Existence of finitely optimal solutions for infinite-horizon optimal control problems

In this paper, we investigate the existence of finitely optimal solutions for the Lagrange problem of optimal control defined on [0, ) under weaker convexity and seminormality hypotheses than those of previous authors. The notion of finite optimality has been introduced into the literature as the weakest of a hierarchy of types of optimality that have been defined to permit the study of Lagrange problems, arising in mathematical economics, whose cost functions either diverge or are not bounded below. Our method of proof requires us to analyze the continuous dependence of finite-interval Lagrange problems with respect to a prescribed terminal condition. Once this is done, we show that a finitely optimal solution can be obtained as the limit of a sequence of solutions to a sequence of corresponding finite-horizon optimal control problems. Our results utilize the convexity and seminormality hypotheses which are now classical in the existence theory of optimal control.This research forms part of the author's doctoral dissertation written at the University of Delaware, Newark, Delaware under the supervision of Professor Thomas S. Angell.     

Partial molar volumes of cryptand-222 in organic solvents at 25°C

The partial molar volumes at infinite dilution of cryptand-222 (C-222) in water, methanol, acetonitrile, ethanol, dimethylsulfoxide, propanol, 2-propanol, chloroform, benzene, 1-butanol, cyclohexane, butyl-methylketone, hexane, tetrahydronaphthalene, heptane, octane, cyclohexylbenzene and decane were measured at concentrations ranging from 0.01 to 0.1 mol-L^–1 at 25°C. The partial molar volumes at infinite dilution showed remarkable dependency on the molar volume of the solvent. The partial molar volumes at infinite dilution for C-222 increase as the solvent molar volume increases.     

Ab initio calculations of vibronic activity in phosphorescence microwave double resonance spectra of p-dichlorobenzene

The phosphorescence spectrum of p-dichlorobenzene has been calculated using multiconfiguration self-consistent-field wave functions and the quadratic response technique. Attention has been paid to the intensity distribution of the singlet–triplet (³B_1u¹A_g) transition through a number of vibronic subbands. The second order spin–orbit coupling (SOC) contribution to the spin splitting of the ³B_1u (^3*) state is found to be almost negligible, and the calculations therefore provide a good estimate for the zero-field splitting (ZFS) parameters based only on the electron spin–spin coupling expectation values. Nuclear quadrupole resonance constants for the different Cl isotopes are also calculated to accomplish the ZFS assignment. The electric dipole activity of the spin sublevels in the triplet–singlet transitions to the ground-state vibrational levels is estimated by calculations of derivatives using distorted geometries which are shifted from the equilibrium position along different vibrational modes. A vibrational analysis of the phosphorescence spectrum, based on the SOC-induced mixing of the singlet and triplet states calculated along different vibrational modes, provides reasonable agreement with experimental data.Acknowledgment O. R.-P. would like to thank the European MOLPROP network for support. The authors thank Alexander Baev for fruitful discussions. This work was supported by the Swedish Royal Academy of Science (KVA).     

Synthesis of a Stimuli‐Responsive P‐Chiral Polymer with Chiral Phosphorus Atoms and Azobenzene Moieties in the Main Chain

A reaction of the P‐chiral compound (S,S)‐1,2‐bis(boranato(tert‐butyl)methylphosphino)ethane with an azobenzene derivative gave stimuli‐responsive polymers with P‐chiral phosphines in the main chain. This is the first example of a stimuli‐responsive P‐chiral polymer. The polymer isomerized from the trans to the cis form upon UV irradiation and reverted to the trans form reversibly. The polymer was able to coordinate to platinum, and the resulting polymer complex exhibited the Cotton effect owing to the chirality of the phosphorus atoms. The structure of the P‐chiral polymer obtained could be changed reversibly by light and thermal stimuli, and the polymer chain was induced to rotate helically when complexed with transition metals through the chiral phosphorus atoms.     

Use of cluster expansion techniques in quantum chemistry. A linear response model for calculating energy differences

In this paper we have reviewed the theoretical framework of the coupled-cluster (cc) based linear response model as a tool for directly calculating energy differences of spectroscopic interest like excitation energy (ee), ionisation potential (ip) or electron affinity (ea). In this model, the ground state of a many-electron system is described as in a coupled cluster theory for closed shells. The electronic ground state is supposed to interact with an external photon field of frequencyw, and the poles of the linear response function as a function ofw furnish with the elementary excitations of the system. Depending on the general form of the coupling term chosen, appropriate difference energies like ee, ip or EA may be generated. Pertinent derivations of the general working equations are reviewed, and specific details as well as approximations for ee, ip or ea are indicated. It is shown that the theory bears a close resemblance to the equation of motion (eom) method but is superior to the latter in that the ground state correlation is taken to all orders and may be looked upon as essentially a variant of renormalisedtda. A perturbative analysis elucidating the underlying perturbative structure of the formulation is also given which reveals that the theory has a hybrid structure: the correlation terms are treated akin to an open shellmbpt, while the relaxation terms are treated akin to a Green function theory. A critique of the methodvis-a-vis other cc-based approaches for difference energies forms the concluding part of our review.     

Optimization of culture parameters for production of podophyllotoxin in suspension culture of Podophyllum hexandrum

The root explants of the germinated seedlings of Podophyllum hexandrum were grown in MS medium supplemented with indole acetic acid (IAA) (2 mg/L) and activated charcoal (0.5%), and healthy callus culture was obtained after incubation for 3 wk at 20°C. The cultivation of plant cells in shake flask was associated with problems such as clumping of cells and browning of media, which were solved by the addition of pectinase and polyvinylpyrrolidone. The effect of major media components and carbon source was studied on the growth and podophyllotoxin production in suspension culture. It was found that glucose was a better carbon source than sucrose and that NH₄ ⁺:NO₃ ⁻ ratio (total nitrogen concentration of 60 mM) and PO₄ ³⁻ did not have much effect on the growth and product formation. The relative effect of culture parameters (inoculum level, pH, IAA, glucose, NH₄ ⁺:NO₃ ⁻ ratio, and PO₄ ³⁻) on the overall growth and product response of the plant cell suspension culture was further investigated by Plackett-Burman design. This indicated that inoculum level, glucose, IAA, and pH had significant effects on growth and production of podophyllotoxin. To identify the exact optimum concentrations of these parameters on culture growth and podophyllotoxin production, central composite design experiments were formulated. The overall response equations with respect to growth and podophyllotoxin production as a function of these culture parameters were developed and used to determine the optimum concentrations of these parameters, which were pH 6.0, 1.25 mg/L of IAA, 72 g/L of glucose, and inoculum level of 8 g/L.     

Determination of Copper at a Glassy Carbon Electrode Modified with Langmuir–Blodgett Film of p‐tert‐Butylthiacalix[4]arene

A new type of voltammetric sensor, Langmuir–Blodgett film of p‐tert‐butylthiacalix[4]arene modified glassy carbon electrode, was advanced and used for determining copper at trace levels by differential pulse stripping voltammetry. Calibration plot was found to be linear in the range of 2×10^?8 M to 5×10^?6 M; the detection limit was 2×10^?9 M. Possible recognition mechanism was also discussed. From determination of Copper in real samples (river, lake and tap water) it can be concluded that the method is rapid, sensitive in determining of copper and can be used in the analysis of natural water samples.     

Variable Mott-Schottky plots acquisition by potentiodynamic electrochemical impedance spectroscopy

Potentiodynamic electrochemical impedance spectroscopy provides extraction of potential-dependent space charge layer capacitance from potentiodynamic impedance spectra of non-stationary semiconductor–electrolyte interface. The new technique has been applied for acquisition of Mott-Schottky plots of cathodically treated TiO₂ anodic films. Cathodic treatment in 1 M H₂SO₄ increases donor density and flat band potential of TiO₂. Freshly doped films show hysteresis in the space charge layer capacitance in cyclic potential scans. The subsequent cycling eliminates the hysteresis but preserves the greater part of the doping effect. Presented at the 4th Baltic Conference on Electrochemistry, Greifswald, 13–16 March 2005     

Thermody namic functions of 1,2-alkanediols in dilute aqueous solutions

The heat capacities of binary aqueous solutions of 1,2-ethanediol, 1,2-propanediol and 1,2-butanediol were measured at temperatures ranging from 283.15 to 338.15 K by differential scanning calorimetry. The partial molar heat capacities at the infinite dilution were then calculated for the respective alkanediols. For 1,2-ethanediol or 1,2-propanediol, the partial molar heat capacities at the infinite dilution of increased with increasing temperature. In contrast, the partial molar heat capacities of 1,2-butanediol at the infinite dilution decreased with increasing temperature. Heat capacity changes by dissolution of the alkanediols were also determined. Heat capacity changes caused by the dissolution of 1,2-ethanediol or 1,2-propanediol were increase with increasing temperature. On the other hand, heat capacity changes caused by the dissolution of 1,2-butanediol are decrease with increasing temperature. Thus our results indicated that the structural changes of water caused by the dissolution of 1,2-butanediol differed from that of the two other alkanediols. This revised version was published online in July 2006 with corrections to the Cover Date.     

聚4-重氮基苯乙烯与聚苯乙烯磺酸钠的自组装

1991年Ｄｅｃｈｅｒ等将带相反电荷的聚电解质 ,于水溶液中交替沉积在片基上 ,制备了多层超薄膜[1] ,这种制膜方法现称为静电自组装 .它操作简单 ,无需专用设备 ;一般在水体系进行 ,对环境友好 ;静电力比范德华力强 ,使它比ＬＢ膜稳定 ,所以近年来有很大发展[2 ] .现在自组装成膜驱动力已从静电力扩展到氢键力、电荷转移相互作用、疏水相互作用等 ,用于组装的组分也从聚电解质扩展到多官能团小分子、胶体粒子、无机纳米颗粒 ,ＤＮＡ、蛋白质等生物大分子等[3～ 11] .虽然自组装膜比ＬＢ膜稳定 ,但它也不耐极性溶剂、电解质水溶液等侵蚀 .如…