The generalised vector dominance/colour-dipole picture of deep-inelastic scattering at low x

We give a detailed account of the recently formulated generalised vector dominance/colour-dipole picture (GVD/CDP) of deep-inelastic scattering at low , including photoproduction. The approach, based on transitions, propagation and diffractive scattering via the generic structure of the two-gluon exchange, provides a unique and quantitatively successful theory for the total cross section, , at low x. The GVD/CDP is shown to imply the empirical low-x scaling law, with , that was established by a model-independent analysis of the experimental data. Received: 16 February 2001 / Published online: 3 May 2001     

Dual bounding procedures lead to convergent Branch–and–Bound algorithms

Branch–and–Bound methods with dual bounding procedures have recently been used to solve several continuous global optimization problems. We improve results on their convergence theory and give a condition that enables us to detect infeasible partition sets from the dual optimal value. Received: May 5, 1999 / Accepted: April 19, 2001?Published online September 17, 2001     

On Copositive Programming and Standard Quadratic Optimization Problems

A standard quadratic problem consists of finding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semidefinite programming relaxation is strengthened by replacing the cone of positive semidefinite matrices by the cone of completely positive matrices (the positive semidefinite matrices which allow a factorization FF ^T where F is some non-negative matrix). The dual of this cone is the cone of copositive matrices (i.e., those matrices which yield a non-negative quadratic form on the positive orthant). This conic formulation allows us to employ primal-dual affine-scaling directions. Furthermore, these approaches are combined with an evolutionary dynamics algorithm which generates primal-feasible paths along which the objective is monotonically improved until a local solution is reached. In particular, the primal-dual affine scaling directions are used to escape from local maxima encountered during the evolutionary dynamics phase.     

Determination of the cubic to hexagonal structure transition in the metastable system TiN-AlN

Structural transitions of metastable Ti_1–xAl_xN coatings on technically relevant substrates were determined as a function of the Ti/Al ratio. Ti_1–xAl_xN films with different Ti/Al ratios were deposited on high speed steel (HSS) substrates at substrate temperatures of 300?° and 500?°C by means of reactive magnetron sputtering ion plating (MSIP). A Ti/Al compound target was used as well as a cluster arrangement of one Ti and one Al target for comparison. The composition of the films was determined by electron probe microanalysis (EPMA), the crystallographic structure by thin film X-ray diffraction (XRD). The analyses revealed that films deposited with Ti/Al ratios of 44/56 and 36/64 had grown in cubic NaCl structure, a film with a Ti/Al ratio of 32/68 was two-phase, and a Ti/Al ratio of 25/75 led to a hexagonal film in wurtzite structure. Only small differences of the lattice parameters could be observed in dependence of temperature: At 300?°C the lattice parameters of the cubic structure corresponded exactly to Vegard‘s law, whereas they slightly decreased in the films deposited at 500?°C. The application of a cluster arrangement instead of a compound target resulted in nearly the same lattice parameters and peak shapes.     

Universal area product formulas for rotating and charged black holes in four and higher dimensions

We present explicit results for the product of all horizon areas for general rotating multicharge black holes, both in asymptotically flat and asymptotically anti-de Sitter spacetimes in four and higher dimensions. The expressions are universal, and depend only on the quantized charges, quantized angular momenta and the cosmological constant. If the latter is also quantized these universal results may provide a "looking glass" for probing the microscopics of general black holes.     

Direct enantioselective access to 4-substituted tetrahydroquinolines by catalytic asymmetric transfer hydrogenation of quinolines

A convenient protocol for the enantioselective synthesis of 4-substituted tetrahydroquinolines has been developed. Chiral BINOL phosphoric acids promote the reduction of a wide range of 4-substituted quinolines with Hantzsch esters with good to high levels of enantioselectivity.     

Practical estimation of the uncertainty of analytical measurement standards

Nowadays, a lot of time and resources are used to determine the quality of goods and services. As a consequence, the quality of measurements themselves, e.g., the metrological traceability of the measured quantity values is essential to allow a proper evaluation of the results with regard to specifications and regulatory limits. This requires knowledge of the measurement uncertainties of all quantity values involved in the measurement procedure, including measurement standards. This study shows how the uncertainties due to the preparation, as well as the chemical and compositional stability of a chemical measurement standard, or calibrator, can be estimated. The results show that the relative standard uncertainty of the concentration value of a typical analytical measurement standard runs up to 2.8% after 1 year. Of this, 1.9% originates from the preparation of the measurement standard, while 2.0 and 0.53% originate from the chemical and compositional stability during storage at −20 °C. The monthly preparation of working calibrators stored at 4 °C and used on a weekly basis, results in an additional standard uncertainty of the analyte concentration value of 0.35% per month due to compositional stability. While the preparation procedure is the major contributor to the total measurement uncertainty, the uncertainties introduced by the stability measurements are another important contributor, and therefore, the measurement procedure to evaluate stability is important to minimize the total measurement uncertainty.