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An equitable graph coloring is a proper vertex coloring of a graph G where the sizes of the color classes differ by at most one. The equitable chromatic number is the smallest number k such that G admits such equitable k-coloring. We focus on enumerative algorithms for the computation of the equitable coloring number and propose a general scheme to derive pruning rules for them: We show how the extendability of a partial coloring into an equitable coloring can be modeled via network flows. Thus, we obtain pruning rules which can be checked via flow algorithms. Computational experiments show that the search tree of enumerative algorithms can be significantly reduced in size by these rules and, in most instances, such naive approach even yields a faster algorithm. Moreover, the stability, i.e., the number of solved instances within a given time limit, is greatly improved.
Since the execution of flow algorithms at each node of a search tree is time consuming, we derive arithmetic pruning rules (generalized Hall-conditions) from the network model. Adding these rules to an enumerative algorithm yields an even larger runtime improvement.
We prove characterizations of the existence of perfect ƒ-matchings in uniform mengerian and perfect hypergraphs. Moreover, we investigate the ƒ-factor problem in balanced hypergraphs. For uniform balanced hypergraphs we prove two existence theorems with purely combinatorial arguments, whereas for non-uniform balanced hypergraphs we show that the ƒ-factor problem is NP-hard.
We present a new Min-Max theorem for an optimization problem closely connected to matchings and vertex covers in balanced hypergraphs. The result generalizes Kőnig’s Theorem (Berge and Las Vergnas in Ann N Y Acad Sci 175:32–40, 1970; Fulkerson et al. in Math Progr Study 1:120–132, 1974) and Hall’s Theorem (Conforti et al. in Combinatorica 16:325–329, 1996) for balanced hypergraphs.
Replacement tissues, designed to fill in articular cartilage defects, should exhibit the same properties as the native material. The aim of this study is to foster the understanding of, firstly, the mechanical behavior of the material itself and, secondly, the influence of cultivation parameters on cell seeded implants as well as on cell migration into acellular implants. In this study, acellular cartilage replacement material is theoretically, numerically and experimentally investigated regarding its viscoelastic properties, where a phenomenological model for practical applications is developed. Furthermore, remodeling and cell migration are investigated.
The aim of this work was to perform a detailed investigation of the use of Selective Laser Melting (SLM) technology to process eutectic silver-copper alloy Ag 28 wt. % Cu (also called AgCu28). The processing occurred with a Realizer SLM 50 desktop machine. The powder analysis (SEM-topography, EDX, particle distribution) was reported as well as the absorption rates for the near-infrared (NIR) spectrum. Microscope imaging showed the surface topography of the manufactured parts. Furthermore, microsections were conducted for the analysis of porosity. The Design of Experiments approach used the response surface method in order to model the statistical relationship between laser power, spot distance and pulse time.
The performance and biomass yield of the perennial energy plant Sida hermaphrodita (hereafter referred to as Sida) as a feedstock for biogas and solid fuel was evaluated throughout one entire growing period at agricultural field conditions. A Sida plant development code was established to allow comparison of the plant growth stages and biomass composition. Four scenarios were evaluated to determine the use of Sida biomass with regard to plant development and harvest time: (i) one harvest for solid fuel only; (ii) one harvest for biogas production only; (iii) one harvest for biogas production, followed by a harvest of the regrown biomass for solid fuel; and (iv) two consecutive harvests for biogas production. To determine Sida's value as a feedstock for combustion, we assessed the caloric value, the ash quality, and melting point with regard to DIN EN ISO norms. The results showed highest total dry biomass yields of max. 25 t ha⁻¹, whereas the highest dry matter of 70% to 80% was obtained at the end of the growing period. Scenario (i) clearly indicated the highest energy recovery, accounting for 439 288 MJ ha⁻¹; the energy recovery of the four scenarios from highest to lowest followed this order: (i) ≫ (iii) ≫ (iv) > (ii). Analysis of the Sida ashes showed a high melting point of >1500 °C, associated with a net calorific value of 16.5–17.2 MJ kg⁻¹. All prerequisites for DIN EN ISO norms were achieved, indicating Sida's advantage as a solid energy carrier without any post-treatment after harvesting. Cell wall analysis of the stems showed a constant lignin content after sampling week 16 (July), whereas cellulose had already reached a plateau in sampling week 4 (April). The results highlight Sida as a promising woody, perennial plant, providing biomass for flexible and multipurpose energy applications.
Sensitivity of turbulent Schmidt number and turbulence model to simulations of jets in crossflow
(2016)
Environmental discharges have been traditionally designed by means of cost-intensive and time-consuming experimental studies. Some extensively validated models based on an integral approach have been often employed for water quality problems, as recommended by USEPA (i.e.: CORMIX). In this study, FLOW-3D is employed for a full 3D RANS modelling of two turbulent jet-to-crossflow cases, including free surface jet impingement. Results are compared to both physical modelling and CORMIX to better assess model performance. Turbulence measurements have been collected for a better understanding of turbulent diffusion's parameter sensitivity. Although both studied models are generally able to reproduce jet trajectory, jet separation downstream of the impingement has been reproduced only by RANS modelling. Additionally, concentrations are better reproduced by FLOW-3D when the proper turbulent Schmidt number is used. This study provides a recommendation on the selection of the turbulence model and the turbulent Schmidt number for future outfall structures design studies.
Four members of a homologous series of chlorinated poly(vinyl ester) oligomers CCl₃–(CH₂CH (OCO(CH₂)ₘCH₃))ₙ–Cl with degrees of polymerization of 10 and 20 were prepared by telomerisation using carbon tetrachloride. The number of side chain carbon atoms ranges from 2 (poly(vinyl acetate) to 18 (poly(vinyl stearate)). The effect of the n-alkyl side chain length and of the degree of polymerization on the thermal stability and crystallization behaviour of the synthesized compounds was investigated.
All oligomers degrade in two major steps by first losing HCl and side chains with subsequent breakdown of the backbone. The members with short side chains, up to poly(vinyl octanoate), are amorphous and show internal plasticization, whereas those with high number of side chain carbon atoms are semi-crystalline due to side-chain crystallization. A better packing for poly(vinyl stearate) is also noticeable. The glass transition and melting temperatures as well as the onset temperature of decomposition are influenced to a larger extent by the side chain length than by the degree of polymerization. Thermal stability is improved if both the size and number of side chains increase, but only a long side chain causes a significant increase of the resistance to degradation. This results in a stabilization of PVAc so that oligomers from poly(vinyl octanoate) on are stable under atmospheric conditions. Thus, the way to design stable, chlorinated PVEs oligomers is to use a long n-alkyl side chain.
Robots are widely used as a vehicle to spark interest in science and technology in learners. A number of initiatives focus on this issue, for instance, the Roberta Initiative, the FIRST Lego League, the World Robot Olympiad and RoboCup Junior. Robotic competitions are valuable not only for school learners but also for university students, as the RoboCup initiative shows. Besides technical skills, the students get some project exposure and experience what it means to finish their tasks on time. But qualifying students for future high-tech areas should not only be for students from developed countries. In this article, we present our experiences with research and education in robotics within the RoboCup initiative, in Germany and South Africa; we report on our experiences with trying to get the RoboCup initiative in South Africa going. RoboCup has a huge support base of academic institutions in Germany; this is not the case in South Africa. We present our ‘north–south’ collaboration initiatives in RoboCup between Germany and South Africa and discuss some of the reasons why we think it is harder to run RoboCup in South Africa.
The light-addressable potentiometric sensor (LAPS) has the unique feature to address different regions of a sensor surface without the need of complex structures. Measurements at different locations on the sensor surface can be performed in a common analyte solution, which distinctly simplifies the fluidic set-up. However, the measurement in a single analyte chamber prevents the application of different drugs or different concentrations of a drug to each measurement spot at the same time as in the case of multi-reservoir-based set-ups. In this work, the authors designed a LAPS-based set-up for cell culture screening that utilises magnetic beads loaded with the endotoxin (lipopolysaccharides, LPS), to generate a spatially distributed gradient of analyte concentration. Different external magnetic fields can be adjusted to move the magnetic beads loaded with a specific drug within the measurement cell. By recording the metabolic activities of a cell layer cultured on top of the LAPS surface, this work shows the possibility to apply different concentrations of a sample along the LAPS measurement spots within a common analyte solution.