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.     

Sol-gel approach to in situ creation of high pH-resistant surface-bonded organic-inorganic hybrid zirconia coating for capillary microextraction (in-tube SPME)

A novel zirconia-based hybrid organic-inorganic sol-gel coating was developed for capillary microextraction (CME) (in-tube SPME). High degree of chemical inertness inherent in zirconia makes it very difficult to covalently bind a suitable organic ligand to its surface. In the present work, this problem was addressed from a sol-gel chemistry point of view. Principles of sol-gel chemistry were employed to chemically bind a hydroxy-terminated silicone polymer (polydimethyldiphenylsiloxane, PDMDPS) to a sol-gel zirconia network in the course of its evolution from a highly reactive alkoxide precursor undergoing controlled hydrolytic polycondensation reactions. A fused silica capillary was filled with a properly designed sol solution to allow for the sol-gel reactions to take place within the capillary for a predetermined period of time (typically 15-30 min). In the course of this process, a layer of the evolving hybrid organic-inorganic sol-gel polymer got chemically anchored to the silanol groups on the capillary inner walls via condensation reaction. At the end of this in-capillary residence time, the unbonded part of the sol solution was expelled from the capillary under helium pressure, leaving behind a chemically bonded sol-gel zirconia-PDMDPS coating on the inner walls. Polycyclic aromatic hydrocarbons, ketones, and aldehydes were efficiently extracted and preconcentrated from dilute aqueous samples using sol-gel zirconia-PDMDPS coated capillaries followed by thermal desorption and GC analysis of the extracted solutes. The newly developed sol-gel hybrid zirconia coatings demonstrated excellent pH stability, and retained the extraction characteristics intact even after continuous rinsing with a 0.1 M NaOH solution for 24 h. To our knowledge, this is the first report on the use of a sol-gel zirconia-based hybrid organic-inorganic coating as an extraction medium in solid phase microextraction (SPME).     

Outer product analysis of electronic nose and visible spectra: application to the measurement of peach fruit characteristics

Visual aspect and aroma are among the most important features of fruit that determine consumer preferences. Electronic nose and spectroscopic techniques have shown positive results in evaluating some basic analytical parameters of fruit and global features such as the cultivar.In this paper, we illustrate and discuss a study aimed at evaluating the improvement derived by the fusion of visible spectra and electronic nose data. These experiments were performed on a population of yellow peaches belonging to two cultivars. Each sample was measured by visible optical spectroscopy and by electronic nose. In addition, a number of reference parameters were also measured by conventional destructive methodologies.Collected data were analysed individually and then fused together in order to classify the two cultivars and to estimate the reference parameters. Data fusion was performed building the outer product matrix for each measurement. The set of matrices was then successively unfolded and analysed by conventional chemometrics tools.Results were improved using outer products, for instance in classification average percentage errors of 25, 10, and 7 for electronic nose, spectra, and outer product, respectively was achieved. Regression analysis provides the evidence of a substantial orthogonal appearance of the datasets, which offer former hidden information on fruit classification.     

Applications of Thermal Analysis and Coupled Techniques in Pharmaceutical Industry

Thermal analysis methods are well-established techniques in research laboratories of pharmaceutical industry. The robustness and sensitivity of instrumentation, the introduction of automation and of reliable software according to the industrial needs widened considerably the areas of applications in the last decade. Calibration of instruments and validation of results follow the state of the art of cGMP as for other analytical techniques. Thermal analysis techniques are especially useful for the study of the behavior of the poly-phasic systems drug substances and excipients and find a unique place for new delivery systems. Since change of temperature and moisture occur by processing and storage, changes of the solid state may have a considerable effect on activity, toxicity and stability of compounds. Current requirements of the International Conference of Harmonisation for the characterization and the quantitation of polymorphism in new entities re-enforce the position of thermal analysis techniques. This challenging task needs the use of complementary methods. Combined techniques and microcalorimetry demonstrate their advantages. This article reviews the current use of thermal analysis and combined techniques in research and development and in production. The advantage of commercially coupled techniques to thermogravimetry is emphasized with some examples. This revised version was published online in August 2006 with corrections to the Cover Date.     

A comparative study on the single-scan and multiple-scan techniques in differential scanning calorimetry: Application to the crystallization of the semiconducting Ge0.13Sb0.23Se0.64 alloy

A method has been developed for analysing the evolution with time of the volume fraction transformed and for calculating the kinetic parameters at non-isothermal reactions in materials involving formation and growth of nuclei. By considering the assumptions of extended volume and random nucleation, a general expression of the fraction transformed as a function of time has been obtained in isothermal crystallization processes. Considering the mutual interference of regions growing from separate nuclei the Johnson–Mehl–Avrami equation has been deduced as a particular case. The application of the transformation rate equation to the non-isothermal processes has been carried out under the restriction of a nucleation which takes place early in the transformation and the nucleation frequency is zero thereafter. Under these conditions, the kinetic parameters have been deduced by using the techniques of data analysis of single-scan and multiple-scan. The theoretical method developed has been applied to the glass-crystal transformation kinetics of the semiconducting Ge_0.13Sb_0.23Se_0.64 alloy. The kinetic parameters obtained according to both techniques differ by only about 2.5%, which confirms the reliability and accuracy of the single-scan technique when calculating the above-mentioned parameters in non-isothermal transformation processes. The phases at which the above-mentioned semiconducting glass crystallizes after the thermal process have been identified by X-ray diffraction. The diffractogram of the transformed material shows that microcrystallites of Sb₂Se₃ and GeSe are associated with the crystallization process, remaining a residual amorphous matrix.     

Identification of anthraquinone coloring matters in natural red dyestuffs by high performance liquid chromatography with ultraviolet and electrospray mass spectrometric detection

Reversed phase liquid chromatography with diode array detection (DAD) and electrospray mass spectrometric (ESI MSD) methods were developed for the identification of anthraquinone color components of cochineal, lac dye, and madder – red natural dyestuffs. Electrospray mass spectrometry was found to be more suitable than diode array detection for such analysis because of its higher sensitivity (detection limits in the range 30–90 ng mL^–1) and selectivity. The developed method permitted unequivocal identification of carminic acid and laccaic acid A as coloring matters in examined preparations of cochineal and lac dye, respectively. In madder more chemical color species were found: alizarin, purpurin, lucidin, ruberythric acid, and also aluminum and calcium alizarin lake. Among the methods recommended so far, the present one allows fast, direct, and unequivocal identification of components of very complicated natural products used in art.     

Blood cell separation using crosslinkable copolymers containing N,N‐dimethylacrylamide

Amphiphilic copolymers using hydrophilic N,N‐dimethylacrylamide (DMA), hydrophobic methyl methacrylate (MMA) and a crosslinkable monomer, 3‐methacryloyloxypropyl trimethoxysilane (MTSi), were synthesized and evaluated as coating materials for leukocyte removal filters for whole blood. When filters composed of non‐woven fabrics were coated with crosslinked synthesized copolymers, the elution ratios of the copolymers to water were adequately low because of the crosslinking with trimethoxysilane groups of MTSi units in the copolymers. Filters coated with crosslinked poly(DMA‐co‐MTSi) having a 0.96 mole fraction of DMA units showed a 0.35 ± 0.44% platelet permeation ratio and a logarithmic reduction of 4.0 ± 0.68 for leukocytes. On the other hand, an increase in the content of MMA units in the DMA‐containing copolymers improved the permeation ratio of the platelets dramatically. Filters coated with crosslinked poly(DMA‐co‐MMA‐co‐MTSi) containing a 0.39 mole fraction of MMA units and a 0.58 mole fraction of DMA units showed an 86 ± 3.0% platelet permeation ratio and a logarithmic reduction of 2.1 ± 1.2 for leukocytes. This indicates that an adequate content of hydrophobic monomer units, such as MMA units, is necessary for effective platelet permeation. Copyright © 2007 John Wiley & Sons, Ltd.     

On the convergence of the LJ search method

The convergence of the Luus-Jaakola search method for unconstrained optimization problems is established.Notation E _n Euclideann-space - f Gradient off(x) - ² f Hessian matrix - (·) ^T Transpose of (·) - I Index set {1, 2, ...,n} - [x _i1 ^*(j) ] Point around which search is made in the (j + 1)th iteration, i.e., [x _1l ^*(j) ,x _2l ^*(j) ,...,x _n1 ^*(j) ] - r _i ⁽ⁱ⁾ Range ofx _il ^*(i) in the (j + 1)th iteration - l ₁ min_i {r _i ⁽⁰⁾ } - l ₂ min_i {r _i ⁽⁰⁾ } - A _j Region of search in thejth iteration, i.e., {x E _n:x _il ^*(j-1) –0.5r _i ^(j-1) x _ix _il ^*(j-1) +0.5r _i ^(j-1) ,i I} - S _j Closed sphere with center origin and radius _j - Reduction factor in each iteration - 1– - (·) Gamma function Many discussions with Dr. S. N. Iyer, Professor of Electrical Engineering, College of Engineering, Trivandrum, India, are gratefully acknowledged. The author has great pleasure to thank Dr. K. Surendran, Professor, Department of Electrical Engineering, P.S.G. College of Technology, Coimbatore, India, for suggesting this work.     

Labelling and Fractionating of Black Mamba Venom using 131I and Gel-Filtration Technique

Separation of Black Mamba (Dendroaspis polylepis) venom into three fractions was achieved by the use of Sephadex G-100 filtration method. The first and highest peak of the three separated bands proved to be the lethally toxic. Labelling the venom with nascent¹³¹ I prior to fractionating facilitated the detection and the evaluation of three well resoluted fractions. Comparative separation of non-labelled venom was also carried out side by side with the labelled one to study the advantage of radioactivity on extinction measurements.     

Radiotracer Investigation of the Copper Ore Concentration Process

One of the most difficult operations for control and identification in copper ore concentration process is grain classification in hydrocyclone batteries. In the paper radiotracer investigations of the classification process immediately give values of hydrocyclones parameters with higher accuracy than obtained from conventional methods. Presented paper includes the results of the investigation which was carried out in “Lubin” Copper Mine in Poland.