We report here a case of torsion of the gallbladder in a 73-year-old woman. The patient was admitted to our hospital with right hypochondralgia. Ultrasonography and computed tomography demonstrated a distended gallbladder, with a multilayered wall, which contained no stones. Since the symptoms did not respond to antibiotics, laparotomy was performed. The gallbladder was found to be twisted around its pedicle and to be gangrenous. Cholecystectomy was performed, and the patient had an uneventful postoperative course. We also reviewed 245 cases reported in the Japanese literature. The clinical features of gallbladder torsion, which include low frequency of fever and jaundice, poor response to antibiotic therapy, and acute onset of abdominal pain, may be helpful in the differential diagnosis from acute cholecystitis. Moreover, a highly suggestive sign of gallbladder torsion observed by ultrasonography or computed tomography is a markedly enlarged "floating" gallbladder with a continuous hypoechoic line indicating edematous change in the wall.

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We study the spectral properties of Schrödinger operators on perturbed lattices. We shall prove the non-existence or the discreteness of embedded eigenvalues, the limiting absorption principle for the resolvent, construct a spectral representation, and define the S-matrix. Our theory covers the square, triangular, diamond, Kagome lattices, as well as the ladder, the graphite and the subdivision of square lattice.

Let a physical body in R 2 or R 3 be given. Assume that the electric conductivity distribution inside consists of conductive inclusions in a known smooth background. Further, assume that a subset ⊂ ∂ is available for boundary measurements. It is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on . More precisely: given a ball B with center outside the convex hull of and satisfying (B ∩ ∂ ) ⊂ , boundary measurements on with explicitly given Dirichlet data are enough to determine whether B intersects the inclusion. An approximate detection algorithm is introduced based on the theory. Numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion-free domain near and is robust against measurement noise.

Since −∆e ix·ξ = |ξ| 2 e ix·ξ , e ix·ξ is an eigenfunction of −∆. Therefore (0.1) and (0.2) illustrate the expansion of arbitrary functions in terms of eigenfunctions (more appropriately generalized eigenfunctions since they do not belong to L 2 (R n )) of the Laplacian.There are two directions of development of the above fact. One is quantum mechanics, where the Schrödinger operator H = −∆ + V (x) is the most basic tool to decribe the physical system of atoms or molecules. If H has the continuous spectrum, it is known that there exists a system of generalized eigenfunctions of H which play the same role as e ix·ξ . Moreover, by using these generalized eigenfunctions one can define an operator called the scattering matrix or the S-matrix, which is the fundamental object to study the physical properties of quantum mechanical particles through the scattering experiment.The other direction is the Fourier transform on manifolds, especially on homogeneous spaces of Lie groups, which is a central theme in the representation theory. Hyperbolic manifolds, one of the deepest sources of classical mathematics, appear also in this context. In particular, hyperbolic quotient manifolds by the action of discrete subgroups of SL(2, R) and the associated S-matrix are important objects in number theory. 0.2. Perturbation of the continuous spectrum. The aim of the perturbation theory of continuous spectrum is, given an operator H 0 whose spectral property is rather easy to understand, to study the spectral properties of H 0 + V , where V is the perturbation deforming the operator H 0 . When H = H 0 + V has the continuous spectrum, an effective way of studying its spectral properties is to construct a generalized Fourier tranform associated with H. To accomplish this idea, it is necessary that the Fourier transform for H 0 can be constructed easily. For example, it is the case for the Laplacian −∆ on R n . If the perturbation term V is an operator on the same Hilbert space as for H 0 and is not so strong, one can construct the Fourier transform associated with H 0 + V by using the technique of functional analysis and partial differential equations. This is not so easy for operators on hyperbolic manifolds. Even the construction of the Fourier transform associated with the Laplace-Beltrami operator on the hyperbolic space is no longer a trivial work. To construct the Fourier transform on hyperbolic spaces based on the upper half space model or the ball model, one needs deep knowledge of Bessel functions. Under the action of discrete subgroups, the properties of groups will reflect on the structure of manifolds or the construction of generalized eigenfunctions. 0.3. Spectral and scattering theory on hyperbolic manifolds. In the present note, we deal with the spectral theory and the associated forward and inverse problems for Laplace-Beltrami operators on hyperbolic manifolds. Since we are mainly interested in its spectral properties, Selberg's work [Se56] and its developments are beyond our scope. As an approach to the hyperbolic man...

Physical results after pylorus-preserving gastrectomy (PPG) with preservation of the vagus nerve were evaluated. The status of 15 patients with early gastric cancer after PPG was compared with that of 14 patients after distal gastrectomy (DG). The postoperative/preoperative body-weight ratio of the PPG group (0.99) was significantly greater than that of the DG group (0.92). Patients who had PPG had fewer postoperative abdominal symptoms than those who underwent DG. The gastric emptying pattern of patients who had a pylorus-preserving procedure was slower than that of those who had conventional gastrectomy, and more similar to the preoperative pattern. Contraction of the gallbladder after PPG was better than after DG. Gastroscopy revealed that the mucosa of the stomach remnant after PPG was less abnormal than after DG. In conclusion, PPG is a more physiological operation than conventional DG and should be applied in carefully selected cases of early gastric cancer.

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T1 and sN0 patients may be a target group for the study of SLN-guided surgery. A larger multicenter trial should be performed to clarify the application of sentinel node navigation surgery for gastric cancer.