Dynamics of constrained systems

The dynamics on the final constraint submanifold of a constrained system is discussed: a system of equations of motion is induced by the initial ones, whose consistency originates this submanifold, and there is also a dynamics which is the geometrically natural one of this (presymplectic) submanifold. Their compatibility and possible equivalence are analyzed. As a consequence, another justification of Dirac's conjecture is obtained.     

Properties of the sequential gradient-restoration algorithm (SGRA), part 1: Introduction and comparison with related methods

The sequential gradient-restoration algorithm (SGRA) was developed in the late 1960s for the solution of equality-constrained nonlinear programs and has been successfully implemented by Miele and coworkers on many large-scale problems. The algorithm consists of two major sequentially applied phases. The first is a gradient-type minimization in a subspace tangent to the constraint surface, and the second is a feasibility restoration procedure. In Part 1, the original SGRA algorithm is described and is compared with two other related methods: the gradient projection and the generalized reduced gradient methods. Next, the special case of linear equalities is analyzed. It is shown that, in this case, only the gradient-type minimization phase is needed, and the SGRA becomes identical to the steepest-descent method. Convergence proofs for the nonlinearly constrained case are given in Part 2.Partial support for this work was provided by the Fund for the Promotion of Research at Technion, Israel Institute of Technology, Haifa, Israel.     

Invariant forms and Hamiltonian systems: A geometrical setting

A geometric proof is given of Lee Hwa Chung's theorem for regular Hamiltonian systems, which identifies all the possible differential forms left invariant by the dynamics. Applications of this theorem in the area of canonical transformations are also remarked in a purely geometrical context.     

Kinetic determination of copper(II) by its catalytic effect on the atmospheric oxidation of 1,3-cyclopentanedione bis(4-methylthiosemicarbazone) monohydrochloride

The kinetic method is based on the catalytic effect of copper(II) on the atmospheric oxidation of 1,3-cyclopentanedione bis(4-methylthiosemicarbazone) monohydrochloride. The reaction is followed spectrophotometrically at 390 nm. The kinetic parameters of the reaction are reported and a rate equation is suggested. The calibration graphs are linear in the range 0.05–0.5 μg Cu ml^?1. Interference by other ions is studied.     

Encapsulation of sodium nimesulide and precursors in beta-cyclodextrin

Crystalline 1:1 inclusion complexes with beta-cyclodextrin (beta-CD) and the sodium salt of nimesulide (4-nitro-2-phenoxymethanesulfonanilide), and the sodium salt of the derivative 2-phenoxymethanesulfonanilide, have been prepared by co-precipitation from aqueous solution. The presence of true inclusion complexes was supported by elemental analysis, thermogravimetry and powder X-ray diffraction. FTIR and 13C CP MAS NMR spectroscopy confirmed that no chemical modification of the guests occurred upon formation of inclusion complexes. The reaction of the precursors 2-phenoxynitrobenzene and 2-phenoxyaniline with beta-CD was also studied and crystalline inclusion complexes with a 2:1 (host-to-guest) stoichiometry were isolated. The interaction of the different guest species with beta-CD host molecules was studied theoretically by carrying out ab initio calculations. Favourable inclusion geometries were obtained for the four guests mentioned above. On the other hand, it was found that the inclusion of the neutral guests nimesulide and 2-phenoxymethanesulfonanilide was considerably less favourable. This is in agreement with the experimentally observed difficulty in isolating true inclusion complexes containing these guests and beta-CD. The calculated lower stability is attributed to the different steric hindrance arising from the different conformational preferences of neutral and anionic forms.     

Tangential-flow ultrafiltration: a versatile methodology for determination of complexation parameters in refractory organic matter from Brazilian water and soil samples

In this work the copper(II) complexation parameters of aquatic organic matter, aquatic and soil humic substances from Brazilian were determined using a new versatile approach based on a single-stage tangential-flow ultrafiltration (TF-UF) technique (cut-off 1 kDa) and sensitive atomic spectrometry methods. The results regarding the copper(II) complexation capacity and conditional stability constants obtained for humic materials were compared with those obtained using direct potentiometry with a copper-ion-selective electrode. The analytical procedure based on ultrafiltration is a good alternative to determine the complexation parameters in natural organic material from aquatic and soil systems. This approach presents additional advantages such as better sensibility, applicability for multi-element capability, and its possible to be used under natural conditions when compared with the traditional ion-selective electrode.