On the Curvature of the Central Path of Linear Programming Theory

We prove a linear bound on the average total curvature of the central path of linear programming theory in terms of the number of independent variables of the primal problem, and independent of the number of constraints.     

The effect of hydrogen adsorption on the electronic structure of gold nanoparticles

It has been demonstrated that hydrogen adsorption has an effect on the electronic structure of gold nanoparticles. The physicochemical properties of separate gold nanoparticles have been studied under an ultrahigh vacuum scanning tunneling microscope. The structure and electronic structure of gold–hydrogen clusters were modeled by the quantum-chemical density functional theory method. Hydrogen adsorption onto gold nanoparticles 4–5 nm is size at room temperature was experimentally revealed, and the lower limit of 1.7 eV for the Au–H bond energy was determined. The interaction of hydrogen with gold leads to a considerable rearrangement of the electronic subsystem of nanoparticles. The experimentally observed effects were supported by quantum-chemical calculations. The rearrangement mechanism is related to strong correlations in the electronic subsystem.     

Molecular nitrogen adsorption on individual platinum and titanium nanoclusters

Molecular nitrogen adsorption on single platinum and titanium nanoclusters is investigated by scanning tunneling microscopy and spectroscopy, including the use of an inverse scheme of spectroscopic measurements. Some regularities of the occurring processes are found.     

Tunneling spectroscopy of single electron spin

The possibility of detection of the electron spin of a single paramagnetic species (an atom, a radical, or an ion) on the surface was discussed. The analysis was based on spin chemistry laws taking into account the statistics of the spin states of both the tunneling electron and paramagnetic center. The equations for the tunneling current as a function of temperature and magnetic field strength were derived. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1732–1734, September, 1998.     

Ammonia decomposition on a platinum nanocoating at various electric potentials

It was shown that the rate of ammonia decomposition on a platinum nanocoating can be controlled by applying an external electrostatic field to the coating to create a negative or positive platinum potential of variable magnitude. In experiments conducted with a contact time of 15 min between platinum and ammonia at a temperature of 700 K and a pressure of 5 × 10^–7 Torr, the decomposition rate increased by 44% at a negative potential of the coating of–6 V and by 70% at a positive potential of +6 V.     

Newton's method on Riemannian manifolds and a geometric model for the human spine

To study a geometric model of the human spine we are led tofinding a constrained minimum of a real valued function definedon a product of special orthogonal groups. To take advantgeof its Lie group structure we consider Newton's method on thismanifold. Comparisons between measured spines and computed spinesshow the pertinence of this approach.     

Determination of the thermal desorption kinetic parameters for samples with a temperature gradient

An application of the thermal desorption technique to the study of desorption from the samples with a temperature gradient is discussed. The kinetics of first- and second-order desorption from linearly and exponentially heated samples with a parabolic temperature profile is considered. It is shown that the low-temperature part of the thermal desorption curve is described by the same equations as those for the desorption from the nongradient surface with the less effective area and with the temperature equal to that at the center of the nonuniformly heated sample. The approximate analytical expressions for the amount of adsorbed surface species as a function of time are derived. These expressions enable to find the kinetics order, the activation energy E and the preexponential factor k₀ for the desorption process from thermal desorption spectra. In a first approximation the corrections for the nonuniformity of the sample temperature do not substantially change the value of E but slightly increase the value of k₀. The correction procedure for k₀ is described in detail. The possible application of the proposed method to various experimental conditions is discussed.