An analytical and numerical study of the two-dimensional Bratu equation

Bratu's problem, which is the nonlinear eigenvalue equationu+ exp(u)=0 withu=0 on the walls of the unit square and as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance ofsymmetry: because of invariance under the C₄ rotation group and parity in bothx andy, one can slash the size of the basis set by a factor of eight and reduce the CPU time by three orders of magnitude. Second, the pseudospectral method is ananalytical as well as a numerical tool: the simple approximation3.2A exp(–0.64A), whereA is the maximum value ofu(x, y), is derived via collocation with but a single interpolation point, but is quantitatively accurate for small and moderateA. Third, the Newton-Kantorovich/Chebyshev pseudospectral algorithm is so efficient that it is possible to compute good numerical solutions—five decimal places—on amicrocomputer inbasic. Fourth, asymptotic estimates of the Chebyshev coefficients can be very misleading: the coefficients for moderately or strongly nonlinear solutions to Bratu's equations fall off exponentially rather than algebraically withv untilv is so large that one has already obtained several decimal places of accuracy. The corner singularities, which dominate the behavior of the Chebyshev coefficients in thelimit v, are so weak as to be irrelevant, and replacing Bratu's problem by a more complicated and realistic equation would merely exaggerate the unimportance of the corner branch points even more.     

Quadratic approximate dynamic programming for input‐affine systems

We consider the use of quadratic approximate value functions for stochastic control problems with input‐affine dynamics and convex stage cost and constraints. Evaluating the approximate dynamic programming policy in such cases requires the solution of an explicit convex optimization problem, such as a quadratic program, which can be carried out efficiently. We describe a simple and general method for approximate value iteration that also relies on our ability to solve convex optimization problems, in this case, typically a semidefinite program. Although we have no theoretical guarantee on the performance attained using our method, we observe that very good performance can be obtained in practice.Copyright © 2012 John Wiley & Sons, Ltd.     

Water as a Promoter of the Complete Oxidation of Volatile Organic Compounds over Uranium Oxide Catalysts

The effect of water addition on the complete oxidation of benzene and propane VOCs by uranium oxide catalysts has been investigated. Benzene oxidation was studied using a silica supported U₃O₈ catalyst. Complete oxidation is promoted by the addition of 2.6% water compared with the reactivity when no water is added to the reactant feed. Increasing the water concentration to 12.1% resulted in a suppression of oxidation activity. Investigation of propane oxidation using U₃O₈ shows a dramatic promotion of activity. Propane conversion was ca. 50% at 600 °C without added water, whilst it increased to 100% at 400 °C with the addition of 2.6% water. A comparison of oxidation activity has been made with Mn₂O₃, an oxide recognised for complete oxidation. In contrast to the U₃O₈ catalysts the addition of 2.6% water suppresses the activity of Mn₂O₃. In situ powder X-ray diffraction studies showed that the bulk U₃O₈ structure was stable under all the reaction conditions. The origin of the increased activity is not clear but may be due to modification of the catalyst surface and the contribution from new reaction pathways such as steam reforming.     

Approximate dynamic programming via iterated Bellman inequalities

In this paper, we introduce new methods for finding functions that lower bound the value function of a stochastic control problem, using an iterated form of the Bellman inequality. Our method is based on solving linear or semidefinite programs, and produces both a bound on the optimal objective, as well as a suboptimal policy that appears to works very well. These results extend and improve bounds obtained in a previous paper using a single Bellman inequality condition. We describe the methods in a general setting and show how they can be applied in specific cases including the finite state case, constrained linear quadratic control, switched affine control, and multi‐period portfolio investment. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of two authorization protocols using Colored Petri Nets

To prevent unauthorized access to protected trusted platform module (TPM) objects, authorization protocols, such as the object-specific authorization protocol (OSAP), have been introduced by the trusted computing group (TCG). By using OSAP, processes trying to gain access to the protected TPM objects need to prove their knowledge of relevant authorization data before access to the objects can be granted. Chen and Ryan’s 2009 analysis has demonstrated OSAP’s authentication vulnerability in sessions with shared authorization data. They also proposed the Session Key Authorization Protocol (SKAP) with fewer stages as an alternative to OSAP. Chen and Ryan’s analysis of SKAP using ProVerif proves the authentication property. The purpose of this paper was to examine the usefulness of Colored Petri Nets (CPN) and CPN Tools for security analysis. Using OSAP and SKAP as case studies, we construct intruder and authentication property models in CPN. CPN Tools is used to verify the authentication property using a Dolev–Yao-based model. Verification of the authentication property in both models using the state space tool produces results consistent with those of Chen and Ryan.     

Thermodynamic magnetization discontinuity between the A and B phases of superfluid3he

We present data for the magnitude of the thermodynamic magnetization discontinuity at the equilibrium A-B transition in superfluid³He, M_AB, over its entire pressure-temperature-magnetic field phase diagram. The data was taken by measuring flux changes in a SQUID pick-up coil, which was calibrated by a novel first-principles technique. We compare our results with those of NMR experiments, and find that the two types of measurements yield different values, and this discrepancy is not the result of thermometry or field errors.     

The effect of combined antenatal vitamin K and phenobarbital therapy on umbilical blood coagulation studies in infants less than 34 weeks' gestation

OBJECTIVE: To determine if antenatal vitamin K and phenobarbital therapy affect coagulation studies in umbilical blood at birth, and to provide 95% reference ranges for umbilical blood coagulation parameters in premature gestations. METHODS: Patients at imminent risk for spontaneous or indicated premature delivery less than 34 weeks' gestation were randomized to receive either placebo or vitamin K and phenobarbital. Prothrombin time (PT), activated partial thromboplastin time (PTT), functional coagulation factors, and decarboxylated prothrombin assays were performed on umbilical blood specimens. Decarboxylated prothrombin, also known as "protein induced by vitamin K absence-factor II" or precursor prothrombin, is a sensitive marker for vitamin K deficiency. Standardized values of PT and PTT are reported in seconds and standardized values of factor assays in percentage of normal adult functional activity (mean +/- one standard deviation). RESULTS: Newborns in the placebo and treatment groups had similar umbilical blood PT (12.6 +/- 1.2 versus 12.7 +/- 1.4 seconds), PTT (48.8 +/- 13.4 versus 49.6 +/- 13.8 seconds), and functional activity of factor II (40.3 +/- 12.5 versus 42.0 +/- 12.1%), factor VII (67.0 +/- 20.9 versus 66.8 +/- 18.9%), factor IX (27.4 +/- 12.8 versus 25.8 +/- 8.9%), and factor X (47.0 +/- 12.8 versus 49.2 +/- 11.6%). Newborns in the treatment group were about half as likely as those in the placebo group to have detectable decarboxylated prothrombin levels in umbilical blood at birth (gestational age-adjusted odds ratio 0.47, 95% confidence interval 0.22-1.01; P = .05). CONCLUSIONS: Combined maternal therapy with vitamin K and phenobarbital before premature delivery does not affect umbilical blood PT, PTT, or functional activity of vitamin K-dependent coagulation factors II, VII, IX, and X. However, it is associated with the reduced presence of decarboxylated prothrombin in umbilical blood at birth. There is significant improvement in umbilical blood coagulation tests as gestational age advances from 24 to 34 weeks.     

Solid-state 2H NMR study of methyl-d3-cobalamin

A solid-state 2H NMR study of methyl-d3-cobalamin has been performed as a function of temperature to provide information concerning the character and energetics of the motion performed by this unique bioorganometallic methyl group. Analysis of the 2H NMR line shape indicates that the methyl group undergoes rapid three-fold rotation, and that the Co-C-2H angle lies between 105.9 and 109.5 degrees. Determination of the spin-lattice relaxation times T1 shows that the relaxation is anisotropic, consistent with a "jumping" motion of the methyl group rather than rotational diffusion. This also provides the activation energy to methyl jumps as 8.3 +/- 1.3 kJ/mol. It is proposed that this energetic barrier may be a useful probe of changes in the electronic character of the Co-C bond that accompany the biological role of this molecule in such enzymes as methionine synthase.     

Immunomicroscopy: resin techniques and on-section labelling with immunocolloidal gold or immunoperoxidase--planning a protocol

On-section immunocytochemistry is divided into two parts: (i) processing of biological tissue for section microscopy and (ii) immunolabelling of sections. Many of the more successful microscopical methods employ delicate aldehyde fixation of biological tissue followed by "sympathetic" processing into an acrylic resin. Processing regimens do not have to be complicated. Simple and cost effective room temperature protocols utilising partial dehydration have been devised and they can be as effective as the more complex low temperature techniques in preserving both ultrastructure and antigenic reactivity. The embedded material can be investigated by either light or electron microscopy. Frozen sections can be cut and immunolabelled but only if the tissue is chemically fixed first, as in resin embedding. Fixation with low concentrations of aldehyde will normally better preserve tissue immunoreactivity but this may be at the expense of good ultrastructure with these protocols. If so, low temperature resin embedding methods or rapid freezing and cryosubstitution can be tried. The choice of processing protocol will determine which acrylic resin to use, as will the preference for subsequent immunolabelling with either colloidal gold or peroxidase/diaminobenzidine (DAB). Both types of labelling system offer advantages to localisation studies and can be used in combination for double or even triple labelling. Silver enhancement of the colloidal gold or DAB allows for improved observation by light microscopy.