Lie symmetries and CR geometry

This paper is divided into three parts. Part I develops a general, new theory (inspired by modern CR geometry) of Lie symmetries of completely integrable pde systems, viewed from their associated submanifolds of solutions. Part II constructs general combinatorial formulas for the prolongations of vector fields to jet spaces. Part III explicitly characterizes the flatness of some systems of the second order. The results presented here are original and were not published elsewhere; most formulas of Parts II and III were verified by means of Maple Release 7. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 47, Complex Analysis, 2007.     

Locating seam minima for macromolecular systems

The performance of three different functions (penalty, Lagrange–Newton, and projection) used in combination with three different Newton-based optimization algorithms for solving large-scale constrained optimizations is investigated. The test cases correspond to locating minima on seams between two force field energy functions, which can be used to model transitions structures in chemical reactions. The Lagrange–Newton function used in combination with a standard Newton–Raphson optimization is found to be the most efficient for systems up to ～500 atoms, while an iterative algorithm becomes preferable for larger systems.     

Mössbauer study of amorphous and crystallized Fe1-xCx alloys

Fe_1?xC_x amorphous alloys have been studied with Mössbauer Spectroscopy for 0.19<-x<-0.31. For x>-0.286, new carbides are formed by crystallization of such alloys. The chemical twinning model allows describing their structures.     

Effect of particle size on carburization of Fe-Co alloy catalysts

Bimetallic Fe-Co alloy catalysts supported on silica have been studied by use of combined Mössbauer absorption and emisson spectroscopy. Effects of carburization on samples with different particle size are discussed.     

Optical properties of TiN1-x single crystals

The reflectance spectra of TiN_1–x single crystals were measured at room temperature. The chemical composition of the crystals was varied between TiN_1–0.00 and TiN_1–0.43. The experimental data are analyzed on the basis of a Lorentz-Drude model in order to determine the influence of nitrogen vacancies on the electrical conductivity, on the carrier concentration, and on the collision time.     

Geometry of random sequential adsorption

By sequentially adding line segments to a line or disks to a surface at random positions without overlaps, we obtain configurations of the one- and two-dimensional random sequential adsorption (RSA) problem. We have simulated the one- and two-dimensional problem with periodic boundary condition. The one-dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation. In two dimensions the geometrical properties of the RSA configuration are discussed and in addition known results of the RSA process are reproduced. Various statistical distributions of the Voronoi-Dirichlet (VD) network corresponding to the RSA disk configuration are analyzed. In order to characterize pores in the RSA configuration, we introduce circular holes. There is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and these holes. The hole size distribution is found to be a parabola. We also find general relations that connect the asymptotic behavior of the surface coverage, the correlation function, and the hole size distribution.     

Reaction of naphthalene‐2,3‐dicarbaldehyde with cyanide; A unique oxidative condensation product

Naphthalene‐2,3‐dicarbaldehyde (NDA), a reagent used for the fluorescent detection of amino acids in the presence of cyanide, self‐condenses in the presence of cyanide ion and methanol at room temperature to yield a unique crystalline product 2, 15‐hydroxybenzo[g]benzo[6,7]isochromeno[4,3‐c]isochromen‐7(15H)‐one. The product is proposed to result from facile air oxidation of NDA to a methyl ester in combination with benzoin condensation. Product 2 does not to form in the absence of air. The gHMBC spectrum of 2 distinguishes it from a possible alternative isomeric condensation product.     

Internet protocol network design with uncertain demand

We present a case study concerning the design and dimensioning of the internet protocol network of TDC, the largest Danish network operator. Due to historical reasons the number of points of presence (POPs) in the network has reached a level, believed to be too high. To point out potential POPs for dismantling, we consider a network planning problem concerning dimensioning of the POPs and capacity expansion of the transmission links of the network. This problem is formulated as a two-stage stochastic program using a finite number of scenarios to describe the uncertain outcome of future demand. The problem is then solved by an L-shaped algorithm, and we report results of our computational experiments.