Averaging in the Autoresonance Model

Mathematical Notes -     

Slow Solutions of a Differential Inclusion and Vector Optimization

The present work develops a new approach for studying the dynamic evolution of a vector optimization problem. We introduce a convenient differential inclusion that rules the dynamics of the optimization problem. Actually we consider a sort of ‘gradient system’ defined by vector valued functions. The main tool used is a completely new adaptation to the vector problem of the notion of pseudogradient, which is a well-known concept in the modern critical point theory. Finally we study a special class of solutions of the above quoted differential inclusion: the slow solutions.     

过模慢波结构频率反射特性及谐振腔的影响

 利用有限元方法求解:S-参数矩阵，研究了过模慢波结构对圆波导TM₀₁，TM₀₂模的反射特性，分析了在慢波结构末端加入谐振腔后，由于两端口的不对称性而造成的对反射特性影响。结果表明，在TM₀₁的π模频率附近，慢波结构和谐振腔组成的系统对无谐振腔一侧端口入射TM₀₁模的反射增大，而对有谐振腔一侧端口入射TM₀₁模的反射减小。根据计算结果，解释了普通多波切伦柯夫振荡器所用慢波结构周期数较多的原因，说明了在多波切伦柯夫振荡器中引入谐振腔后，不但可以减少所用慢波结构周期数，而且有利于提高微波输出效率。     

Wave Properties of A Free Elliptical Helix Slow-Wave Structure with Arbitrary Eccentricity

This paper gives the investigations of the fundamental wave of a free elliptical helix slow-wave structure (SWS) with arbitrary eccentricity. The wave properties including the phase velocity characteristics, interaction impedance and the longitudinal electric field distribution of this mode has been fully studied. It is found that, when the eccentricity increases, the interaction impedance and the operating frequency of such SWS will be improved, which allows to have a higher gain and operating in a higher frequency band. Furthermore, the field configuration is different from that of a round helix; the azimuthal distribution of the E-field follows with the angular Mathieu function of the first kind, even with mode of zero. In radial, E-field is elliptical surface wave. When the eccentricity tends to zero, all the characteristics will be smoothly degenerates to the case of round helix correspondingly.     

正二阶快-慢系统中的奇性同宿轨道和极限环

本文研究一类正二阶快-慢系统中奇性同宿轨道和极限环,并且给出了此系统存在奇性同宿轨道和极限环的充分条件.     

Chiral ligand-controlled catalytic asymmetric epoxidation of α,β-unsaturated carbonyl compounds with peroxide

Asymmetric epoxidation reaction of α,β-unsaturated carbonyl compounds with alkylperoxide was catalyzed by an external chiral tridentate aminodiether-lithium peroxide giving epoxides with good enantiomeric excess. Slow addition of alkylhydroperoxide was beneficial for a catalytic asymmetric reaction. Lone pair electron-differentiating coordination of a carbonyl oxygen to lithium is another critical factor for high enantioselectivity.     

Repro-Modelling Based Generation of Intrinsic Low-Dimensional Manifolds

Effective procedures for the reduction of reaction mechanisms, including the intrinsic low-dimensional manifold (ILDM) and the repro-modelling methods, are all based on the existence of very different time scales in chemical kinetic systems. These two methods are reviewed and the advantages and drawbacks of them are discussed. An algorithm is presented for the repro-modelling based generation of ILDMs. This algorithm produces an unstructured table of ILDM points, which are then fitted using spline functions. These splines contain kinetic information on the behaviour of the chemical system. Combustion of hydrogen in air is used as illustrative example. Simulation results using the fitted model are compared with the outcome of calculations based on the detailed reaction mechanism for homogeneous explosions and 1D laminar flames.     

Synthesis of a slow‐release and superabsorbent nitrogen fertilizer and its properties

A slow‐release and superabsorbent nitrogen fertilizer (SSNF) was synthesized by aqueous solution copolymerization of acrylic acid and maleic anhydride using N,N′‐methylene bisacrylamide as a crosslinker, ammonium persulfate and sodium sulfite as an initiator in the presence of urea. The effects on water absorbency such as amount of crosslinker, initiator, urea and maleic acid, degree of neutralization, etc. were investigated. To improve slow release and water retention properties, the product was surface‐crosslinked with trihydroxymethyl propane glycidol ether (6360). The nitrogen content of the SSNF synthesized under optimal conditions was 28.5%, and the water absorbencies were about 900 (g/g) in distilled water and 180 (g/g) in tap water. The nitrogen slow release behavior of the SSNF in water and water retention capacity of the soil with SSNF were also investigated. The results showed that the surface‐crosslinked product not only had good slow release property but also excellent soil moisture preservation capacity, which could effectively improve the utilization of fertilizer and water resources simultaneously. The results of the present work indicated that the SSNF could be found an application in agriculture and horticulture, especially in drought‐prone areas where the availability of water is insufficient. Copyright © 2006 John Wiley & Sons, Ltd.     

Extending the Scope of Singlet‐State Spectroscopy

Different decoupling sequences are tested—using various shaped radio‐frequency (RF) pulses—to achieve the longest possible lifetimes of singlet‐state populations over the widest possible bandwidths, that is, ranges of offsets and relative chemical shifts of the nuclei involved in the singlet states. The use of sinc or refocusing broadband universal rotation pulses (RE‐BURP) for decoupling during the intervals where singlet‐state populations are preserved allows one to extend the useful bandwidth with respect to prior state‐of‐the‐art methods based on composite‐pulse WALTZ decoupling. The improved sinc decoupling sequences afford a more reliable and sensitive measure of the lifetimes of singlet states in pairs of spins that have widely different chemical shifts, such as the two aromatic protons H⁵ and H⁶ in uracil. Similar advantages are expected for nucleotides in RNA and DNA. Alternative approaches, in particular frequency‐modulated decoupling sequences, also appear to be effective in preserving singlet‐state populations, even though the profiles of the apparent relaxation rate constants as a function of the offset are somewhat perturbed. The best decoupling sequences prove their utility in sustaining longer lifetimes of singlet states than previously achieved for the side‐chain tyrosine protons in bovine pancreatic trypsin inhibitor (BPTI) at 600 MHz (14.1 T), where the differences of chemical shifts between coupled protons are a challenge.     

MANAGING INTERACTING POPULATIONS UNDER TIME SCALE SEPARATION

Renewable resource modeling is usually characterized by different time scales where some state variables such as biomass may evolve relatively faster than other state variables such as carrying capacity. A strong form of time scale separation (STSS) means that a slowly changing variable is treated as constant over time. Management rules that assume STSS do not account for a time scale externality and this may induce inefficiencies in resource management. In the current work, we study multispecies resource management under time scale separation by adopting the framework of singular perturbation reduction methods. By extending recent work by Vardas and Xepapadeas [2015] to interacting populations, we study regulation with full internalization of the time scale externality. We further study regulation and noncooperative outcomes under STSS and identify deviations in harvesting and biomass paths among these cases. Deviations indicate the inefficiencies associated with adopting STSS.