A tabu search heuristic for solving the CLSP with backlogging and set-up carry-over

In this paper, the multi-item, single-level, capacitated, dynamic lot sizing problem with set-up carry-over and backlogging, abbreviated to CLSP⁺, is considered. The problem is formulated as a mixed integer programming problem. A heuristic method consisting of four elements: (1) a demand shifting rule, (2) lot size determination rules, (3) checking feasibility conditions and (4) set-up carry-over determination, provides us with an initial feasible solution. The resulting feasible solution is improved by adopting the corresponding set-up and set-up carry-over schedule and re-optimizing it by solving a minimum-cost network flow problem. Then the improved solution is used as a starting solution for a tabu search procedure, with the value of moves assessed using the same minimum-cost network problem. Computational results on randomly generated problems show that the algorithm, which is coded in C++, is able to provide optimal solutions or solutions extremely close to optimal. The computational efficiency makes it possible to solve reasonably large problem instances routinely on a personal computer.     

A facile synthesis of new 3-(2-benzimidazolyl)-2-alkyl-4-(3H)-quinazolinones under microwave irradiation

Preparation of 2-amino-N-(1-H-benzimidazol-2-yl)benzamide and a variety of new 3-(2-benzimidazolyl)-2-alkyl-4-(3H)-quinazolinones using isatoic anhydride, 2-aminobenzimidazole and orthoesters under microwave irradiation are described.     

Efficient intermolecular 3+2 trapping of the Nazarov intermediate with vinyl sulfides

Cross-conjugated 1,4-pentadien-3-ones undergo electrocyclization to 2-oxidocyclopentenyl cations upon treatment with BF₃·OEt₂. When these reactions are carried out in the presence of electron-rich vinyl sulfides, nucleophilic trapping followed by ring-closure furnishes bridged bicyclic products that can be viewed as formal 3+2 cycloadducts. This process results in three new carbon-carbon bonds and establishes up to five new stereocenters.     

1‐Methyl‐1H‐imidazo[4,5‐f]quinolin‐6‐ium chloride monohydrate

The title compound, C₁₁H₁₀N₃⁺·Cl^?·H₂O, belongs to the N1‐methyl‐substituted imidazo­[4,5‐f]­quinoline family, in which the heterocyclic ring is protonated at the pyridine rather than at the imidazole N atom. The mol­ecule as a whole is almost exactly planar. The molecular structure has been compared with that of the 2‐amino analogue described in the literature, and it was found that the extra amino group of the latter is involved in conjugation with the adjacent double bond, i.e. the conjugation does not extend over the entire heterocyclic system. The cation of the title compound forms a strong hydrogen bond with the Cl^? anion and the anions are interconnected by the water solvent mol­ecule.     

Synthesis of imidazoles as novel emivirine and S‐DABO analogues

5‐Alkyl‐4‐benzyl‐1,3‐dihydroimidazol‐2‐ones ( 3a‐d ) and 5‐alkyl‐4‐benzyl‐1,3‐dihydroimidazole‐2‐thiones (7a‐d) were prepared via Dakin West reaction on DL‐phenylalanine with the appropriate aliphatic acid anhydrides followed by hydrolysis and reaction with potassium cyanate or potassium thiocyanate. Compounds 3a‐d were alkylated with ethoxymethyl chloride to give the alkylated imidazoles 5a‐d which were considered analogues of Emivirine with deletion of carbonyl group at the 4‐position. Alkylation of 7a‐d afforded the corresponding S‐alkylated derivatives 8a‐p which in a similar way were considered analogues of S‐DABO. However all the imidazole derivatives were devoid of activity against HIV.     

Flow injection chemiluminescence determination of hydrazine by oxidation with chlorinated isocyanurates

A rapid and sensitive flow injection chemiluminescence (CL) method is described for the determination of hydrazine based on the CL generated during its reaction with either sodium dichloroisocyanurate (SDCC) or trichloroisocyanuric acid (TCCA) in alkaline medium. The emission intensity is greatly enhanced if dichlorofluorescein (DCF) as sensitizer is present in the reaction medium. The presence of citrate prevents the precipitation of some cations in the reaction medium and also causes an enhancement in emission intensity. The effect of analytical and flow injection variables on these CL systems and determination of hydrazine are discussed. The optimum parameters for the determination of hydrazine were studied and were found to be the following: SDCC and TCCA both 1x10(-3) M; NaOH, 2x10(-1) M; DCF, 5x10(-6) M; citrate, 1x10(-3) M and flow rate, 3.8 ml min(-1). The optimized method yielded 3sigma detection limits of 2x10(-7) and 3x10(-7) M for hydrazine with SDCC and TCCA oxidants, respectively. The method is simple, fast, sensitive, and precise and was applied to the determination of hydrazine in water samples.     

On the Cauchy problem for some abstract nonlinear differential equations

In the present paper, we study the Cauchy problem in a Banach spaceE for an abstract nonlinear differential equation of form $$\frac{{d^2 u}}{{dt^2 }} = - A\frac{{du}}{{dt}} + B(t)u + f(t,W)$$ whereW = (A ₁(t)u,A ₂(t)u,?,A _?(t)u), (A _i (t),i = 1, 2, ?,?), (B(t),t ∈I = [0,b]) are families of closed operators defined on dense sets inE intoE, f is a given abstract nonlinear function onI ×E ^? intoE and ?A is a closed linear operator defined on dense set inE intoE, which generates a semi-group. Further, the existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the families (A _i(t),i = 1, 2, ?,?), (B(t),t ∈I). An application and some properties are also given for the theory of partial diferential equations.