On the convergence of the Zassenhaus formula

The domain of convergence of the Zassenhaus formula in a Banach algebra is studied. This domain is shown to be strictly larger than the one which was already known.     

Synthesis of polypyrrole nanoparticles and its grafting with silica gel for selective binding of chromium(VI)

Polypyrrole nanoparticles of desired structure have been synthesized through simple micelle technique. It is then grafted with functionalized silica gel to develop a novel organic-inorganic hybrid material. The role of dimethyl dichloro silane (coupling agent) in grafting is demonstrated. The nanoparticles are characterized by TEM, SEM and TGA. Grafting reactions are evaluated by spectral (FTIR) analysis and chemical test. The Cr(VI) binding behavior of the composite is studied in various pH of the medium. The selectivity in binding Cr(VI) is monitored. The metal ion adsorption capacity and surface area of the material are found to be 38 mg/g and 235 m²/g, respectively.     

Localizability of massless particles in the framework of the conformal group

Localizability of massless particles in the framework of the conformal group is given by means of imprimitivity systems for particular representations of the Sitter groupSO ₀(4, 1).Dedicated to Professor Ivan Úlehla on the ocassion of his sixtieth birthday.The authors wish to thank Professors M. Flato and W. Schmid for stimulating discussions.     

Facile synthesis of polyacrylate directed silver nanoparticles for pH sensing through naked eye

Poly(acrylic acid) (PAA) and its salt poly(acrylate) (PA) have been synthesized through modified free radical polymerization in environmentally begin aqueous medium under ultrasound to make the process robust. The synthesized polymer is well-characterized through conventional techniques. Its salt is employed to produce highly stable and stimuli sensitive colloidal silver (Ag-PA sol) without using any additional reducing chemical reagents like sodium borohydride, ascorbic acid, hydrazine, etc or UV/Gamma radiation. A detailed mechanistic path of the polymerization and reduction of Ag⁺ on polyacrylate chains has been evaluated. Finally Ag-PA sol is used for pH sensing through naked eye to eliminate the need for sophisticated instrument for data collection. The present work focuses mainly the development of a low cost pH sensing system based on colorimetric ‘smart polymer’ having high practical utility. The unique structural and photo-physical features of nano-scaled materials open new opportunities for the applications of colorimetric pH sensor. In the present work, Ag nano-clusters capped by PA^? are employed as an effective colorimetric pH sensor for the first time, requiring no further functionalization.     

The permeation liquid membrane as a sensor for free nickel in aqueous samples

There are currently a limited number of techniques to study nickel speciation in aqueous samples. This work reports on the use of the permeation liquid membrane (PLM) for that objective. In this paper, the composition of the organic phase was studied to maximize the Ni flux (thus the sensitivity of the device) over a wide Ni2+ concentration range (50 nM to 100 microM) in order to verify its ability to determine free Ni2+ in the presence of Ni complexes. A mixture containing 1,10-didecyl-1,10-diaza-18-crown-6 ether (22DD) and di(2-ethylhexyl)phosphoric acid (D2EHPA) in toluene/phenylhexane was selected as the optimized organic phase for the PLM. The PLM was shown to be a reliable tool to measure free nickel concentrations down to 10(-7) M. The effect of pH on Ni transport was also studied. Fluxes below pH 6 were reduced significantly, i.e. an order of magnitude smaller than fluxes above pH 7.8. Finally, as part of a broader study examining the ability of trace metals to induce antibiotic resistance in bacteria, we used the PLM to quantify the formation, at pH = 7.2, of a weak complex between Ni and Imipenem (a member of the carbapenem class of beta-lactam antibiotics) or its hydrolysis product(s).     

Analysis of an Optimal Control Problem Related to the Anaerobic Digestion Process

Our aim in this work is to synthesize optimal feeding strategies that maximize, over a time period, the biogas production in a continuously filled bioreactor controlled by its dilution rate. Such an anaerobic process is described by a four-dimensional dynamical system. Instead of modeling the optimization of the biogas production as a Lagrange-type optimal control problem, we propose a slightly different optimal control approach in this paper: We study the minimal time control problem to reach a target point, which is chosen in such a way that it maximizes the biogas production at steady state. Thanks to the Pontryagin maximum principle and the geometric control theory, we provide an optimal feedback control for the minimal time control problem, when the initial conditions are taken within the invariant and attractive manifold of the system. The optimal synthesis exhibits turnpike and anti-turnpike singular arcs and a cut locus.     

Mass transfer with chemical reaction in a laminar falling film

Zusammenfassung Es wird eine analytische Lösung für die Absorption in einem laminaren Rieselfilm mit homogener und heterogener chemischer Reaktion 1. Ordnung vorgestellt, wobei der Stofftransportwiderstand auf der Gasseite liegt. Die Lösung ist eine Funktion von drei dimensionslosen ParameternBi, und, welche die BiotZahl und einen homogenen bzw. heterogenen Reaktionsparameter darstellen. Es wird gezeigt, daß für feste Werte vonBi und die Absorptionsrate (bezogen auf die Breite 1 des Rieselfilms) über eine gewisse Länge (dimensionslos) des Rieselfilms unabhängig von ist, wenn, < 0,6 ist. Die laufende Länge wird von der Stelle aus gemessen, an der die Absorption beginnt. Für b 0,6 nimmt der FlußQ mit zu, erreicht aber einen Sättigungswert bei=10, wonachQ nurmehr sehr langsam anwächst. Jedoch für ein gegebenes und ohne Übergangswiderstand im Film (Bi ) nimmtQ mit für alle 0 zu.

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Mass transfer with chemical reaction in a laminar falling film

An analytical solution is presented for gas absorption in a laminar falling film with first-order homogeneous and heterogeneous chemical reaction and external gas-phase mass transfer resistance. The solution depends on three dimensionless parametersBi, and, wich represent the Biot number, homogeneous and heterogeneous reaction parameters, respectively. It is shown that for fixed values ofBi and, the rate of gas absorption (per unit breadth) over a certain length; (dimensionless) along the falling film measured from the point where surface absorption begins is independent of if < 0.6. For 0.6, this fluxQ increases with but reaches a saturation value at=10 beyond whichQ increases very slowly. But for given and zero gas film resistance (Bi ),Q increases with for all 0.

     

Star exponentials of the elements of the inhomogeneous symplectic Lie algebra

We compute the star exponential of any element of the inhomogeneous symplectic Lie algebra on a 2l-dimensional phase space and show the existence of classical trajectories for a quantum system whose Hamiltonian belongs to this Lie algebra.     

Studies on kinetics and mechanism of oxidation of D‐sorbitol and D‐mannitol by cerium(IV) in aqueous micellar sulfuric acid media

The kinetics and mechanism of cerium(IV) oxidation of hexitols, i.e. D ‐sorbitol and D ‐mannitol, in aqueous sulfuric acid media have been studied in the presence and absence of surfactants. Under the kinetic conditions, [S]_T ? [Ce(IV)]_T, where [S]_T is the total substrate (D ‐sorbitol or D ‐mannitol) concentration, the overall process shows a first‐order dependence on [Ce(IV)]_T and [S]_T. The process is acid catalyzed and inhibited by [HSO]. From the [HSO] dependence, it has been noted that the both Ce(SO₄)²⁺ and Ce(SO₄)₂ have been found kinetically active. The different rate constants in the presence and absence of surfactants have been estimated with the activation parameters. N‐cetylpyridinium chloride has been found to retard the oxidation process of hexitols, whereas sodium dodecyl sulfate has been found to accelerate the rate process. All these findings including the micellar effects have been interpreted in terms of the proposed reaction mechanism and partitioning behavior of the kinetically active different species of Ce(IV) between the aqueous and pseudomicellar phase. © 2008 Wiley Periodicals, Inc. 40: 445–453, 2008