Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

Dynamic modification of the capillary wall for electrophoretic separations of small ions

Separations of small ions were carried out under nonequilibrated conditions using capillaries treated with NaOH, HCl, or tris(hydroxymethyl)aminomethane (Tris) prior to analysis. For separations of benzoic acid isomers or acids and amines under weakly acidic conditions, capillaries flushed with 0.1 M NaOH and subsequently with running buffers prior to analysis were used. Separations of six benzoic acid isomers were accomplished in 4 min in 1 mM phosphate buffers, pH 4.01, containing 2.5 mM hydroxypropyl-beta-cyclodextrin. Without additives, the separation of biological amines and acids were also achieved in 10 min at pH 4.01. Capillaries treated with 0.1 M HCl prior to analysis were tested in separations of six phenols in 5 mM Tris solutions at pH 7.0. As a result of small electrophoretic mobilities of phenols against a small electroosmotic flow, resolution was optimized. We also found that reproducibility was improved using capillaries treated with HCl. The relative standard deviations of migration mobility of phenols were less than 1%, which were smaller than those obtained using capillaries treated with 0.1 M NaOH or Tris.     

Optimizing separation conditions for polycyclic aromatic hydrocarbons in micellar electrokinetic chromatography

We report the separation of polycyclic aromatic hydrocarbons (PAHs) using 0.1% poly(ethylene oxide) (PEO) in micellar electrokinetic chromatography (MEKC). In the presence of PEO, adsorption of PAHs on the capillary wall was reduced, leading to better resolution and reproducibility. Effects of tetrapentylammonium iodide (TPAI), dextran sulfate (DS), methanol, and sodium lauryl sulfate (SDS) on the separation of PAHs were elucidated. In terms of resolution and speed, DS, compared to TPAI, is a better additive for separation of PAHs. When using 0.1% PEO solution containing 45% methanol, 50 mM SDS, and 0.02% DS, separation of 10 PAHs containing 2 to 5 benzene rings was accomplished in less than 12 min at 15 kV in a commercial CE system. The method has also been tested for separating seven PAHs with high quantum yields when excited at 325 nm using a He-Cd laser. Unfortunately, separation of the seven PAHs was not achieved and sensitivity diminished under the same conditions. To optimize sensitivity, resolution and speed, a stepwise technique in MEKC has been proposed. The seven PAHs were resolved in 35 min at 15 kV when separation was performed in 0.1% PEO solution containing 35 mM SDS, 40% methanol and 0.02% DS for 2 min, and subsequently in 0.1% PEO solution containing 20 mM SDS, 50% methanol, and 0.02% DS.     

Insertion Reactions of Carbon Disulfide into Mg‐C and Mg‐N Bonds: Syntheses and Structural Determinations of Mg(S2CY)2(THF)n(Y=NEt2, NiPr2, iPr,Ph) and BrMg(S2CZ)(THF)3(Z=Ph,iPr)

The insertion reaction of CS₂ with Mg(NR₂)₂ (R= Et, ⁱPr), MgR′₂ (R′= Et, Ph) and R″MgBr (R″= ⁱPr, Ph) respectively lead solid products, Mg(S₂CNR₂)₂(THF)_n ( 1 : R= Et, n=2; 2 : R= ⁱPr, n=1), Mg(S₂C′R)₂(THF)₂ ( 3 : ′R= Et, 4 : ′R= Ph), BrMg(S₂C″R) (THF)₃ ( 5 : ″R= ⁱPr, 6 : ″R= Ph) in which the inserted carbon disulfides act as terminal chelating ligands. These compounds were characterized with ¹H, ¹³C NMR, IR spectroscopy, mass spectrometry, elemental analyses, and X‐ray crystallography.     

Synthesis and Crystal Structure of 3-（2-Hydroxy-phenyl）-5-（2-methylphenyl）-6-thoxycarbonyl-cyclohexen-2-one

1 INTRODUCTION The molecular assembly of one- or multi-dimen-sional aggregation by hydrogen bonds is now an im-portant subject of supramolecular chemistry and crys-tal engineering[1, . Supramolecular structures formed 2]via intermolecular hydrogen bonds X–H…X or C–H…X (X = O, Cl, N, et al.) are very common inorganic compounds[3~12], and they generally possessdifferent properties due to these hydrogen bonds. Concerning about the spectra of benzene-contai-ning…     

Performance improvement of electrochromic display devices employing micro-size precipitates of tungsten oxide

In this paper, we studied the effect of micro-size WO₃ precipitates on the electrochromic characteristics based on aging test. The electrochromic mechanism can be effectively investigated by a solid-state TaN/WO₃/ITO capacitor. The experimental results reveal that WO₃ electrochromic devices with optimized aging time of 4 days exhibit a higher optical contrast and longer retention time, which is mainly attributed to the formation of micro-size WO₃ precipitates during aging process. The performance improvement using micro-size WO₃ precipitates has the potential in future large-area window or energy efficient display applications.