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.     

Effects of Silk Fibroin Enzyme Hydrolysates on Memory and Learning: A Review

Silk protein products have been used for a wide range of applications. This review focuses on the studies conducted relative to cognitive functions with silk fibroin enzyme hydrolysates (FEH) in humans and animals. All known studies reported in PubMed and Google Scholar have been included. Studies have been conducted on children, high school and college students, adults and seniors, ranging in ages from 7–92 years. Doses of 200–600 mg silk FEH per day for three weeks to 16 weeks have been used. Based on these studies, it can be concluded that silk FEH exhibit beneficial cognitive effects with respect to memory and learning, attention, mental focus, accuracy, memory recall, and overall memory and concentration. These conclusions are supported by studies in rats and mice. Mechanistic studies that have been conducted in animals and cell culture systems are also reviewed. These studies indicate that silk FEH exerts its positive effects on memory and learning by providing neuroprotection via a complex mechanism involving its potent antioxidant and inflammation-inhibiting activities. Acetylcholine (ACh) is secreted by cholinergic neurons, and plays a role in encoding new information. Silk FEH were shown to decrease the levels of the pro-oxidant and pro-inflammatory mediators interlukin-1 (IL-1β), IL-6 and tumor necrosis factor-alpha (TNF-α), protecting the cholinergic system from oxidative stress, thus enhancing ACh levels in the brain, which is known to promote cognitive functions. In addition, the expression of brain-derived neurotrophic factor (BNDF), which is involved in the survival of neurons, is enhanced, and an increase in the expression of the phosphorylated cAMP response element-binding protein (p-CREB) occurs, which is known to play a positive role in cognitive functions. No adverse effects have been reported in association with the use of silk FEH.     

Integrating a Luminescent Porous Aromatic Framework into Indicator Papers for Facile,Rapid, and Selective Detection of Nitro Compounds

Porous aromatic framework materials with high stability, sensitivity, and selectivity have great potential to provide new sensors for optoelectronic/fluorescent probe devices. In this work, a luminescent porous aromatic framework material (LNU-23) was synthesized via the palladium-catalyzed Suzuki cross-coupling reaction of tetrabromopyrene and 1,2-bisphenyldiborate pinacol ester. The resulting PAF solid exhibited strong fluorescence emission with a quantum yield of 18.31%, showing excellent light and heat stability. Because the lowest unoccupied molecular orbital (LUMO) of LNU-23 was higher than that of the nitro compounds, there was an energy transfer from the excited LNU-23 to the analyte, leading to the selective fluorescence quenching with a limit of detection (LOD) ≈ 1.47 × 10⁻⁵ M. After integrating the luminescent PAF powder on the paper by a simple dipping method, the indicator papers revealed a fast fluorescence response to gaseous nitrobenzene within 10 s, which shows great potential in outdoor fluorescence detection of nitro compounds.     

Iron-catalysed alkene and heteroarene H/D exchange by reversible protonation of iron-hydride intermediates

C–H functionalisation reactions offer a sustainable method for molecular construction and diversification. These reactions however remain dominated by precious metal catalysis. While significant interest in iron-catalysed C–H activation reactions has emerged, the isolation, characterisation and mechanistic understanding of these processes remain lacking. Herein the iron-catalysed C(sp²)–H bond hydrogen/deuterium exchange reaction using CD₃OD is reported for both heterocycles and, for the first time, alkenes (38 examples). Isolation and characterisation, including by single-crystal X-ray diffraction, of the key iron-aryl and iron-alkenyl C–H metallation intermediates provided evidence for a reversible protonation of the active iron hydride catalyst. Good chemoselectivity was observed for both substrate classes. The developed procedure is orthogonal to previous iron-catalysed H/D exchange methods which used C₆D₆, D₂, or D₂O as the deuterium source, and uses only bench-stable reagents, including the iron(ii) pre-catalyst. Further, a new mechanism of iron-hydride formation is reported in which β-hydride elimination from an alcohol generates the iron hydride. The ability to produce, isolate and characterise the organometallic products arising from C–H activation presents a basis for future discovery and development.

The iron-catalysed C(sp²)–H bond H/D exchange reaction using CD₃OD is reported for both heterocycles and alkenes. Characterisation of the key C–H metallation intermediates provided evidence for reversible protonation of the iron hydride catalyst.     

Applying Unconventional Spectroscopies to the Single-Molecule Magnets,Co(PPh3)2X2 (X=Cl,Br, I): Unveiling Magnetic Transitions and Spin-Phonon Coupling

Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single-molecule magnets (SMMs). Spin-phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin-phonon coupling in molecules is challenging. We have found that far-IR magnetic spectra (FIRMS) of Co(PPh₃)₂X₂ ( Co-X ; X=Cl, Br, I) reveal rarely observed spin-phonon coupling as avoided crossings between magnetic and u-symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero-field split (ZFS) levels of the S=3/2 electronic ground state were probed by INS, high-frequency and -field EPR (HFEPR), FIRMS, and frequency-domain FT terahertz EPR (FD-FT THz-EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) and g values. Ligand-field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities in Co-X , showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spin-phonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.