Design of Hyperbolic Billiards

We formulate a general framework for the construction of hyperbolic billiards. Spherical symmetry is exploited for a simple treatment of billiards with spherical caps and soft billiards in higher dimensions. Other examples include the Papenbrock stadium. Reproduction of the entire article for non-commercial purposes is permitted without charge.     

A numerical model of multimode fiber PON frequency response

Frequency response of passive optical network (PON) based on multimode fibers is investigated. The network comprises fibers, connectors and splitters/couplers. It is shown that due to mode filtering at splitters, the frequency response is different for different network nodes in otherwise symmetrical network.     

Proton hydration in aqueous solution: Fourier transform infrared studies of HDO spectra

This paper attempts to elucidate the number and nature of the hydration spheres around the proton in an aqueous solution. This phenomenon was studied in aqueous solutions of selected acids by means of Fourier transform infrared spectroscopy of semiheavy water (HDO), isotopically diluted in H(2)O. The quantitative version of difference spectrum procedure was applied for the first time to investigate such systems. It allowed removal of bulk water contribution and separation of the spectra of solute-affected HDO. The obtained spectral data were confronted with ab initio calculated structures of small gas-phase and polarizable continuum model (PCM) solvated aqueous clusters, H+(H2O)n, n=2-8, in order to help in establishing the structural and energetic states of the consecutive hydration spheres of the hydrated proton. This was achieved by comparison of the calculated optimal geometries with the interatomic distances derived from HDO band positions. The structure of proton hydration shells outside the first hydration sphere essentially follows the model structure of other hydrated cations, previously revealed by affected HDO spectra. The first hydration sphere complex in diluted aqueous solutions was identified as an asymmetric variant of the regular Zundel cation [The Hydrogen Bond: Recent Developments in Theory and Experiments, edited by P. Schuster, G. Zundel, and C. Sandorfy (North-Holland, Amsterdam, 1976), Vol. II, p. 683], intermediate between the ideal Zundel and Eigen structures [E. Wicke et al., Z. Phys. Chem. Neue Folge 1, 340 (1954)]. Evidence was found for the existence of strong and short hydrogen bonds, with oxygen-oxygen distance derived from the experimental affected spectra equal 2.435 A on average and in the PCM calculations about 2.41-2.44 A. It was also evidenced for the first time that the proton possesses four well-defined hydration spheres, which were characterized in terms of hydrogen bonds' lengths and arrangements. Additionally, an outer hydration layer, shared with the anion, as well as loosely bound water molecules interacting with free electron pairs of the central complex were detected in the affected spectra.     

Optimal partitioning of a measurable space into countably many sets

Summary A notion of an optimal partition of a measurable space into countably many sets according to given nonatomic probability measures is defined. It is shown that the set of optimal partitions is nonempty. Bounds for the optimal value are given and the set of optimal partitions is characterized. Finally, an example related to statistical decision theory is presented.     

An analysis of mean life and lifetime of unstable elementary particles

A theoretical analysis of the concept of lifetime and mean life of unstable elementary particles is presented. New analytic formulas for lifetime and mean life as a function of decay width and the mass of unstable particle are derived for Breit-Wigner and Matthews-Salam energy distributions. It is demonstrated that, for unstable particles with a larger width or decay energy threshold, the deviation from the generally accepted mean life ^m = ^–1 is significant. The behavior of the decay law P(t) for small times is analyzed, and it is shown that the Breit-Wigner distribution violates the condition P(t = 0) = 0, whereas the Matthews-Salam distribution satisfies it.     

The continuous solution of a functional equation of Abel

Summary The functional equation(x) + (y) = (xf(y) + yf(x)) (1) for the unknown functionsf, and mapping reals into reals appears in the title of N. H. Abel's paper [1] from 1827 and its differentiable solutions are given there. In 1900 D. Hilbert pointed to (1), and to other functional equations considered by Abel, in the second part of his fifth problem. He asked if these equations could be solved without, for instance, assumption of differentiability of given and unknown functions. Hilbert's question was recalled by J. Aczél in 1987, during the 25th International Symposium on Functional Equations in Hamburg-Rissen. In particular Aczél asked for all continuous solutions of (1). An answer to his question is contained in our paper. We determine all continuous functionsf: I ,: A _f (I × I) and: I that satisfy (1). HereI denotes a real interval containing 0 andA _f (x,y) := xf(y) + yf(x), x, y I. The list contains not only the differentiable solutions, implicitly described by Abel, but also some nondifferentiable ones.Applying some results of C. T. Ng and A. Járai we are able to obtain even a more general result. For instance, the assertion (i.e. the list of solutions) remains unchanged if we replace continuity of and by local boundedness of orf(0)I from above or below. Strengthening a bit the assumptions onf we can preserve a large part of the assertion requiring only the measurability of either orf(0)I.     

A look at multiparticle production via modified combinants

The European Physical Journal A - The transverse momentum ($$p_{T}$$) distribution of strange hadrons ($$K_{S}^{0}$$ and $$\varLambda $$) and multi-strange hadrons( $$\varXi $$ and $$\varOmega $$)...     

Living ring-opening metathesis polymerization of norbornenes bay-functionalized perylene diimides

Ring-opening metathesis polymerization (ROMP)-derived poly(oxanorbornene imide)s bearing bay-linked mono - alkoxy -M1 and 1,7-di-alkoxy M2 functionalized perylene diimides (PDIs) were synthesized using Grubb's third ( G3 ) and Hoveyda-Grubbs second generation ( HG2 ) ruthenium-alkylidene metathesis initiators. The mono-alkoxy-derived PDI-based non-ladderphane polymer poly M1 displayed 67% to 77% of the trans olefin content in the polymer chain depending on the initiator used for the polymerization. When using the symmetrical 1,7-di-alkoxy-derived PDI-based polymer poly M2 having the ladderphane type-structure, this displayed a significant amount of cis and trans olefin contents in the polymer chains, irrespective of the type of initiators used for the polymerization. ROMP of both monomers M1 and M2 proceeded in a well-controlled manner with a linear dependence of molecular weight on the monomer/initiator ratio using G3 as initiator. Optical properties of the ladderphane-based poly M2 and non-ladderphane-based poly M1 were characterized in both solution and the film state. X-ray diffraction (XRD) analysis for all the polymers showed significant π-stacking in the thin film state with ordered molecular packing and closer values of d-spacing for both poly M1 and poly M2 . Film morphology examined by AFM elucidated homogenous smooth polymer surface for both polymers in general, but with some irregularities observed for poly M1 . In addition, CV analysis revealed both polymers could be good candidates as electron-accepting materials, with excellent film-forming ability, and thermal stability.     

Cooperative Chemotaxis of Magnesium Microswimmers for Corrosion Spotting

Numerous artificial micro- and nanomotors, as well as various swimmers have been inspired by living organisms that are able to move in a coordinated manner. Their cooperation has also gained a lot of attention because the resulting clusters are able to adapt to changes in their environment and to perform complex tasks. However, mimicking such a collective behavior remains a challenge. In the present work, magnesium microparticles are used as chemotactic swimmers with pronounced collective features, allowing the gradual formation of macroscopic agglomerates. The formed clusters act like a single swimmer able to follow pH gradients. This dynamic behavior can be used to spot localized corrosion events in a straightforward way. The autonomous docking of the swimmers to the corrosion site leads to the formation of a local protection layer, thus increasing corrosion resistance and triggering partial self-healing.     

Structural studies of 4-aryloctahydro-pyrido[1,2-c]pyrimidine derivatives

¹³C cross-polarisation magic angle spinning NMR data have been reported for four derivatives of 4-aryl-octahydro-pyrido[1,2-c]pyrimidine-1,3-dione and the X-ray diffraction data for two (with 2′-Me and 2′-OMe). The crystal structures show the presence of centrosymmetric cyclic dimers with intermolecular C1O?H-N or C3O?H-N hydrogen bonds, the configuration at the chiral centres (C4 and C4_a) was determined as RR (SS). The twisting of aromatic ring at C4 with respect to the pyrido[1,2-c]pyrimidine skeleton is about 68-109°.