The activity of cobalt aluminum catalyst in reaction of nitrous oxide decomposition

Data of activity of cobalt aluminum catalysts with various content of active component in reaction of nitrous oxide decomposition obtained both on laboratory equipment and model catalytic reactor are presented.     

Local rules for quasiperiodic tilings of quadratic 2-planes inR 4

We prove that quasiperiodic tilings of the plane, appearing in the strip projection method always admit local rules, when the linear embedding ofR ² inR ⁴ has quadratic coefficients. These local rules are constructed and studied. The connection between Novikov quasicrystallographic groups and the quasiperiodic tilings of Euclidean space is explained. All the point groups in Novikov's sense, compatible with these local rules, are enlisted. The two-dimensional quasicrystals with infinite-fold rotational symmetry are constructed and studied.Address after September 1, 1992: Dept. of Physics, Harvard University, Cambridge, MA 02138, USA     

Mathematical Model of Ice Melting on Transmission Lines

During ice storms, ice forms on high voltage electrical lines. This ice formation often results in downed lines and has been responsible for considerable damage to life and property as was evidenced in the catastrophic ice storm of Quebec recently. There are two main aspects, viz., the formation of ice and its timely mitigation. In this paper, we mathematically model the melting of ice due to a higher current applied to the transmission wire. The two dimensional cross-section contains four layers consisting of the transmission wire, water due to melting of ice, ice, and the atmosphere. The model includes heat equations for the various regions with suitable boundary conditions. Heat propagation and ice melting are expressed as a Stefan-like problem for the moving boundary between the layers of ice and water. The model takes into account gravity which leads to downward motion of ice and to forced convection of heat in the water layer. In this paper, the results are applied to the case when the cross-sections are concentric circles to yield melting times for ice dependent on the increase in intensity of the electrical flow in the line. This research has been supported in part by Manitoba Hydro and NSERC.     

A Logarithmic Inequality

Mathematical Notes - The inequality $$\ln {\kern 1pt} \ln \left( {r - \ln r} \right) + 1 < \mathop {\min }\limits_{0 < x \leqslant r - 1} \left( {\ln x + {x^{ - 1}}\ln \left( {r - x}...     

On Shallit’s Minimization Problem

Mathematical Notes - In Shallit’s problem (SIAM Review, 1994), it was proposed to justify a two-term asymptotics of the minimum of a rational function of $$n$$ variables defined as the sum of...     

Characterization of Carleson measures by the Hausdorff-Young property

It is shown that the Laplace transform of an L ^p (1 < p ≤ 2) function defined on the positive semiaxis satisfies the Hausdorff-Young type inequality with a positive weight in the right complex half-plane if and only if the weight is a Carleson measure. In addition, Carleson’s weighted L ^p inequality for the harmonic extension is given with a numeric constant.     

Width of parametric resonance regions for equations on a torus

We present new proofs of the theorem on the width of the forbidden regions for the Hill equation with a small potential and the theorem on the width of the parametric resonance regions for a first-order differential equation on a torus. These results are special cases of the theorem proved in this paper by the normal form method.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 129–135, July, 1998.The author wishes to thank M. F. Kondrat'eva, V. V. Sidorenko, and the referee for useful remarks.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01411.