Lower semicontinuous solutions of the Bellman equation for the minimum time problem

The minimum time problem associated with a nonlinear control system is considered, and the unicity of the lower semicontinuous solution of the corresponding Bellman equation is investigated. A main tool in our approach is the Kruzkov transformation that enables us to work on ⁿ –{0}, where {0} is the target set, instead of the unknown reachable set.This research was carried out while the first author was visiting the Department of Mathematics, University of Genova, Genova, Italy.     

Effect of conformational parameters on physical properties of polymers containing pendant phenoxyphthalonitrile substituents

Heteroaromatic polymers are considered to be high performance organic materials due to their unique and highly attractive properties, including outstanding thermal and mechanical resistance, that arise from their aromatic structure and strong interactions between macromolecular chains. Modification or designing new molecular architectures with tailored physico-chemical characteristics allows expanding the applications of these materials in various advanced technologies. Herein, a series of polymers containing bulky phenoxyphthalonitrile pendant units was synthesized and their physical properties were studied and correlated with their conformational parameters, as well as free and van der Waals volumes. For comparison, the related polymers without lateral moieties were also investigated to highlight the effect of bulky substituent on the polymer rigidity. Thus, it is shown that conformational rigidity determines the packing of macromolecules in solid state, and, therefore, the free volume, glass transition, and decomposition temperatures. The values found experimentally for T _g correlate well with those obtained using the conformational rigidity parameters. The dependence of T _g of these polymers on Kuhn segment is described by linear equations, with very good factors of convergence. The correlations established by Monte Carlo method allow obtaining the T _g values for related polymers where the experimental measurement of this parameter is difficult.     

Contingent Solutions for the Bellman Equation in Infinite Dimensions

The present paper is concerned with the study of the Hamilton–Jacobi–Bellman equation for the time optimal control problem associated with infinite-dimensional linear control systems from the point of view of continuous contingent solutions.     

On constraint controllability of linear systems in Banach spaces

In this paper, we give an addendum to a result of Dolecki and Russell (Ref. 1) related to the duality relationship between observation and control for linear systems in Banach spaces. Our results relate the controllability of a system to the constraint controllability of that system and to the observability of an adjoint system. The main tool used here is an extension of the classical open mapping theorem.     

Thermal Degradation and Kinetic Studies of New Flame-Retardant Phosphorus-Containing Polymers with Liquid Crystalline Properties

In this study, two new thermotropic liquid crystalline phosphorus-containing polymers were prepared by polycondensation reaction of 1,4-phenylene-bis((6-oxido-6H-dibenz[c,e][1,2]oxaphosphorinyl)carbinol) with two different phosphonic dichlorides, namely ethyl dichlorophosphate and phenyl dichlorophosphate. The polymers were characterized by means of FT-IR, ¹H NMR, differential scanning calorimetry, polarized light microscopy, wide-angle X-ray diffraction, and thermogravimetric analysis. Thermogravimetric analysis was performed in nitrogen atmosphere by heating the samples over a range of temperatures from 25° to 700°C using five different heating rates. The kinetic processing of data was achieved using the Freeman-Carroll, ASTM E1641, and Kissinger methods.     

Correlation between physical properties and conformational rigidity of some aromatic polyimides having pendant phenolic groups

Soluble polyimides based on an aromatic diamine containing pendant phenolic group and four different dianhydrides have been synthesized by two-step polycondensation reaction in solution. The polyimides were easily soluble in polar organic solvents and even in less polar solvents and showed high thermal stability, with initial decomposition temperature being above 420 °C. Monte Carlo method was used to calculate conformational rigidity parameters of these polyimides. Some physical properties such as solubility, glass transition temperature and initial decomposition temperature were investigated and compared with those of related polyimides which did not contain any pendant groups based on the same dianhydrides and a diamine without pendant phenolic group. All data were discussed in relation to the rigidity of the chain.

     

Constraint controllability for linear control systems

Summary We investigate some controllability properties of linear control systems in finite or infinite dimensions.     

Phthalonitrile‐containing aromatic polyimide thin films with nano‐actuation properties

Polymer films of some polyimides containing pendant phthalonitrile groups were prepared by casting the corresponding poly(amic acid) solutions onto glass plates, followed by thermal imidization under controlled temperature conditions. The poly(amic acid)s were synthesized by polycondensation reaction of 4,4′‐diamino‐4″‐(3,4‐dicyanophenoxy)triphenylmethane, 1, or of different amounts of 1 and 4,4′‐bis(4‐aminophenoxybiphenyl), with two aromatic dianhydrides, 4,4′‐oxydiphthalic anhydride or benzophenone‐3,3′,4,4′‐tetracarboxylic dianhydride. Most of the films were flexible and tough and exhibited high thermal stability, having the initial decomposition temperature above 400 °C. Dynamic mechanical analysis and dielectric spectroscopy revealed the influence of phthalonitrile group content on the relaxation processes of polyimides. The values of the dielectric constant at 10 kHz and 20 °C were in the range of 3.25–3.61. The films exhibited nano‐actuation in the range of 240–480 nm, depending on the phthalonitrile group content, when an electric voltage was applied on their surface. Copyright © 2012 John Wiley & Sons, Ltd.     

Nanoparticles of nickel oxide: growth and organization on zinc-substituted anionic clay matrix by one-pot route at room temperature

A room temperature nanocarving strategy is developed for the fabrication of nanoparticles of nickel oxide on zinc-substituted anionic clay matrix (Ni/ZnLDH). It is based on the growth and organization of nanoparticles of nickel oxide which occur during the structural reconstruction of the layered structure of the anionic clay in NiSO₄ aqueous solution. No organic compounds are used during the fabrication. The described material was characterized by X-ray diffraction (XRD), IR spectroscopy (FTIR), transmission electron microscopy (TEM), field-emission scanning electron microscopy (FESEM), energy dispersive X-ray (EDX) spectroscopy, and X-ray photoelectron spectroscopy (XPS). Results show that the nickel-clay nanoarchitecture consists of small nanoparticles of nickel oxide (average size 7 nm) deposited on the larger nanoparticles (average size 90 nm) of zinc-substituted clay. The optical properties of the new nickel-zinc formulation are studied by UV–Vis.