Explicit formula for singular vectors of the Virasoro algebra with central charge less than 1

We calculate explicitly the singular vectors of the Virasoro algebra with the central charge $c\leq 1$. As a result, we have an infinite sequence of the singular vectors for each Fock space with given central charge and highest weight, and all its elements can be written in terms of the Jack symmetric functions with rectangular Young diagram.Comment: 10 pages, revised versio

Emergent Supersymmetry in Warped Backgrounds

We show that quantum mechanical supersymmetries are emerged in Kaluza-Klein spectrum of linearized gravity in several warped backgrounds as a consequence of higher-dimensional general coordinate invariance. These emergent supersymmetries play an essential role for the spectral structure of braneworld gravity. We show that for the case of braneworld models with two codimension-1 branes the spectral pattern is completely determined only through the supersymmetries

Studies on Bile Pigments II. Seperation of Natural Direct Bilirubins

Separation of both forms of the direct bilirubin were carried out from the dog's gallbladder bile, and further isolations of them were also done. 1. The natural salt-form bilirubin was isolated after separation on the column of aluminium oxide with a n-propanolic aqueous solution. 2. The natural salt-form bilirubin was obtained in amorphous yellow powders which were strongly hygroscopic and easily soluble in water and methanol but not in chloroform or carbon tetrachloride. An aqueous solution of these powders showed both the direct diazo and Gmelin reaction, but neither Ehrlich's aldehyde nor Schlesinger reaction. The salt-form bilirubin was transferred into chloroform only when some quantities of hydrochloric acid were added to a mixture of chloroform and an aqueous solution of it. 3. The absorption maxima of the natural salt-form bilirubin existed at 420 to 430 m&#956; in a methanolic solution and at 425 or 435m&#956; in 50% or 10% n-propanol. 4. The natural ester-form bilirubin was isolated after separating on the column of silica gel with a chloroformethanolic mixture. 5. The natural ester-form bilirubin was obtained in amorphous greenish yellow powders. It was further hygroscopic and easily soluble in water and methanol but not in chloroform or carbon tetrachloride. An aqueous solution of it showed the direct diazo and Gmelin reaction, but neither Ehrlich's aldehyde nor Schlesinger's reaction. No pigment was transferred into chloroform even if some quantities of hydrochloric acid were added to a mixture of chloroform and an aqueous solution of it, but did by saponification with 5% methanolic potash. 6. The absorption maxima of the natural ester-form bilirubin existed at 415 m&#956; in both methanolic and aqueous solutions.</p

The Japan - U.S. bilateral trade

International trade ; Japan ; Balance of payments

Inter-regional spillovers in Fukuoka Prefecture: Using VAR model

This paper examines the question of inter-regional spillovers in Fukuoka Prefecture. Fukuoka Prefecture is located on the west side of Japan, and is near the Korean peninsula. There are two government-designated major cities in Fukuoka Prefecture. One is Fukuoka City, which is the central city in Fukuoka Prefecture. The other is Kitakyushu City, which is a big city with a population of about one million. The relationship between Fukuoka City and Kitakyushu City is not without problems. Because the two cities are independently administered, each government can execute the policy that best suits its own interest. On the other hand, it is important for Fukuoka Prefecture that both cities economy cooperate. We analyze this question within the framework of three or more than three regions vector-autoregressive (VAR) model. To express the economic relationship in this study, Fukuoka Prefecture is divided into Fukuoka City, Kitakyushu City, and the rest of Fukuoka Prefecture. We subject to extensive sensitivity analysis, with particular attention paid to the effects on the results of strong common output movements.