ON FINITE TIME STOPPING PHENOMENA FOR ONE-HARMONIC MAP FLOW

Abstract. For a very strong diffusion equation like total variation flow it is often observed that the solution stops at a steady state in a finite time. This phenomenon is called a finite time stopping or a finite time extinction if the steady state is zero. Such a phenomenon is also observed in one-harmonic map flow from an interval to a unit circle when initial data is piecewise constant. However, if the target manifold is a unit two-dimensional sphere, the finite time stopping may not occur. An explicit example is given in this paper. 1

Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation

We consider a gradient flow system of total variation with constraint. Our system is often used in the color image processing to remove a noise from picture. In particular, we want to preserve the sharp edges of picture and color chromaticity. Therefore, the values of solutions to our model is constrained in some fixed compact Riemannian manifold. By this reason, it is very difficult to analyze such a problem, mathematically. The main object of this paper is to show the global solvability of a constrained singular diffusion equation associated with total variation. In fact, by using abstract convergence theory of convex functions, we shall prove the existence of solutions to our models with piecewise constant initial and boundary data

Combined Gastrectomy with Adjacent Organs in T4 Gastric Cancer : Therapeutic Results and Indication

The postoperative morbidity, mortality and survival of 244 T4 gastric cancer patients were examined to assess the therapeutic results and to clarify the indication for combined gastrectomy with adjacent (T4) organs. A total of 190 combined and 54 simple gastrectomies were performed during the 25-year period between 1969 and 1994. Fourteen (7.4%) and 7 (13.0%) patients died of the complications after combined and simple gastrectomies respectively. No statistical significant difference was found in the mortality rates between the gastrectomies. The histological examination of 190 resected specimens by the combined gastrectomy with T4 organs revealed that gastric resections with conclusive curability A, B and C were performed in 33 (17.4%), 84 (44.2%) and 73 (38.4%) cases respectively. Significant differences (P < 0.01) among 3 survival curves of the patients with curability A, B and C were found, and the 5-year survival rates were 65.5%, 35.4% and 9.2% respectively. The survival curve of 176 patients with combined gastrectomy was significantly (P < 0.01) higher than that of 47 patients with simple gastrectomy, and the 5-year survival rates were 31.3% and 4.3%. However, the survival curve and the 5-year survival rate of the patients with simple gastrectomy were not statistically different from those of the patients with curability C. These results suggest that combined gastrectomy with T4 organs in T4 gastric cancer may be indicated for the patients with surgical curability B, but not surgical curability C

Fractional time differential equations as a singular limit of the Kobayashi-Warren-Carter system

This paper is concerned with a singular limit of the Kobayashi-Warren-Carter system, a phase field system modelling the evolutions of structures of grains. Under a suitable scaling, the limit system is formally derived when the interface thickness parameter tends to zero. Different from many other problems, it turns out that the limit system is a system involving fractional time derivatives, although the original system is a simple gradient flow. A rigorous derivation is given when the problem is reduced to a gradient flow of a single-well Modica-Mortola functional in a one-dimensional setting.Comment: 24 page

Spin relaxation in CdTe/ZnTe quantum dots

We have measured photoluminescence (PL) spectra and time-resolved PL in CdTe quantum dots (QDs) under the longitudinal magnetic field up to 10T. Circular polarization of PL increases with increasing magnetic field, while its linear polarization is absent under linearly polarized excitation. Time-resolved PL measurements clarified that this behavior is caused by the suppression of spin relaxation induced by the longitudinal magnetic field. We believe that this behavior is related to the hyperfine interaction of electron spin with magnetic momenta of lattice nuclei

Clinical Impact of Down-Regulated Plasma miR-92a Levels in Non-Hodgkin's Lymphoma

Background: We undertook a study to evaluate the clinical relevance of miR-92a in plasma obtained from non-Hodgkin’s lymphoma (NHL) patients, because the miR-17-92 polycistronic miRNA cluster plays a crucial role in lymphomagenesis and affects neo-angiogenesis. Methodology/Principal Findings: Plasma miR-92a values in NHL were extremely low (,5%), compared with healthy subjects (P,.0001), irrespective of lymphoma sub-type. The very low plasma level of miR-92a increased in the complete response (CR) phase but did not reach the normal range, and the plasma level was lower again in the relapse phase. Patients in CR or CR unconfirmed with a plasma miR-92a level of less than the cut-off level showed a significantly high relapse rate compared with patients with normalized plasma miR-92a level. Conclusions/Significance: The current results therefore indicate that the plasma miR-92a value could be a novel biomarke