The improper infinite derivatives of Takagi's nowhere-differentiable function

Let T be Takagi's continuous but nowhere-differentiable function. Using a representation in terms of Rademacher series due to N. Kono [Acta Math. Hungar. 49 (1987) 315-324], we give a complete characterization of those points where T has a left-sided, right-sided, or two-sided infinite derivative. This characterization is illustrated by several examples. A consequence of the main result is that the sets of points where T^′(x)=±∞ have Hausdorff dimension one. As a byproduct of the method of proof, some exact results concerning the modulus of continuity of T are also obtained.     

Computation of symbolic dynamics for one-dimensional maps

In this paper we design and implement rigorous algorithms for computing symbolic dynamics for piecewise-monotone-continuous maps of the interval. The algorithms are based on computing forwards and backwards approximations of the boundary, discontinuity and critical points. We explain how to handle the discontinuities in the symbolic dynamics which occur when the computed partition element boundaries are not disjoint. The method is applied to compute the symbolic dynamics and entropy bounds for the return map of the singular limit of a switching system with hysteresis and the forced Van der Pol equation.     

Synthesis and characterization of long perylenediimide polymer fibers: from bulk to the single-molecule level

The synthesis and characterization of perylenediimide polyisocyanides is reported. In addition to short oligomers, our synthetic approach results in the formation of extremely long, well-defined, and rigid perylenediimide polymers. Ordering and close-packing of the chromophores in these long polymers is guaranteed by attachment to a polyisocyanide backbone with amino acid side chains. Hydrogen bonding interactions between those groups stabilize and rigidify the helical polymer structure. The rodlike nature of the synthesized long perylenediimide pendant polyisocyanides as well as the helical arrangement of the chromophores is demonstrated by means of atomic force microscopy. Remarkably, polymer fibers up to 1 mum in length have been visualized, containing several thousands of perylenediimide molecules. Circular dichroism spectroscopy reveals the chiral organization of the chromophore units in the polymer, whereas absorption and emission measurements prove the occurrence of excited-state interactions between those moieties due to the close packing of the chromophore groups. However, an intricate optical behavior is encountered in bulk as a result of the coexistence of short oligomers and long polymers of perylenediimide, a situation subsequently uncovered by means of single-molecule experiments. Individual long helical perylenediimide polyisocyanides exhibit a typical red-shifted fluorescence spectrum, which, together with depolarized emission continuously decreasing in time, demonstrate that fluorescence arises from multiple excimer-like species in the polymer. Upon continuous irradiation of these long polymers, a fast decay in fluorescence lifetime is observed, a situation explained by photoinduced creation of quenching sites. Radical/ion formation by intramolecular electron transfer between close-by perylenediimide moieties is the most probable mechanism for this process. Appropriate control of the electron-transfer process might open the possibility of applying these polymers as perylenediimide-based supramolecular nanowires.     

Identification of CO adsorption sites in supported Pt catalysts using high-energy-resolution fluorescence detection X-ray spectroscopy

High-energy-resolution fluorescence detection (HERFD) X-ray spectroscopy is presented as a new tool for the identification of the bonding sites of reactants in supported metal catalysts. The type of adsorption site of CO on an alumina-supported platinum catalyst and the orbitals involved in the bonding are identified. Because X-ray absorption spectroscopy (XAS) is element-specific and can be used under high pressures and temperatures, in situ HERFD XAS can be applied to a swathe of catalytic systems, including alloys.     

Boxlike filter response based on complementary photonic bandgaps in two-dimensional microresonator arrays

We propose that a boxlike filter response can be obtained by utilizing complementary photonic bandgap properties of the column and row configurations in two-dimensional microresonator arrays. The filters are fabricated using deep-UV lithography in silicon-on-insulator technology. The observed sidelobes reduction is approximately 10 dB, and the usable bandwidth can be as high as 500-750 GHz.     

Computation and efficiency of potential function minimizers of combinatorial congestion games

Mathematical Programming - We study the computation and efficiency of pure Nash equilibria in combinatorial congestion games, where the strategies of each player i are given by the binary vectors...     

An analysis of generalised heuristics for vehicle routing and personnel rostering problems

The present study investigates the performance of heuristics while solving problems with routing and rostering characteristics. The target problems include scheduling and routing home care, security and maintenance personnel. In analysing the behaviour of the heuristics and determining the requirements for solving the aforementioned problems, the winning hyper-heuristic from the first International Cross-domain Heuristic Search Challenge (CHeSC 2011) is employed. The completely new application of a hyper-heuristic as an analysis tool offers promising perspectives for supporting dedicated heuristic development. The experimental results reveal that different low-level heuristics perform better on different problems and that their performance varies during a search process. The following characteristics affect the performance of the heuristics: the planning horizon, the number of activities and lastly the number of resources. The body of this paper details both these characteristics and also discusses the required features for embedding in an algorithm to solve problems particularly with a vehicle routing component.