Adiabatic Theorems for Quantum Resonances

We study the adiabatic time evolution of quantum resonances over time scales which are small compared to the lifetime of the resonances. We consider three typical examples of resonances: The first one is that of shape resonances corresponding, for example, to the state of a quantum-mechanical particle in a potential well whose shape changes over time scales small compared to the escape time of the particle from the well. Our approach to studying the adiabatic evolution of shape resonances is based on a precise form of the time-energy uncertainty relation and the usual adiabatic theorem in quantum mechanics. The second example concerns resonances that appear as isolated complex eigenvalues of spectrally deformed Hamiltonians, such as those encountered in the N-body Stark effect. Our approach to study such resonances is based on the Balslev-Combes theory of dilatation-analytic Hamiltonians and an adiabatic theorem for nonnormal generators of time evolution. Our third example concerns resonances arising from eigenvalues embedded in the continuous spectrum when a perturbation is turned on, such as those encountered when a small system is coupled to an infinitely extended, dispersive medium. Our approach to this class of examples is based on an extension of adiabatic theorems without a spectral gap condition. We finally comment on resonance crossings, which can be studied using the last approach.     

Multi-objectives Tabu Search based algorithm for progressive resource allocation

Military course of action planning involves time and space synchronization as well as resource and asset allocation. A mission could be seen as a defined set of logical ordered tasks with time and space constraints. The resources to task rules require that available assets should be allocated to each task. A combination of assets might be required to execute a given task. The couple (task, resources) constitutes an action. This problem is formulated as a multi-objectives scheduling and resource allocation problem. Any solution is assessed based on a number of conflicting and heterogeneous objectives. In fact, military planning officers should keep perfecting the plan based on the Commander’s criteria for success. The scheduling problem and resource allocation problem are considered as NP-Hard Problems [A. Guitouni, B. Urli, J.-M. Martel, Course of action planning: A project based modelling, Working Paper, Faculté des sciences de l’ administration, Université Laval, Québec, 2005]. This paper is concerned with the multi-objectives resource allocation problem. Our objective is to find adequate resource allocation for given courses of action schedule. To optimize this problem, this paper investigates non-exact solution methods, like meta-heuristic methods for finding potential efficient solutions. A progressive resource allocation methodology is proposed based on Tabu Search and multi-objectives concepts. This technique explores the search space so as to find a set of potential efficient solutions without aggregating the objectives into a single objective function. It is guided by the principle of maximizing the usage of any resource before considering a replacement resource. Thus, a given resource is allocated to the maximum number of tasks for a given courses of action schedule. A good allocation is a potential efficient solution. These solutions are retained by applying a combination of a dominance rule and a multi-criteria filtering method. The performance of the proposed Pareto-based approach is compared to two aggregation approaches: weighted-sum and the lexicographic techniques. The result shows that a Pareto-based approach is providing better solutions and allowing more flexibility to the decision-maker.     

A constraint generation algorithm for large scale linear programs using multiple-points separation

In order to solve linear programs with a large number of constraints, constraint generation techniques are often used. In these algorithms, a relaxation of the formulation containing only a subset of the constraints is first solved. Then a separation procedure is called which adds to the relaxation any inequality of the formulation that is violated by the current solution. The process is iterated until no violated inequality can be found. In this paper, we present a separation procedure that uses several points to generate violated constraints. The complexity of this separation procedure and of some related problems is studied. Also, preliminary computational results about the advantages of using multiple-points separation procedures over traditional separation procedures are given for random linear programs and survivable network design. They illustrate that, for some specific families of linear programs, multiple-points separation can be computationally effective.     

Identification of source terms in wave equation with dynamic boundary conditions

This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fréchet differentiability of the Tikhonov functional is studied, and a gradient formula is obtained via the solution of an associated adjoint problem. Then, the Lipschitz continuity of the gradient is proved. Furthermore, the existence and the uniqueness for the minimization problem are discussed. Finally, some numerical experiments for the reconstruction of an internal wave force are implemented via a conjugate gradient algorithm.     

Ion-Pair LC Method for Simultaneous Determination of Aliskiren Hemifumarate,Amlodipine Besylate and Hydrochlorothiazide in Pharmaceuticals

A rapid and precise LC method was developed for the simultaneous determination of aliskiren hemifumarate (ALS), amlodipine besylate (AML) and hydrochlorothiazide (HCZ) using acetonitrile:25 mM octane sulfonic acid sodium salt monohydrate in water (60:40 v/v) as the mobile phase. The flow rate was maintained at 1.2 mL min^?1 on a stationary phase composed of Supelco, Discovery^® HS (C18) column (25 cm × 4.6 mm, 5 μm). Isocratic elution was applied throughout the analysis. Detection was carried out at λ _max (232 nm) at ambient temperature. The method was validated according to ICH guidelines. Linearity, accuracy and precision were satisfactory over the concentration ranges of 32–320, 2–44 and 4–64 μg mL^?1 for ALS, AML and HCZ, respectively. LOD and LOQ were estimated and found to be 0.855 and 2.951 μg mL^?1, respectively, for ALS, 0.061 and 0.202 μg mL^?1, respectively, for AML as well as 0.052 and 0.174 μg mL^?1, respectively, for HCZ. The method was successfully applied for the determination of the three drugs in their co-formulated tablets. The results were compared statistically with reference methods and no significant difference was found. The developed method is specific and accurate for the quality control and routine analysis of the cited drugs in pharmaceutical preparations.     

Kinetics of the Reaction of 2-Chloro-quinoxaline with Hydroxide Ion in ACN–H2O and DMSO–H2O Binary Solvent Mixtures

The kinetics of alkaline hydrolysis of 2-chloroquinoxaline (QCl) with hydroxide ion was investigated spectrophotometrically at different percentages of aqueous–organic solvent mixtures with acetonitrile (10–60% v/v) and with dimethylesulphoxide (10–80%) over the temperature range from 25 to 45 °C. The reaction was performed under pseudo first order conditions with respect to 2-chloroquinoxaline (QCl). An increase in the percentage of organic solvent (v/v) has different effects on the reaction rate constants, presumably due to hydrogen bond donor and acceptor differences of the media and other solvatochromic parameters. The data were discussed in terms of the Kamelt-Taft parameter and E _T(30). A nonlinear relation between the logarithm of the rate constant and reciprocal of the dielectric constant suggests the presence of selective solvation by the polar water molecules. Activation parameters ΔH ^#, ΔS ^# and ΔG ^# were determined and discussed.     

Simultaneous HPLC determination of thiocolchicoside and glafenine as well as thiocolchicoside and floctafenine in their combined dosage forms

Sensitive and accurate high-performance liquid chromatographic methods have been developed for the simultaneous determination of thiocolchicoside (TC)-glafenine (GF) (Mix I) and thiocolchicoside-floctafenine (FN) (Mix II) in their pharmaceutical formulations. The analysis for both mixtures was performed using 250 mm × 4.6 mm i.d., 5 μm particle size C18 Waters Symmetry column. The mobile phase consisted of methanol-0.035 M phosphate buffer (50:50, v/v) of pH 4.5 for Mix I and methanol-0.03 M phosphate buffer (70:30, v/v) of pH 4 for Mix II with flow rate of 1 mL/min and UV detection at 400 nm in both cases. The calibration plots were rectilinear over the concentration range of 0.2-2 μg/mL for TC in both mixtures and 20-200 μg/mL for each of GF and FN . The limits of detection for TC and GF were 0.05 μg/mL and 0.62 μg/mL, respectively, and for TC and FN were 0.02 μg/mL and 0.70 μg/mL, respectively. Additionally, the proposed methods were successfully applied to their combined tablets with average percentage recoveries of 100.35 ± 0.61 and 100.57 ± 0.72% for TC and GF respectively and for TC and FN the percentage recoveries were 101.2 ± 0.72 and 100.36 ± 0.67%, respectively. The results obtained were favorably compared with those given using the comparison methods.