We study the linear system =Ax+Bu from a differential geometric point of view. It is well-known that controllability of the system is related to the one-parameter family of operators etB. We use this to give a proof of the classical controllability conditions in terms of the differential geometry of certain curves in n. We then view (t)=Im(etB) as a curve in appropriate Grassmannian and see that, in local coordinates, is an integral curve of the flow induced by a matrix Riccati equation. We obtain qualitative geometric conditions on that are equivalent to the controllability of the system. To get quantitiative results, we lift to a curve l' in a splitting space, a generalized Grassmannian, which has the advantage of being a reductive homogeneous space of the general linear group, GL(n). Explicit and simple expressions concerning the geometry of are computed in terms of the Lie algebra of GL(n), and these are related to the controllability of the system.James Wolper was a visiting professor in the Department of Mathematics at Texas Tech University while much of this research was conducted. He would like to express appreciation for the hospitality he received during his visit. 相似文献
SCF calculations utilizing a basis of all s-type Gaussians have been performed to investigate the dimerization of BH3 to B2H6. Localized molecular orbitals and pseudonatural orbitals are calculated. The dimerization energy obtained (11.5 kcal/mole) supports the assumption that the non-Hartree-Fock interactions (electron correlation) play a dominant role (Exp = 40–60 kcal/mole). The energy of the principal type of resonance structure based on the SCF-MO 's of the separated-but-distorted BH3 systems is rigorously calculated and found to be 150 kcal/mole higher in energy than the SCF energy of B2H6. Thus, resonance stabilization (delocalization) is shown to be extremely important to the stability of the “three-center” bonds in B2H6, as has been suspected for many years. 相似文献
We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems. 相似文献
We report gas-phase electronic spectra of formamide, N-methyformamide, acetamide, and N-methylacetamide at 300 K calculated using a combination of classical molecular dynamics and time-dependent density functional theory (TDDFT). In comparison to excitation energies computed using the global minima structures, the valence npi* and pi(nb)pi* states show a significant red-shift of 0.1-0.35 eV, while smaller shifts are found for the n3s and pi(nb)3s Rydberg states. In this work, we have identified the physical origin of these shifts arising from variations of the molecular structure. We present simple relationships between key geometrical parameters and spectral shifts. Consequently, electronic spectra can be generated directly from ground-state structures, without additional quantum chemical calculations. The electronic spectrum of formamide in aqueous solution is computed using TDDFT using an explicit solvent model. This provides a quantitative determination of the condensed-phase spectrum. In general, this study shows that temperature effects can change the predicted excitation energies significantly and demonstrates how electronic spectra at elevated temperatures can be computed in a computationally efficient way. 相似文献
We report the first successful design of a self-associating antiparallel coiled coil, APH. The simultaneous application of Coulombic and hydrophobic components results in a decided preference for the antiparallel alignment as judged by HPLC, sedimentation equilibrium, and chemical denaturation data. The designed peptide is of comparable stability to naturally occurring leucine zipper peptides and can be expressed in bacteria. These properties of APH suggest potential in vivo protein fusion and biomaterials applications. 相似文献
A convenient and highly convergent method for the synthesis of new imidazo[1,2-a]pyridine-based coelenterazine analogues is reported. The imidazo[1,2-a]pyridine core was constructed through a condensation between 2-aminopyridine analogues and arylglyoxals. Additionally, a new approach to the synthesis of benzylglyoxals was introduced. The imidazo[1,2-a]pyridines display moderate antioxidant activities at a low micromolar level in 2,2-diphenyl-1-picrylhydrazyl (DPPH). 相似文献