Linear Quadratic Gaussian Homing for Markov Processes with Regime Switching and Applications to Controlled Population Growth/Decay

Methodology and Computing in Applied Probability - The problem of optimally controlling one-dimensional diffusion processes until they enter a given stopping set is extended to include Markov...     

Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

Normal forms for nonlinear control systems with scalar output

We propose a normal form for nonlinear control systems with scalar output. We follow an approach proposed by Poincaré and adapted for control systems by Kang and Krener which consists of analyzing, step-by-step, the action of the change of coordinates on the system. To cite this article: I.A. Tall, M. Balde, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Comment: Towards a Complete Classification of Spherically Symmetric Lorentzian Manifolds According to Their Ricci Collineations

General expressions for the components of the Ricci collineation vector are derived and the related constraints are obtained. These constraints are then solved to obtain Ricci collineations and the related constraints on the Ricci tensor components for all spacetime manifolds (degenerate or non-degenerate, diagonal or non-diagonal) admitting symmetries larger than so(3) and already known results are recovered. A complete solution is achieved for the spacetime manifolds admitting so(3) as the maximal symmetry group with non-degenerate and non diagonal Ricci tensor components. It is interesting to point out that there appear cases with finite number of Ricci collineations although the Ricci tensor is degenerate and also the cases with infinitely many Ricci collineations even in the case of non-degenerate Ricci tensor. Interestingly, it is found that the spacetime manifolds with so(3) as maximal symmetry group may admit two extra proper Ricci collineations, although they do not admit a G ₅ as the maximal symmetry group. Examples are provided which show and clarify some comments made by Camci et al. [Camci, U., and Branes, A. (2002). Class. Quantum Grav. 19, 393–404]. Theorems are proved which correct the earlier claims made in [Carot, J., Nunez, L. A., and Percoco, U. (1997). Gen. Relativ. Gravit. 29, 1223–1237; Contreras, G., Núñez, L. A., and Percolo, U. (2000). Gen. Relativ. Gravit. 32, 285–294].     

Fractal analysis of hydroxyapatite from nitrogen isotherms

Samples of calcium hydroxyapatite, CaHap, were prepared via a wet method and subjected to thermal treatment in air in the temperature range 100-900 degrees C. Nitrogen adsorption-desorption isotherms were obtained on different samples, and their data points were used to analyze the fractal properties of the obtained solids. Both FHH and Neimark's equations were used for such purpose, and the agreement or disagreements between obtained results on using both equations are discussed. Considering the appropriate values of the obtained surface fractal dimensions D, it was concluded that an appreciable defractalization of the prepared hydroxyapatite is only noted upon calcinations at 900 degrees C. Below this temperature the loss in surface area and pore volume result from simultaneous bulk and surface mass transport, which conserve the initial surface roughness and average pore radius. Calcination at 900 degrees C caused sintering to proceed via bulk mass transport, with a consequent pore widening and a decrease in surface roughness.     

Adsorption of Molybdenum on Titania from Aqueous Solutions

The adsorption of Mo from dilute aqueous solutions (10(-3) to 3x10(-2) M) is effected on three samples of titania, two are anatase and the third is P25, which is composed of rutile and anatase. The adsorption isotherms at 298, 318, and 338 K are analyzed using a Langmuir linear equation. The isotherms on P25 showed a distinct inflection point that is reproduced by two linear portions, indicating different adsorption regimes. This adsorption behavior is explained as follows: with low amount adsorbed the adsorption is initiated by protonation of the basic hydroxyls on which the negatively charged MoO(4)(2-')s are adsorbed, and this is accompanied by an increase in the pH of the impregnating solution. At higher adsorption the coordinatively unsaturated Ti(4+) sites participate in the process, leading to a decline in the initial increase in pH. In the case of the two anatase samples the low surface area resulted in poor distribution of adsorption sites; consequently, the distinction between the two modes of adsorption was not entirely clear. The higher adsorption site density in the case of anatase is accompanied by a lower surface coverage, θ, than that for P25. The heat of adsorption, Q, on the three titania samples showed a linear increase with θ, which is represented by the regression equation: -Q=95.77θ-4.25 (R(2)=0.993). Copyright 2001 Academic Press.     

On-column trace enrichment by sequential frontal and elution electrochromatography II. Enhancement of sensitivity by segmented capillaries with z-cell configuration--application to the detection of dilute samples of moderately polar and nonpolar pesticides

An on-column trace enrichment method for capillary electrochromatography of dilute samples is described. It involves the sequential use of frontal and elution electrochromatography on a segmented capillary column comprising of two contiguous segments each packed with a different sorbent. While the entering segment is for preconcentration by frontal electrochromatography the second segment is much longer and is meant for separation of the enriched analytes in the subsequent elution electrochromatography step. The preconcentration segment is usually packed with a sorbent that affords the highest affinity towards the solutes of interest while the separation segment is packed with a stationary phase that exhibits the highest selectivity and separation efficiency for the analytes. The detection is performed in the UV using a z-cell configuration for achieving an increased path length for detection. The effectiveness of this on-column trace enrichment is demonstrated on dilute samples of moderately polar solutes (e.g., carbamate insecticides) and nonpolar solutes (e.g., pyrethroid insecticides). Under optimal frontal and elution electrochromatography conditions. 817- and 1100-fold sensitivity increase are achieved for permethrin (a pyrethroid insecticide) and methiocarb (a carbamate insecticide), respectively, with a UV detector. The method is demonstrated with real water samples (e.g., tap and lake water samples) spiked with carbamate and pyrethroid insecticides. The limits of detection for the pesticides achieved in tap and lake waters reached 10(-8) to 10(-9) M.     

Adsorption of Some Essential Amino Acids on Hydroxyapatite

Samples of synthetic hydroxyapatite, Ca(10)(PO(4))(6)(OH)(2), obtained by wet method and calcined at 1173 K in air were used in an adsorption study of some essential amino acids, mainly histidine, methionine, and tryptophan. Adsorption isotherms were obtained using aqueous solutions of concentration range 2.7x10(-2)-1.3x10(-3) M at 303, 318, and 343 K, under near neutral conditions. The mode of adsorption was studied using IR spectroscopy. The results are discussed in terms of the dependence of the adsorption process both on the functional groups on the hydroxyapatite and on the solution chemistry of the aqueous amino acids solutions. Copyright 2001 Academic Press.     

Capillary electrochromatography with monolithic silica columns III. Preparation of hydrophilic silica monoliths having surface-bound cyano groups: chromatographic characterization and application to the separation of carbohydrates, nucleosides, nucleic acid bases and other neutral polar species

Two synthetic routes have been introduced and evaluated for the preparation of hydrophilic silica-based monoliths possessing surface-bound cyano functions. In one synthetic scheme, the silica monolith was reacted in a single step with 3-cyanopropyldimethylchlorosilane to yield a cyano phase referred to as CN-monolith. In a second synthetic route, the silica monolith was first reacted with gamma-glycidoxypropyltrimethoxysilane (gamma-GPTS), followed by a reaction with 3-hydroxypropionitrile (3-HPN) to give a stationary phase denoted CN-OH-monolith. Although the gamma-GPTS was intended to play the role of a spacer arm to link the 3-HPN to the silica surface, this spacer arm became an integral part of the hydrophilic stationary phase. Thus, the CN-OH-monolith can be viewed as a double-layered stationary phase (i.e., stratified phase) with a hydroxy sub-layer and a cyano top layer. Due to its stronger hydrophilic character, the CN-OH-monolith yielded higher retention and better selectivity than the CN-monolith. The CN-OH-monolith was demonstrated in the normal-phase capillary electrochromatography (CEC) of various polar compounds including phenols and chloro-substituted phenols, nucleic acid bases, nucleosides, and nitrophenyl derivatives of mono- and oligosaccharides. The CN-OH-monolith yielded a relatively strong electroosmotic flow over a wide range of mobile phase composition, thus allowing rapid separation of the polar compounds studied.