Optimisation of fault-tolerant fabric-cutting schedules using genetic algorithms and fuzzy set theory

In apparel industry, manufacturers developed standard allowed minutes (SAMs) databases on various manufacturing operations in order to facilitate better scheduling, while effective production schedules ensure smoothness of downstream operations. As apparel manufacturing environment is fuzzy and dynamic, rigid production schedules based on SAMs become futile in the presence of any uncertainty. In this paper, a fuzzification scheme is proposed to fuzzify the static standard time so as to incorporate some uncertainties, in terms of both job-specific and human related factors, into the fabric-cutting scheduling problem. A genetic optimisation procedure is also proposed to search for fault-tolerant schedules using genetic algorithms, such that makespan and scheduling uncertainties are minimised. Two sets of real production data were collected to validate the proposed method. Experimental results indicate that the genetically optimised fault-tolerant schedules not only improve the operation performance but also minimise the scheduling risks.     

Half-sandwich titanium(IV) complexes with Kläui's tripod ligand

Treatment of [Ti(O-i-Pr)(2)Cl(2)] with NaL(OEt) (L(OEt)(-) = [CpCo[P(O)(OEt)(2)](3)](-), Cp = eta(5)-C(5)H(5)) afforded [L(OEt)Ti(O-i-Pr)(2)Cl] that reacted with HCl in ether to give [L(OEt)TiCl(3)] (1). The average Ti-O and Ti-Cl distances in 1 are 1.975 and 2.293 A, respectively. Reaction of titanyl sulfate with NaL(OEt) in water followed by addition of HBF(4) afforded [L(OEt)TiF(3)] (2), the Ti-O and Ti-F distances of which are 2.020(2) and 1.792(2) A, respectively. The Zr(IV) analogue [L(OEt)ZrF(3)] (3) was prepared similarly from zirconyl nitrate, NaL(Oet), and HBF(4) in water. The Zr-O and average Zr-F distances in 3 are 2.139(2) and 1.938(2) A, respectively. Treatment of 1 with tetrachlorocatechol (H(2)Cl(4)cat) afforded [L(OEt)Ti(Cl(4)cat)Cl] (4). The average Ti-O(P), Ti-O(C), and Ti-Cl distances in 4 are 1.972, 1.926, and 2.334 A, respectively. Hydrolysis of 4 in the presence of Et(3)N yielded the mu-oxo dimer [(L(OEt))(2)Ti(2)(Cl(4)cat)(2)(mu-O)] (5). The average Ti-O(P), Ti-O(C), and Ti-O(Ti) distances in 5 are 2.027, 1.926, and 1.7977(9) A. Treatment of 1 with 1,1'-binaphthol (BINOLH(2)) in the presence of Et(3)N afforded [(L(OEt))(2)Ti(2)(mu-O)(2)(mu-BINOL)] x 2BINOLH(2) (6.2BINOLH(2)). Complex 1 is capable of catalyzing ring opening of epoxides with Me(3)SiN(3) under solvent-free conditions presumably via a Ti-azide intermediate.     

Synthesis,characterization, X-ray structural analysis and study of oxidative properties of propyltriphenylphosphonium bromochromate

The complex of propyltriphenylphosphonium bromochromate(VI), PrPh₃P[CrO₃Br] is easily synthesized in nearly quantitative yield using a direct reaction of chromium(VI) oxide and propyltriphenylphosphonium bromide. This compound is a versatile reagent for the efficient and selective oxidation of organic substrates, in particular for alcohols to their corresponding aldehydes or ketones, under mild conditions. This compound was characterized by IR, UV/Visible, ¹³C-n.m.r. and ¹H-n.m.r. techniques. It crystallized in the monoclinic form and its crystal and molecular structure have been determined by X-ray crystallography.     

Intermolecular rhodium-catalyzed [2+2+2] carbocyclization reactions of 1,6-enynes with symmetrical and unsymmetrical alkynes

The crossed intermolecular rhodium-catalyzed [2+2+2] carbocyclization of carbon and heteroatom tethered 1,6-enynes can be accomplished with symmetrical and unsymmetrical alkynes, to afford the corresponding bicyclohexadienes in an efficient and highly selective manner.     

A novel class of amide-derived air-stable P,O-ligands for Suzuki cross-coupling at low catalyst loading

The benzamide-derived P,O-ligands efficiently promoted the Pd-catalyzed Suzuki cross-coupling reactions of aryl bromides with phenylboronic acid at 0.01 mol % of Pd loading at 60-80 °C to form biaryls in excellent yields. A sterically hindered arylboronic acid gave a quantitative yield of the coupling product at 110 °C with 1 mol % Pd.     

Mixed-Metal Clusters of Palladium

The importance of palladium complexes in catalytic processes is well-demonstrated by its applications in hydrogenation processes in industry. Mixed metal clusters of palladium are of interest as the palladium ion can attain either a 16- or 18-electron configuration which is an important feature for catalytic processes. Recent developments in the preparation, characterization, chemical and physical properties of these clusters are discussed in this review.     

Singular Sturm—Liouville problems with nonnegative and indefinite weights

This article is concerned with the oscillatory properties of the eigenfunctions of a class of singular Sturm—Liouville problems—(p y)+q y=w y on (a, b), where the weight functionw vanishes on a subinterval of positive measure, or where the weight functionw changes sign on (a, b).This work was supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38.     

The synthesis and reactivity of the heptanuclear dianion [Os7(CO)20]2− including the synthesis and structural characterizations of the compounds [Os7(CO)20(AuPEt)3 2] and [Os8(CO)20(η6-C6H6]

Reduction of the heptaosmium cluster [Os₇(CO)₂₁] With [Et₄N][NH₄) gives the cluster dianion [Os₇(CO)₂₀]^2–,1, in high yield. The reaction of the dianion with [AuPR ₃Cl] (R=Et or Ph) in the presence of TlPF₆ forms [Os₇((CO)₂₀(AuPR ₃)₂] [R=Et (2a);R = Ph(2b)] in 80% yield, while the corresponding reaction with (Os(C₆H₆)(CH₃CN)₃]²⁺ gives [Os₈(CO)₂₀ ( ⁶-C₆H₆)] (3) in reasonable yield (ca. 30%). The dianion,1, and the clusters2 and3 have been fully characterized by bout spectroscopic and crystallographic methods. The crystal structure of the [Ph₄P]⁺ salt of1 shows that the metals in the anion adopt a capped octahedral geometry, with all twenty carbonyl ligands in terminal sites. The metal core geometry in2a is best described as a tricapped octahedron, and is based on the structure of the dianion1 with two adjacent octahedral faces capped by the Au atoms of the two AuPEt₃ groups. In a similar fashion, the geometry of3 is related to that of1 with the addition of an Os(C₆H₆) unit capped to a triangular face, to give a bicapped octahedral framework.