Labeling algorithm for the shortest path problem with turn prohibitions with application to large-scale road networks

In real road networks, the presence of no-left, no-right or no U-turn signs, restricts the movement of vehicles at intersections. These turn prohibitions must be considered when calculating the shortest path between a starting and an ending point in a road network. We propose an extension of Dijkstra’s algorithm to solve the shortest path problem with turn prohibitions. The method uses arc labeling and a network structure with low memory requirements. We compare the proposed method with the dual graph approach in a set of randomly generated networks and Bogotá’s large-scale road network. Our computational experiments show that the performance of the proposed method is better than that of the dual graph approach, both in terms of computing time and memory requirements. We co-developed a Web-based decision support system for computing shortest paths with turn prohibitions that uses the proposed method as the core engine.     

Confinement into a state with persistent current by thermal quenching of loop of Josephson junctions

We study a loop of Josephson junctions that is quenched through its critical temperature. For three or more junctions, symmetry breaking states can be achieved without thermal activation, in spite of the fact that the relaxation time is practically constant when the critical temperature is approached from above. The probability for these states decreases with quenching time, but, for a large number of junctions, cooling does not have to be fast. For this case, we evaluate the standard deviation of the induced flux. Our results are consistent with the available experimental data.     

Copolymerization of styrene and methacrylic acid in concentrated emulsions

Copolymerization of styrene and methacrylic acid was carried out by the concentrated emulsion polymerization method, using sodium dodecylsulfate and AIBN as emulsifier and initiator, respectively. Compared to conventional emulsion polymerization, a much smaller amount of water (5–25 vol %) is employed as the continuous phase and thus the loss of methacrylic acid, which is very soluble in water, is minimized. The concentrated emulsion, which has the appearance of a gel, was prepared at room temperature, and was polymerized at 40°C. The size of copolymer latexes is affected by the internal phase ratio, and was in the range of 0.2–0.3 μm in diameter. Potentiometric titration was used to determine the surface density of the carboxylic groups of the copolymer latexes and its dependence on the feed molar ratio of methyacrylic acid to styrene. NMR and IR spectroscopies have been employed to determined the composition of the copolymer latexes.     

A non-analytic proof of the newman—znám result for disjoint covering systems

A direct combinatorial proof is given to a generalization of the fact that the largest modulusN of a disjoint covering system appears at leastp times in the system, wherep is the smallest prime dividingN. The method is based on geometric properties of lattice parallelotopes. This research was supported by grant 85-00368 from the United States-Is rael Binational Science Foundation, Jerusalem, Israel.     

Projective objects in categories of locally convex spaces

Mathematical Notes -     

IR and SFM study of PTCDA thin films on different substrates

FT-IR spectroscopy and SFM were used to investigate the growth of thin films of the organic semiconductor 3,4,9,10-perylenetetracarboxylicdianhydride (PTCDA) deposited by vacuum sublimation onto various substrates, i.e. Ag(111) layers on mica, KBr(100), mica, oxidized Si, and TiO₂ nanoparticles on Si. Layer thicknesses of PTCDA varied from 10 to 1500 nm.The anhydride vibrations of PTCDA differ for the used substrates, which can be connected to the orientation of the molecules relative to the substrate surface and the film morphology as detected in the SFM pictures.     

Neutron diffraction investigation of the structural transition in HgSe1−x Sx ternary mercury chalcogenide systems at high pressures

The structure of HgSe_1?x S_x ternary mercury chalcogenides at high pressures up to 35 kbar is investigated by neutron diffraction. It is found under pressure, that the HgSe_1?x S_x compounds undergo, a phase transition from the cubic sphalerite-type to the hexagonal cinnabar-type structure, which is accompanied by a jump-wise change in the unit cell volume and interatomic distances. The unit cell parameters and the positional parameters of Hg and Se (S) atoms in the high-pressure hexagonal phase are determined. A two-phase state is revealed in the phase transition region.     

Bijective proofs of two broken circuit theorems

We prove, by means of explicit bijections, theorems of Whitney and Stanley that express the coefficients of the chromatic polynomial of a graph G and the number of acyclic orientations of G in terms of numbers of sets of edges that contain no broken circuits of G.     

A definition of spectrum for differential equations on finite time

Hyperbolicity of an autonomous rest point is characterised by its linearization not having eigenvalues on the imaginary axis. More generally, hyperbolicity of any solution which exists for all times can be defined by means of Lyapunov exponents or exponential dichotomies. We go one step further and introduce a meaningful notion of hyperbolicity for linear systems which are defined for finite time only, i.e. on a compact time interval. Hyperbolicity now describes the transient dynamics on that interval. In this framework, we provide a definition of finite-time spectrum, study its relations with classical concepts, and prove an analogue of the Sacker-Sell spectral theorem: For a d-dimensional system the spectrum is non-empty and consists of at most d disjoint (and often compact) intervals. An example illustrates that the corresponding spectral manifolds may not be unique, which in turn leads to several challenging questions.