Multiple cover formula of generalized DT invariants I: Parabolic stable pairs

In this paper, we introduce the notion of parabolic stable pairs on Calabi–Yau 3-folds and invariants counting them. By applying the wall-crossing formula developed by Joyce–Song, Kontsevich–Soibelman, we see that they are related to generalized Donaldson–Thomas invariants counting one dimensional semistable sheaves on Calabi–Yau 3-folds. Consequently, the conjectural multiple cover formula of generalized DT invariants is shown to be equivalent to a certain product expansion formula of the generating series of parabolic stable pair invariants. The application of this result to the multiple cover formula will be pursued in the subsequent paper.     

Noncommutative resolution, F-blowups and D-modules

We explain the isomorphism between the G-Hilbert scheme and the F-blowup from the noncommutative viewpoint after Van den Bergh. In doing this, we immediately and naturally arrive at the notion of D-modules. We also find, as a byproduct, a canonical way to construct a noncommutative resolution at least for a few classes of singularities in positive characteristic.     

Light scattering from crystalline superstructure in tubular-extruded polybutene-1 films

Light scattering from polybutene-1 films prepared by tubular extrusion was studied in order to investigate its crystalline superstructure and the deformation mechanism. Analysis of the light-scattering patterns together with electron micrographs, indicate the existence of sheaflike crystalline superstructures. The sheaves are aligned nearly side by side with their axes preferentially oriented perpendicular to the machine direction. The H_v scattering patterns exhibit a “butterfly” appearance. Analysis of the patterns in terms of scattering and azimuthal angles at which the scattering intensity is a maximum yields information on the size and shape of the sheaflike texture. The information should be of importance in studies of anisotropic crystal growth caused by molecular orientation in the melt and of the deformation mechanism of the texture. The deformation behavior should be representative of that of different parts of spherulites, at least qualitatively; the deformation of the texture along the machine and transverse directions corresponds to deformation of equatorial and meridional regions of a spherulite, respectively.     

Tilting generators via ample line bundles

It is known that a tilting generator on an algebraic variety X gives a derived equivalence between X and a certain non-commutative algebra. In this paper, we present a method to construct a tilting generator from an ample line bundle, and construct it in several examples.     

Neutron diffraction data and molecular dynamics simulations of the molten mixture Ag(Br0.7I0.3)

The structure factors of the ionic liquid mixture Ag(Br(0.7)I(0.3)) at three temperatures, 723, 923, and 1023 K, as well as of the pure molten AgI at 923 K and the pure molten AgBr at 773 and 923 K, were studied experimentally and by means of molecular dynamics simulations. The experiments were carried out using the high intensity total scattering time-of-flight spectrometer, HIT-II, at the KENS spallation neutron source in Japan. The experimental data are very reliable, with the possible exception of the small momentum transfer region, whose accessibility is limited by neutron energy and detector positions. The simulations made use of the semiempirical rigid ion potentials of the Vashishta-Rahman [Phys. Rev. Lett. 40, 1337 (1978)] type using a new set of parameters appropriate for the mixture. Within the known constraints of the pairwise rigid ion potentials, the simulated structure factors are in fair agreement with experiment. The results for the pair distribution functions suggest that the molten mixture retains the superionic character found in previous calculations of both the AgI and AgBr melts. This suggestion is confirmed by the results for the self-diffusion coefficients. Values obtained for the ionic conductivities are also presented.     

Certain sequences with compact closure

This paper deals with a question which is stated by quite simple definitions. A sequence {xn} in a space X is called a β-sequence if every subsequence of it has a cluster point in X. The closure of the sequence {xn} means the closure of in X. Here we consider the question when a β-sequence has compact closure. We give several answers to this question.     

Ferroelectric order and phase transition in polytrifluoroethylene

Polarization-reversal currents and x-ray profiles under a high dc field were measured on polytrifluoroethylene (PTrFE) samples prepared by melt crystallization at different cooling rates. The results for PTrFE were found to be analogous to those for copolymers of vinylidene fluoride and trifluoroethylene [P(VDF/TrFE)] with low VDF content. Slow-cooled and quenched samples showed different x-ray profiles but the same IR spectra. For the slow-cooled samples, a polarization reversal was clearly observed as a peak in polarization current, offering evidence for ferroelectric order in PTrFE. The ferroelectric behavior was found to be unlike that of typical ferroelectric polymers. There are two processes in a polarization reversal, i.e., partial depolarization reversal, accompanied by crystalline phase transitions. It is noted that no ferroelectric order was observed for the quenched sample which, however, becomes pyroelectric by poling as revealed by our previous studies. We speculate on possible crystal structures of PTrFE based on the published structure models and the present results. The relation between the ferroelectricity and the previously reported pyroelectricity is also discussed.     

The influence of light sources on sunitinib measurements with photoisomerization

Sunitinib is an orally administered tyrosine kinase inhibitor. Therapeutic drug monitoring is an important component of the follow‐up of patients because of high interpatient variability in the pharmacokinetics of sunitinib and large variabilities in its efficacy and toxicity. The aim of the present study was to examine the light stability of sunitinib and confirm the effects of light exposure on sunitinib measurements by LC–MS/MS. Sunitinib and its active metabolite, SU12662, convert Z isomers to E isomers with exposure to light. The Z–E photoisomerization ratio reached a plateau at 35% for both E isomers in methanol within 15 min of normal light exposure (700 lx). However, the Z isomer of the sunitinib and SU12662 peak area ratios in plasma decreased by 10% within 15 min. These results suggest that sunitinib samples need to be handled without light exposure in all sample preparation steps. Alternatively, it should be measured sunitinib and SU12662 after the sample has reached photoisomerical equilibrium. These results suggest that the sunitinib therapeutic range changes depending on light conditions during sample handling in sunitinib and SU12662 measurements.