Singular problems on the infinite interval modelling phenomena in draining flows

Existence results are presented for singular boundary-valueproblems on the infinite interval. In particular our theoryincludes a discussion of a problem which arises in the theoryof draining flows. Received 10 February 2001.     

Singular initial and boundary value problems with sign changing nonlinearities

A variety of new existence results are presented for both singularinitial and boundary value problems where the nonlinearity is allowed to change sign. Our theory is then applied to anexample which arises naturally in nonlinear mechanics (thatis, in the membrane response of a spherical cap). Received 17 May, 1999.     

Effect of gallium, aluminium, and chromium on silica supported V-Mg-O catalysts during oxidative dehydrogenation of propane: Kinetic study

The oxidative dehydrogenation （ODH） of propane was conducted on gallium, aluminum, and chromium doped Si30VMgO catalysts. On doping, the concentrations of the phases responsible for the activity and selectivity increased in their concentrations. The reaction studies were conducted in a tubular steel reactor at temperatures of 753, 783, 813, and 843 K and atmospheric pressure. The total flow rates of the feed were chosen as 30, 40, 50, and 60 ml/min. The propane to oxygen ratios were chosen at 1 ： 1, 2 ： 1, and 3 ： 1, respectively. The effect of various dopants on the activity and selectivity of the catalysts was studied. Deactivation studies were conducted over all the catalysts. The kinetic data were analyzed in terms of power law models and Langmuir-Hinshelwood （LH） models. The kinetic data results were analyzed by comparing the effect of dopants. Statistical model discrimination was done for the proposed models. AIC and BIC criteria were used for discrimination of the models.     

Synthesis and characterization of functional polysilanes [RMe2Si(CH2)x(Me)Si]n (R = 2‐Fu, 5‐Me‐2‐Fu, 2‐Th, 4‐Me‐2‐Th; x = 2, 3) with appended furyl/thienyl groups on the carbosilyl side chains and their application in the generation and stabilization of palladium nanoparticles

The polysilanes [RMe₂Si(CH₂)_x(Me)Si]_n [x = 2, 3; R = 2‐Fu ( 1, 2 ), 5‐Me‐2‐Fu ( 3, 4 )] bearing furyl‐substituted carbosilyl side chains have been synthesized by dehalocondensation reaction (Wurtz coupling) of the corresponding carbosilanes using sodium dispersion in refluxing toluene. On the other hand, analogous polysilanes with appended thienyl groups [x = 2, 3; R = 2‐Th ( 5, 6 ), 4‐Me‐2‐Th ( 7, 8 )] are only accessible by the reaction of the corresponding carbosilane precursors under mild Wurtz coupling conditions (THF, RT). These polysilanes reveal monomodal molecular weight distribution with M_w/PDI = 3.3–5.4 × 10⁴/1.22–1.47 ( 1–4 ) and 9.1–14.4 × 10⁴/1.45–1.61 ( 5–8 ) and are characterized by FT‐IR, multinuclear (¹H, ¹³C{¹H}, ²⁹Si{¹H}) NMR, and UV/PL spectral studies as well as thermogravimetric analysis (TGA). Preliminary studies on the reactivity of polysilane 2 with palladium acetate (toluene, RT) reveal the formation of spherical palladium nanoparticles of size 8.2 ± 0.6 nm, which remain stable in solution for several weeks. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7816–7826, 2008     

A switched controller for an underactuated underwater vehicle

We present a switched control law for stabilizing an underactuated underwater vehicle (UUV) moving in a horizontal plane in a neutrally buoyant condition. The control law consists of a sequential series of control actions, each of which achieves a certain objective, finally resulting in the system being moved to the origin. Finite-time controllers are employed at each stage to achieve the desired objective. Simulation results are presented to validate the control law.     

Preparation of polymandelide by reaction of α-bromophenylacetic acid and triethylamine

Polymandelide was prepared in 77% yield by reaction of α-bromophenylacetic acid and triethylamine. The product was characterized by ¹H- and ¹³C-NMR and IR spectra and isolation and identification of mandelic acid from hydrolysis of the polymer. The NMR spectra indicate the presence of tacticity at CH in the polymer. Molecular weights were determined by GPC and viscosity measurements; n values of 12–20 are comparable to those reported for polymandelides prepared by other methods. The x-ray powder diffraction pattern showed the product to be completely amorphous. Thermal decomposition was studied using DSC.     

Generalized jump-type Ornstein-Uhlenbeck processes as limits of infinite-particle systems

We prove the existence and uniquencess of the solution to the martingale problem associated with jump-type Ornstein-Uhlenbeck processes in the Schwartz space of distributions onR ^d. An example of a noninteracting infinite-particle system is given, which after rescaling has such a process as a limit. Cases when such a process has an invariant measure are identified.