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.     

Computability of Self-Similar Sets

We investigate computability of a self-similar set on a Euclidean space. A nonempty compact subset of a Euclidean space is called a self-similar set if it equals to the union of the images of itself by some set of contractions. The main result in this paper is that if all of the contractions are computable, then the self-similar set is a recursive compact set. A further result on the case that the self-similar set forms a curve is also discussed.     

A New Family of Anionic FeIII Spin Crossover Complexes Featuring a Weak‐Field N2O4 Coordination Octahedron

Unprecedented anionic Fe^III spin crossover (SCO) complexes involving a weak‐field O,N,O‐tridentate ligand were discovered. The SCO transition was evidenced by the temperature variations in magnetic susceptibility, Mössbauer spectrum, and coordination structure. The DFT calculations suggested that larger coefficients on the azo group in the HOMO?1 of a ligand might contribute to the enhancement of a ligand‐field splitting energy. The present anionic SCO complex also exhibited the light‐ induced excited‐spin‐state trapping effect.     

Rapid determination of five antibiotic residues in swine wastewater by online solid-phase extraction–high performance liquid chromatography–tandem mass spectrometry

A simple and quick online solid-phase extraction (SPE) coupled to liquid chromatography (LC)/tandem mass spectrometry (MS/MS) for the determination of the five antibiotics (florfenicol, FF; lincomycin, LCM; oxytetracyclin, OTC; tylosin, TS; valnemulin, VLM) in swine wastewater has been developed. After filtration, aliquots (100 μl) of wastewater samples were directly injected to a column-switching LC system. Some matrix interference was removed by washing up SPE column with 0.2% formic acid solution and acetonitrile. Antibiotics eluted from SPE column were separated on analytical column by converting switching valve and were detected by MS/MS. Calibration curves using the method of standard addition had very good correlation coefficients (r > 0.99) in the range of 0.1 to 2 ng/ml. The intra-day precision of the method was less than 12% and the inter-day precision was between 6 to 17%. The detection limits were 0.01–0.1 ng/ml. When this method was applied to wastewater samples in swine facilities, four compounds (LCM, OTC, TS, and VLM) were detected.     

Dimensions of the coordinate functions of space-filling curves

The graphs of coordinate functions of space-filling curves such as those described by Peano, Hilbert, Pólya and others, are typical examples of self-affine sets, and their Hausdorff dimensions have been the subject of several articles in the mathematical literature. In the first half of this paper, we describe how the study of dimensions of self-affine sets was motivated, at least in part, by these coordinate functions and their natural generalizations, and review the relevant literature. In the second part, we present new results on the coordinate functions of Pólya's one-parameter family of space-filling curves. We give a lower bound for the Hausdorff dimension of their graphs which is fairly close to the box-counting dimension. Our techniques are largely probabilistic. The fact that the exact dimension remains elusive seems to indicate the need for further work in the area of self-affine sets.     

Status report on theGALLEX experiment

Summary The GALLEX collaboration is performing an experiment for the detection of neutrinos coming principally from the p-p fusion reaction in the Sun, via the reaction ν_e+⁷¹Ga→⁷¹Ge+e⁻. The experiment is running in the Gran Sasso Underground Laboratory of INFN, using as a target 30.3 tons of gallium in the form of 8.13 molar aqueous GaCl₃ solution. A report is given of the status of GALLEX after the end of the operations devoted to the removal from the solution of the cosmogenically formed Ge isotopes, completed in the middle of 1991. The experiment is now collecting data on solar neutrinos and the data analysis is in progress. Preliminary results concerning the first year of measurement are presented. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

Chiral information transfer by solid-solid interaction: application for absolute configuration assignment

Host-guest complexes of calix[4]resorcarene with chiral molecules were efficiently formed by solid-solid grinding and exhibited CD Cotton effects reflecting the absolute configuration of the guest.     

A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals

Modeling of scale-dependent characteristics of mechanical properties of metal polycrystals is studied using both discrete dislocation dynamics and continuum crystal plasticity. The initial movements of dislocation arc emitted from a Frank-Read type dislocation source and bounded by surrounding grain boundaries are examined by dislocation dynamics analyses system and we find the minimum resolved shear stress for the FR source to emit at least one closed loop. When the grain size is large enough compared to the size of FR source, the minimum resolved shear stress levels off to a certain value, but when the grain size is close to the size of the FR source, the minimum resolved shear stress shows a sharp increase. These results are modeled into the expression of the critical resolved shear stress of slip systems and continuum mechanics based crystal plasticity analyses of six-grained polycrystal models are made. Results of the crystal plasticity analyses show a distinct increase of macro- and microscopic yield stress for specimens with smaller mean grain diameter. Scale-dependent characteristics of the yield stress and its relation to some control parameters are discussed.