Dynamic optimization problems with bounded terminal conditions

Bounded terminal conditions of nonlinear optimization problems are converted to equality terminal conditions via the Valentine's device. In so doing, additional unknown parameters are introduced into the problem. The transformed problems can still be easily solved using the sequential gradient-restoration algorithm (SGRA) via a simple augmentation of the unknown parameter vector . Three example problems with bounded terminal conditions are solved to verify this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant No. NCC 2-106.     

Sufficient conditions for a strong relative minimum in an optimal control problem

In this paper, on the basis of Young's method (Ref. 1), sufficient conditions for a strong relative minimum in an optimal control problem are given. Young's method generalizes geodesic coverings and the simplest Hilbert integral from the standard variational calculus. This paper carries Young's method over to nonparametric problems.     

Syntheses of TiO2(B) nanowires and TiO2 anatase nanowires by hydrothermal and post-heat treatments

TiO₂(B) nanowires and TiO₂ anatase nanowires were synthesized by the hydrothermal processing in 10 M NaOH aq. at 150 °C followed by the post-heat treatment at 300-800 °C. As-synthesized Na-free titanate nanowires (prepared by the hydrothermal treatment and repeated ion exchanging by HCl (aq.) were transformed into TiO₂(B) structure with maintaining 1-D morphology at 300-500 °C, and further transformed into anatase structure at 600-800 °C with keeping 1-D shape. At 900 °C, they transformed into rod-shaped rutile grains. Microstructure of these 1-D TiO₂ nanomaterials is reported.     

A novel layered bimetallic phosphite intercalating with organic amines: Synthesis and characterization of Co(H2O)4Zn4(HPO3)6·C2N2H10

A new layered cobalt-zinc phosphite, Co(H₂O)₄Zn₄(HPO₃)₆·C₂N₂H₁₀ has been synthesized in the presence of ethylenediamine as the structure-directing agent. The compound crystallizes in the monoclinic system, space group Cc (No. 9), a=18.2090(8), b=9.9264(7), c=15.4080(7) Å, β=114.098(4)°, V=2542.3(2) Å³, Z=4, R=0.0323, wR=0.0846. The structure consists of ZnO₄ tetrahedra, CoO₆ octahedra and HPO₃ pseudopyramids through their vertices forming bimetallic phosphite layers parallel to the ab plane. Organic cations, which reside between the inorganic layers, are mobile and can be exchanged by NH₄⁺ cations without the collapse of the framework.     

Self-assembly of lanthanide mixed-carboxylates coordination polymers

Two new mixed-ligands lanthanide coordination polymers, [Ln(Ac)(ip)(H₂O)₂]·0.5H₂O (Ln=La (1); Ln=Eu (2); Ac=acetate; ip=isophthalate) have been synthesized under hydrothermal condition. Single-crystal X-ray analyses show that complexes 1 and 2 are three-dimensional structure in which lanthanide ions are bridged by monocarboxylate ligand, acetate or dicarboxylate ligand, isophthalate. And the central lanthanide ions, La³⁺ and Eu³⁺, are both nine-coordinate with oxygen atoms. The thermogravimetric analysis was carried out to examine the thermal stability of the title complexes. And the photoluminescence property of complex 2 was also investigated.     

Isoperichoric focusing field-flow fractionation and thin layer isoperichoric focusing based on coupling of gradient generated by primary field with secondary field action: general principles and performances

The primary field forces can generate spatially oriented gradient of the effective property of a continuum or pseudo-continuum fluid (carrier liquid). When this gradient is coupled with the action of a secondary field of identical or different nature the isoperichoric focused zones of the dispersed species can appear. Consequently, they can be separated according to differences responding to the property gradient of the carrier liquid. This concept can be applied under static (non-flow) conditions in thin layer focusing as well as under dynamic conditions with the elution due to the carrier liquid flow in focusing field-flow fractionation. The gradient established by the action of the primary field and the concentration distribution of the isoperichoric focused zone formed by the coupled effect of the gradient and of the primary or secondary field are described theoretically. The rigorous relationship describing the shape of the focused zone is compared with the approximate solutions. The performances of the proposed principle were evaluated by model calculations. Potential experimental configurations considering the implementation of the static and dynamic conditions are discussed. The generalized isoperichoric focusing theory can be applied to describe the particular processes operating in analytical and preparative focusing separations of the particles of various, but especially of biological origin.     

Syntheses and characterization of two new zinc phosphites with 1D chains decorated by Zn-centered complexes

Two inorganic-organic hybrid solids, Zn₂(phen)(HPO₃)₂ (1) and Zn(phen)(HPO₃) (2), have been synthesized under solvothermal conditions in the presence of 1,10-phenanthroline (phen) ligands. Their structures were determined by single-crystal X-ray diffraction and further characterized by FTIR, elemental analysis, powder X-ray diffraction, thermogravimetric analysis and fluorescent spectra. Compound 1 crystallizes in the triclnic system, space group P-1, , , , α=75.609(1)°, β=79.145(2)°, γ=67.157(2)°, , Z=2. Compound 2 is monoclinic, C2/c, , , , β=94.175(4)°, , Z=8. Both structures consist of 1D chains constructed from strictly alternating ZnO₄ and HPO₃ polyhedra through sharing vertices. The chains are further decorated by Zn-centered complex architectures, [Zn(phen)]²⁺ for 1 and [Zn(phen)₂]²⁺ for 2. The 2D and 3D supramolecular arrays for 1 and 2 are stably stacked via strong π-π interactions of the phen groups, respectively.     

配位聚合物{[Co2(HBTC)2(H2O)6]·C4H10N2·2H2O}n的水热合成、结构表征及荧光性质

采用水热法合成了配位聚合物[Co2(HBTC)2(H2O)6]·C4H10N2·2H2O}n(H3BTC为1,3,5-均苯三羧酸,C4H10N2为哌嗪),通过X射线单晶衍射、红外光谱和荧光光谱进行表征,并用TGA研究了该配位聚合物的热稳定性.晶体属三斜晶系,P1空间群,a=1.05437(9)nm,b=1.05485(9)nm,c=0.71482(5)nm,α=102.4623(28)°,β=91.3500(42)°,γ=111.0186(29)°,V=0.72018(10)nm3,Mr=764.37,Dc=1.762g·cm-3,Z=1,μ(MoKα)=1.25mm-1,F(000)=394,R=0.0307,wR=0.0815.晶体的基本构建单元中包含2个Co()中心、2个配位的HBTC分子和6个配位的水分子.基本构建单元通过相互链接形成具有“Z”型结构的一维配位聚合链,链间通过两种不同的氢键(O—H…O和N—H…O)相互作用,进而形成具有三维骨架结构的微孔晶体,微孔大小为0.71nm×0.82nm.荧光光谱表明,常温下用λex=312nm的光激发后,配位聚合物在329nm处出现强烈的荧光发射.     

Inductively coupled plasma atomic emission spectrometry — Optimization of the operating conditions in the determination of trace of elements in line-rich emission matrices

Radial viewing 40.68 MHz inductively coupled plasma atomic emission spectrometer was used in the determination of Y, Sc and rare earth elements in Eu₂O₃ or Lu₂O₃ as pure rare earth matrices. The Mg II 280.270 nm/Mg I 285.213 nm line intensity ratio was measured to evaluate the robustness of the operating conditions. The operating conditions were affected by varying the incident power and sheathing gas flow rate. The carrier gas flow rate remained a constant value. The relationship between the Mg II 280.270 nm/Mg I 285.213 nm ratio and the excitation temperature was obtained. A dependence of the magnesium ratio in the pure solvent and the corresponding values in the presence of the above matrices was established.     

Selective cleavage of acetals with ZnBr2 in dichloromethane

A selective cleavage of acetals of 1,2- and 1,3-diols has been achieved under mild conditions using ZnBr₂ in dichloromethane at room temperature. Acetal types cleavable by this procedure include benzylidene, isopropylidene and cyclohexylidene acetals. This method is compatible with several other types of hydroxyl protecting groups such as Bn, Bz, TBDPS, TIPS and TBDMS.