SMOOTHNESS OF INERTIAL MANIFOLDS FOR SEMILINEAR EVOLUTION EQUATIONS IN COMPLEX BANACH SPACES

Abstract. We study inertial manifolds for a semilinear evolution equation du/dt + Au = F (t, u) in a complex Banach space. It is known that various conditions ensure existence of inertial manifolds for the equation, however, Miklavčič gave a sharp but simple condition so as to show the existence of inertial manifolds. In this paper, we show smoothness of inertial manifolds using the sharp condition with additional assumptions on F , and also apply to a scalar reaction diffusion equation ut − uxx = f (t, x, u, ux) with the Dirichlet boundary conditions

非線形偏微分方程式における弱解の再正規化理論についての研究

制度:新 ; 文部省報告番号:乙1985号 ; 学位の種類:博士(学術) ; 授与年月日:2005/9/27 ; 早大学位記番号:新410

Clinical impact of lipid injectable emulsion in internal medicine inpatients exclusively receiving parenteral nutrition: a propensity score matching analysis from a Japanese medical claims database

Background Although guidelines recommend lipid injectable emulsions (ILEs) be used as a part of parenteral nutrition, many patients in Japan receive lipid-free parenteral nutrition. Furthermore, little is known about the effect of ILEs on clinical outcomes in medical inpatients managed with parenteral nutrition. The aim of this study was to investigate the clinical impact of ILEs on internal medicine inpatients receiving parenteral nutrition. Methods A propensity score matching (PSM) analysis was performed using a medical claims database covering 451 hospitals in Japan. Participants included the following internal medicine inpatients, ages >= 18 years, fasting > 10 days, and receiving exclusively parenteral nutrition, between 2011 and 2020. Participants were divided into 2 groups: those who did and did not receive ILEs. The primary endpoint was in-hospital mortality. The secondary endpoints included intravenous catheter infection, activities of daily living (ADL), hospital length of stay (LOS), and total medical costs. To adjust for energy doses, logistic or multiple regression analyses were performed using energy dose as an additional explanatory variable. Results After PSM, 19,602 matched pairs were formed out of 61,437 patients. The ILE group had significantly lower incidences than the non-ILE group of in-hospital mortality (20.3% vs. 26.9%; odds ratio [OR], 0.69; 95% confidence interval [CI], 0.66-0.72; p < 0.001), deteriorated ADL (10.8% vs. 12.5%; OR, 0.85; 95% CI, 0.79-0.92; p < 0.001), and shorter LOS (regression coefficient, - 0.8; 95% CI, - 1.6-0.0; p = 0.045). After adjusting for energy dose, these ORs or regression coefficients demonstrated the same tendencies and statistical significance. The mean total medical costs were $21,009 in the ILE group and$21,402 in the non-ILE group (p = 0.08), and the adjusted regression coefficient for the ILE vs. the non-ILE group was - $860 (95$1252 to - $47). Conclusions ILE use was associated with improved clinical outcomes, including lower in-hospital mortality, in internal medicine inpatients receiving parenteral nutrition

Dose-Dependent Effects of Amino Acids on Clinical Outcomes in Adult Medical Inpatients Receiving Only Parenteral Nutrition: A Retrospective Cohort Study Using a Japanese Medical Claims Database

The majority of inpatients requiring parenteral nutrition (PN) do not receive adequate amino acid, which may negatively impact clinical outcomes. We investigated the influence of amino acid doses on clinical outcomes in medical adult inpatients fasting >10 days and receiving only PN, using Japanese medical claims database. The primary endpoint was in-hospital mortality, and the secondary endpoints included deterioration of activities of daily living (ADL), intravenous catheter infection, hospital readmission, hospital length of stay (LOS), and total medical costs. Patients were divided into four groups according to their mean prescribed daily amino acid doses from Days 4 to 10 of fasting: Adequate (>= 0.8 g/kg/day), Moderate (>= 0.6-= 0.4-<0.6 g/kg/day), and Very low (<0.4 g/kg/day). Multivariate logistic or multiple regression analyses were performed with adjustments for patient characteristics (total n = 86,702). The Adequate group was used as the reference in all analyses. For the Moderate, Low, and Very low groups, adjusted ORs (95% CI) of in-hospital mortality were 1.20 (1.14-1.26), 1.43 (1.36-1.51), and 1.72 (1.62-1.82), respectively, and for deterioration of ADL were 1.21 (1.11-1.32), 1.34 (1.22-1.47), and 1.22 (1.09-1.37), respectively. Adjusted regression coefficients (95% CI) of hospital LOS were 1.2 (0.4-2.1), 1.5 (0.6-2.4), and 2.9 (1.8-4.1), respectively. Lower prescribed doses of amino acids were associated with worse clinical outcomes including higher in-hospital mortality

Introduction to University Calculus for “Bunkei’’ Students in Waseda

In these days, mathematics is one of the most important tools for any person. However, in Japan, many students hate and avoid mathematics in their high school age. In Waseda University, one of the biggest and oldest private universities in Japan, special curriculum is constructed for such “Bunkei’’ students who major in social or human science

Three-Dimensional Comparison in Palatal Forms Between Modified Presurgical Nasoalveolar Molding Plate and Hotz's Plate Applied to the Infants With Unilateral Cleft Lip and Palate

AbstractThe presurgical nasoalveolar molding plate appliance with stent (PNAM) extended from the palatal molding plate; to correct the nostril shape of infants with cleft lip and palate is well known. The PNAM appliance is based on the finding that a high degree of plasticity is maintained in the cartilage of infants during the first 6 weeks after birth. However, on the current PNAM protocol described by Grayson et al. the nasal stent is supposed to be an adjunct to the palatal molding plate after reducing the severity of the alveolar cleft width. We have used the modified Hotz's plate from the setup model and built up the nasal stent even before reducing the severity of the alveolar deformity. In this study we assess the effects of the modified Hotz's plate and the modified PNAM appliance for the alveolar and palatal form. The lateral deviation of the incisal point, the width of the palatal cleft, and the degree of curvature of the palatal vault were first evaluated on plaster models. The PNAM group is smaller on the lateral deviation of the incisal point than the modified Hotz's group. The decreased average width of the palatal cleft and curvature of the palate, was almost the same in both the modified Hotz's and PNAM groups. In comparison with the modified Hotz's plate, the modified PNAM appliance also improves the molding of the alveolar segments and reduces cleft width