Recursive solution of linear-quadratic Nash games for weakly interconnected systems

A recursive method is developed for the solution of coupled algebraic Riccati equations and corresponding linear Nash strategies of weakly interconnected systems. It is shown that the given algorithm converges to the exact solution with the rate of convergence ofO(²), where is a small coupling parameter. In addition, only low-order systems are involved in algebrdic computations; the amount of computations required does not grow per iteration and no analyticity assumption is imposed on the system coefficients.This work was supported by Rutgers University Research Council under Grant No. 2-02188.     

Note on the application of the reduced graph model in conjunction with search trees to the enumeration ofKekulé structures

The reduced graph model, when used in conjunction with the search trees method, provides a novel combinatorial procedure for the enumeration and generation ofKekulé structures. The procedure is suited for large benzenoid hydrocarbons consisting of cata- and thin peri-condensed parts.

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Zur Anwendung des Reduced Graph Model im Zusammenhang mit Search Trees zur Ermittlung der Anzahl möglicherKekulé-Strukturen

Zusammenfassung Das Modell erlaubt mit der im Titel genannten Kombination eine neuartige Methode zur Ermittlung und Generierung vonKekulé-Strukturen. Das Verfahren ist für große benzoide Kohlenwasserstoffe geeignet, die aus cata- und (dünnen) peri-kondensierten Teilstrukturen bestehen.

     

A simple and efficient one-step, regioselective, enzymatic glucosylation of arbutin by α-glucosidase

4-Hydroxyphenyl-β-isomaltoside has been synthesized by α-glucosidase assisted transglycosylation between arbutin as acceptor and sucrose as donor molecules, respectively. Optimum conditions for the transglucosylation reaction were 40 °C for 20 h with 10 mM arbutin and 1.5 M sucrose in a 100 mM sodium citrate/phosphate buffer at pH 5.0. The new glucoside was obtained in a 50% molar yield with respect to arbutin.     

Atomic walk counts of negative order

Atomic walk counts (awc's) of order k (k > or = 1) are the number of all possible walks of length k which start at a specified vertex (atom) i and end at any vertex j separated by m (0 < or = m < or = k) edges from vertex i. The sum of atomic walk counts of order k is the molecular walk count (mwc) of order k. The concept of atomic and molecular walk counts was extended to zero and negative orders by using a backward algorithm based on the usual procedure used to obtain the values of mwc's. The procedure can also be used in cases in which the adjacency matrix A related to the actual structure is singular and therefore A(-1) does not exist. awc's and mwc's of negative order may assume noninteger and even negative values. If matrix A is singular, atomic walk counts of zero order may not be equal to one.     

Assessment of Chemical Composition and Anti-Penicillium Activity of Vapours of Essential Oils from Abies Alba and Two Melaleuca Species in Food Model Systems

The possibilities of the practical utilization of essential oils (EOs) from various plant species in the food industry have attracted the attention of the scientific community. Following our previous studies, the antifungal activities of three further commercial EOs, Melaleuca armillaris subsp. armillaris (rosalina; REO), Melaleuca quinquenervia (niaouli; NEO), and Abies alba (fir; FEO), were evaluated in the present research in respect to their chemical profiles, over four different concentrations, 62.5 μL/L, 125 μL/L, 250 μL/L, and 500 μL/L. The findings revealed that the major compounds of REO, NEO, and FEO were linalool (47.5%), 1,8-cineole (40.8%), and α-pinene (25.2%), respectively. In vitro antifungal determinations showed that the inhibition zones of a Penicillium spp. mycelial growth ranged from no inhibitory effectiveness (00.00 ± 00.00 mm) to 16.00 ± 1.00 mm, indicating a very strong antifungal activity which was detected against P. citrinum after the highest REO concentration exposure. Furthermore, the in situ antifungal efficacy of all EOs investigated was shown to be dose-dependent. In this sense, we have found that the highest concentration (500 µL/L) of REO, NEO, and FEO significantly reduced (p < 0.05) the growth of all Penicillium strains inoculated on the bread, carrot, and potato models. These results indicate that the investigated EOs may be promising innovative agents in order to extend the shelf life of different types of food products, such as bread, carrot and potato.     

Dynamics of water adsorption on TiO2 monitored by work function spectroscopy

Water adsorption dynamics on two TiO₂ (1 1 0) rutile surfaces at room temperature has been investigated using the work function (WF) change as a function of time. The first surface was prepared in a standard way using sputtering/annealing cycles, whereas the second one was long term annealed at 620 K in moderate vacuum conditions (the residual gas pressure of about 1 × 10⁻⁷ mbar) and cleaned afterwards. The WF change show striking difference as compared to those obtained for highly reduced TiO₂ (1 1 0) rutile or the (2 × 1) reconstructed surfaces. For the first kind of surface we show that the observed adsorption dynamics can be qualitatively explained by the present understanding of the water adsorption on non-reconstructed TiO₂ (1 1 0) rutile surface according to which the bridging oxygen vacancies and Ti rows are the main adsorption sites. Although generally similar to the former results, water adsorption dynamics on the second kind of the surface has an additional feature that can be only explained by a new adsorption site, which we suggest to be due to (2 × 1) reconstructed regions coexisting with the non-reconstructed TiO₂ (1 1 0) surface.