On nonlinear programming with support functions

Optimality conditions are derived for a nonliear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various dualityresults are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semidefinite quadratic form or anLp norm. It is pointed out that these special cases can easily be generated from our results.     

Separation and determination of m-phenoxybenzaldehyde reaction products by capillary gas chromatography

A capillary GC method employing an internal standard has been developed and successfully used for quantitative determination both of the raw materials used for the manufacture of m-phenoxybenzaldehyde and for the components of the reaction mixtures obtained at various stages of the development of the process. A complete analysis can be performed in a single temperature programmed run.     

Determination of arsenic, selenium, and antimony in cloud water by inductively coupled plasma mass spectrometry

The capability of inductively coupled plasma mass spectrometry in determining trace levels of As, Se, and Sb in cloud water was evaluated. Preliminary studies focused on identifying and eliminating potential interferences in the cloud water matrix, the choice of appropriate internal standards, and system optimization. The detection limits for As, Se, and Sb were 20, 100, 20 pg/mL using pneumatic nebulization, and 5, 25, 5 pg/mL, respectively, using ultrasonic nebulization with a precision of better than 5% RSD. The accuracy was demonstrated by the analysis of a NIST commercial reference material, SRM 1643d. In all cases, the results from ICP-MS analysis agreed within 4% of the certified values. Comparative analysis of cloud water samples obtained from a site downwind from large pollution sources (Whiteface Mountain, New York) and Changlagali Pakistan, a rural mountain peak, was carried out by hydride generation atomic absorption (HGAA) spectrometry. There was excellent agreement between the ICP-MS and HGAA results. Received: 31 July 1997 / Revised: 28 October 1997 / Accepted: 31 October 1997     

Collisional behaviour of electronically excited silicon atoms,Si(3p2(D1D2)), by atomic absorption spectroscopy

The collisional behaviour of electronically excited silicon atoms in the optically metastable 3p²(¹D₂) state (0.781 eV) is investigated by time-resolved resonance absorption in the ultraviolet. Si(3 ¹D₂) was generated by the repetitive pulsed irradiation of SiCl₄ at λ > 165 nm in a flow system, and monitored by attenuation of resonance radiation at λ = 288.16 nm (4s(¹P⁰₁) ← ep²(¹D₂)) using signal averaging. Absolute second-order rate constants (k_R, cm³ molecule^?1 s^?1, 300 K) are reported for the gases: H₂[(8.1 ± 1.5) × 10^?11], O₂[(2.3 ± 0.4) × 10^?11], He (? 10^?15) and SiCl₄ [(2.9 ± 0.4) × 10^?10]. These results are compared with the analogous data reported hitherto for Si(3³P_J) and Si(3 ¹S₀). Those for H₂ and O₂ are discussed within the context of symmetry arguments on the nature of the potential surfaces involved using the weak spin orbit coupling approximation. Finally, pulsed stimulated emission operating on the transition Si(3P²)(¹So → ¹D₂) (λ = 1.0995 μ) was not detected in high energy pulse experiments using a confocal cavity, despite the population inversion between Si(3 ¹S₀ and Si(3 ¹D₂) observed by resonance absorption following the photolysis of SiCl₄.     

Kinetic study of electronically excited silicon atoms,Si(3p2(1S0)), by time-resolved attenuation of atomic resonance radiation

The collisional behaviour of electronically excited silicon atoms in the 3p²(¹S₀) state, 1.909 eV above the 3p²(³P₀) ground state, is investigated by time-resolved attenuation of atomic resonance radiation at λ = 390.53 nm (4s(¹P^o₁)←3p² (¹S₀)). The optically metastable Si(3¹S₀) atoms were generated by the repetitive pulsed irradiation of SiCl₄ and their decay monitored in the presence of added gases. Absolute quenching rate constants (k_Q, cm³ molecule^?1 s^?1, 300 K) are reported for the following collision partners: He (?1.3 × 10^?15), SiCl₄ ((9.1 ± 1.4) × 10^?11), O₂ ((1.5 ± 0.2) × 10^?11) and N₂O ((4.3 ± 0.4) × 10^?11). The results for O₂ and N₂O are compared with analogous data reported hitherto for Si(3p²(³P_J)) and with those for the other np²(¹S₀) states of the group IV atoms C, Ge, Sn and Pb. The rate data for the silicon atoms are considered in terms of the nature of the potential surfaces arising from symmetry arguments based on the weak spin orbit coupling approximation.     

Thin layer chromatography of 57 metal ions on an inorganic ion-exchanger in mixed solvent systems

Summary Thin layers of stannic arsenate have been used to study the chromatographic behaviour of 57 metal ions in different mixed solvents. Au³⁺, Hg²⁺, UO ₂ ²⁺ , Be²⁺ and Al³⁺ and others can be easily separated from numerous metal ions. Fast quaternary, ternary and binary separations have been also achieved. Important separations are discussed. The effect of pH, duration of heating of ionexchanger plates and layer thickness on the R_f values has been studied and discussed. It is shown that Lederer's equation is also obeyed by thin layers of stannic arsenate, if instead of concentration of Na⁺ ion its activity is taken into consideration.     

Effects of laser irradiation on optical properties of a-Se100−x Te x thin films

The effect of laser irradiation on the optical properties of thermally evaporated Se_100?x Te _x (x=8, 12, 16) chalcogenide thin films has been studied. The result shows that the irradiation causes a shift in the optical gap. The results have been analyzed on the basis of laser irradiation-induced defects in the film. The width of the tail of localized state in the band gap has been evaluated using the Urbach edge method. As the irradiation time increases, the values of the optical energy gap for all compositions decrease, while tail energy width increases. It is also observed that the optical energy gap decreases with increasing Te content in the alloy. These changes are a consequence of an increment in disorder produced by laser irradiation in the amorphous structure of thin film.