Pharmazeutische Pr?parate

Ohne Zusammenfassung     

Ueber Bestimmung der Eiweissstoffe und nicht eiweissartigen Stickstoffverbindungen in Futtermitteln

Ohne Zusammenfassung     

Zur Analyse der Legirungen

Ohne Zusammenfassung     

Note on the computational complexity ofj-radii of polytopes in ℝ n

We show that, for fixed dimensionn, the approximation of inner and outerj-radii of polytopes in ℝ ⁿ , endowed with the Euclidean norm, is in ℙ. Our method is based on the standard polynomial time algorithms for solving a system of polynomial inequalities over the reals in fixed dimension.     

Submodular linear programs on forests

A general linear programming model for an order-theoretic analysis of both Edmonds' greedy algorithm for matroids and the NW-corner rule for transportation problems with Monge costs is introduced. This approach includes the model of Queyranne, Spieksma and Tardella (1993) as a special case. We solve the problem by optimal greedy algorithms for rooted forests as underlying structures. Other solvable cases are also discussed.     

On the feasibility of heat-exchange processes in uninsulated equipment

Strictly speaking, the common two-fluid heat exchanger is a special version of a three-fluid exchanger because the environment also participates in the energy exchange. In a number of situations this effect is significant and leads to either reduced or increased area requirements, depending on the purpose of the exchange operation. With certain combinations of the system parameters it is even impossible to achieve an envisaged temperature change. For some typical flow arrangements these combinations are established in an analytic form so that one can rapidly assess the feasibility of a desired process without actually performing the rather tedious design calculations.     

Multiply periodic real functions and their period sets

Multiply periodic real functions are rather pathological; continuous ones have to be constant and, as will be shown, measurable ones must be constant a.e. Beyond this, some other properties of these functions are discussed, and examples are given. Since the set of periods of a real function is a subgroup of (R,+), it is possible to apply algebraic methods to get a better survey. It will be shown that the homogeneous sets defined by Borel are just cosets of these subgroups; this leads to a transfer of theorems about homogeneous sets to results about period sets (and, at the same time, subgroups of (R,+)).     

High-resolution electron microscopy of polyethylene and paraffin crystals: Stability in the electron beam

Uncollapsed polyethylene pyramids (200–1500 Å) in length are irradiated with the electron beam of a 100-kV transmission electron microscope. Their high stability is remarkable compared to the stability of 1–10 μm crystals collapsed on the substrate, usually taken as a reference. Therefore, the maximum magnifications (300,000–750,000 X) of the microscope can be used and high-resolution images can be obtained. No lattice defects can be detected in the images of PE pyramids. Irradiation with D_c > 800 C/m² induces the orthorhombic → hexagonal transition, and slight lattice distortions appear in the high-resolution image of the hexagonal phase. For an irradiation dose D_c ≈ 2400 C/M², the diffraction pattern disappears. Normal C₃₆ orthorhombic and monoclinic paraffins have the same stability as orthorhombic PE and high-resolution patterns are obtained. These exceptional stabilities are discussed in detail. From the diffraction pattern of these uncollapsed pyramids, the fold surfaces of PE pyramids have been indexed as the {111} and paracrystalline distortions in the orthorhombic PE have been measured at low irradiation dose. Along the a and b axes g is ca. 5% and along the chain axis c it is ca. 17%; these values agree with the previous x-ray determinations of PE crystallized from the melt. The large difference between these two distortion factors may be interpreted in terms of packing.