Testing goodness of fit for the distribution of errors in multivariate linear models

In this paper, to test goodness of fit to any fixed distribution of errors in multivariate linear models, we consider a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residuals and the characteristic function under the null hypothesis. We study the limiting behaviour of this test statistic under the null hypothesis and under alternatives. In the asymptotics, the rank of the design matrix is allowed to grow with the sample size.     

Determination of bromide by low power surfatron microwave induced plasma after bromine continuous generation

A simple continuous flow generation of volatile bromine is described for the determination of low concentrations of the elements by atmospheric-pressure argon microwave induced plasma (MIP) surfatron. Bromine is continuously generated by mixing the bromide with sulphuric acid and hypochlorite solutions. The bromine vapor is separated from the aqueous phase by a gas-liquid separator and is desiccated by passing it through concentrated sulphuric acid. The detection limit attained was 2 microg/l. and the precision was +/-0.7% (at the 80 microg/l. level). The proposed determination is very selective if oxidizing/reducing agents are absent. The procedure has been tested for bromide determination in two drug preparations. Good agreement between the experimental results and the certified values has been obtained.     

Ab initio rotational constants of interstellar species: Cyanoacetylene hydrogenated derivatives

By means of ab initio calculations, the rotational constants and dipole moments of H_nC₃N (n = 1, 3, 5, 7, and 9) species have been calculated at the HF / 6-31G * level of theory. Selected cases have been also calculated at the MP 2/6-31G * level and the influence of calculation level on rotational constant values is briefly discussed. Some of these species were discovered in the interstellar medium, while others have still not been detected there, although their existence is very probable. The results given here could help in their detection. © 1993 John Wiley & Sons, Inc.     

Preorganization and reorganization as related factors in enzyme catalysis: the chorismate mutase case

In this paper a deeper insight into the chorismate-to prephenate-rearrangement, catalyzed by Bacillus subtilis chorismate mutase, is provided by means of a combination of statistical quantum mechanics/molecular mechanics simulation methods and hybrid potential energy surface exploration techniques. The main aim of this work is to present an estimation of the preorganization and reorganization terms of the enzyme catalytic rate enhancement. To analyze the first of these, we have studied different conformational equilibria of chorismate in aqueous solution and in the enzyme active site. Our conclusion is that chorismate mutase preferentially binds the reactive conformer of the substrate--that presenting a structure similar to the transition state of the reaction to be catalyzed--with shorter distances between the carbon atoms to be bonded and more diaxial character. With respect to the reorganization effect, an energy decomposition analysis of the potential energies of the reactive reactant and of the reaction transition state in aqueous solution and in the enzyme shows that the enzyme structure is better adapted to the transition structure. This means not only a more negative electrostatic interaction energy with the transition state but also a low enzyme deformation contribution to the energy barrier. Our calculations reveal that the structure of the enzyme is responsible for stabilizing the transition state structure of the reaction, with concomitant selection of the reactive form of the reactants. This is, the same enzymatic pattern that stabilizes the transition structure also promotes those reactant structures closer to the transition structure (i.e., the reactive reactants). In fact, both reorganization and preorganization effects have to be considered as the two faces of the same coin, having a common origin in the effect of the enzyme structure on the energy surface of the substrate.     

Monodromy,center–focus and integrability problems for quasi-homogeneous polynomial systems

This paper deals with planar quasi-homogeneous polynomial vector fields, and addresses three major questions: the monodromy, the center–focus and the integrability problems. We characterize the monodromic planar quasi-homogeneous polynomial vector fields, and we give a condition to distinguish between a center and a focus in this case. Also, we provide conditions which characterize the integrability of quasi-homogeneous polynomial systems under non-resonance conditions. The results obtained allow us to analyse two monodromic planar systems with degenerate linear part: one of them with nilpotent linearization, and another one with null linear part.     

Analysis of Hopf and Takens–Bogdanov Bifurcations in a Modified van der Pol–Duffing Oscillator

We analyze a modified van der Pol–Duffing electronic circuit, modeled by a tridimensional autonomous system of differential equations with Z₂-symmetry. Linear codimension-one and two bifurcations of equilibria give rise to several dynamical behaviours, including periodic, homoclinic and heteroclinic orbits. The local analysis provides, in first approximation, the different bifurcation sets. These local results are used as a guide to apply the adequate numerical methods to obtain a global understanding of the bifurcation sets. The study of the normal form of the Hopf bifurcation shows the presence of cusps of saddle-node bifurcations of periodic orbits. The existence of a codimension-four Hopf bifurcation is also pointed out. In the case of the Takens–Bogdanov bifurcation, several degenerate situations of codimension-three are analyzed in both homoclinic and heteroclinic cases. The existence of a Hopf–Shil'nikov singularity is also shown.     

Theoretical study of catalytic efficiency of a Diels-Alderase catalytic antibody: an indirect effect produced during the maturation process

The Diels-Alder reaction is one of the most important and versatile transformations available to organic chemists for the construction of complex natural products, therapeutics agents, and synthetic materials. Given the lack of efficient enzymes capable of catalyzing this kind of reaction, it is of interest to ask whether a biological catalyst could be designed from an antibody-combining site. In the present work, a theoretical study of the different behavior of a germline catalytic antibody (CA) and its matured form, 39 A-11, that catalyze a Diels-Alder reaction has been carried out. A free-energy perturbation technique based on a hybrid quantum-mechanics/molecular-mechanics scheme, together with internal energy minimizations, has allowed free-energy profiles to be obtained for both CAs. The profiles show a smaller barrier for the matured form, which is in agreement with the experimental observation. Free-energy profiles were obtained with this methodology, thereby avoiding the much more demanding two-dimensional calculations of the energy surfaces that are normally required to study this kind of reaction. Structural analysis and energy evaluations of substrate-protein interactions have been performed from averaged structures, which allows understanding of how the single mutations carried out during the maturation process can be responsible for the observed fourfold enhancement of the catalytic rate constant. The conclusion is that the mutation effect in this studied germline CA produces a complex indirect effect through coupled movements of the backbone of the protein and the substrate.