The application of multivariate analysis to the radioallergosorbent test (RAST)

Multivariate statistical analyses using principal component analyses (PCA) and Mahalanobis' method were applied to the quality control of radioallergosorbent test (RAST). Mites and foods allergen were analyzed by PCA method, and foods allergen were analyzed by Mahalanobis' method. The vast differences in the distribution on titers among the mites and the foods were observed. To evaluate the results of a test and the quality of kits for test statistically, it should be better to use multivariate analyses such as PCA or Mahalanobis' method.     

Measurements of equilibrium water vapor pressures for the dehydration of magnesium, manganese and cobalt formate dihydrates by means of the transpiration method

The equilibrium water vapor pressures for the thermal dehydration of Mg(HCO(2))(2). 2H(2)O, Mn(HCO(2))(2). 2H(2)O and Co(HCO(2))(2). 2H(2)O were measured by means of the transpiration method. These hydrates form isomorphous crystals with space group P21/c. In this structure, the water molecules lie in the planes parallel to the (100) planes. Thermodynamic data such as DeltaG, DeltaH and DeltaS were derived from the values of the water vapor pressures. The relationship between these thermodynamic data and the crystal structures is discussed.     

Structure of liquid-crystalline phases formed by N-acetyl-L-glutamic acid oligomeric benzyl esters –2H NMR study

A series of N-acetyl-L-glutamic acid oligopeptide benzyl esters with exact residue numbers 4, 6, and 12 has been synthesized by a stepwise procedure. For these oligopeptide–dioxane binary systems, the behavior of the liquid-crystalline phases has been examined␣by the use of ²H NMR, and the results indicate that highly ordered aggregates formed by these oligopeptides in dioxane are in an alignment similar to that in a nematic mesophase. Received: 27 February 2001 Accepted: 8 May 2001     

Reverse aromatic cope rearrangement of 2-allyl-3-alkylideneindolines driven by olefination of 2-allylindolin-3-ones: synthesis of alpha-allyl-3-indole acetate derivatives

The reverse aromatic Cope rearrangement of 2-allyl-3-alkylideneindolines obtained by Horner-Wadsworth-Emmons olefination of 2-allylindolin-3-ones was performed. When 2-allylindolin-3-ones were treated with phosphonium ylides in refluxing toluene, domino Wittig reaction and reverse aromatic Cope rearrangement took place to give alpha-allyl-3-indole acetate derivatives in good yields. The aromatization as a new driving force in the Cope rearrangement is preferable to the conjugation with the carbonyl and cyano groups and also to the alkyl substitution pattern, which are well-known driving forces.     

Phlomisflavosides A and B, new flavonol bisglycosides from Phlomis spinidens

From the aerial parts of Phlomis spinidens, two new flavonol bisglycosides, phlomisflavosides A (1) and B (2), were isolated together with the known compounds, astragalin, isoquercitrin, lamiridoside, phlomoside A, shanzhiside methyl ester, 8-O-acetylshanzhiside methyl ester, phlorigidoside C, rodioloside (=salidroside), forsythoside B, citroside A and lariciresinol-4'-O-beta-D-glucoside. The structures of the new compounds were elucidated based on spectral and chemical evidence.     

Cohomological non-rigidity of generalized real Bott manifolds of height 2

We investigate the following problem: When do two generalized real Bott manifolds of height 2 have isomorphic cohomology rings with ?/2 coefficients and also when are they diffeomorphic? It turns out that in general cohomology rings with ?/2 coefficients do not distinguish those manifolds up to diffeomorphism. This gives a negative answer to the cohomological rigidity problem for real toric manifolds posed earlier by Y. Kamishima and the present author. We also prove that generalized real Bott manifolds of height 2 are diffeomorphic if they are homotopy equivalent.     

Rigidity problems in toric topology: A survey

Several rigidity problems in toric topology are addressed in the survey paper by the second and third authors, “Classification Problems of Toric Manifolds via Topology” (in Toric Topology, Am. Math. Soc., Providence, RI, 2008, pp. 273–286). In the present paper, we survey the results on those problems including recent developments.     

Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes

The purpose of this paper is to derive the stochastic expansion of self-normalized-residual functionals stemming from a class of diffusion type processes observed at high frequency, where total observing period may or may not tend to infinity. The result enables us to construct some explicit statistics for goodness of fit tests, consistent against “presence of a jump component” and “diffusion-coefficient misspecification”; then, the acceptance of the null hypothesis may serve as a collateral evidence for using the correctly specified diffusion type model. Especially, our asymptotic result clarifies how to remove the bias caused by plugging in a diffusion-coefficient estimator.     

Kernel identities for van Diejen’s q-difference operators and transformation formulas for multiple basic hypergeometric series

The kernel function of Cauchy type for type BC is defined as a solution of linear q-difference equations. In this paper, we show that this kernel function intertwines the commuting family of van Diejen’s q-difference operators. This result gives rise to a transformation formula for certain multiple basic hypergeometric series of type BC. We also construct a new infinite family of commuting q-difference operators for which the Koornwinder polynomials are joint eigenfunctions.