Min-max game theory and algebraic Riccati equations for boundary control problems with continuous input-solution map. Part II: The general case

We consider the abstract dynamical framework of [LT3, class (H.2)] which models a variety of mixed partial differential equation (PDE) problems in a smooth bounded domain ⁿ , arbitraryn, with boundaryL ₂-control functions. We then set and solve a min-max game theory problem in terms of an algebraic Riccati operator, to express the optimal quantities in pointwise feedback form. The theory obtained is sharp. It requires the usual Finite Cost Condition and Detectability Condition, the first for existence of the Riccati operator, the second for its uniqueness and for exponential decay of the optimal trajectory. It produces an intrinsically defined sharp value of the parameter, here called _c (critical), _c0, such that a complete theory is available for > _c, while the maximization problem does not have a finite solution if 0 < < _c. Mixed PDE problems, all on arbitrary dimensions, except where noted, where all the assumptions are satisfied, and to which, therefore, the theory is automatically applicable include: second-order hyperbolic equations with Dirichlet control, as well as with Neumann control, the latter in the one-dimensional case; Euler-Bernoulli and Kirchhoff equations under a variety of boundary controls involving boundary operators of order zero, one, and two; Schroedinger equations with Dirichlet control; first-order hyperbolic systems, etc., all on explicitly defined (optimal) spaces [LT3, Section 7]. Solution of the min-max problem implies solution of theH -robust stabilization problem with partial observation.The research of C. McMillan was partially supported by an IBM Graduate Student Fellowship and that of R. Triggiani was partially supported by the National Science Foundation under Grant NSF-DMS-8902811-01 and by the Air Force Office of Scientific Research under Grant AFOSR-87-0321.     

Identification of microbial inhibitory functional groups in corn stover hydrolysate by carbon-13 nuclear magnetic resonance spectroscopy

Dilute-acid biomass hydrolysates contain biomass degradation products that are inhibitory to cell growth and fermentation. Overliming with Ca(OH)₂ has been found to be one of the most effective methods for detoxifying the dilute-acid hydrolysate for ethanol production. However, the mechanism of overliming is not well understood. Carbon-13 nuclear magnetic resonance (¹³C-NMR) spectroscopy was used to elucidate the functional groups involved in the overliming reaction. The ¹³C-NMR spectra showed that the major functional groups removed during the overliming process were aliphatic and aromatic acids or esters, and other aromatic and aliphatic compounds. Ketone and aldehyde functionalities were not detected in the spectra. This is the first time that ¹³C-NMR has been used to elucidate the overliming reaction.     

Synthesis, relaxometric and photophysical properties of a new pH-responsive MRI contrast agent: the effect of other ligating groups on dissociation of a p-nitrophenolic pendant arm

Two gadolinium(III) chelates, GdNP-DO3A (1-methlyene-(p-NitroPhenol)-1,4,7,10-tetraazacycloDOdecane-4,7,10-triAcetate) and GdNP-DO3AM (1-methlyene(p-NitroPhenol)-1,4,7,10-tetraazacycloDOdecane-4,7,10-triacetAMide), containing a single nitrophenolic pendant arm plus either three acetate or three amide pendant arms were synthesized and characterized. The properties of the gadolinium, terbium, and dysprosium complexes of these ligands were examined as a function of pH. The extent and mechanism of the changes in water relaxivity with pH of each gadolinium complex was found to differ substantially for the two complexes. The water relaxivity of Gd(NP-DO3A) increases from 4.1 mM(-1) s(-1) at pH 9 to 7.0 mM(-1) s(-1) at pH 5 as a result of acid-catalyzed dissociation of the nitrophenol from the lanthanide. The nitrophenol group in Gd(NP-DO3AM) does not dissociate from the metal center even at pH 5; therefore, the very modest increase in relaxivity in this complex must be ascribed to an increase in prototropic exchange rate of the bound water and/or phenolic protons.     

Identification of inhibitory components toxic toward zymomonas mobilis CP4(pZB5) xylose fermentation

Zymomonas mobilis CP4(pZB5) is a recombinant bacterium that can produce ethanol from both xylose and glucose. The ethanol-producing efficiency of this organism is substantially impeded by toxic substances present in pretreated hydrolyzates or solid biomass substrates. Acetic acid and furfural (a pentose degradation product) are highly toxic to this organism at levels envisioned for a pretreated-hardwood liquid hydrolyzate. In addition, lignin degradation products and 5-hydroxymethylfurfural (a hexose degradation product) have a moderately toxic effect on the organism. Of the compounds studied, organic acids and aldehydes were found to be more inhibitory than lignin acids or the one alkaloid studied. Acetone:water and methanol extracts of solid biomass samples from red oak, white oak, and yellow poplar are toxic toZymomonas cell growth and ethanol production, with the extracts from white oak being the most toxic.     

The nuclear microprobe as an analytical tool

The nuclear microprobe is a spatially sensitive analytical instrument which exploits measurement of the particles or other radiations emitted when specimens are irradiated with beams of energetic charged-particles, most often having energies lying the range 0.5–4 MeV. Factors affecting the analytical and technical performance are discussed and examples given of application of the instrument to the fields of nuclear science and metallurgy, biology and geology.     

Continuous culture studies of xylose-fermentingZymomonas mobilis

The continuous cofermentation performance of xylose-fermentingZymomonas mobilis at 30°C and pH 5.5 was characterized using a pure-sugar feed solution that contained 8 g/L glucose and 40 g/L xylose. Successful chemostat start up resulted in complete utilization of glucose and greater than 85% utilization of xylose, but was only reproducibly achieved using initial dilution rates at or less than 0.04/h; once initiated, cofermentation could be maintained at dilution rates of 0.04 to 0.10/h. Whereas xylose and cell-mass concentrations increased gradually with increasing dilution rate, ethanol concentrations and ethanol yields on available sugars remained approximately constant at 20–22 g/L and 80–90% of theoretical, respectively. Volumetric and specific ethanol productivities increased linearly with increasing dilution rate, rising from approx 1.0 each (g/L/h or g/g/h) at a dilution rate of 0.04/h to approx 2.0 each (g/L/h or g/g/h) at a dilution rate of 0.10/h. Similarly, specific sugar-utilization rates increased from approx 2.0 g/g/h at dilution rate 0.04/h to approx 3.5 g/g/h at dilution rate of 0.10/h. The estimated values of 0.042 g/g for the maximum Z.mobilis cell-mass yield on substrate and 1.13 g/g/h for the minimum specific substrate utilization rate required for cellular maintenance energy are within the range of values reported in the literature. Results are also presented which suggest that long-term adaptation in continuous culture is a powerful technique for developing strains with higher tolerance to inhibitory hemicellulose hydrolyzates.     

Interactive decision software and computer graphics for architectural and space planning

We describe the development and successful implementation of a decision support system now being used by several leading firms in the architecture and space planning industries. The system, which we call SPDS (spatialprogrammingdesignsystem) has the following characteristics: (i) user-friendly convenience features permitting architects and space planners to operate the system without being experienced programmers; (ii) interactive capabilities allowing the user to control and to manipulate relevant parameters, orchestrating conditions to which his or her intuition provides valuable input; (iii) informative and understandable graphics, providing visual displays of interconnections that the computer itself treats in a more abstract methematical form; (iv) convenient ways to change configurations, and to carry out what if analyses calling on the system's decision support capabilities; (v) a collection of new methods, invisible to the user, capable of generating good solutions to the mathematical programming problems that underlie each major design component. These new methods succeed in generating high quality solutions to a collection of complex discrete, highly nonlinear problems. While these problems could only be solved in hours, or not at all, with previously existing software, the new methods obtain answers in seconds to minutes on a minicomputer. Major users, including Dalton, Dalton, Newport, and Marshal Erdwin, report numerous advantages of the system over traditional architectural design methods.     

Composition and polyamorphism in supercooled yttria-alumina melts

By extending recent work on liquid-liquid transitions in supercooled yttria-alumina AYx liquids we draw attention to the compositional dependence of the structure factor of the high density liquid, arguing that this is sufficiently sensitive to discriminate between liquids at the level of a few %. Comparing structure factor differences between liquids of different compositions and in the same liquid AY20 between high and low temperatures straddling the transition at 1788 K between a high density liquid (HDL) and a low density liquid (LDL) enables compositional phase separation to be ruled out. It points instead to kinetic changes in polyhedral configurational order being the drivers for this polyamorphic transformation. Rotor behaviour observed in levitated liquid drops used in the high temperature experiments enables the reversibility of the LLT transition (LLT) and the associated changes in entropy and density to be identified. Evidence for critical-like behaviour in the structural relaxation time and in the fluctuation correlation length is presented. By re-examining recent work which failed to find the structural and thermal signatures for the LLT in liquid AY20 at 1788 K we present evidence for the LLT occurring instead in liquid AY15 at 1940 K, suggesting that the liquid-liquid transition temperature in AYx liquids decreases with increasing yttria content.     

Laser-induced breakdown spectroscopy analysis of complex silicate minerals—beryl

Beryl (Be₃Al₂Si₆O₁₈) is a chemically complex and highly compositionally variable gem-forming mineral found in a variety of geologic settings worldwide. A methodology and analytical protocol were developed for the analysis of beryl by laser-induced breakdown spectroscopy (LIBS) that minimizes the coefficient of variance for multiple analyses of the same specimen. The parameters considered were laser energy/pulse, time delay and crystallographic orientation. Optimal analytical conditions are a laser energy/pulse of 102 mJ and a time delay of 2 μs. Beryl compositions measured parallel and perpendicular to the c axis were identical within analytical error. LIBS analysis of 96 beryls from 16 countries (Afghanistan, Brazil, Canada, China, Colombia, India, Ireland, Italy, Madagascar, Mexico, Mozambique, Namibia, Norway, Russia, Tanzania and United States), Antarctica, and ten US states (AZ, CA, CO, CT, ID, ME, NC, NH, NM and UT) were undertaken to determine whether or not LIBS analysis can be used to determine the provenance of gem beryl.