An improved algorithm for the two machine flow shop problem with several availability constraints

In this paper we deal with the two-machine flow shop scheduling problem with several availability constraints on the first machine, under the resumable scenario. We first develop an improved algorithm with a relative worst-case error bound of 4/3. We then present a polynomially solvable case.     

Existence and controllability results for impulsive partial functional differential inclusions

In this paper we prove the existence and the controllability of mild and extremal mild solutions for first-order semilinear densely defined impulsive functional differential inclusions in separable Banach spaces with local and nonlocal conditions.     

Lithium sulfate: Calorimetric determination of the temperatures and enthalpies of high-temperature phase transitions

Using a high-temperature Calvet calorimeter as a differential enthalpic analyser Li₂SO₄ was investigated in the temperature range 800–1200 K. One transformation in the solid state was observed at 847 K with a corresponding enthalpy increment of 24.2 kJ mol^?1. The solid-liquid transition was found to occur at 1131 K with an enthalpy of fusion of 7.74 kJ mol^?1. Furthermore, the analysis of the corresponding thermograms supports the presence of the premelting effect which was evidenced by other techniques. A critical comparison with previous results in the literature is given.     

Thermodynamic Study of the Molten Salt Binary System KHSO4−NaHSO4

The partial molar enthalpies of mixing of NaHSO₄ and KHSO₄ have been measured at 528 K by dropping samples of pure compounds into molten mixtures of NaHSO₄ and KHSO₄ in Calvet calorimeter. From these values the molar enthalpy of mixing has been deduced. The same method has been used for the determination of the heat capacity of the two pure compounds in the solid and liquid states. The phase diagram of this system has been confirmed by conductometric and thermal analysis methods. By an optimization method the excess entropy of the liquid mixtures was also calculated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Synthesis and Reactions of 3‐Methylthiazolo[3,2‐a]Benzimidazole‐2‐Carboxylic Acid Hydrazide: Synthesis of Some New Pyrazole, 1,3‐Thiazoline, 1,2,4‐Triazole and 1,2,4‐Triazolo[3,4‐b]‐1,3,4‐Thiadiazine Derivatives Pendant to Thiazolo[3,2‐a]Benzimidazole Moiety

The reaction of 3‐methylthiazolo[3,2‐a]benzimidazole‐2‐carboxylic acid ethyl ester (1) with hydrazine hydrate gives the hydrazide 2 which reacts with CS₂/KOH to afford the potassium salt 3. Treatment of 3 with l‐aryl‐2‐bromoethanones 4a,b afforded the 1,3‐thiazoline derivatives 6a,b, respectively, while the reaction of 3 with hydrazine hydrate afforded 1,2,4‐triazole‐3‐thione derivative 9. The reaction of 9 with l‐aryl‐2‐bromoethanones 4a,b and with hydrazonyl chlorides 11a,b gave the 1,2,4‐triazolo[3,4‐b]‐1,3,4‐thiadiazine derivatives 10a,b and 12a,b, respectively. Treatment of hydrazide 2 with phenyl isothiocyanate in refluxing benzene gave the thiosemicarbazide derivative 16. The latter reaction gave 1,3,4‐oxadiazole derivative 17 when benzene was replaced by DMF. Cyclization of the thiosemicarbazide derivative 16 with NaOH resulted in the formation of the 1,2,4‐triazole‐3‐thione derivative 18.     

Optimal estimates for blowup rate and behavior for nonlinear heat equations

We first describe all positive bounded solutions of where \input amstex \loadmsbm $(y,s)\in \Bbb R^N\times \Bbb R$ , 1 < p, and (N − 2)p ≤ N + 2. We then obtain for blowup solutions u(t) of uniform estimates at the blowup time and uniform space-time comparison with solutions of u′ = u^p. © 1998 John Wiley & Sons, Inc.     

Determination of the blow-up rate for a critical semilinear wave equation

In this paper, we determine the blow-up rate for the semilinear wave equation with critical power nonlinearity related to the conformal invariance.Mathematics Subject classification (2000): 35L05, 35L67Membre de lInstitut Universitaire de France