Thickness and morphology of polyelectrolyte coatings on silica surfaces before and after protein exposure studied by atomic force microscopy

Analyte–wall interaction is a significant problem in capillary electrophoresis (CE) as it may compromise separation efficiencies and migration time repeatability. In CE, self-assembled polyelectrolyte multilayer films of Polybrene (PB) and dextran sulfate (DS) or poly(vinylsulfonic acid) (PVS) have been used to coat the capillary inner wall and thereby prevent analyte adsorption. In this study, atomic force microscopy (AFM) was employed to investigate the layer thickness and surface morphology of monolayer (PB), bilayer, (PB-DS and PB-PVS), and trilayer (PB-DS-PB and PB-PVS-PB) coatings on glass surfaces. AFM nanoshaving experiments providing height distributions demonstrated that the coating procedures led to average layer thicknesses between 1 nm (PB) and 5 nm (PB-DS-PB), suggesting the individual polyelectrolytes adhere flat on the silica surface. Investigation of the surface morphology of the different coatings by AFM revealed that the PB coating does not completely cover the silica surface, whereas full coverage was observed for the trilayer coatings. The DS-containing coatings appeared on average 1 nm thicker than the corresponding PVS-containing coatings, which could be attributed to the molecular structure of the anionic polymers applied. Upon exposure to the basic protein cytochrome c, AFM measurements showed an increase of the layer thickness for bare (3.1 nm) and PB-DS-coated (4.6 nm) silica, indicating substantial protein adsorption. In contrast, a very small or no increase of the layer thickness was observed for the PB and PB-DS-PB coatings, demonstrating their effectiveness against protein adsorption. The AFM results are consistent with earlier obtained CE data obtained for proteins using the same polyelectrolyte coatings.     

Optimal service control against worst case admission policies: A multichained stochastic game

In this paper we will consider two-person zero-sum games and derive a general approach for solving them. We apply this approach to a queueing problem. In section 1 we will introduce the model and formulate the Key-theorem. In section 2 we develop the theory that we will use in section 3 to prove the Key-theorem. This includes a general and useful result in Lemma 2.1 on the sufficiency of stationary policies.     

Breaks, cuts, and patterns

We generalize the concept of a break by considering pairs of arbitrary rounds. We show that a set of home-away patterns minimizing the number of generalized breaks cannot be found in polynomial time, unless P=NP. When all teams have the same break set, the decision version becomes easy; optimizing remains NP-hard.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

$$Gamma $$ Γ -evaluations of hypergeometric series

The Ramanujan Journal - In this paper we explore special values of Gaussian hypergeometric functions in terms of products of Euler $$Gamma $$ -functions and exponential functions of linear...     

Scheduling with safety distances

We investigate the problem of Scheduling with Safety Distances (SSD) that consists in scheduling jobs on two parallel machines without machine idle time. Every job is already assigned to its machine, and we just have to specify an ordering of the jobs for each machine. The goal is to find orderings of the jobs such that the minimum time elapsed between any two job completion times is maximized. We prove that this problem is NP-hard in general and give polynomial time algorithms for special cases. These results combined establish a sharp borderline between NP-complete and polynomial solvable versions of the problem SSD.This research was supported by the Christian Doppler Laboratorium für Diskrete Optimierung.On leave from the Mathematics Section, Forestry University Nanjing, Nanjing, PR China.     

The transportation problem with exclusionary side constraints

We consider the so-called Transportation Problem with Exclusionary Side Constraints (TPESC), which is a generalization of the ordinary transportation problem. We confirm that the TPESC is NP-hard, and we analyze the complexity of different special cases. For instance, we show that in case of a bounded number of suppliers, a pseudo-polynomial time algorithm exists, whereas the case of two demand nodes is already hard to approximate within a constant factor (unless P = NP). This research was partially supported by FWO Grant No. G.0114.03.     

On a periodic vehicle routing problem

This paper deals with a study on a variant of the Periodic Vehicle Routing Problem (PVRP). As in the traditional Vehicle Routing Problem, customer locations each with a certain daily demand are given, as well as a set of capacitated vehicles. In addition, the PVRP has a horizon, say T days, and there is a frequency for each customer stating how often within this T-day period this customer must be visited. A solution to the PVRP consists of T sets of routes that jointly satisfy the demand constraints and the frequency constraints. The objective is to minimize the sum of the costs of all routes over the planning horizon. We develop different algorithms solving the instances of the case studied. Using these algorithms we are able to realize considerable cost reductions compared to the current situation.