A comment on 'Stabilization and optimal control for nonlinear systems'

This note presents a counter-example, to demonstrate that thebasis for the proposed solutions to the nonlinear quadraticregulator problem given in the paper ‘Stabilization andoptimal control for nonlinear systems’ is not true ingeneral.     

CLIMATIC CHANGE SINCE LITTLE ICE AGE RECORDED BY DUNDE ICE CAP

The climatic change since the Little Ice Age recorded in the Dunde Ice Cap is presentedin this paper. There have been three cold periods and three warm periods since 1400AD.Among them, the coldest one was in the 17th century. Many evidences verified the three coldand warm variations recorded in the Dundc Ice Cap. But it was found from the comparison between the Dunde Icc Cap climatic record and thewinter temperature record in Shanghai that there was a temporal dfference in climatic changebetween East China and West China. The general trend is that the cooling and warmingprocesses in West China were earlier than that in East China. In the Dunde Ice Cap, it isnow in an anomalous warm period, while it is not as warm as in Dunde Ice Cap recordaccording to the winter temperature in Shanghai. In addition to the possible cause of temporaldifference in climatic change between West China and East China, another possible cause isthat the greenhouse effect of CO_2 may already be recognizable in the Dunde Ice Cap a     

Subharmonic Resonances and Chaotic Motions of a Bilinear Oscillator

A bilinear oscillator with different stiffnesses for positiveand negative deflections arises frequently in off-shore marinetechnology due to the slackening of mooring lines. A limitingcase, in which one of the stiffnesses becomes infinite, is theimpact oscillator which has applications to vessels moored ina harbour. The subharmonic resonances, bifurcations and chaotic motionsof these oscillators are studied using the concepts of topologicaldynamics. Problems of the existence, uniqueness and stabilityof the steady state motions are investigated, and particularuse is made of the Poincaré map. The bilinear oscillatoris shown to have co-existing small amplitude solutions undermost of its subharmonic resonances, showing that one-off andautomated computer integrations could easily miss an importantresonant peak. The domains of attraction of the competing stablesolutions are explored. Cascades of period-doubling bifurcationsand the exponential divergence of adjacent starts indicate thatthe impact oscillator has a régime of chaotic motionsgoverned by a strange attractor.     

A frequency analysis of the ν9 band of CD3CD3: experiment and ab initio calculations

The infrared gaseous spectrum of CD₃CD₃ has been measured in the range of 530–670cm^?1 to investigate vibration—torsion effects in the ν₉ band. Three separate spectra all taken under different experimental conditions were recorded. The lines with (ΔK = ?1) and with high values of K show torsional splittings that are substantially larger than expected from the observed barrier height. These splittings are caused primarily by Coriolis-type interactions between the torsional stack of ν₉ = 1 and the corresponding stack for the ground vibrational state. Because of a near-degeneracy that exists between the states (ν₉ = 0, ν₄ = 3) and (ν₉ = 1, ν₄ = 0), three subbands (K, σ) = (15,1), (16,2), (17,3) are resonantly perturbed. For these cases, perturbation-allowed 3ν₄ torsional transitions have been identified. Here σ= 0, 1, 2 or 3 labels the torsional sublevels. Measurements from the ν₉ and 3ν₄ bands, frequencies from the far-infrared torsional spectra in the ground vibrational state, and lower state combination differences from the ν₉ + ν₄ ? ν₄ band were fitted to within experimental uncertainty using an effective Hamiltonian which considered three torsional stacks; one for the ground vibrational state and two for ν₉ = 1. In all, 22 parameters were determined using a total of 2001 lines. Of these, three parameters were the interstack couplings, eight are from the ground vibrational state and 11 are from the excited vibrational state. Two barrier-dependent torsion—rotation parameters, which were essential for obtaining a satisfactory fit, were calculated by ab initio methods.     

Pd促进ZnO/Al2O3催化乙醇水蒸气重整制氢

采用浸渍法制备了Pd促进ZnO/Al2O3催化剂, 考察了该催化剂作用时, 在水醇摩尔比为3, 常压和450 °C工作条件下乙醇水蒸气重整(SRE)制氢反应性能. 研究结果表明, 在该催化剂体系作用下的SRE反应过程中, H2、CH3CHO为主要产物, 与ZnO/Al2O3催化剂不同, Pd能促使CH3CHO发生C-C键断裂反应, 显著提高C2H5OH转化率及H2选择性, 分别达65%、55%. 还利用BET比表面积、透射电子显微镜(TEM)、热重-差示扫描量热-质谱(TG-DSC-MS)等表征手段考察了催化剂失活以及表面积炭情况, 发现Pd的加入对催化剂总积炭量并无明显影响.     

The near infrared overtone spectrum of propyne taken by diode laser in the 12700 cm−1region

Detailed regions of the near infrared spectrum of propyne between 12737 cm-¹ and 12778cm-¹ have been measured using a simple and inexpensive home-made laser diode spectrometer. This part of the spectrum covers the overlapping 3v₁ + v₃ + v₅ and 3v₁ + v₃ + v₅ + v₁₀—v₁₀ bands. Combining a global fit and an individual profile analysis made possible the determination of the vibrational and rotational constants in each band and in some cases the resolution of the individual K structure in each transition cluster.     

A HYBRID MODEL FOR THE NOISE GENERATION DUE TO RAILWAY WHEEL FLATS

A numerical model is developed to predict the wheel/rail dynamic interaction occurring due to excitation by wheel flats. A relative displacement excitation is introduced between the wheel and rail that differs from the geometric form of the wheel flat due to the finite curvature of the wheel. To allow for the non-linearity of the contact spring and the possibility of loss of contact between the wheel and the rail, a time-domain model is used to calculate the interaction force. This includes simplified dynamic models of the wheel and the track. In order to predict the consequent noise radiation, the wheel/rail interaction force is transformed into the frequency domain and then converted back to an equivalent roughness spectrum. This spectrum is used as the input to a linear, frequency-domain model of wheel/rail interaction to predict the noise. The noise level due to wheel flat excitation is found to increase with the train speed V at a rate of about 20 log₀V whereas rolling noise due to roughness excitation generally increases at about 30 log₀V. For all speeds up to at least 200 km/h the noise from typical flats exceeds that due to normal levels of roughness. When the wheel load is doubled the predicted impact noise increases by about 3 dB.