A case of Budd-Chiari syndrome: Gd-EOB-DTPA-enhanced MR findings

Budd-Chiari syndrome (BCS) is a rare disorder caused by the obstruction of hepatic venous outflow, leading to sinusoidal congestion, ischemic injury to liver cells and portal hypertension. Long-term survival largely depends on whether hepatocellular carcinoma occurs. A recently available liver-specific contrast medium, gadolinium-ethoxybenzyl-diethylenetriamine penta-acetic acid (Gd-EOB-DTPA), reportedly has high diagnostic capability for detection of malignant liver tumors. However, there has been no report of the sue of Gd-EOB-DTPA-enhanced magnetic resonance imaging (MRI) for BCS. We present a case of chronic BCS who underwent both gadopentetate dimeglumine (Gd-DTPA) and Gd-EOB-DTPA-enhanced MRI. Hepatic congestion and edema were seen as slightly hypointense areas on Gd-EOB-DTPA-enhanced hepatobiliary-phase images, although these areas were observed as slightly hyperintense on previously obtained Gd-DTPA-enhanced delayed-phase image. Reduced uptake of Gd-EOB-DTPA by hepatocytes in the region of congestion or edema may account for this difference, which should be recognized in image interpretations.     

Multiple elliptic hypergeometric series. An approach from the Cauchy determinant

A multiple generalization of elliptic hypergeometric series is studied through the Cauchy determinant for the Weierstrass sigma function. In particular, a duality transformation for multiple hypergeometric series is proposed. As an application, two types of Bailey transformations for very well-poised multiple elliptic hypergeometric series are derived.     

Analysis of Spectral Reflectance Using Normalization Method from Endoscopic Spectroscopy System

Objective assessment of gastrointestinal mucosal color is extremely important in the endoscopic diagnosis of digestive tract disease. In this paper, we propose a method to clarify the spectral characteristics of gastric and colon cancer. A large number of spectral reflectance data of mucous membrane are measured by the endoscopic spectroscopy system (ESS) in the National Cancer Center Hospital East, Kashiwa, Japan and the Department of Internal Medicine, Self-Defense Force Center Hospital, Tokyo, Japan. We assume that early cancer appears primarily in the spectral data of short wavelength, because it is usually present in a superficial cell where short wavelength light is scattered more strongly than long wavelength light. To identify the features in the short wavelength components, the spectral reflectance was divided by the reflectance of a long wavelength. We investigated the possibility of distinguishing early cancer from normal spectral data through statistical analysis, employing the projection axis as the mean difference between them. Early cancer and normal spectral data were projected on the projection axis, and the Student’s T-test was applied to evaluate the mean of the distribution between these data.     

On first passage time structure of random walks

For continuous time birth-death processes on {0,1,2,…}, the first passage time T⁺_n from n to n + 1 is always a mixture of (n + 1) independent exponential random variables. Furthermore, the first passage time T_0,n+1 from 0 to (n + 1) is always a sum of (n + 1) independent exponential random variables. The discrete time analogue, however, does not necessarily hold in spite of structural similarities. In this paper, some necessary and sufficient conditions are established under which T⁺_n and T_0,n+1 for discrete time birth-death chains become a mixture and a sum, respectively, of (n + 1) independent geometric random variables on {1,2,…};. The results are further extended to conditional first passage times.     

Computation of multiple eigenvalues of infinite tridiagonal matrices

In this paper, it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues. The computation of such double eigenvalues is enabled by the Newton method of two variables. The three-term recurrence relations obtained from its eigenvalue problem (EVP) subsume the well-known relations of (A) the zeros of ; (B) the zeros of ; (C) the EVP of the Mathieu differential equation; and (D) the EVP of the spheroidal wave equation. The results of experiments are shown for the three cases (A)-(C) for the computation of their ``double pairs'.

     

Canceling branch points and cusps on projections of knotted surfaces in -space

For a knotted surface in -space, its generic projection into -space has branch points as its singularities, and its successive projection into -space has fold points and cusps as its singularities. In this paper, we show that for non-orientable knotted surfaces, the numbers of branch points and cusps can be minimized by isotopy.

     

The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations

We show the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brezis-Gallouet-Wainger and Beale-Kato-Majda. As an application of those inequalities, the regularity problem under the critical condition to the Navier-Stokes equations, the Euler equations in and the gradient flow to the harmonic map to the sphere are discussed. Namely the Serrin-Ohyama type regularity criteria are improved in the terms of the Besov spaces. Received: 21 September 2000; in final form: 16 Feburary 2001 / Published online: 18 January 2002     

Construction of Chiral Tri‐ and Tetra‐Arylmethanes Bearing Quaternary Carbon Centers: Copper‐Catalyzed Enantioselective Propargylation of Indoles with Propargylic Esters

Copper‐catalyzed enantioselective propargylation of indoles with propargylic esters and sequential Huisgen cycloaddition with azides lead to the construction of chiral triarylmethanes, bearing a quaternary carbon center, with high to excellent enantioselectivities. The result described herein can be used in the enantioselective preparation of a tetraarylmethane.