Tight upper bounds for semi-online scheduling on two uniform machines with known optimum.

We consider a semi-online version of the problem of scheduling a sequence of jobs of different lengths on two uniform machines with given speeds 1 and s. Jobs are revealed one by one (the assignment of a job has to be done before the next job is revealed), and the objective is to minimize the makespan. In the considered variant the optimal offline makespan is known in advance. The most studied question for this online-type problem is to determine the optimal competitive ratio, that is, the worst-case ratio of the solution given by an algorithm in comparison to the optimal offline solution. In this paper, we make a further step towards completing the answer to this question by determining the optimal competitive ratio for s between [Formula: see text] and [Formula: see text], one of the intervals that were still open. Namely, we present and analyze a compound algorithm achieving the previously known lower bounds.

Co-encapsulation of human serum albumin and superparamagnetic iron oxide in PLGA nanoparticles: part I. Effect of process variables on the mean size.

PLGA (poly d,l-lactic-co-glycolic acid) nanoparticles (NPs) encapsulating magnetite nanoparticles (MNPs) along with a model drug human serum albumin (HSA) were prepared by double emulsion solvent evaporation method. This Part I will focus on size and size distribution of prepared NPs, whereas encapsulation efficiency will be discussed in Part II. It was found that mean hydrodynamic particle size was influenced by five important process variables. To explore their effects, a five-factorial, three-level experimental design and statistical analysis were carried out using STATISTICA® software. Effect of process variables on the mean size of nanoparticles was investigated and finally conditions to minimize size of NPs were proposed. GAMS™/MINOS software was used for optimization. The mean hydrodynamic size of nanoparticles ranged from 115 to 329 nm depending on the process conditions. Smallest possible mean particle size can be achieved by using low polymer concentration and high dispersion energy (enough sonication time) along with small aqueous/organic volume ratio.

Co-encapsulation of human serum albumin and superparamagnetic iron oxide in PLGA nanoparticles: part II. Effect of process variables on protein model drug encapsulation efficiency.

This study investigates encapsulation efficiency of model drug, encapsulated by magnetic poly d,l-lactic-co-glycolic acid (PLGA) nanoparticles (NPs). This is the following part of our preceding paper, which is referred in this paper as Part I. Magnetic nanoparticles and model drug human serum albumin (HSA)-loaded PLGA NPs were prepared by the double emulsion solvent evaporation method. Among five important process variables, concentration of PLGA and concentration of HSA in the inner aqueous phase along with their cross-effect had the strongest influence on the encapsulation efficiency. Encapsulation efficiency of nanoparticles ranged from 18% to 97% depending on the process conditions. Higher encapsulation efficiencies can be achieved by using low HSA and high PLGA concentrations. The optimization process, carried out by exact mathematical tools using GAMSTM/MINOS software makes it easier to find out optimum process conditions to achieve comparatively high encapsulation efficiency (e.g. 92.3%) for relatively small-sized PLGA NPs (e.g. 155 nm).