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We study a time-varying well-posed system resulting from the additive perturbation of the generator of a time-invariant well-posed system. The associated generator family has the form $$A+G(t)$$ , where $$G(t)$$ is a bounded operator on the state space and $$G(\cdot )$$ is strongly continuous. We show that the resulting time-varying system (the perturbed system) is well-posed and investigate its properties. In the particular case when the unperturbed system is scattering passive, we derive an energy balance inequality for the perturbed system. We illustrate this theory using it to formulate the system corresponding to an electrically conducting rigid body moving in vacuo in a bounded domain, with an electromagnetic field (both in the rigid body and in the vacuum) described by Maxwell’s equations.

We give general results about the identifiability of source terms for infinite-dimensional linear systems that are exactly observable. We allow the source term to be unbounded, i.e., not contained in the state space, but in one of a sequence of extended spaces. We show that the operator from the source term to the output function is bounded from below, in suitable norms. We apply the main result to a system described by the wave equation in a bounded $$n$$ -dimensional domain. We derive results of independent interest concerning the range of the input map of an exactly controllable system, when restricted to various spaces of smooth input functions.

We are well into the third decade of the HIV epidemic. While strides have been made in HIV prevention, rates for African American men who have sex with men (AAMSM) and young AAMSM continue to increase – perhaps indicating that traditional deficit-approaches of HIV prevention are not effective for all populations. Following a recent call to investigate the resiliency of young gay men, this study identifies sources of resilience and strength within the House and Ball communities, a subculture comprised primarily of AAMSM. The mixed-methods design included survey data (N=263) collected at community events, interviews with Ball attendees and focus group data with House members. Survey data indicate a relationship between participating in the House and Ball communities and seeking support, acceptance and entertainment. Qualitative data validate these findings and provide detail on motivations for AAMSM to participate and the perceived benefits of participation. Findings are discussed in relation to building strengths-based interventions, using concepts of resiliency including shamelessness, social creativity, social support and volunteerism.

The SCOLE model is a coupled system consisting of a flexible beam (modelled as an Euler–Bernoulli equation) with one end clamped and the other end linked to a rigid body. Its inputs are the force and the torque acting on the rigid body. It is well-known that the SCOLE model is not exactly controllable with L 2 input signals in the natural energy state space H c , because the control operator is bounded from the input space $${\mathbb{C}^2}$$ to H c , and hence compact. We regard the velocity and the angular velocity of the rigid body as the output signals of this system. Using the theory of coupled linear systems (one infinite-dimensional and one finite-dimensional) developed by us recently in another paper, we show that the SCOLE model is well-posed, regular and exactly controllable in arbitrarily short time when using a certain smoother state space $${\mathcal{X}\subset H^c}$$ .

We investigate two classes of time-varying well-posed linear systems. Starting from a time-invariant scattering-passive system, each of the time-varying systems is constructed by introducing a time-dependent inner product on the state space and modifying some of the generating operators. These classes of linear systems are motivated by physical examples such as the electromagnetic field around a moving object. To prove the well-posedness of these systems, we use the Lax–Phillips semigroup induced by a well-posed linear system, as in scattering theory.

There is growing behavioral and epidemiological evidence to suggest that young men who have sex with men (YMSM) are at high risk for becoming HIV-infected. Unfortunately, relatively little research has been conducted to examine the range of individual, social, and community-level factors that put these young men at increased risk. To address existing gaps in the literature, the Healthy Young Men's (HYM) Study was launched in Los Angeles to examine the range of factors associated with HIV risk and protective behaviors within an ethnically diverse sample of 526 YMSM recruited using a venue-based stratified probability sampling design. In this paper we present findings that demonstrate that YMSM who experience residential instability, who have been forced to leave their home because of their sexuality, and/or who are precariously housed are at significantly greater risk for drug use and involvement in HIV risk-related behaviors.

We consider feedback systems obtained from infinite-dimensional well-posed linear systems by output feedback. Thus, our framework allows for unbounded control and observation operators. Our aim is to investigate the relationship between the open-loop system, the feedback operator K and the spectrum (in particular, the eigenvalues and eigenvectors) of the closed-loop generator AK. We give a useful characterization of that part of the spectrum σ(AK) which lies in the resolvent set of A, the open-loop generator, via the “characteristic equation” involving the open-loop transfer function. We show that certain points of σ(A) cannot be eigenvalues of AK if the input and output are scalar (so that K is a number) and K≠0. We devote special attention to the case when the output feedback operator K is compact. It is relatively easy to prove that in this case, σe(A), the essential spectrum of A, is invariant, that is, it is equal to σe(AK). A related but much harder problem is to determine the largest subset of σ(A) which remains invariant under compact output feedback. This set, which we call the immovable spectrum of A, strictly contains σe(A). We give an explicit characterization of the immovable spectrum and we investigate the consequences of our results for a certain class of well-posed systems obtained by interconnecting an infinite chain of identical systems.

In this paper we consider a class of distributed parameter systems governed by the heat equation on bounded domains in \Bbb Rn. We consider two types of boundary inputs (actuators) and two types of boundary outputs (sensors). Allowing for any possible pairing of these, we consider a totality of four possible arrangements of our system. The first type of input (control) is through the Neumann boundary condition on a part of the boundary, together with a homogenous Neumann boundary condition on the remaining part of the boundary. For this type of input, the input space is infinite-dimensional. The second type of input (with a finite-dimensional input space) is obtained by imposing constant normal derivatives on each element of a finite partition of the boundary. The first type of output (observation) is given by evaluation (trace) of the state of the system on a part of the boundary, so that the output space is infinite-dimensional. For the second type of output (with a finite-dimensional output space), we again consider a partition of the boundary of the spatial domain (which can be different from the one considered for the inputs) and each output channel contains the average of the values of the state of the plant on one element of this partition. Our main result is that any possible combination of the aforementioned inputs and outputs provides a regular linear system.

We give a characterization of infinite-time admissible observation operators for the right-shift semigroup on L 2[0,∞). Our main result is that if A is the generator of this semigroup and C is the observation operator, mapping D(A) into the complex numbers, then C is infinite-time admissible if and only if for all s in the open right half-plane. We derive this using Fefferman's theorem on bounded mean oscillation and Hankel operators. This result solves a special case of a more general conjecture which says that the same equivalence is true for any strongly continuous semigroup acting on a Hilbert space. For normal semigroups the conjecture is known to be true and then it is equivalent to the Carleson measure theorem. We derive some related results and partial results concerning the case when the signals are not scalar but with values in a Hilbert space.

We consider a rather general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in the frequency domain. We introduce and study the concept of admissible feedback operator for such a system and of well-posedness radius. We show that the closed-loop system obtained from a regular linear system with an admissible feedback operator is again regular and we describe the relationship between the generating operators of the open-loop and closed-loop systems.

We give an elementary proof of the well-known fact that shift-invariant operators onL 2[0, ∞) are represented by transfer functions which are bounded and analytic on the right open half-plane. We prove a generalization to Banach space-valuedL p -functions, where 1≤p

We study four transformations which lead from one well-posed lin- ear system to another: time-inversion, flow-inversion, time-flow-inversion and duality. Time-inversion means reversing the direction of time, flow-inversion means interchanging inputs with outputs, while time-flow-inversion means do- ing both of the inversions mentioned before. A well-posed linear system Σ is time-invertible if and only if its operator semigroup extends to a group. The system Σ is flow-invertible if and only if its input-output map has a bounded inverse on some (hence, on every) finite time interval (0 ,τ )( τ> 0). This is true if and only if the transfer function of Σ has a uniformly bounded inverse on some right half-plane. The system Σ is time-flow-invertible if and only if on some (hence, on every) finite time interval (0 ,τ ), the combined operator Στ from the initial state and the input function to the final state and the output function is invertible. This is the case, for example, if the system is conser- vative, since then Στ is unitary. Time-flow-inversion can sometimes, but not always, be reduced to a combination of time- and flow-inversion. We derive a surprising necessary and sufficient condition for Σ to be time-flow-invertible: its system operator must have a uniformly bounded inverse on some left half- plane. Finally, the duality transformation is always possible. We show by some examples that none of these transformations preserves regularity in general. However, the duality transformation does preserve weak regularity. For all the transformed systems mentioned above, we give formulas for their system operators, transfer functions and, in the regular case and under additional assumptions, for their generating operators.

Consider a semigroupT on a Banach spaceX and a (possibly unbounded) operatorC densely defined inX, with values in another Banach space. We give some necessary as well as some sufficient conditions forC to be an admissible observation operator forT, i.e., any finite segment of the output functiony(t)=CTtx,t≧0, should be inLp and should depend continuously on the initial statex. Our approach is to start from a description of the map which takes initial states into output functions in terms of a functional equation. We also introduce an extension ofC which permits a pointwise interpretation ofy(t)=CTtx, even if the trajectory ofx is not in the domain ofC.

The response learning and associative hookup stages of paired-associate learning were studied in 8-year-old children as a function of intralist conceptual similarity. Response learning, as measured by response recall, was facilitated by the presence of similar items, while the associative stage, as measured by a matching test, was somewhat impeded by the use of category instances. These results are similar to those for young adults’ learning, and indicate the utility of the stage-analysis model in the study of paired-associate learning by children.