Transportation problems which can be solved by the use of hirsch-paths for the dual problems

Balinski uses his signature method for the proof of the Hirsch-conjecture for dual transportation polyhedra to obtain an efficient algorithm for the assignment problem. We will show how to extend this method to other primal transportation problems, including transportation problems with unit demands. We then prove that Balinski's assignment algorithm is equivalent, cycle by cycle, to that of Hung and Rom. We demonstrate that, under some assumptions for our probability model, a modification of the latter algorithm has an average complexity of O(n ²logn) and present some computational results confirming this. We also present results that indicate that this modification compares favorably with Balinski's algorithm and other codes. Research of both authors supported, in part, by grants of the Alexander von Humboldt-Stiftung. Supported, in part, by NSF grant DMS-8504050.     

The degenerate C. Neumann system I: symmetry reduction and convexity

The C. Neumann system describes a particle on the sphere S ⁿ under the influence of a potential that is a quadratic form. We study the case that the quadratic form has ℓ +1 distinct eigenvalues with multiplicity. Each group of m _σ equal eigenvalues gives rise to an O(m _σ )-symmetry in configuration space. The combined symmetry group G is a direct product of ℓ + 1 such factors, and its cotangent lift has an Ad*-equivariant momentum mapping. Regular reduction leads to the Rosochatius system on S ^ℓ , which has the same form as the Neumann system albeit for an additional effective potential.     

Self-adjoint Analytic Operator Functions: Local Spectral Function and Inner Linearization

In this note we continue the study of spectral properties of a self-adjoint analytic operator function A(z) that was started in [5]. It is shown that if A(z) satisfies the Virozub–Matsaev condition on some interval Δ₀ and is boundedly invertible in the endpoints of Δ₀, then the ‘embedding’ of the original Hilbert space into the Hilbert space , where the linearization of A(z) acts, is in fact an isomorphism between a subspace of and . As a consequence, properties of the local spectral function of A(z) on Δ₀ and a so-called inner linearization of the operator function A(z) in the subspace are established.      

Decay studies of K isomers in 254No

A detailed $ \gamma$ spectroscopic decay study of two K isomers in ²⁵⁴No was performed. In addition to the previously reported $ \gamma$ lines two new transitions of E = 778 , 856keV could be attributed to the decay pattern of ^254m1No ( T _1/2 = 275±7 ms). The population of an excited band built up on this isomer ( $\ensuremath K^{\pi} =8^{-}$ by the decay of ^254m2No ( T _1/2 = 198±13 μs) could be proven by measuring delayed $ \gamma$ - $ \gamma$ coincidences between transitions stemming from the decay of both isomeric states. The energies of the band members could be established up to $\ensuremath I^{\pi} = 15^{-}$ . A spontaneous fission branch of (2.0±1.2)×10^-4 was measured for ^254m1No , an upper limit of $ \le$ 1.2×10^-4 was estimated for ^254m2No . These values demonstrate the high stability of multi-quasiparticle configurations against spontaneous fission. Evidence for an $ \alpha$ decay branch of ^254m1No in the order of 1×10^-4 was found.     

Thermodynamic assessment of Hg(II)-gibbsite interactions

As discrete particles and/or as surface coatings on other minerals in natural systems, aluminum hydroxides are efficient sinks for Hg(II). The Hg(II) adsorption on gibbsite was determined as a function of temperature (T), pH, and the type of background electrolytes, i.e., NaNO(3), NaClO(4), and NaCl. When the equilibration time t(E) approximately 2 h, the Hg(II) retention on gibbsite was found to be a reversible process, which was ascribed to adsorption. The Hg(II) adsorption capacity, i.e., Gamma(Hg(II)), varied with the type of electrolyte used in accordance with the following order: Gamma(NO(3))(Hg(II)) > or = Gamma(ClO(4))(Hg(II)) > or = Gamma(Cl)(Hg(II)). In all cases, the estimated thermodynamic parameters showed that the Hg(II) adsorption on gibbsite was endothermic and spontaneous. The Hg(II) adsorption data were quantified with the Langmuir or Hill, and Dublin-Radushkevick (DR), isotherms at all temperatures and acidity levels examined. Always, the Hg(II) adsorption data were in compliance with the DR model. However, the Hg(II) adsorption in NaNO(3) or NaClO(4) was interpreted in terms of the Langmuir model. When NaCl was used as electrolyte, the Hg(II) adsorption was modeled well with the Hill equation. The mean free energy values calculated from DR plots concluded that Hg(II)-gibbsite interactions are a result of chemical bonding.     

Nickel(II)-komplexe des unsubstituierten cyclobutadiens

cis- and trans-3,4-Dichlorocyclobutene (I) react with Ni(CO)₄ and AlCl₃ to give (C₄H₄)NiCl₂ · AlCl₃ (II), while the bromo- and iodo-substituted cyclobutenes (III) without AlCl₃ yield the complexes (C₄H₄)NiX₂ (IVa, X  Br; IVb, X  I). Properties of II and IV are discussed and the presence of a C₄H₄ ring attached to nickel is likely from the results obtained.     

Top-down patterning of zeolitic imidazolate framework composite thin films by deep X-ray lithography

For the first time a top-down process was used to control the spatial location of Metal-Organic Frameworks on a surface. Deep X-ray lithography was utilised to micropattern a Zeolitic Imidazolate Framework layer on a sol-gel surface, with exposure hardening the sol-gel by inducing crosslinking while leaving the frameworks intact.     

Epothilone Analogues with Benzimidazole and Quinoline Side Chains: Chemical Synthesis,Antiproliferative Activity,and Interactions with Tubulin

A series of epothilone B and D analogues bearing isomeric quinoline or functionalized benzimidazole side chains has been prepared by chemical synthesis in a highly convergent manner. All analogues have been found to interact with the tubulin/microtubule system and to inhibit human cancer cell proliferation in vitro, albeit with different potencies (IC₅₀ values between 1 and 150 nM ). The affinity of quinoline‐based epothilone B and D analogues for stabilized microtubules clearly depends on the position of the N‐atom in the quinoline system, while the induction of tubulin polymerization in vitro appears to be less sensitive to N‐positioning. The potent inhibition of human cancer cell growth by epothilone analogues bearing functionalized benzimidazole side chains suggests that these systems might be conjugated with tumor‐targeting moieties to form tumor‐targeted prodrugs.