Hypothesis testing in rank-size rule regression

This note examines testing methods for Paretoness in the framework of rank-size rule regression. Rank-size rule regression describes a relationship found in the analysis of various topics such as city population, words in texts, scale of companies and so on. In terms of city population, it is basically an empirical rule that log?(_S(i))$\log ?(S_{(i)})$ is approximately a linear function of log?(i)$\log ?(i)$ where _S(i)$S_{(i)}$ is the number of population of i  th largest city in a country. This is closely related to the so-called Zipf’s law. It is known that this kind of empirical observation is found when the city population is a random variable following a Pareto distribution. Thus one may be willing to test if city size has a Pareto distribution or not. Rosen and Resnick [K.T. Rosen, M. Resnick, The size distribution of cities: an explanation of the Pareto law and primacy, Journal of Urban Economics 8 (1980), 165–186] and Soo [K.T. Soo, Zipf’s law for cities: a cross country investigation, Regional Science and Urban Economics (35) 2005, 239–263] regress log?(_S(i))$\log ?(S_{(i)})$ on log?(i)$\log ?(i)$ and log?²(i)${\log ?}^2(i)$ and test the null of Paretoness by standard t-test for the latter regressor. It is found that t-statistics take large values and the Paretoness is rejected in many countries. We study the statistical properties of the t-statistic and show that it explodes asymptotically, in fact, by simulation and thus the t-test does not provide a reasonable testing procedure. We propose an alternative test statistic which seems to be asymptotically normally distributed. We also propose a test with the null hypothesis that the city size distribution is Pareto with exponent unity, which is a modification of the F-test.     

Preparation of modified poly(vinyl chloride) containing N,N-di(β-hydroxyethyl)dithiocarbamate and its reaction with metal ions

Reaction of N,N-di(β-hydroxyethyl)dithiocarbamate ion with poly(vinyl chloride) (PVC) was undertaken, and the reaction with metal ions of the polymer obtained was investigated. The effect of γ-irradiation on the reaction with metal ion was also studied. The modified PVC (PHDC) obtained from the reaction with N,N-di(β-hydroxyethyl)dithiocarbamate ion is pale yellow even after reaction at 100°C for 5 hr in dimethylformamide (DMF); it is soluble in dipolar solvents and its chlorine content is decreased considerably. This polymer reacted well with acetate salts of copper(II), nickel(II), zinc(II), and silver(I) heterogeneously in aqueous solution because of the introduction of hydrophilic groups (two hydroxy groups). The reactivity of the metal ions toward the polymer was of the order Ag(I) ? Cu(II) > Ni(II) > Zn(II). From the result of the reaction of γ-irradiated polymer with cupric ion, the polymer was judged to have fairly good antiradiation property.     

Structure and Nonlinear Optical Properties of Lanthanide Borate Glasses

The third–order nonlinear optical susceptibility, χ⁽³⁾, of lanthanide (lanthanum, praseodymium, neodymium, and samarium) borate glasses has been measured by the third harmonic generation method. The structure of the present glass system has been studied by infrared and Raman spectroscopic methods. The network structures of the present Ln₂O₃–B₂O₃ glasses have been confirmed to be basically similar to each other. Praseodymium, neodymium, and samarium borate glasses exhibit χ⁽³⁾ values that are larger than lanthanum borate glasses, because of the optical resonance effect, in accordance with the f – f transition. Especially, the χ⁽³⁾ value for 30Pr₂O₃·70B₂O₃ glass is 1.8 × 10⁻¹² esu, which is a factor of ∼60 larger than that of SiO₂ glass. This striking enhancement of χ⁽³⁾ is mainly attributed to the large transition moment to the first excitation state.     

Fabrication of single-wall carbon nanotubes within the channels of a mesoporous material by catalyst-supported chemical vapor deposition

Diameter-controlled single-wall carbon nanotubes (SWCNTs) have been synthesized using Co, Fe/Co and Rh/Pd alloy nanoparticles trapped within the one-dimensional channels of a mesoporous materials (Folded Sheets Mesoporous material: FSM-16) by catalyst-supported chemical vapor deposition (CCVD) using ethanol as carbon source at 973-1173 K. The SWCNTs synthesized are characterized by transmission electron microscopy, Raman spectroscopy and photoluminescence spectroscopy. The yield, diameter distribution and quality of the SWCNTs strongly depend on the reaction temperature during CCVD. The product synthesized at 1173 K contains only SWCNTs, in marked contrast to those synthesized at lower temperatures. As the reaction temperature decreases, the relative abundance of multi-wall carbon nanotubes against SWCNTs significantly increases, whereas the mean diameter of SWCNTs increases as reaction temperature increases. The results show that a careful control of the reaction temperature is crucial to fabricate diameter-controlled SWCNTs from the channels of FSM-16.     

Effects of the incorporation of silver and gold nanoparticles on the photoanodic properties of rose bengal sensitized TiO2 film electrodes prepared by sol-gel method

Rose bengal-deposited TiO₂ film electrodes bearing dispersed Ag or Au nanoparticles were prepared by the sol-gel method. The dye-induced visible region photoresponse of the electrodes decreased with increasing Ag content up to a mole ratio of Ag/TiO₂ = 0.0207, while the UV photoresponse increased. On the other hand, the dye-induced visible region photoresponse decreased to a less extent by incorporation of a larger amount of Au particles of Au/TiO₂ = 0.06, along with decreased UV photoresponse. The effects of the metal particles on the dye sensitization of the electrodes were discussed in terms of band edge fluctuation induced by the surface metal particles, Schottky barriers at TiO₂/metal interfaces, and surface plasma resonance.     

Determination of substances in polylactic acid products for food-contact use and mutagenicity of their migration solutions

Specification tests defined in the Japanese Food Sanitation Law were conducted on 7 polylactic acid food-contact products. Moreover, the content and migration of other compounds were examined by means of ICP-AES, GC/MS and mutagenicity tests. All products met their specifications, and migration levels of heavy metals were negligible. No notable peak was observed in GC/MS analysis. Moreover, all products gave negative results in both rec-assay and the umu-test. An increase in the β-galactosidase activity in the umu-test observed with the migration solution of soup bowl was due not to polylactic acid, but to the polyurethane coating.     

Metals in recycled polyethylene terephthalate and discrimination method for its use

Metals in recycled polyethylene terephthalate (PET) were analyzed by ICP-MS following microwave digestion with nitric acid. Physically and superclean-like recycled PET contained both Ge and Sb, and sometimes contained Co, P or Si. In contrast, the chemically recycled PET contained only Ge or Sb, and some samples contained Co. The recycled PETs did not contain Pb or Cd. Ge and Sb were catalysts of the polymerization, and the other metals also originated from the PET resin as additives. It was concluded that there is no safety concern about metals in recycled PET. It became clear that the presence of both Ge and Sb could identify products formed using physically or superclean-like recycled PET. According to this discrimination method, about half of the sheet molding products used recycled PET.     

Characteristics of neutralization of acids by newly isolated fungal cells

Soil microorganisms play an important role in maintaining soil pH at levels suitable for other soil organisms. To clarify the biological neutralization mechanism in soil, we isolated soil microorganisms showing a high ability to neutralize acids and studied their characteristics. From our taxonomic study, three isolated strains were identified as filamentous fungi, namely Mucor sp., Aspergillus fumigatus, and Aureobasidium pullulans. These strains could secrete basic materials, such as ammonia, for neutralization, grow in the medium at pH 4.0 and increase the pH of the medium to approximately 8.0. These microbial cells could neutralize not only nitric acid but also sulfuric and hydrochloric acids. The strains could also grow by utilizing nitric acid as a sole nitrogen source. In the soil containing these organisms, the pH was maintained in the neutral range by the buffering action of basic materials that they secrete. These results suggest that these fungal cells are useful for protecting the soil from acidification by acid rain.