Funktionen mit Stammfunktion

The aim of this note is to analyze the class \(St[a,b]\) of all real functions on \([a,b]\) with primitive with respect to its size and its relations to other function classes. Apart from recalling previously known results and discussing new results we put a particular emphasis on examples and counterexamples.     

Complex Inorganic/Organic Core-Shell Particles by an Inverse Emulsion Technique

Two synthetic approaches to modify the surface of inorganic particles are presented. In the first approach the inorganic particles are prepared in-situ in a confined space in inverse emulsions. The used amphiphilic statistical copolymers act not only as emulsifiers, but they also hydrophobize the remaining inorganic particles after the precipitation. This approach represents a versatile method to obtain various inorganic nanoparticles as well as more complex inorganic materials like core-multiple shell and perovskite-based nanoparticles. The second procedure uses preformed inorganic particles, as an aqueous dispersion, to modify them with surface active amphiphilic copolymers in a multicomponent solvent system. This method turns out to be a simple but highly efficient method to modify preformed inorganic nanoparticles. The particles are characterized by SEM, TEM and dynamic light scattering. The modified inorganic nanoparticles are suitable to be homogenously incorporated into a polymer matrix to form transparent nanocomposite materials.     

NZ‐flows in strong products of graphs

We prove that the strong product G₁? G₂ of G₁ and G₂ is ?₃‐flow contractible if and only if G₁? G₂ is not T? K₂, where T is a tree (we call T? K₂ a K₄‐tree). It follows that G₁? G₂ admits an NZ 3 ‐flow unless G₁? G₂ is a K₄ ‐tree. We also give a constructive proof that yields a polynomial algorithm whose output is an NZ 3‐flow if G₁? G₂ is not a K₄ ‐tree, and an NZ 4‐flow otherwise. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 267–276, 2010     

Corresponding-states laws for protein solutions

The solvent around protein molecules in solutions is structured and this structuring introduces a repulsion in the intermolecular interaction potential at intermediate separations. We use Monte Carlo simulations with isotropic, pair-additive systems interacting with such potentials. We test if the liquid-liquid and liquid-solid phase lines in model protein solutions can be predicted from universal curves and a pair of experimentally determined parameters, as done for atomic and colloid materials using several laws of corresponding states. As predictors, we test three properties at the critical point for liquid-liquid separation: temperature, as in the original van der Waals law, the second virial coefficient, and a modified second virial coefficient, all paired with the critical volume fraction. We find that the van der Waals law is best obeyed and appears more general than its original formulation: A single universal curve describes all tested nonconformal isotropic pair-additive systems. Published experimental data for the liquid-liquid equilibrium for several proteins at various conditions follow a single van der Waals curve. For the solid-liquid equilibrium, we find that no single system property serves as its predictor. We go beyond corresponding-states correlations and put forth semiempirical laws, which allow prediction of the critical temperature and volume fraction solely based on the range of attraction of the intermolecular interaction potential.     

Molecular dynamics simulation of hydrogen fluoride mixtures with 1-ethyl-3-methylimidazolium fluoride: a simple model for the study of structural features

Mixtures of hydrogen fluoride with ionic liquids show unique physicochemical properties, including their ability to form polyfluoride species (pointed out for the first time in this media by von Rosenvinge et al. J. Chem. Phys. 1997, 107, 8012). Among those systems the acidic 1-ethyl-3-methylimidazolium fluoride (EMIF.2.3HF) has been widely studied experimentally since it is the more promising for electrochemical applications. Recent studies (Hagiwara et al. J. Electrochem. Soc. 2002, 149, D1), while yielding many results, raised some questions about structural features of the liquid: absence of hydrogen bonds between the EMI+ ring hydrogen atoms and the fluoride anions, persistence of stacks and layers of cations similar to those existing in the crystal, and interpretation of the X-ray diffraction spectra. To address these questions, we have developed a simple molecular dynamics model. Our simulations are very consistent with experimental results and complete them, providing an atomic scale interpretation.     

Controlling the energy transfer in dipole chains

Processing digital signals on the molecular scale is of great interest. In this paper, we discuss the control of pulselike energy propagation through one-dimensional arrays of dipoles. Three systems are explored. In the first system, a chain of coaxial dipoles is gated by two control dipoles. Changing the orientation of these control dipoles lets us control the transfer of energy in the chain. In the other two systems, the chain-branch system and the two-branch system, two chains are used as an input and the propagation of energy is controlled by sending one or two signals toward the junction. Both systems can operate as a logical AND port. Their geometrical configurations are key to a well-defined control and operation of the AND port.     

Probing the limits of rate acceleration mediated by hydrogen bonds

[Structure: see text] A simple receptor and substrate are used to probe the relationship between transition-state charge and the level of rate acceleration that can be created by stabilizing the transition state through hydrogen bonding. Pericyclic reactions are accelerated less than 2-fold by the receptor, whereas a conjugate addition reaction is accelerated more than 30-fold. Therefore, substrate polarization by hydrogen bonding would only appear to be effective for reactions that generate significant charge at the transition state.     

Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle

We prove that for any n×n matrix, A, and z with |z|A, we have that . We apply this result to the study of random orthogonal polynomials on the unit circle.     

A general ultrasound-assisted access to room-temperature ionic liquids

The replacement of common organic solvents by room-temperature ionic liquids (RTILs) is a topical subject in both academia and industry. In the last decades, the number of applications for RTILs has followed an exponential curve and spilled over the boundaries of chemistry. Still, one of the main drawbacks of these compounds is their difficult access. The present ultrasound-assisted method affords a general and easy access to a large variety of room-temperature ionic liquids.     

An improved Interior-Point Algorithm for Large-Scale Shakedown Analysis

This work focuses on the calculation of shakedown load-factors of structures by using the lower-bound theorem of shakedown analysis. The resultant optimization problem is solved by an interior-point algorithm. In general, the application of shakedown analysis to practical problems leads to large-scale problems with large numbers of unknowns and constraints. Thus the solution turns out to be computationally intensive. For this reason it is important to reduce the dimension of the considered problem. Therefore, the major improvement of the presented algorithm consists of a problem-oriented reformulation of the problem reducing the size of the system to be solved. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)