Chordal decomposition in operator-splitting methods for sparse semidefinite programs

Mathematical Programming - We employ chordal decomposition to reformulate a large and sparse semidefinite program (SDP), either in primal or dual standard form, into an equivalent SDP with smaller...     

An Alternative Model for Queueing Systems with Single Arrivals,Batch Services and Customer Coalescence

In this paper we consider a queueing system with single arrivals, batch services and customer coalescence and we use it as a building block for constructing queueing networks that incorporate such characteristics. Chao et al. (1996) considered a similar model and they proved that it possesses a geometric product form stationary distribution, under the assumption that if the number of units present at a service completion epoch is less than the required number of units, then all the units coalesce into an incomplete (defective) batch which leaves the system. We drop this assumption and we study a model without incomplete batches. We prove that the stationary distribution of such a queue has a nearly geometric form. Using quasi-reversibility arguments we construct a network model with such queues which provides relevant bounds and approximations for the behaviour of assembly processes. Several issues about the validity of these bounds and approximations are also discussed.     

One-pot synthesis of novel fused pentacyclic chromenopyrimidobenzimidazolones and benzimidazolyl-chromenyl-substituted thiazolidinones

The ultrasound promoted synthesis of a number of novel fused pentacyclic chromenopyrimido[1,2-α]benzimidazolones by the one-pot reaction of 3-formylchromones with 2-aminobenzimidazole is described. Moreover, the isolated pentacyclic chromone derivatives upon microwave irradiation with 2-mercaptocarboxylic acids afforded benzimidazolyl-chromenylthiazolidinones incorporating three pharmacophoric heterocycles; the same thiazolidinones were also formed through a multicomponent reaction under microwave irradiation involving 3-formylchromones, aminobenzimidazole and 2-mercaptocarboxylic acids. The structural elucidation of the products was accomplished by 1D and 2D NMR experiments and for thiazolidinones was also confirmed by X-ray crystallographic analysis. Full assignment of all ¹H and ¹³C NMR chemical shifts has been unambiguously achieved. The proposed reaction mechanism is also discussed.     

A wavelet smoothing method to improve conditional sales forecasting

This article proposes a wavelet smoothing method to improve conditional forecasts generated from linear regression sales response models. The method is applied to the forecasted values of the predictors to remove forecast errors and thereby improve the overall forecasting performance of the models. Eight empirical studies are presented in which the purpose was to forecast detergent sales in the Netherlands, and wavelet smoothing was compared with a moving average and a band-pass filter. All methods were found to improve forecasts. Wavelet smoothing provided the best results when applied on highly volatile marketing time series. In contrast, it was less effective when applied on highly aggregated and smooth time series. An advantage of wavelets is that they are flexible enough to allow for data characteristics like abrupt changes, spikes and cyclical changes that are usually associated with price changes and promotions.     

Ring transformation of 5-aroyl-3(2H)-isothiazolones to 1,2,5-oxathiazole and 1,2,3-thiadiazole derivatives

Reaction of 2-substituted-5-aroyl-3(2H)-isothiazolones 2 with hydroxylamine and phenylhydrazine was found to give (N-substituted-carboxamido)methylene derivatives of 1,2,5-oxathiazole and 1,2,3-thiadiazole, 5 and 7 , respectively. The formation of these heterocycles was ascribed to a mononuclear heterocyclic rear-rangement of the initially formed ketone derivatives, oximes and hydrazones, through a nucleophilic attack of the = N-OH and = N-NH- groups on the S N bond of the isothiazolone ring. In a similar manner, reaction of isothiazolones 2 with hydrazine was found to give 4-aryl-5-(N-substituted-carboxamido)methyl-1,2,3-thiadiazoles 17 .     

The importance of the plume ejection time for the fragmentation yields observed in the UV ablation of molecular van der Waals films. Ablation of chlorobenzene films at 248 nm

The efficiency of photolysis in the ablation of thick C₆H₅Cl films at 248 nm is probed over 40–300 mJ/cm² by means of time-of-flight quadrupole mass spectrometry. Up to ≈ 150 mJ/cm², the photolysis yield is considerably smaller than that in the gas-phase. We argue that because of plume ejection well after the laser pulse, photolysis occurs exclusively in the film, and as a result, permanent dissociation is limited by the operation of efficient recombination processes characteristic of condensed phases. Fragmentation starts being important only at higher fluences, at which desorption during the laser pulse is indicated to be significant.     

Conformation and coordination of β-diketonates in mixed-ligand copper(II) chelates of 1,2-diamines. Theoretical approach and experimental verification. Crystal structure of [bis(N,N′-dimethyl-1,2-diaminoethane) bis(3-cyano-2,4-pentanedionate)copper(II)]dihydrate

The reaction of the bis(2,4-pentanedionato)copper(II), Cu(acac)₂, and its substituted derivatives (Cu(NC-acac)₂, Cu(O₂N-acac)₂, and Cu(tfac)₂), with 1,2-diaminoethane (en), 1,2-diaminopropane (pn) and certain N-substituted derivatives of 1,2-diaminoethane, enR, is reported. The reaction products were found to depend on the reaction conditions, the extent of N-substitution of the diamine and the nature of the β-diketonate anion, β⁻. The [Cu(enR)β₂] addition compounds are not always sufficiently stable and in most instances the tetragonal species [Cu(enR)₂β₂] prevail as the final product. The 1,2-diamine molecules in [Cu(enR)₂β₂] form chelate rings attaining the gauche conformation while the β-diketonato anions essentially confer electrical neutrality. Density functional theory (DFT) calculations suggest that the active sites of the β-diketonato anion and its conformation depend on their ability to create hydrogen bonds and on the substituents in 3-position. The Fukui indices of chemical reactivity favor the carbonyl oxygens as binding sites of most anions while in the case of the 3-cyano-2,4-pentanedionato anion, NC-acac⁻, bonding through the cyano nitrogen is envisaged with the S(E, Z) conformer having the lowest energy. These findings are in accord with experimental data and further proof is given by single crystal X-ray diffraction analysis of the structure of [Cu(MeenMe)₂(NC-acac)₂] · 2H₂O (MeenMe denoting N,N′-dimethyl-1,2-diaminoethane). In this compound the NC-acac⁻ attains the S(E, Z) conformation and interacts with the square-planar entity [Cu(MeenMe)₂]²⁺ through the cyano nitrogen, while intermolecular hydrogen bonding involving the water molecules leads to supramolecular structure.     

Formation of 5-aroyl-3-(2H)isothiazolones from the reaction of 3-aroylpropionamides with thionyl chloride

Reaction of N-substituted-3-aroylpropionamides with excess thionyl chloride was found to give sulfur-nitrogen heterocyclic compounds, which were characterized as 2-substituted-5-aroyl-3-(2H)isothiazolones.     

The synthesis of n‐substituted isothiazol‐3(2h)‐ones from nsubstituted 3‐benzoylpropionamides

N‐Substituted isothiazol‐3(2H)‐ones can be easily prepared from N‐substituted 3‐benzoylpropi‐onamides in two experimentally simple steps, in satisfactory overall yields. Reaction of the amides with excess thionyl chloride results in the formation of N‐substituted 5‐benzoylisothiazol‐3(2H)‐ones, which are readily debenzoylated with alkali to the corresponding N‐substituted isothiazol‐3(2H)‐ones. This method has now been successfully applied to the synthesis of isothiazolones N‐substituted with a bulky alkyl group, such as the tert‐butyl group, and with a phenyl group bearing either a strong electron‐withdrawing substituent, such as the 3‐nitrophenyl and 4‐nitrophenyl group, or an electron‐releasing substituent, such as the 4‐methylphenyl and 4‐methoxyphenyl group.