Can between-session (homework) activities be considered a common factor in psychotherapy?

A common goal for psychotherapies is to enable patients to improve their functioning and reduce distress in the situations and interpersonal contexts in which their problems exist. Although generally associated with behavioral, cognitive, couples, and family therapies, the use of the time between consultation sessions through therapeutic activities is implicit to all psychotherapies. This special series in Journal of Psychotherapy Integration represents an initial effort to make explicit the role of between-session 'homework' assignments in behavioral, client centered, cognitive, experiential, interpersonal, psychodynamic, and systemic approaches. Expert theoreticians, researchers, and practitioners present theoretical and clinical case examples to illustrate homework's role in assisting patient therapeutic progress. We synthesize themes from the issue in a concluding piece in the interests of facilitating future theoretical and empirical work on homework in psychotherapy integration. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Fibrous hydroxyapatite–carbon nanotube composites by chemical vapor deposition: In situ fabrication,structural and morphological characterization

Fibrous hydroxyapatite (HA)–carbon nanotube composites were synthesized by the catalytic decomposition of acetylene over Fe–Co bimetallic catalysts supported on the fibrous HA. Two forms of fibrous HA (distinct needle-like monocrystals and spherulitic aggregates of needles) were synthesized using a simple precipitation method and loaded with bimetallic catalysts (from 2 up to 20 wt%) by a wet chemical impregnation method. The HA supported catalysts were evaluated for the in situ growth of carbon nanotubes using the catalytic chemical vapor deposition method. The effect of reaction temperature and metal loading on the yield, structural perfection and morphology of the carbon products were investigated using a combination of X-ray diffraction, thermal analysis, Raman spectroscopy and scanning and transmission electron microscopies. The results revealed that both the selection of the growing conditions and the metal loading determine the yield and overall quality of the synthesized carbon nanotubes, which exhibit high graphitization degree when synthesized in high yields.     

A new Lyapunov design approach for nonlinear systems based on Zubov's method

The present research work proposes a new nonlinear controller synthesis approach that is based on the methodological principles of Lyapunov design. In particular, it relies on a short-horizon model-based prediction and optimization of the rate of “energy dissipation” of the system, as it is realized through the time derivative of an appropriately selected Lyapunov function. The latter is computed by solving Zubov's partial differential equation based on the system's drift vector field. A nonlinear state feedback control law with two adjustable parameters is derived as the solution of an optimization problem that is formulated on the basis of the aforementioned Lyapunov function and closed-loop performance characteristics. A set of system-theoretic properties of the proposed control law are examined as well. Finally, the proposed Lyapunov design method is evaluated in a chemical reactor example which exhibits nonminimum-phase behaviour.     

Singular PDEs and the single-step formulation of feedback linearization with pole placement

The present work proposes a new formulation and approach to the problem of feedback linearization with pole placement. The problem under consideration is not treated within the context of geometric exact feedback linearization, where restrictive conditions arise from a two-step design method (transformation of the original nonlinear system into a linear one in controllable canonical form with an external reference input, and the subsequent employment of linear pole-placement techniques). In the present work, the problem is formulated in a single step, using tools from singular PDE theory. In particular, the mathematical formulation of the problem is realized via a system of first-order quasi-linear singular PDEs and a rather general set of necessary and sufficient conditions for solvability is derived, by using Lyapunov's auxiliary theorem. The solution to the system of singular PDEs is locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package. Under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear state feedback law computed through the solution of the system of singular PDEs, both feedback linearization and pole-placement design objectives may be accomplished in a single step, effectively overcoming the restrictions of the other approaches by bypassing the intermediate step of transforming the original system into a linear controllable one with an external reference input.     

Nonlinear discrete-time observer design with linearizable error dynamics

A necessary and sufficient condition for the existence of a discrete-time nonlinear observer with linearizable error dynamics is provided. The result can be applied to any real analytic nonlinear system whose linear part is observable. The necessary and sufficient condition is the solvability of a nonlinear functional equation. Furthermore, the well-known Siegel's theorem on the linearizability of a mapping is naturally reproduced in a corollary. The proposed observer design method is constructive and can be applied approximately to any sufficiently smooth, linearly observable system yielding a local observer with approximately linear error dynamics.     

Integrating process safety with molecular modeling-based risk assessment of chemicals within the REACH regulatory framework: benefits and future challenges

Registration, evaluation and authorization of chemicals (REACH) represents a recent regulatory initiative by the European union commission to protect human health and the environment from potentially hazardous chemicals. Under REACH, all stakeholders must submit (thermo)physical, thermochemical, and toxicological data for certain chemicals. The commission's impact assessment studies estimate that the costs of REACH will be approximately 3-5 billion Euros. The present study advocates the systematic incorporation of computational chemistry and computer-assisted chemical risk assessment methods into REACH to reduce regulatory compliance costs. Currently powerful computer-aided ab initio techniques can be used to generate predictions of key properties of broad classes of chemicals, without resorting to costly experimentation and potentially hazardous testing. These data could be integrated into a centralized IT decision and compliance support system, and stored in a retrievable, easily communicable manner should new regulatory and/or production requirements necessitate the introduction of different uses of chemicals under different conditions. For illustration purposes, ab initio calculations are performed on heterocyclic nitrogen-containing compounds which currently serve as high energy density materials in the chemical industry. Since investigations of these compounds are still in their infancy, stability studies are imperative regarding their safe handling and storage, as well as registration under REACH.     

Nonlinear observer design using Lyapunov’s auxiliary theorem

The present work proposes a new approach to the nonlinear observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer theory, the proposed approach develops a nonlinear analogue. The formulation of the observer design problem is realized via a system of singular first-order linear PDEs, and a rather general set of necessary and sufficient conditions for solvability is derived by using Lyapunov’s auxiliary theorem. The solution to the above system of PDEs is locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package.     

Time-discretization of non-affine nonlinear system with delayed input using taylor-series

In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sampled-data representation of a non-affine nonlinear system with constant input time-delay. The mathematical expressions of the discretization scheme are presented and the ability of the algorithm is tested for some of the examples. The proposed scheme provides a finite-dimensional representation for nonlinear systems with time-delay enabling existing controller design techniques to be applied to them. For all the case studies, various sampling rates and time-delay values are considered.     

A new approach to the zero-dynamics assignment problem for nonlinear discrete-time systems using functional equations

The present research work aims at the development of a systematic method to arbitrarily assign the zero dynamics of a nonlinear discrete-time real analytic system by constructing the requisite synthetic output maps. The problem under consideration is motivated by the need to adequately address the control problem of nonminimum-phase nonlinear discrete-time systems, since the latter represent a rather broad class of systems due to the well-known effect of sampling on the stability of zero-dynamics. In the proposed approach, the above control objective can be attained through: (i) a systematic computation of synthetic output maps that induce minimum-phase behavior while being statically equivalent to the original output maps (both vanish on the equilibrium manifold) and (ii) the subsequent integration into the methodological framework of currently available nonminimum-phase compensation schemes for nonlinear discrete-time systems that rely on output redefinition. The mathematical formulation of the zero-dynamics assignment problem is realized via a system of nonlinear functional equations, and a rather general set of necessary and sufficient conditions for solvability is derived. The solution to the above system of functional equations can be proven to be locally analytic, and this enables the development of a solution method that is easily programmable with the aid of a symbolic software package. The synthetic output maps that induce the prescribed zero dynamics for the original nonlinear discrete-time system can be explicitly computed on the basis of the solution to the aforementioned system of functional equations.     

Managing uncertainties in a safety-constrained process system for solvent selection and usage: an optimization approach with technical, economic, and risk factors

This paper addresses the problem of managing uncertainties in a safety-constrained process system for economic performance enhancement. Within such a context, a typical solvent selection problem involves a number of different solvents with nominal property values that are utilized in various process units and requires the minimization of the total operating cost while satisfying certain technical performance criteria and process safety constraints. Practically, in any process system, property values of streams are not exact; they are usually functions of operating variables and market conditions that change over time inevitably introducing irreducible uncertainties in system performance. A key aim of the present study is to systematically explore the effect of volatility in solvent prices on the economic performance of the process. Appropriate sensitivity analysis and Monte Carlo simulation work have been carried out to assist the decision maker in taking into account the continuously changing market conditions, while identifying operationally safe feasibility regions for solvents with different risk characteristics in the underlying optimization problem. The aforementioned uncertain inputs are shown to cause shifts of the associated Pareto front of optimal solutions toward feasibility regions that can be characterized in a more realistic manner. Finally, an illustrative case study that uses the permissible exposure limit as a risk factor is considered to evaluate the proposed method.