Normal-form preemption sequences for an open problem in scheduling theory

Structural properties of optimal preemptive schedules have been studied in a number of recent papers with a primary focus on two structural parameters: the minimum number of preemptions necessary, and a tight lower bound on shifts, i.e., the sizes of intervals bounded by the times created by preemptions, job starts, or completions. These two parameters have been investigated for a large class of preemptive scheduling problems, but so far only rough bounds for these parameters have been derived for specific problems. This paper sharpens the bounds on these structural parameters for a well-known open problem in the theory of preemptive scheduling: Instances consist of in-trees of n unit-execution-time jobs with release dates, and the objective is to minimize the total completion time on two processors. This is among the current, tantalizing “threshold” problems of scheduling theory: Our literature survey reveals that any significant generalization leads to an NP-hard problem, but that any significant, but slight simplification leads to tractable problem with a polynomial-time solution. For the above problem, we show that the number of preemptions necessary for optimality need not exceed \(2n-1\); that the number must be of order \({\varOmega }(\log n)\) for some instances; and that the minimum shift need not be less than \(2^{-2n+1}.\) These bounds are obtained by combinatorial analysis of optimal preemptive schedules rather than by the analysis of polytope corners for linear-program formulations of the problem, an approach to be found in earlier papers. The bounds immediately follow from a fundamental structural property called normality, by which minimal shifts of a job are exponentially decreasing functions. In particular, the first interval between a preempted job’s start and its preemption must be a multiple of 1 / 2, the second such interval must be a multiple of 1 / 4, and in general, the i-th preemption must occur at a multiple of \(2^{-i}\). We expect the new structural properties to play a prominent role in finally settling a vexing, still-open question of complexity.     

The Role of TiO<Subscript>2</Subscript> in Ceramic Bulk Interference Suppressing Resistor Integrated with Car Spark Plug

Spark plug resistors operate under extreme conditions (200°C, 4.2 MPa, peak-to-peak working voltage U_p-p of 15 to 30 kV, and instantaneous power of 26 kW). The dissipated heat has to be distributed evenly in the entire structure. The deciding factor for the homogeneity of the structure of a resistive body, which also influences the resistance value of resistors, is titanium dioxide. Its influence on the phase transition of the glass binding the components of the resistive body has been investigated by means of differential thermal analysis (DTA). Homogeneity assessment of the structure has been carried out by means of a scanning electron microscope. Titanium undergoes partial reduction during thermal processing of the resistor. The oxidation number of titanium has been determined by means of electron spectroscopy for chemical analysis–x-ray photoelectron spectroscopy (ESCA-XPS). Electrical stability of the resistors has been measured using a simulator device for the car ignition system. The resistors with no TiO₂ content get damaged and those with TiO₂ exhibit electrical stability.     

A Study on the Copper Recovery from the Slag of the Outokumpu Direct-to-Copper Process

The work was aimed at the investigation of the influence of the carbon reducer’s surface on the rate of copper removal from the slag obtained from the flash direct-to-blister process at the G?ogów smelter in Poland. It was found that, under our experimental conditions, the copper recovery from the slag slightly increases as the slag/carbon interface increases. It is very likely that the results depend on the geometry of the investigated system as well as the slag foaming phenomenon. The increase of the slag/carbon interface does not noticeably change the final copper content in the slag. The obtained results do not follow any of the reaction rate equations. Therefore, it can be suggested that the slag foaming plays the key role in the experiments by increasing the reduction surface. In addition, the investigated slag has a high viscosity, which hampers the mass transfer in this slag. This hypothesis is supported by the fact that the slag layer situated below the graphite penetrator was found to be of a different color than the slag in the vicinity of that penetrator, where it was agitated by the CO and CO₂ gases generated by the reactions of the slag reduction. Also, the slag in the layer under the penetrator contained more copper than the slag above this layer.     

Mixed finite element method for contact problems

In the paper the model of finite elements for elastic contact problems was used. Real structures are modeled by finite elements and rigid finite elements. We calculate stresses in the surface of two substructures using Coulomb model of friction.The method given here is an iterative procedure which is planed to incorporate this technique in the system allowing for incremental elastic solution. The computer program is adapted to solving spatial problems.     

ENRICHMENT OF GAS-FLAMING COAL BY THE AGGREGATIVE FLOTATION METHOD

Abstract

Aggregative flotation tests of gas-flaming coal were carried out in a laboratory flotation machine and a flotation column. Aggregation of coal feeds was carried out using as a collector unemulsified and emulsified kerosene at dosages of 130 and 10 kg/t, respectively. The results of the aggregative flotation showed that it is possible to beneficate gas-flaming coal at a huge dosage of the collector, the flotation response of which is very low. Preemulsification of kerosene caused a distinct decrease of its consumption. The efficiency of aggregative flotation of coal was higher in the flotation machine; however, the flotation selectivity of the finest feeds (?0.13 and ?0.23 mm) in the column was a little better. The influence of the size of coal grains on coal recovery and ash reduction both in the flotation machine and flotation column was interpreted as dependent on the decrease of the contact plane of aggregates formed by coal grains with air bubbles and on the size of these aggregates.     

The tricalcium silicate hydration in the presence of active silica

The influence of active silica upon the tricalcium silicate hydration was studied. On the microcalorimetric curves a considerable acceleration of the process with dormant period elimination was observed. The reason for this is the lowering of calcium ions concentration in the solution as they are consumed, rapidly by the CSH phase formation of a low C/S ratio. Basing on these results the authors presume that the delaying factor of C₃S hydration process is the quasi-stationary layer supersaturated with calcium ions surrounding the anhydrous grains of tricalcium silicate.     

Comparison of flavonoids profile in sprouts of common buckwheat cultivars and wild tartary buckwheat

In this study, major types of flavonoids in 7‐day sprouts of five common buckwheat cultivars grown in Poland (Hruszowska, Kora, Panda, Luba and Emka) and wild tartary buckwheat were investigated. Results demonstrated that sprouts of common buckwheat cultivars and wild tartary buckwheat contained both known and a newly discovered flavonol: quercetin 3‐O‐galactosyl‐rhamnoside. An exceptionally high content of this flavonoid was found in cotyledons of wild tartary buckwheat (30.79 ± 0.14 mg g^?1 DW), exceeding about 10 times level of rutin (3.16 ± 0.07 mg g^?1 DW). The results are not consistent with the data published so far on the content of flavonoids in sprouts of tartary buckwheat. Higher levels of flavonoids were measured in cotyledons than in hypocotyls with the exception of anthocyanins, which were present in higher amounts in hypocotyls. Cotyledons of common buckwheat sprouts were rich in C‐glycosides of luteolin and apigenin, the total content of which exceeded ca. 5 times the concentration of rutin.