreted as a delay-independent robust stability condition for linear discrete-time systems subjected to uniformly bounded time-varying delays. The required quasi-dominance condition for stability is the same as an analogous continuous-time result derived earlier; however there are some significant differences discussed in this note. >

A New Method in Wave Diffraction Theory by Thin Screens

Abstract: There exist many methods of analyzing electromagnetic fields scattered by thin unclosed screens of arbitrary configuration. But all these methods as a rule result in ill-conditioned matrices; that is the condition number of these matrices rapidly increases together with the matrix size. So far these methods cannot guarantee the solution with the settled accuracy. These paper presents a new mathematically correct method which equivalently reduces initial boundary value problems to the infinite algebraic system of the second kind. The truncated matrices condition numbers of this system are uniformly bounded. It enables us to solve the considered problem with an arbitrary settled accuracy. Theoretical estimates and numerical experiments demonstrated higher quality of the algorithms obtained. We also present some numerical results illustrating the possible applications of the method.

Decay of solutions for the equations of isothermal gas dynamics

Abstract: The equations of isothermal gas dynamics are expressed as a 2×2-system of genuinely nonlinear hyperbolic conservation laws which possesses a convex entropy. Existence of weak global solutions is known for even large initial data via Glimm’s difference scheme. We show that the total variation of such (large) solutions decays strongly to zero. The proof consists in showing that the total amount of wave interaction in the Glimm approximations is uniformly bounded.

Model reference adaptive control for nonlinear systems with unknown degrees and with unknown relative degrees 1 or 2

Abstract: In most of the studies of model reference adaptive control, it is assumed that an upper bound on the degree of the controlled system is known. It makes the scope of application of model reference adaptive control too restrictive, since the reasonable upper bound on the degree cannot be specified a priori in many cases. In the present paper, we propose a design method of model reference adaptive control systems for nonlinear systems with unknown degrees and with unknown relative degrees 1 or 2. Even if the degree of the controlled system varies, and even if the relative degree also varies between 1 and 2, the structure of the proposed adaptive controller does not change. It is shown that the resulting control system is uniformly bounded, and that the tracking error converges to an arbitrarily small residual region. Finally, several simulation studies also show the effectiveness of the proposed method. >

Theory of P-type learning control with implication for the robot manipulator

Abstract: The robustness and convergence of P-type learning control algorithms for a class of time-varying, nonlinear systems with state disturbances, measurement noise at the output, and reinitialization errors at each iteration is studied. The uniform boundedness of the system states with respect to the existence of errors of initialization, measurement noises and fluctuations of system dynamics is proved. The system output is shown to converge uniformly to the desired output whenever all disturbances tend to zero. Implications of the results for robot manipulator and linear systems are presented. >

Equivalence of two Series of Spherical Representations of a Free Group (

Abstract: The spherical principal series of a non-commutative free group may be analytically continued to yield a series of uniformly bounded representations, much as the spherical representations π(in1/2) + it of SL (2,R) may be analytically continued in the strip 0 < Rez < 1. This series of uniformly bounded representations was constructed and studied by A. M.Mantero and A.Zappa. Independently T.Pytlik and R.Szwarc introduced and studied representations of the free group which contain a series of subrepresentations indexed by spherical functions. Both series consist of irreducible representations and include the spherical complementary series. The aim of this paper is to prove that the non-unitary uniformly bounded representations of the two series are also equivalent.

Robust discrete-time adaptive control subject to a control input amplitude constraint

Abstract: Subject to a control input amplitude constraint, an adaptive algorithm is proposed to control discrete-time plants with unmodelled dynamics. By introducing an additional feedback signal, it is shown that the uniform boundedness of all signals in the adaptive loop can be guaranteed. The nominal plant is assumed to be stable but unnecessarily minimum phase. Various properties of this adaptive algorithm are analysed. It is shown that the performance which can be achieved with no control input amplitude constraint in the non-adaptive case (i.e. the case when the true nominal plant is known a priori) is asymptotically well maintained in the adaptive system. The analysis is supported by computer simulation results.

A new design for model reference robust control using state space techniques

Abstract: Proposes a model reference control (MRC) structure which is different from existing MRC structures. This new approach is based on state space techniques, but is not simply an alternative form of the input-output transfer function approach. It has the advantage of being a unified structure that processes systems with either time-invariant (TIV) or time-varying (TV) parameters. For systems with TV parameters, it requires a lower number of assumptions compiled with the input-output operator approach. This result can be achieved due to a new concept called dynamic coordinate transformation. This dynamic coordinate transformation has the effect of transforming the plant into a "big" system which is composed of two subsystems One subsystem has the matching property which is not enjoyed by the original plant, while all the unmatched unmodeled dynamics, as well as TV parameters which we do not like in the original plant, are drawn into the other unmatched subsystem. The control objective for the original plant is transformed into the control of the matched subsystem while the unmatched subsystem remains uniformly bounded as long as all the unmodeled dynamics, TV parameters, plant input, and the plant output are bounded. For simplicity, the authors discuss only systems with TIV parameters. A robust control approach and the backstepping method are used to guarantee that the overall states are globally uniformly bounded (GUB) and that the output tracking error is globally uniformly ultimately bounded (GUUB). >