Primal separation for 0/1 polytopes

 The 0/1 primal separation problem is: Given an extreme point xˉ of a 0/1 polytope P and some point x ^*, find an inequality which is tight at xˉ, violated by x ^* and valid for P or assert that no such inequality exists. It is known that this separation variant can be reduced to the standard separation problem for P. We show that 0/1 optimization and 0/1 primal separation are polynomial time equivalent. This implies that the problems 0/1 optimization, 0/1 standard separation, 0/1 augmentation, and 0/1 primal separation are polynomial time equivalent. Then we provide polynomial time primal separation procedures for matching, stable set, maximum cut, and maximum bipartite graph problems, giving evidence that these algorithms are conceptually simpler and easier to implement than their corresponding counterparts for standard separation. In particular, for perfect matching we present an algorithm for primal separation that rests only on simple max-flow computations. In contrast, the known standard separation method relies on an explicit minimum odd cut algorithm. Consequently, we obtain a very simple proof that a maximum weight perfect matching of a graph can be computed in polynomial time. Received: August 20, 2001 / Accepted: April 2002 Published online: December 9, 2002 RID="⋆" ID="⋆" This research was developed while the author was on leave at the Istituto di Analisi dei Sistemi ed Informatica, Viale Manzoni 30, 00185 Roma, supported by the project TMR-DONET nr. ERB FMRX-CT98-0202 of the European Union. Mathematics Subject Classification (2000): 90C10, 90C60, 90C57     

Families of Structures on Spherical Fibrations

Let SF(n) be the usual monoid of orientation- and base point-preserving self-equivalences of the n-sphere ${\mathbb{S}^n}$ n. If Y is a (right) SF(n)-space, one can construct a classifying space B(Y, SF(n), *)=B _n for ${\mathbb{S}^n}$ n-fibrations with Y-structure, by making use of the two-sided bar construction. Let k: B _n →BSF(n) be the forgetful map. A Y-structure on a spherical fibration corresponds to a lifting of the classifying map into B _n . Let K _i =K $\left( {{\mathbb{Z}_2 }} \right)$ , i) be the Eilenberg–Mac Lane space of type $\left( {{\mathbb{Z}_2 }} \right)$ , i). In this paper we study families of structures on a given spherical fibration. In particular, we construct a universal family of Y-structures, where Y=W _n is a space homotopy equivalent to ∏ _i≥1 K _i . Applying results due to Booth, Heath, Morgan and Piccinini, we prove that the universal family is a spherical fibration over the space map{B _n , B _n }×B _n . Furthermore, we point out the significance of this space for secondary characteristic classes. Finally, we calculate the cohomology of B _n .     

A data-analysis method for identifying differential effects of time-delayed feedback forces and periodic driving forces in stochastic systems

In this work a method is developed for analyzing time series of periodically driven stochastic systems involving time-delayed feedback. The proposed data-analysis method yields dynamical models in terms of stochastic delay differential equations. On the basis of these dynamical models differential effects of driving forces and time-delayed feedback forces can be identified.     

Contamination of therapeutic human immunoglobulin preparations with apolipoprotein H (β2‐glycoprotein I)

Polyclonal immunoglobulin (Ig) concentrates are important biological medicinal products and the assurance of their quality and safety is crucial. In our present approach we used proteomic methods to check the purity of commercial Ig products of different origin. The experimental setup included nonreducing 2DE or DIGE combined with MALDI‐TOF and the thrombin generation assay, a routine safety test for pharmaceutical Ig preparations, and was complemented by a specific immunoassay. 2DE patterns displayed contaminations with trace amounts of human apolipoprotein H (Apo‐H), transferrin, albumin, and its fragments. In contrast to the latter, Apo‐H is a protein that is active in the coagulation cascade, and thus a potential involvement in thromboembolic events in vivo cannot be excluded. It was found by 2DE and MALDI‐TOF to be a contaminant of several Ig preparations. Spiking experiments of Ig preparations with pure Apo‐H demonstrated an Apo‐H concentration dependent increase in thrombin generation assay values. Traces of Apo‐H are possibly also contributing to unwanted side effects, as already known for factor XIa. The significance of Apo‐H contaminations for these side effects might be verified by detailed analyses of pharmacovigilance data.     

High-temperature oxygen sensors for glass-forming melts

Electrochemical sensors are reported for the on-line measurement of oxygen partial pressures of oxidic glass-forming melts on a laboratory and technical scale. Based on the principle of solid electrolyte cells without transference, they are principally simple units. The extreme chemical and temperature conditions of their applications, however, demanded extensive fundamental investigations and resulted in specific forms of reference and measuring electrodes, a thermo-dynamic procedure of verifying the correct functioning of such cells, and a method of measuring thermoelectric voltages of non-isothermal glass melts.     

On static and radiative space-times

The conformal constraint equations on space-like hypersurfaces are discussed near points which represent either time-like or spatial infinity for an asymptotically flat solution of Einstein's vacuum field equations. In the case of time-like infinity a certain radiativity condition, is derived which must be satisfied by the data at that point. The case of space-like infinity is analysed in detail for static space-times with non-vanishing mass. It is shown that the conformal structure implied here on a slice of constant Killing time, which extends analytically through infinity, satisfies at spatial infinity the radiativity condition. Thus to any static solution exists a certain radiative solution which has a smooth structure at past null infinity and is regular at past time-like infinity. A characterization of these solutions by their free data is given and non-symmetry properties are discussed.     

Kalorimetrische Messungen an Mischungen von Nichtelektrolyten, 1. Mitt.: Molwärme des Systems 1,2-Dibromäthan-Benzol

Zusammenfassung Es wird der Aufbau eines Kalorimeters zur Bestimmung der spezif. Wärme von Flüssigkeiten beschrieben. Die Messungen werden nach einem kontinuierlichen adiabatischen Aufheizverfahren durchgeführt. Der Fehler in der Molwärme beträgt ca. ±0,4%. Die Methode erlaubt auch innerhalb relativ kleiner Temperaturbereiche eine Aussage über die Temperaturabhängigkeit der Wärmekapazität.Die Molwärme des Systems 1,2-Dibromäthan-Benzol wird zwischen 24 und 29°C über den ganzen Konzentrationsbereich vermessen. Die Mischungen zeigen negative C _p-Werte mit unsymmetrischem Konzentrationsverlauf. Für höhere Temperaturen ist eine Zunahme der Symmetrie zu erwarten.

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A calorimeter has been described which serves to determine the heat capacities of liquids. In the measurements the calorimeter and the surroundings are heated continuously, so that adiabatic conditions prevail. The experimental error in the molar heat capacities is ca. ±0,4%. The method also permits the estimation of the temperature dependence of the heat capacities, even within relatively small temperature intervals.The molar heat capacity of the system 1,2-dibromoethane-benzene has been measured between 24° and 29°C for all concentrations. The C _p-values of the mixtures are negative and show an asymmetrical dependence on the concentration. For higher temperatures it is expected that the concentration dependence will become more nearly symmetrical.

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Mit 3 Abbildungen     

Polymer-bound osmium oxide catalysts

Polymer-supported oxidic osmium catalysts based on cross-linked poly(4-vinyl pyridine) were synthesized by various routes and characterized by a number of physical techniques (Raman, IR, XPS, ¹³C and ¹⁵N solid-state NMR spectroscopy). Model compounds of type Os₂O₆L₄ (L = pyridine, 4-iso-propyl pyridine, and 4-tert-butyl pyridine) were obtained under the conditions of the catalyst synthesis. The catalytic systems were successful in the dihydroxylation of alkenes.     

The efficient and selective oxidation of alcohols with zeolite NaY-supported sodium ruthenate

Primary and internal alcohols are efficiently oxidised to their corresponding oxidation products at room temperature by a newly synthesized zeolite NaY-supported sodium ruthenate. Advantages of this system include simple catalyst removal and product isolation, in addition to easy recycling of this catalyst.