Inclusive spectra of electroproduced K+ mesons

We report measurements of kaon electroproduction from a hydrogen target carried out at DESY. The invariant cross section for the reaction ep → eK⁺ + anything is given as a function of the variables q², W, x, p²_⊥ and φ in the following region:

$\text{?0.5 ? q}{}^2\text{? ?0.1 GEV}{}^2\text{, 2.0 ? W ? 2.8 GEV, 0.3 ? x ? ? 1.0, p}{}^2{}_{\mathrm{\perp }}\text{? 0.25 GEV}{}^2\text{, 0° ? ø ? 360°}$

. Finally we compare our data with a quark-parton model.     

Two results in metric fixed point theory

We establish two fixed point theorems for certain mappings of contractive type. The first result is concerned with the case where such mappings take a nonempty, closed subset of a complete metric space X into X, and the second with an application of the continuation method to the case where they satisfy the Leray–Schauder boundary condition in Banach spaces.     

LBB stability of a mixed Galerkin finite element pair for fluid flow simulations

We introduce a new mixed finite element for solving the 2- and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as $\text{P}{1}_{\text{D}}''–''\text{P}2$, uses discontinuous piecewise linear functions for velocity and continuous piecewise quadratic functions for pressure. The aim of introducing the mixed formulation is to produce a new flexible element choice for triangular and tetrahedral meshes which satisfies the LBB stability condition and hence has no spurious zero-energy modes. The advantage of this particular element choice is that the mass matrix for velocity is block diagonal so it can be trivially inverted; it also allows the order of the pressure to be increased to quadratic whilst maintaining LBB stability which has benefits in geophysical applications with Coriolis forces. We give a normal mode analysis of the semi-discrete wave equation in one dimension which shows that the element pair is stable, and demonstrate that the element is stable with numerical integrations of the wave equation in two dimensions, an analysis of the resultant discrete Laplace operator in two and three dimensions on various meshes which shows that the element pair does not have any spurious modes. We provide convergence tests for the element pair which confirm that the element is stable since the convergence rate of the numerical solution is quadratic.     

Präkompakte gruppen und fastperiodizität

Ohne ZusammenfassungDiese Arbeit wurde von der Deutschen Forschungsgemeinschaft unterstützt.     

Recognizing chromatographic peaks with pattern recognition methods : Part 2. Evaluation of different distance measures

The proposed method for the recognition of peaks in a chromatogram is based on the k-nearest neighbour (KNN) algorithm, in which the chromatogram is compared with a predefined peak profile. A critical part of the KNN algorithm is the selection of the distance measure used to calculate the similarity between points in the pattern space. Here, five different distance functions are evaluated. In addition to the euclidian distance, which was used in the initial tests of the algorithm, the correlation coefficient, the cross-correlation, and the angle between two vectors and its cosine are tested. All these distance measures show satisfactory behaviour. Their different characteristics are discussed.