A multi-step reaction model for ignition of fully-dense Al-CuO nanocomposite powders

A multi-step reaction model is developed to describe heterogeneous processes occurring upon heating of an Al-CuO nanocomposite material prepared by arrested reactive milling. The reaction model couples a previously derived Cabrera-Mott oxidation mechanism describing initial, low temperature processes and an aluminium oxidation model including formation of different alumina polymorphs at increased film thicknesses and higher temperatures. The reaction model is tuned using traces measured by differential scanning calorimetry. Ignition is studied for thin powder layers and individual particles using respectively the heated filament (heating rates of 10³–10⁴ K s^?1) and laser ignition (heating rate ～10⁶ K s^?1) experiments. The developed heterogeneous reaction model predicts a sharp temperature increase, which can be associated with ignition when the laser power approaches the experimental ignition threshold. In experiments, particles ignited by the laser beam are observed to explode, indicating a substantial gas release accompanying ignition. For the heated filament experiments, the model predicts exothermic reactions at the temperatures, at which ignition is observed experimentally; however, strong thermal contact between the metal filament and powder prevents the model from predicting the thermal runaway. It is suggested that oxygen gas release from decomposing CuO, as observed from particles exploding upon ignition in the laser beam, disrupts the thermal contact of the powder and filament; this phenomenon must be included in the filament ignition model to enable prediction of the temperature runaway.     

Regulation of catalytic behaviour of hydrolases through interactions with functionalized carbon-based nanomaterials

The interaction of enzymes with carbon-based nanomaterials (CBNs) is crucial for the function of biomolecules and therefore for the design and development of effective nanobiocatalytic systems. In this study, the effect of functionalized CBNs, such as graphene oxide (GO) and multi-wall carbon nanotubes (CNTs), on the catalytic behaviour of various hydrolases of biotechnological interest was monitored and the interactions between CBNs and proteins were investigated. The enzyme–nanomaterial interactions significantly affect the catalytic behaviour of enzymes, resulting in an increase up to 60 % of the catalytic efficiency of lipases and a decrease up to 30 % of the esterase. Moreover, the use of CNTs and GO derivatives, especially those that are amine-functionalized, led to increased thermal stability of most the hydrolases tested. Fluorescence and circular dichroism studies indicated that the altered catalytic behaviour of enzymes in the presence of CBNs arises from specific enzyme–nanomaterial interactions, which can lead to significant conformational changes. In the case of lipases, the conformational changes led to a more active and rigid structure, while in the case of esterases this led to destabilization and unfolding. Kinetic and spectroscopic studies indicated that the extent of the interactions between CBNs and hydrolases can be mainly controlled by the functionalization of nanomaterials than by their geometry.     

Series and product representations for some mathematical constants

We present several series and product representations for γ, π, and other mathematical constants. One of our results states that, for all real numbers μ s>0, we have

Site‐Selective C−H Oxygenation via Aryl Sulfonium Salts

Herein, we report a two‐step process forming arene C?O bonds in excellent site‐selectivity at a late‐stage. The C?O bond formation is achieved by selective introduction of a thianthrenium group, which is then converted into C?O bonds using photoredox chemistry. Electron‐rich, ‐poor and ‐neutral arenes as well as complex drug‐like small molecules are successfully transformed into both phenols and various ethers. The sequence differs conceptually from all previous arene oxygenation reactions in that oxygen functionality can be incorporated into complex small molecules at a late stage site‐selectively, which has not been shown via aryl halides.     

Inequalities for E k(X,Y) when the marginals are fixed

When k(x, y) is a quasi-monotone function and the random variables X and Y have fixed distributions, it is shown under some further mild conditions that k(X, Y) is a monotone functional of the joint distribution function of X and Y. Its infimum and supremum are both attained and correspond to explicitly described joint distribution functions.Research supported by the Air Force Office of Scientific Research under Grant AFOSR-75-2796Research supported by the National Science Foundation     

On the Partial Sums of a Fourier Series

We give sharp lower estimates for the partial sums of the Fourier series

Stable processes: moving averages versus fourier transforms

Summary We study the relationship between Fourier transforms and moving averages of stable processes. The two classes have a large intersection, however as soon as the noise is required to be bounded they become disjoint.Research supported by the Air Force Office of Scientific Research Contract No. F49620 85C 0144 and by the Office of Naval Research Grant No. N00014 86C 0227This work was done in part when the author was visiting the Center for Computational Statistics, George Mason University, Fairfax, VA 22030-4444     

Remarks on some completely monotonic functions

Applying the Euler-Maclaurin summation formula, we obtain upper and lower polynomial bounds for the function , x>0, with coefficients the Bernoulli numbers Bk. This enables us to give simpler proofs of some results of H. Alzer and F. Qi et al., concerning complete monotonicity of certain functions involving the gamma function Γ(x), the psi function ψ(x) and the polygamma functions ψ(n)(x), n=1,2,… .