An adaptive control scheme for a continuous plant under Known output delay, unmodelled dynamics, and input saturation

This paper deals with robustness of adaptive control of continuoussystems subject to known output delay, input saturation, unmodelledlinear dynamics, and bounded disturbances. A simple gradient-typealgorithm with a relative deadzone is used. The relative deadzoneis built with an estimated contribution of the unmodelled dynamicsto the system output. The basic tool used for stability androbustness analysis is Gronwall's lemma.     

Noncommutative geometry-inspired rotating black hole in three dimensions

We find a new rotating black hole in three-dimensional anti-de Sitter space using an anisotropic perfect fluid inspired by the noncommutative black hole. We deduce the thermodynamical quantities of this black hole and compare them with those of a rotating BTZ solution and give corrections to the area law to get the exact nature of the Bekenstein-Hawking entropy.     

S matrix poles and the second virial coefficient

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S matrix is meromorphic. It may be expressed in terms of its poles, and then the quantum mechanical second virial coefficient of a neutral gas may be calculated. This paper takes another look at this approach, and discusses the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the ‘pole’ expansion and the physical significance of the ‘higher’ poles.     

Atomic additivity of the correlation energy in molecules—an ab initio MP4 and G3 study

It is shown that the closed shell valence electron molecular correlation energy of organic molecules in their ground states is a homogeneous multilinear function of the numbers of neutral atoms in their canonical hybridization state. The additivity is a robust feature, which holds for MP2(fc), MP3(fc) and MP4(fc) model calculations. The latter results obtained on a test set of 91 widely different organic molecules, exhibiting a whole gamut of electronic structure patterns, are excellent as evidenced by the absolute average deviation from the additivity values (AAD) of only 1.4 kcal mol^?1 and R ² = 0.999 93. The maximum absolute deviation (MAD) is 5.3 kcal mol^?1. The additivity formula for the total molecular electron correlation retrieved from G3 calculations also has an excellent performance (AAD = 1.2 kcal mol^?1, R ² = 0.999 98 and MAD = 7.2 kcal mol^?1). If it is taken into account that the additivity formulae require only back of the envelope calculations, these results are remarkable indeed, in particular since the G3 correlation energies span a very large range from 180.7 (methane) to 1642.8 (hexafluorocyclopropane) kcal mol^?1. Comparison of the exact electron correlation energies in free atoms with the corresponding average correlation energies in molecules reveals that a substantial increase in the latter provides an important contribution in overcoming a very strong Coulomb repulsion between the nuclei. It is shown that the additivity formulae are useful in detecting some special molecular features such as strong resonance and anti-aromaticity.     

A theoretical analysis of the excited states in 2-benzoylthiophene

The lower excited states of 2-benzoylthiophene have been studied using ab initio quantum chemical methods based on multiconfigurational wave functions. Six singlet and six triplet excited states have been characterized. The geometry has been optimized for the two lowest triplet states, which are responsible for the photoreactivity of the chromophore in the photosensitizing drug tiaprofenic acid. The T¹(π → π?) and T₂(n → π?) states have been found to be close in energy with the π → π? state slightly lower. The excited states have been characterized using density difference and spin density plots. The different photochemical behaviour of the two triplet states can be rationalized from the theoretical data.     

Thermochemistry of the reactions between CN+ and H2O in the gas phase

The [H₂, C, N, 0]⁺ potential energy surface (PES) has been explored by means of high-level ab initio calculations, carried out in the framework of the G2 theory. From this survey we concluded that the predominant products of the CN⁺ + H₂O reaction are the result of the dissociation of HNCOH⁺ species and to a much lesser extent of the CNHOH⁺ cation to yield CNH⁺ + OH. According to our results HCN⁺ should not be a product of this reaction because all pathways leading to its formation are unfavourable with regards to other competitive processes. Other reactive channels lead to the formation of the H₂ONC⁺ structure which dissociates into CN + H₂O⁺. The loss of NH(3σ) and O(³P) seems to take place following spin-forbidden reaction paths through an intersystem crossing between the singlet and the triplet PESs. The global minimum of the PES, H₂NCO⁺ is easily accessible and should lead to the loss of carbon monoxide which has not been experimentally observed in CN⁺ + H₂O reactions. We cannot offer a clear explanation for this disagreement between theory and experiment.     

Split Malcev algebras

We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras M is of the form $M={\mathcal U} +\sum_{j}I_{j}$ with ${\mathcal U}$ a subspace of the abelian Malcev subalgebra H and any I _j a well described ideal of M satisfying [I _j ,I _k ]?=?0 if j????k. Under certain conditions, the simplicity of M is characterized and it is shown that M is the direct sum of a semisimple split Lie algebra and a direct sum of simple non-Lie Malcev algebras.     

FEATURES AND APPLICATIONS OF BERTALANFFY-RICHARDS‘ AND SCHNUTE'S GROWTH EQUATIONS

ABSTRACT. Based on various ranges of the parameter m (or b), the paper analyzes the features and the integral forms of the Schnute and the Bertalanffy-Richards growth equations as well as the two aspects of their special cases (such as Gompertz, logistic and monomolecular models). It is a first attempt to investigate all the corresponding relationships among parameters of the models derived from the Schnute and the Bertalanffy-Richards growth equations. All the models from the two are empirically fitted by different data sets for eucalypt plantations. Unlike earlier papers, the results of this paper show that either of the two growth equations can be considered as a model for estimating forest growth given a parameter range, and both can produce similar growth performances. Some other aspects of the two growth equations are discussed so that the two can be used correctly.     

The reactions of Cl+ (3P) and Cl+ (1D) with hydrogen sulphide. A G2 molecular orbital study

G2 ab initio molecular orbital calculations have been performed to study the potential energy surfaces (PESs) associated with the reactions of Cl⁺ in its ³P ground state and in its ¹D first excited state with hydrogen sulphide. [H₂, Cl, S]⁺ singlet and triplet state cations present very different bonding characteristics. The latter are systematically ion-dipole or hydrogen-bonded weakly bound species, while the former are covalent molecular ions. As a consequence, although the Cl⁺(³P) is 34.5 kcal mol^?1 more stable than Cl⁺(¹D), the global minimum of the singlet PES lies 37.3 kcal mol^?1 below the global minimum of the triplet PES. Both singlet and triplet potential energy surfaces show significant differences with respect to those associated with Cl⁺ + H₂O reactions as well as with SH₂ reactions with F⁺. In both cases, the major product should be SH⁺ ₂; SH⁺ and HCl⁺ being the minor products, in agreement with the experimental evidence. The estimated heat of formation for the most stable H₂SCl⁺ singlet state species is 198 ± 1 kcal mol^?1.