Perturbation method for determining the group of invariance of hierarchical models

We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in [S. Aoki, A. Takemura, The largest group of invariance for Markov bases and toric ideals, J. Symbolic Comput. 43 (5) (2008) 342–358]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof by Aoki and Takemura which was based on stabilizers of a subset of indeterminates, the perturbation method gives a much simpler proof of the group of invariance. In particular, we determine the group of invariance for a general hierarchical model of contingency tables in statistics, under the assumption that the numbers of the levels of the factors are generic. We prove that it is a wreath product indexed by a poset related to the intersection poset of the maximal interaction effects of the model.     

Formation of 1,2-dioxolanes using Mn(III)-based reaction of various arylacetylenes with 2,4-pentanedione and related reaction

The manganese(III)-based aerobic oxidation of arylacetylenes with 2,4-pentanedione at ambient temperature unexpectedly gave the 1,2-dioxolane derivatives in moderate yields together with a small amount of the oxiranes. The 1,2-dioxolanes underwent silica gel-assisted contraction to quantitatively give the oxiranes. The reaction pathway for the formation of the 1,2-dioxolanes and the by-product was discussed.     

Formation of Metal‐Assisted Stable Double Helices in Dimers of Cyclic Bis‐Tetrapyrroles that Exhibit Spring‐Like Motion

Bidipyrrin‐bridged macrocycles, prepared from Ni^II‐bridged dipyrrin‐based nanorings by intramolecular oxidative biaryl coupling reactions, yielded [2+4]‐type Zn^II‐assisted stable twisted‐ring dimers comprising two double helices. These [2+4]‐type metal complexes can be optically resolved by chiral HPLC and exhibit tunable electronic and optical properties as a result of spring‐like motions. The double helices behave as glue to connect two macrocycles and as the screws of hinges to form thermally responsive synchronized spring systems.     

Swelling-induced Mechanochromism in Multinetwork Polymers

We report a novel and versatile approach to achieving swelling-induced mechanochemistry using a multinetwork (MN) strategy that enables polymer networks to repeatedly swell with monomers and solvents. The isotropic expansion of the first network (FN) provides sufficient force to drive the mechanochemical scission of a radical-based mechanophore, difluorenylsuccinonitrile (DFSN). Although prompt recombination generally occurs in such highly mobile environments, the resulting pink radicals are kinetically stabilized in the gels, probably due to limited diffusion in the extended polymer chains. Moreover, the DFSN embedded in the isotropically strained chain exhibits increased thermal reactivity, which can be reasonably explained by an entropic contribution of the FN to the dissociation. The utility of the MN polymers is demonstrated not only in terms of swelling-force-induced network modification, but also in the context of tunable reactivity of the dissociative unit through proper design of the hierarchical network architecture.     

Influence of adding carbon nanotubes on photoelectric conversion properties of dye-doped titania gel

Multiwalled carbon nanotubes (MWCNTs) were incorporated into amorphous dye-doped titania gel by the sol?Cgel method at room temperature. The working electrodes were prepared by coating the ITO glass with the sol?Cgel titania precursor containing the dye and MWCNTs. The photoelectric conversion properties of the electrodes were examined by simple spectroscopic and electric measurements. The photocurrent spectrum originated from the absorption of the dye. The short circuit photocurrent was enhanced by adding a small amount of MWCNTs evenly to the amorphous dye-doped titania gel. The open circuit voltage was due to the semiconducting characteristics property of the titania gel. The experimental results indicated the electron transport from the dye excited states to the MWCNTs through the titania gel. The MWCNTs functioned as bridges between the titania and ITO. Steam treatment of the titania gel electrodes significantly increased the photoelectric performance due to crystallization of the titania and enhancement of the dye?Ctitania interaction forming the chelate complex on the titania particle surface.     

Thermal extrusion of cellulose using hydroxypropyl methylcellulose

Cellulose - Hydroxypropyl methylcellulose (HPMC), a cellulose derivative, is highly water soluble, viscoelastic, and thermoplastic. However, the thermoplasticity of HPMC has not yet been studied in...     

Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE

We consider goodness-of-fit tests of the Cauchy distribution based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard Cauchy distribution. For standardization of data Gürtler and Henze (2000,Annals of the Institute of Statistical Mathematics,52, 267–286) used the median and the interquartile range. In this paper we use the maximum likelihood estimator (MLE) and an equivariant integrated squared error estimator (EISE), which minimizes the weighted integral. We derive an explicit form of the asymptotic covariance function of the characteristic function process with parameters estimated by the MLE or the EISE. The eigenvalues of the covariance function are numerically evaluated and the asymptotic distributions of the test statistics are obtained by the residue theorem. A simulation study shows that the proposed tests compare well to tests proposed by Gürtler and Henze and more traditional tests based on the empirical distribution function.     

Influence of radial electric field on trajectories of plug potential bounce ion in the tandem mirror

Bouncing ions between the plug potentials play an important role in improvement of the axial confinement in the tandem mirror. We examined the influence of the radial electric field on the trajectories of the ions passed through the anchor cell with nonaxisymmetric magnetic configuration on the assumption that the shape of the magnetic flux tube was shifted from the shape of the equipotential surface of the plasma at the mirror throats of the anchor cells. The discrepancy between the shapes enhanced the radial drift of the bounce ion. Radial potential profile of the core plasma was controlled by adjustment of the radially separated endplate potentials, and it was found that the flattened radial potential profile was effective for the decrease of the radial drift. Presented at 5th Workshop “Role of Electric Fields in Plasma Confinement and Exhaust”, Montreux, Switzerland, June 23–24, 2002.