A new method for constructing a minimal PERT network

A project is an enterprise consisting of several activities which are to be carried out in some specific order. The activities and the order in which they need to be carried out can be represented by a PERT network. The PERT technique is a traditional, well-known approach to the expert of project management. When networks are used, it often becomes necessary to draw dummy activities. Since the computation of project completion time is proportional to the number of arcs, including dummy arcs, it is desirable to draw a network with as few dummy activities as possible.In this paper, we propose a new method for constructing, for a given project scheduling problem, a PERT network having as small as possible the number of dummy arcs by using some results on line graphs. This algorithm deals with the existence of transitive arcs. The paper contains illustrative examples, proofs of some theoretical results as well as a comparative study with a similar algorithm known in the literature. Computational results showed the superiority of our algorithm.     

Utility of 2‐[4‐(3‐oxobenzo[f]‐2H‐chromen‐2‐yl)‐1,3‐thiazol‐2‐yl]ethanenitrile in heterocyclic synthesis

Pyrazolo[4,3‐d]pyrimidines, pyrazolo[4,3‐d]triazolino[4,3‐a]pyrimidines, 3‐(2‐thiazolyl)thiophenes, thiazolo[3,2‐a]pyridine and pyrazolo[1,5‐a]pyrimidines were synthesized from 2‐[4‐(3‐oxobenzo[f]‐2H‐chromen‐2‐yl)‐1,3‐thiazol‐2‐yl]ethanenitrile. The newly synthesized compounds were elucidated by elemental analysis, spectral data, chemical transformation and alternative synthesis route whenever possible.     

Modification of Surface and Structural Properties of Ordered Mesoporous Silicates

Two simple modification methods for ordered mesoporous silicas were examined and compared. MCM-41 molecular sieve was physically coated with 4-cyano-4-biphenyl [4(4-pentenyloxy)]benzoate (CBPB) and chemically modified using trimethylethoxysilane. The structural and surface properties of the obtained materials were characterized using elemental analysis, thermogravimetry and nitrogen adsorption over a wide pressure range.It was shown that the pore size of the MCM-41 material was not decreased significantly after the coating procedure, even for high loadings of CBPB. Moreover, low pressure adsorption measurements indicated that significant fractions of the MCM-41 surface were not covered by CBPB, even for high CBPB loadings, which suggests that the attained coverage may be very nonuniform. The chemical bonding procedure led to a marked decrease in the pore size and change of surface properties.It was demonstrated that nitrogen adsorption measurements provide a means of a thorough characterization of modified MCM-41 materials, allowing to estimate the surface area, pore volume and pore size distribution. Moreover, low pressure adsorption data can be used to qualitatively or semiquantitatively assess the surface coverage of the coated/bonded organic groups, which may be used to estimate the uniformity of the coverage and therefore, the usefulness of the modification procedure.     

Nitrogen Adsorption Study of MCM-41 Molecular Sieves Synthesized Using Hydrothermal Restructuring

Nitrogen desorption scanning hysteresis loops (DSHLs) for large-pore MCM-41 silicas (pore diameter from 4.0 to 6.5 nm) are reported for the first time. DSHLs for MCM-41 were compared with those of conventional mesoporous silicas and no appreciable differences were found, although hysteresis loops and DSHLs for the latter were usually broader. Since desorption behavior of conventional porous silicas is appreciably influenced by pore connectivity, the observed similarity in hysteresis behavior suggests single-pore blocking effects for MCM-41 due to variation of pore diameter along its nonintersecting channels. It was also shown that the steepness of nitrogen desorption branches at relative pressures close to 0.4 often results from proximity of the lower pressure limit of adsorption-desorption irreversibility and consequently it is not justified to consider it as an indication of narrow pore size distribution. Thus, application of desorption data in calculations of pore size distributions may be grossly misleading.     

Equations des variétés de Kummer

Sans résumé

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A two parameter mixed interior-exterior penalty algorithm

In this paper, we analyze the mixed penalty methods introduced in the classic book of Fiacco and McCormick usingtwo distinct penalty parametersr, t. The two penalty coefficients induce a two-parameter differentiable trajectory. We analyze the numerical behaviour of an extrapolation strategy that follows the path of the two-parameter trajectory. We show also how to remove the ill-conditioning by suitable transformations of the equations. In the resulting theory, we show that function values as well as distances to the optimum are both governed by the same behaviour as interior methods (two-step superlinearly convergent, with limiting exponent 4/3).Research partially supported by NSERC grant OGP0036512.Research partially supported by NSERC grant OGP0005491.     

Bioactive Chemical Constituents of Cladiella Species

From the methanolic extract of Cladiella sp., collected from the Andaman Island, India, a new sesquiterpene, cladidiol ( 2 ), and three known diterpenes, cladiellaperoxide ( 3 ), (6E)‐2α,9α‐epoxyeunicella‐6,11(12)‐dien‐3β‐ol ( 4 ), and polyanthellin A ( 5 ) were isolated. The structures of these compounds were established by extensive spectroscopic studies. Compound 2 exhibited modest acetylcholinesterase‐inhibition activity, and compounds 3 – 5 showed antibacterial activities against Streptococcus pyogenes, Escherichia coli, and Pseudomonas aeruginosa.     

Polarographic reduction and tautomeric structure of 2-amino-5-arylazothiazoles

The polarographic behaviour of a series of 2-amino-4-phenyl-5-arylazothiazoles has been investigated at a dropping mercury electrode. Each of the compounds studied exhibits one wave which was shown to correspond to the reductive cleavage of the azo linkage by a 4e irreversible step. On the basis of the polarographic data, it was concluded that the compounds exist only in one tautomeric form, namely the aminoazo structure 1 . The results of E_1/2 — σ_X correlations and HMO calculations of bonding energies of the various possible tautomeric forms 1–3 indicate that the aminoazo form 1 is the most stable structure of the compounds examined.     

Facile synthesis of thiadiazolo [2,3-b] quinazoline derivatives via the Japp-Klingemann Reaction

Diazotized anathranilic acid and its methyl ester react with substituted α-thiocyanatoacetoacetanilides3a–c to give in both cases the corresponding thiadiazolo [2,3-b] quinazolines6a–c, respectively. A mechanism is proposed and it is substantiated by synthesis of6a from N-(2-car?yphenyl)-C-phenylcarbamoyl hydrazidoyl chloride8a or its N-(2-methoxycarbonylcarbonylphenyl) analogue8d.     

A one step synthesis of thiadiazolo[2,3-b]quinazoline derivatives

Diazotized anthranilic acid and its methyl ester react with substituted phenacyl thiocyanates 3 to give in both cases the corresponding thiadiazolo[2,3-b]quinazolines 7a-e . A mechanism is proposed and it is substantiated by alternate synthesis of 7a from the hydrazidoyl chlorides 9a,b and potassium thiocyanate.