On the invariants of coloured Petri Nets

In this paper, we develop a theorem that enables computation of the place invariants of the union of a finite collection of coloured Petri Nets when the individual nets satisfy certain conditions and their invariants are known. We consider the illustrative examples of the Readers-Writers problem, a resource sharing system, and a network of databases and show how this theorem is a valuable tool in the analysis of concurrent systems.

Coloured Petri net models for automated manufacturing systems

In this paper, we propose an approach, using Coloured Petri Nets (CPN) for modelling flexible manufacturing systems. We illustrate our methodology for a Flexible Manufacturing Cell (FMC) with three machines and three robots. We also consider the analysis of the FMC for deadlocks using the invariant analysis of CPNs.

Li2MnO3: a rare red-coloured manganese(IV) oxide exhibiting tunable red-yellow-green emission

An experimental assessment of Li2MnO3 has been conducted, in conjunction with related Mn(IV) oxides, to investigate its red colour and photoluminescence. Optical absorption spectra revealed strong band gap absorption, with a sharp edge at similar to 610 nm and a transparent region between similar to 610 and similar to 650 nm, giving rise to the red colour of this compound. Octahedral Mn(IV) ligand field transitions have been observed in the excitation spectra of Li2MnO3, corresponding both to Mn(IV) at ideal sites and displaced in Li sites in the rock salt-based layered structure of Li2MnO3. Optical excitation at ligand field transition energies produces tunable emission in the red-yellow-green region, rendering Li2MnO3 a unique Mn(IV) oxide. The honeycomb-ordered LiMn6] units in its structure are probably the origin of both the absorption and the photoluminescent properties of Li2MnO3.

Modeling of sonochemical decomposition of CCI4 in aqueous solutions

In the context of removal of organic pollutants from wastewater, sonolysis of CCl4 dissolved in water has been widely investigated. These investigations are either completely experimental or correlate data empirically. In this work, a quantitative model is developed to predict the rate of sonolysis of aqueous CCl4. The model considers the isothermal growth and partially adiabatic collapse of cavitation bubbles containing gas and vapor leading to conditions of high temperatures and pressures in them, attainment of thermodynamic equilibrium at the end of collapse, release of bubble contents into the liquid pool, and reactions in the well-mixed pool. The model successfully predicts the extent of degradation of dissolved CCl4, and the influence of various parameters such as initial concentration of CCl4, temperature, and nature of gas atmosphere above the liquid. in particular, it predicts the results of Hua and Hoffmann (Environ. Sci Technol, 1996, 30, 864-871), who found that degradation is first order with CCl4 and that Argon as well as Ar-O-3 atmospheres give the same results. The framework of the model is capable of quantitatively describing the degradation of many dissolved organics by considering all the involved species.

Efficient use of correlation entropy for analysing time series data

The correlation dimension D 2 and correlation entropy K 2 are both important quantifiers in nonlinear time series analysis. However, use of D 2 has been more common compared to K 2 as a discriminating measure. One reason for this is that D 2 is a static measure and can be easily evaluated from a time series. However, in many cases, especially those involving coloured noise, K 2 is regarded as a more useful measure. Here we present an efficient algorithmic scheme to compute K 2 directly from a time series data and show that K 2 can be used as a more effective measure compared to D 2 for analysing practical time series involving coloured noise.

Synthesis, characterization and photocatalytic activity of MxCe1-xVO4 (M = Li, Ca and Fe)

Non-stoichiometric substituted cerium vanadates, MxCe1-xVO4 (M = Li, Ca and Fe), were synthesized by solid-state reactions. The crystal structure was analyzed by powder X-ray diffraction and it exhibits a tetragonal zircon Structure, crystallizing in the space group I4(1)/amd with a = 7.3733(4) and c = 6.4909(4) angstrom and Z = 4. Particle sizes were in the range of 600-800 nm, as observed by scanning electron microscopy. The thermal analysis of the compounds showed phase stability up to 1100 degrees C. The UV diffuse reflectance spectra indicated that the compounds have band gaps in the range of 2.6-2.9 eV. The photocatalytic activity of these Compounds was investigated for the first time for the degradation of different dyes, and organics, the oxidation of cyclohexane and the hydroxylation of benzene. The degradation of dyes was modeled using the Langmuir-Hinshelwood kinetics, while the oxidation of cyclohexane and hydroxylation of benzene were modeled using a free radical mechanism and a series reaction mechanism, respectively.

Electrophilic Addition of Phenylisocyanate at gamma-CH of Thio-beta-diketonates of Some Transition Metals

The quasi-aromatic property of metal chelates of thio-beta-diketones has been studied by reacting them with phenylisocyanate, where addition takes place at the gamma-CH in a stepwise manner. Mono-thiodiketonates of Ni(II), Pd(II), cu(II) and Co(III) and the dithio-acetylacetonate of Ni(II) react with phenylisocyanate to produce mono-, di- and triphenylamido [with cobalt (III) only] substituted derivatives. In the case of tris (ethylthioacetoacetato) cobalt (III), it is found that the reaction with phenylisocyanate gives two isomers, a chocolate coloured isomer in which the phenylamido carbonyl is not coordinated while the green coloured isomer has bonding through phenylemido carbonyl oxygen. The reactions of the thiodiketonates have been compared with those of beta-diketonates and beta-ketoiminates. The reaction products have been characterised by elemental analyses, magnetic moments, and electronic, IR and 1H NMR spectral studies.

Study of solids and surfaces by photoacoustic spectroscopy

Photoacoustic spectroscopy has been employed to study the electronic spectra of a variety of solids. The systems studied include powders of intensely coloured dyes, amorphous chalcogenides and oxide gels besides polycrystalline samples of several oxide materials. Surface sensitivity of the technique has been examined by study of dye adsorption on oxide surfaces and determination of surface areas of active oxides. Acidic and basic sites on catalyst surfaces have also been estimated by this technique.

Constrained linear filter and its relation to singular optimal control

This paper presents an analysis of an optimal linear filter in the presence of constraints on the moan squared values of the estimates from the viewpoint of singular optimal control. The singular arc has been shown to satisfy the generalized Legcndrc-Clebseh condition and Jacobson's condition. Both the cases of white measurement noise and coloured measurement noise are considered. The constrained estimate is shown to be a linear transformation of the unconstrained Kalman estimate.

Nature of the colour-forming species in peroxy titanium sulphate

ALTHOUGH titanium is determined colorimetrically in aqueous sulphuric acid medium in presence of excess of hydrogen peroxide, the nature of the colour-forming species is not known definitely. Schwarz1 suggested that the colour was due to the peroxo-disulphato titanate anion [O 2Ti(SO4)2]2-. On the other hand, Jahr2 and later Gastinger3 considered that the colour of the compound was due to the peroxy titanyl cation [TiO2 aq.] 2+, and suggested the following equilibrium in solution: Schaeppi and Treadwell4 attributed the colour bo O2TiSO4 or [O2Ti(SO4)2]2-, whereas Babko and Volkova5 represented the coloured complex ion as [Ti(H 2O2)]4+. Mori, Shibata, Kyuno and Ito 6 regarded the coloured species as [TiO2 aq.]2+ or [Ti(OH)2 (H2O)(H2O2)] 2+, assuming the co-ordination number of titanium to be four. Thus, a variety of constitutions has been proposed to explain the colour-forming species of the titanium complex, based on the investigations carried out in dilute sulphuric acid medium, but the complex has not been isolated so far.

Amido binding to ReO3+ core: Synthesis, structure and intermolecular interactions

The light green coloured complexes of general formula [(ReO)-O-V(L)CI(OH2)]Cl have been synthesised in good yields by reacting [RcvOCl(3)(AsPh3)21 with HL in dichloromethane in dinitrogen atmosphere. Here, L- is the deprotonated form of N',N'-bis(2-pyridylmethyl)amine (HL1); N-(2-pyridylmethyl)-N',N'-dimethylethylenediamine (HL2) and N-(2-pyridylmethyl)-N',N-diethylethylenediamine (HL3). Single crystal X-ray structure determination of [(ReO)-O-V(L-1)Cl(OH2)Cl confirms the amido binding of ReO3+ species. In the solid state of [(ReO)-O-V(L-1)Cl(OH2)]Cl, the coordinated and counter chloride ions are engaged in Re-Cl... H-C(ring), Cl...H-C(ring) and Re(OH2)...Cl hydrogen bonding and forming of a supramolecular network in the solid state. The subunit of the supramolecular network consists of one eight-membered and two nine-membered hydrogen bonded rings. The average diameters of eight-membered and nine-membered rings are similar to 3.70 and similar to 5.26 angstrom, respectively.

Algorithms for Colouring Random k-colourable Graphs

The k-colouring problem is to colour a given k-colourable graph with k colours. This problem is known to be NP-hard even for fixed k greater than or equal to 3. The best known polynomial time approximation algorithms require n(delta) (for a positive constant delta depending on k) colours to colour an arbitrary k-colourable n-vertex graph. The situation is entirely different if we look at the average performance of an algorithm rather than its worst-case performance. It is well known that a k-colourable graph drawn from certain classes of distributions can be ii-coloured almost surely in polynomial time. In this paper, we present further results in this direction. We consider k-colourable graphs drawn from the random model in which each allowed edge is chosen independently with probability p(n) after initially partitioning the vertex set into ii colour classes. We present polynomial time algorithms of two different types. The first type of algorithm always runs in polynomial time and succeeds almost surely. Algorithms of this type have been proposed before, but our algorithms have provably exponentially small failure probabilities. The second type of algorithm always succeeds and has polynomial running time on average. Such algorithms are more useful and more difficult to obtain than the first type of algorithms. Our algorithms work as long as p(n) greater than or equal to n(-1+is an element of) where is an element of is a constant greater than 1/4.

Signal subspace approach in localization of sound source in shallow water

A new algorithm based on signal subspace approach is proposed for localizing a sound source in shallow water. In the first instance we assumed an ideal channel with plane parallel boundaries and known reflection properties. The sound source is assumed to emit a broadband stationary stochastic signal. The algorithm takes into account the spatial distribution of all images and reflection characteristics of the sea bottom. It is shown that both range and depth of a source can be measured accurately with the help of a vertical array of sensors. For good results the number of sensors should be greater than the number of significant images; however, localization is possible even with a smaller array but at the cost of higher side lobes. Next, we allowed the channel to be stochastically perturbed; this resulted in random phase errors in the reflection coefficients. The most singular effect of the phase errors is to introduce into the spectral matrix an extra term which may be looked upon as a signal generated coloured noise. It is shown through computer simulations that the signal peak height is reduced considerably as a consequence of random phase errors.

Synthesis, structure and redox properties of (?-oxo)bis(?-carboxylato)diruthenium(III) complexes containing three different terminal ligands

Blue coloured, unstable, essentially diamagnetic and non-electrolytic diruthenium(III) complexes of the formation [Ru2O(O2CR)4(en)2(PPh3)2] were prepared by reacting [Ru2O(O2CR)4(PPh3)2] with 1,2-diaminoethane (en) in CH2Cl2 (R = C6H4-p-X; X = H, Me and OMe). The molecular structure of the complexes is proposed as [{(?1-O2CR)(?1-en)(PPH3)Ru}2(?-O)(?-O2CR)2] based on the 1H NMR spectral data. The electronic spectra of the complexes display a band near 569 nm with a shoulder at 630 nm. In CH2Cl2-0.1 M [Bun4N]ClO4, the complexes exhibit redox couples Ru2III,III/Ru2III,IV and Ru2III,IV/Ru2IV,IV near 0.1 and 1.2 V (vs SCE), respectively. The potentials are the lowest among diruthenium(III) complexes with a similar core structure.