All-electron time-dependent density functional theory with finite elements: time-propagation approach

We present an all-electron method for time-dependent density functional theory which employs hierarchical nonuniform finite-element bases and the time-propagation approach. The method is capable of treating linear and nonlinear response of valence and core electrons to an external field. We also introduce (i) a preconditioner for the propagation equation, (ii) a stable way to implement absorbing boundary conditions, and (iii) a new kind of absorbing boundary condition inspired by perfectly matched layers.     

Conditions for strong Morita equivalence of partially ordered semigroups

We investigate when a partially ordered semigroup (with various types of local units) is strongly Morita equivalent to a posemigroup from a given class of partially ordered semigroups. Necessary and sufficient conditions for such equivalence are obtained for a series of well-known classes of posemigroups. A number of sufficient conditions for several classes of naturally ordered posemigroups are also provided.     

Controlled lateral spreading and pinning of oil droplets based on topography and chemical patterning

Geometric pinning sites can be used to control the lateral spreading and pinning of oils on surfaces. The geometric pinning effect combined with lithographic surface chemistry patterning allows controlling the shapes of oil droplets. We study the confinement effect on test structures of various protruding and intruding geometries, and employ scanning electron microscopy analysis to study the shape of the meniscus at the edges of the chemical patterns. Nanopillar and micropillar topographies are compared, revealing that it is a necessity for accurate oil patterns that the length scale of the roughness is smaller than the resolution of the surface chemistry pattern. We also find that there exists a critical, geometry-dependent threshold contact angle, below which the geometric confinement does not work, as olive oil with a static advancing contact angle of 57° accurately replicated the chemical pattern on top of nanopillar topography, but hexadecane with a static advancing contact angle of 50° penetrated the pinning sites and wetted the whole surface.     

Routing by ranking: A link analysis method for the constrained dial-a-ride problem

The dial-a-ride problem involves the dispatching of a fleet of vehicles in order to transport a set of customers from specific pick-up nodes to specific drop-off nodes. Using a modified version of hyperlink-induced topic search (HITS), we characterize hubs as nodes with many out-links to other hubs and calculate a hub score for each pick-up and drop-off node. Ranking the nodes by hub score gives guidance to a backtracking algorithm for efficiently finding feasible solutions to the dial-a-ride problem.     

Determination of Chlorine by Aluminium Monochloride Molecular Absorption Spectrometry Using Lead Atomic Lines

In earlier studies the methods for determination of chlorine by aluminium monochloride molecular absorption spectrometry have been based on the use of the continuous light sources.

In this study we investigated the molecular absorption of AlCl in a carbon rod furnance for determination of chlorine, by using the lead atomic line at 261.418 nm emitted from a Pb-hollow cathode lamp. A deuterium lamp was used for simultaneous back-ground correction.     

The Measurement of the SO2 Molecular Absorption in the Graphite Furnace for the Possible Determination of Sulfur.

The present study was conducted to investigate the molecular absorption of sulfur dioxide in a carbon rod furnace for the determination of sulfur. The arsenic atomic line at 206.98 nm emitted from an As-hollow cathode lamp was used as an irradiation source in the measurements. The interferences caused by molecular absorption of some other molecules present in these conditions was also examined. Using the ionexchange as the pretreatment for the sample the method can be applied for a great variety of inorganic samples.     

Integral Representation with Adapted Continuous Integrand with Respect to Fractional Brownian Motion

We show that if a random variable is a final value of an adapted Hölder continuous process, then it can be represented as a stochastic integral with respect to fractional Brownian motion, and the integrand is an adapted process, continuous up to the final point.     

Note on multidimensional Breeden–Litzenberger representation for state price densities

In this note, we consider European options of type $h(X^1_T, X^2_T,\ldots , X^n_T)$ depending on several underlying assets. We give a multidimensional version of the result of Breeden and Litzenberger (J Bus 51:621–651, 1978) on the relation between derivatives of the call price and the risk-neutral density of the underlying asset. The pricing measure is assumed to be absolutely continuous with respect to the Lebesgue measure on the state space.     

Analytical instrumentation in the 18th century

Summary Two basically simple and ancient instruments — the balance and blowpipe — were the most successful tools of an 18th century analyst. The development of blowpipe analysis by the Swedish school of mineralogists and chemists is discussed in detail.