Isolated rational curves on K3-fibered Calabi–Yau threefolds

In this paper we study 16 complete intersection K3-fibered Calabi--Yau variety types in biprojective space ℙ ^{n 1}}×ℙ¹. These are all the CICY-types that are K3 fibered by the projection on the second factor. We prove existence of isolated rational curves of bidegree (d,0) for every positive integer d on a general Calabi–Yau variety of these types. The proof depends heavily on existence theorems for curves on K3-surfaces proved by S. Mori and K. Oguiso. Some of these varieties are related to Calabi–Yau varieties in projective space by a determinantal contraction, and we use this to prove existence of rational curves of every degree for a general Calabi–Yau variety in projective space. Received: 14 October 1997 / Revised version: 18 January 1998     

Some Methods for Calculating Stiffness Properties of Periodic Structures

We present a general numerical method for calculating effective elastic properties of periodic structures based on the homogenization method. Some concrete numerical examples are presented.     

An algorithm for large scale 0–1 integer programming with application to airline crew scheduling

We present an approximation algorithm for solving large 0–1 integer programming problems whereA is 0–1 and whereb is integer. The method can be viewed as a dual coordinate search for solving the LP-relaxation, reformulated as an unconstrained nonlinear problem, and an approximation scheme working together with this method. The approximation scheme works by adjusting the costs as little as possible so that the new problem has an integer solution. The degree of approximation is determined by a parameter, and for different levels of approximation the resulting algorithm can be interpreted in terms of linear programming, dynamic programming, and as a greedy algorithm. The algorithm is used in the CARMEN system for airline crew scheduling used by several major airlines, and we show that the algorithm performs well for large set covering problems, in comparison to the CPLEX system, in terms of both time and quality. We also present results on some well known difficult set covering problems that have appeared in the literature.     

Calamitic bolaamphiphiles with (semi)perfluorinated lateral chains: polyphilic block molecules with new liquid crystalline phase structures

Novel bolaamphiphiles consisting of a rigid biphenyl unit, two terminal polar 1,2-diol units and laterally attached (semi)perfluorinated chains have been synthesized via palladium-catalyzed cross coupling reactions as the key step. The thermotropic liquid crystalline behavior of these compounds was investigated by polarized light optical microscopy, DSC, and X-ray scattering, and the influences of the length, number, structure, and position of the lateral chain on the mesomorphic properties were studied. A wide variety of unique liquid crystalline phases were found upon elongation of the lateral semiperfluorinated chains. For short- and medium-chain length a series of columnar phases were observed, and upon further elongation of the lateral chain a series of novel mesophases with layer structures were found. In the columnar phases, the nonpolar lateral chains segregate into columns, which are embedded in honeycomb-like networks of cylinders consisting of the biphenyl units. Strings of hydrogen-bonding networks of the diol groups provide cohesive forces, which maintain the overall structure. Changing the length of the lateral chains influences the diameter of the columns and thus determines the number of biphenyl units which are required to surround these columns. The number of these units [four (c2mm, p4mm), five (p2gg), six (p6mm), eight (c2mm) or 10 (p2gg)] defines the shape of the cylinders as well as the lattice type of the columnar phase. It is proposed that the columnar phases with a p2gg lattice result from the regular organization of pairs of cylinders which have a pentagonal cross sectional shape. In the mesophases with layer structure the aromatic rodlike cores are arranged parallel to the layer planes, and the onset of orientational and positional ordering of the biphenyl segments leads to a sequence of subtypes for these lamellar phases (Lam(Iso)-Lam(N)-Lam(X)).     

Bonding and stability of the hydrogen storage material Mg(2)NiH(4)

Structural stability and bonding properties of the hydrogen storage material Mg(2)NiH(4) (monoclinic, C2/c, Z = 8) were investigated and compared to those of Ba(2)PdH(4) (orthorhombic, Pnma, Z = 8) using ab initio density functional calculations. Both compounds belong to the family of complex transition metal hydrides. Their crystal structures contain discrete tetrahedral 18 electron complexes T(0)H(4)(4-) (T = Ni, Pd). However, the bonding situation in the two systems was found to be quite different. For Ba(2)PdH(4), the electronic density of states mirrors perfectly the molecular states of the complex PdH(4)(4-), whereas for Mg(2)NiH(4) a clear relation between molecular states of TH(4)(4-) and the density of states of the solid-state compound is missing. Differences in bonding of Ba(2)PdH(4) and Mg(2)NiH(4) originate in the different strength of the T-H interactions (Pd[bond]H interactions are considerably stronger than Ni[bond]H ones) and in the different strength of the interaction between the alkaline-earth metal component and H (Ba[bond]H interactions are substantially weaker than Mg[bond]H ones). To lower the hydrogen desorption temperature of Mg(2)NiH(4), it is suggested to destabilize this compound by introducing defects in the counterion matrix surrounding the tetrahedral Ni(0)H(4)(4-) complexes. This might be achieved by substituting Mg for Al.     

Neutron-activation determination of vanadium in oils and catalysts

Summary Vanadium in crude and residual oils and in catalysts at the concentration levels of 0.2–200 and 400–2000 ppm respectively has been determined by means of neutron-activation analysis based on measurement of the nuclide⁵²V. The aim was to apply the technique to industrial or general routine analysis. Four samples were analysed simultaneously in less than 15 minutes.

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Zusammenfassung In Rohöl, Rückstandöl und in Katalysatoren wurde Vanadin in Konzentrationen von 0,2 bis 200 bzw. 400 bis 2000 ppm mit Hilfe der Neutronenaktivierungsanalyse bestimmt, indem das Nuklid⁵²V gemessen wurde. Die Absicht war, dieses Verfahren für industrielle Routineanalysen anzuwenden. In weniger als 15 Minuten lassen sich gleichzeitig vier Proben analysieren.

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Work supported under the International Atomic Energy Agency (IAEA) Technical Assistance Programme.     

Structures and thermochemistry of ions formed by methane chemical ionization of Fe(CO)5. Site of protonation and determination of Fe?H and Fe?CO bond dissociation energies of HFe(CO)n+ ions

High-energy collisional activation mass spectrometry of HFe(CO)₅⁺ ions shows that Fe(CO)₅ is protonated on the iron atom rather than on one of the ligands. This finding is supported by ab initio quantum chemical calculations. The value of the proton affinity of Fe(CO)₅ was measured by high-pressure mass spectrometry to be 857 kJ mol^?1. The Fe? CO bond dissociation energies for HFe(CO)_n⁺ (n = 1–5) were measured by energy-variable low-energy collisional activation mass spectrometry. The Fe? H bond dissociation energies in HFe(CO)_n⁺ ions were also determined. A synergistic effect on the strengths of the Fe? H and Fe? CO bonds in HFe(CO)⁺ is noticed. It is demonstrated that the electronically unsaturated species HFe(CO)_n⁺ (n = 3, 4) formed in exothermic proton-transfer reactions with Fe(CO)₅ form adducts with CH₄. Adducts between C₂H₅⁺ or C₃H₅⁺ and Fe(CO)_n are observed. These adducts are probably formed in direct reactions between the respective carbocations and Fe(CO)₅.