Algorithms for Finite and Semi-Infinite Min–Max–Min Problems Using Adaptive Smoothing Techniques

We develop two implementable algorithms, the first for the solution of finite and the second for the solution of semi-infinite min-max-min problems. A smoothing technique (together with discretization for the semi-infinite case) is used to construct a sequence of approximating finite min-max problems, which are solved with increasing precision. The smoothing and discretization approximations are initially coarse, but are made progressively finer as the number of iterations is increased. This reduces the potential ill-conditioning due to high smoothing precision parameter values and computational cost due to high levels of discretization. The behavior of the algorithms is illustrated with three semi-infinite numerical examples.     

Effect of Mobile Phase pH* on Chromatographic Behaviour in Chiral Ligand-Exchange Thin-Layer Chromatography (CLETLC) of Amino Acid Enantiomers

The enantiomers of some amino acids have been separated on commercial chiral TLC plates in reversed-phase mode. The effect of the pH* of the aqueous-organic mobile phase on the retention and mobility of the enantiomers and on selectivity was investigated. It was shown that for most of the amino acids investigated the highest enantioselectivity was obtained at pH* 3–4 or 6–7. The drift and disturbance of the baseline on the chromatograms were also much smaller at pH* 3–4 and 6–7.     

Description of oxygen permeability in various high polymers using a graph theoretical approach

Graph theory methods are shown to complement group additivity methods of predicting oxygen permeability in certain types of polymers. Graph theory is a topological approach that assigns a set of indices to a molecule to describe its structure. Since many physical properties of molecules depend upon their structure, graph theory indices can be used to describe important properties of molecules. In this work a set of graph theory indices are used to describe the property of a polymer based on a modified representation of the monomer unit. More specifically, Randic indices are used to describe the log of the oxygen permeability with 3.2% average relative error. Polymers comprising the basis set contain backbones of sp², sp³, or aromatic carbons, oxygen, or silicon and have substituents that contain chloride, fluoride, alkyl groups, hydrogen, oxygen, aromatic carbons, or chloro and/or fluoro substituted alkyl groups. The correlation coefficient (R²) (0 ≤ R² ≤ 1) of a nonlinear model is 0.91. The graph theory method for describing the oxygen permeability of these selected groups of polymers is in good agreement with that predicted by the permachor model. The permachor method makes oxygen permeability predictions based upon group additivity and distinguishes the degree of crystallinity of a polymer by empirically assigning different permachor (π) values to identical groups based upon the polymer crystallinity. The inability of graph theory to explain the remaining 9% of the scatter in the data is probably due to failure to incorporate into the graph theory model terms which quantify crystallinity.     

Pulverized coal plasma gasification

A number of experiments on the plasma-vapor gasification of brown coals of three types have been carried out using an experimental plant with an electric-arc reactor of the combined type. On the basis of the material and heat balances, process parameters have been obtained: the degree of carbon gasification (_c), the level of sulfur conversion into the gas phase (_s), the synthesis gas concentration (CO+Hz) in the gaseous products, and the specific power consumption for the gasification process. The degree of gasification was 90.5-95.0%, the concentration of the synthesis gas amounted to 84.7–85.7%, and the level of sulfur conversion into the gas phase was 94.3–96.7%. Numerical study of the process of plasma gasification of coals was carried out using a mathematical model of motion, heating, and gasification of polydisperse coal particles in an electric-arc reactor of the combined type with an internal heat source (arc). The initial conditions for a conjugate system of nonlinear differential equations of the gas dynamics and kinetics of a pulverized coal stream interacting with the electric arc and oxidizer (water vapor) agree with the initial conditions of the experiments. The computation results satisfactorily correlate with the experimental data. The mathematical model can be used for the determination of reagent residence time and geometrical dimensions of the plasma reactor for the gasification of coals.Nomenclature c _i volume concentration of components (kmol m^–3) - x longitudinal coordinate (m) - f _i source members, determined by variation of the ith component due to chemical reactions in unit volume in unit time (kmol m^–3s^–1) - velocity (m s^–1) - M _s ash mass in one particle (kg) - C _D particle drag coefficient - 3.14 - r _s particle radius (m) - d particle diameter (m) - density (kg m^–3) - C _p heat capacity of components (J mol^t– K^–1) - Q _j thermal effect of reaction (J kmol^–1) - E_j activation energy of reaction - N _l volume concentration of particles of thelth fraction (m^–3) - T temperature (K) - emissivity factor of coal particles - 5.67 × 10^–8, blackbody emissivity coefficient (W m^–2 K^–4) - P pressure (Pa) - S reactor cross section (m²) - D reactor diameter (m) - V reactor volume (m³) - L _R reactor length (m) - F _W friction force on the wall (N) - f _g friction coefficient - residence time (s) - Nu Nusselt number - Re Reynolds number - Pr Prandtl number - thermal conductivity of gas (J m^– s^–1 K^–1) - R 8.3 × 10³, universal gas constant (J kmol K^–1) - µ _i molecular mass of component (kg kmol^–1) - dynamic viscosity coefficient of gas (kg m^–1 s^–1) - thermal efficiency of plasma reactor - q_arc specific heat flow from arc (W m^–3) - P ₁ heat supplied in vapor at T = 405 K (W) - P ₂ heat loss to wall (W) - P ₃ heat loss in the gas and slag separator chamber (W) - P ₄ heat loss in the synthesis gas oxidation chamber (W) - P ₅ heat loss in the slag catcher (W) - P ₆ heat carried away in the off-gas (W) - P heat input of arc (W) - P _arc electric power of arc (W) - Q_sp specific power consumption (kw Hr kg^–1) - d _w specific heat flow to wall (W m^–2) - _c degree of carbon gasification (%) - _s level of sulfur conversion into gas phase (%)     

Interactions of vibrationally excited CO2 with oxygen and sulfur atoms

The classical-path method has been used in calculations on O+CO₂ CO+ O₂ and S+CO₂ CO+SO for vibrational-translational disequilibrium. The vibrational-energy localization in various modes in CO₂ affects the reaction cross section and rate constant. The energy distributions in the products have been calculated.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 4, pp. 428–434, July–August, 1988.     

Nondifferential optimization via adaptive smoothing

The problem of minimizing a nondifferential functionx f(x) (subject, possibly, to nondifferential constraints) is considered. Conventional algorithms are employed for minimizing a differential approximationf off (subject to differentiable approximations ofg). The parameter is adaptively reduced in such a way as to ensure convergence to points satisfying necessary conditions of optimality for the original problem.This research was supported by the UK Science and Engineering Research Council, the National Science Foundation under Grant No. ECS-8121149, and the Joint Services Electronics Program, Contract No. F49620-79-C-0178.     

Electrodeposition on copper powder as a means of separation for trace analysis of noble metals in activation analysis: A tracer study

Studies are reported to illustrate surface adsorption of¹⁴⁴Ce,⁵⁹Fe,²³⁴Th,²³³U,²³⁷Np,²³⁹Pu and²⁴¹Am on a dextran gel made by crosslinkage of the polysaccharide dextran (Sephadex). Fixation of such elements was studied from aqueous solution and was found to depend on pH, age of the tracer solution, hydrolytic behaviour of the adsorbed species, concentration and the valency of the adsorbed element.