Decay and Continuity of Boltzmann Equation in Bounded Domains

Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: inflow, bounce-back reflection, specular reflection, and diffuse reflection. We establish exponential decay in $L^{\infty}$ norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set of the velocity at the boundary. Our contribution is based on a new $L^{2}$ decay theory and its interplay with delicate $$ decay analysis for the linearized Boltzmann equation, in the presence of many repeated interactions with the boundary.Comment: 89 pages

Impact of catheter ablation for atrial fibrillation on cardiac disorders in patients with coexisting heart failure

AIMS: We sought to investigate the time course of cardiac disorders after catheter ablation for atrial fibrillation (AF) in patients with coexisting heart failure (HF) during long-term follow-up. METHODS AND RESULTS: We analysed consecutive 280 patients undergoing first-time catheter ablation for AF who had coexisting HF, which was defined as prior HF hospitalization, estimated right ventricular systolic pressure ≥45 mmHg, or B-type natriuretic peptide (BNP) ≥200 pg/dL before the procedure. The primary endpoints were improvements in left ventricular ejection fraction (LVEF), E/e', BNP, left atrial dimension (LAD), and mitral regurgitation (MR) at 1 year. The secondary endpoints were serial changes of LVEF, E/e', BNP, LAD, and MR at 6 months, 1 year, and 5 years and cumulative incidence of HF hospitalization. During the mean follow-up of 5.1 ± 3.0 years, 70.7% of patients were free from recurrent AF. Among patients with LVEF < 50%, E/e' ≥ 15, BNP ≥ 200 pg/dL, LAD ≥ 40 mm, and moderate-to-severe MR, changes in those parameters from baseline to 1 year were 34.5 ± 9.9% to 43.2 ± 14.4% (P < 0.001), 19.7 ± 3.9 to 12.5 ± 6.6 (P < 0.001), 290 to 85 pg/dL (P < 0.001), and 100% to 37.8% (P < 0.001), respectively. The improvements in the cardiac disorders were maintained up to 5 years except for E/e'. In patients with LVEF < 40%, significant delayed improvement of LVEF beyond 1 year was observed (ΔLVEF = 10.5 ± 18.5, P = 0.001), but not in patients with LVEF of 40-49%. The cumulative incidence of HF hospitalization was 12.6% at 5 years. Baseline diastolic dysfunction was the only independent predictor for subsequent HF hospitalization. CONCLUSIONS: In patients undergoing AF ablation with coexisting HF, all cardiac disorders significantly improved after the procedure, which was mostly maintained during 5 year follow-up

Cloning of cDNA and genomic DNA for human cytochrome P-45011β

AbstractA full-length cDNA clone encoding steroid 11β-hydroxylase (P-45011β) has been isolated from a cDNA library derived from human adrenal tumor. The insert of the clone contains an open reading frame encoding a protein of 503 amino acid residues together with a 4 bp 5'-untranslated region and a 576 bp 3'-untranslated region to which a poly(A) tract is attached. The promoter region of the P-45011β gene has also been isolated from a genomic library derived from human pre-B cells. It contains a TATA box, a putative cAMP-responsive element, several repeated sequences and two sequence elements similar to the consensus sequence for binding of AP-1. A transient expression assay in Y-1 adrenal tumor cells demonstrates that the promoter activity is remarkably enhanced by treatment of the cells with cAMP. In addition, analysis using deletion mutants containing various lengths of the 5'-flanking region of the gene suggests that several cis-acting elements participate in transcriptional regulation of human P-45011β gene

On the One-dimensional Stability of Viscous Strong Detonation Waves

Building on Evans function techniques developed to study the stability of viscous shocks, we examine the stability of viscous strong detonation wave solutions of the reacting Navier-Stokes equations. The primary result, following the work of Alexander, Gardner & Jones and Gardner & Zumbrun, is the calculation of a stability index whose sign determines a necessary condition for spectral stability. We show that for an ideal gas this index can be evaluated in the ZND limit of vanishing dissipative effects. Moreover, when the heat of reaction is sufficiently small, we prove that strong detonations are spectrally stable provided the underlying shock is stable. Finally, for completeness, the stability index calculations for the nonreacting Navier-Stokes equations are includedComment: 66 pages, 7 figure

Global classical solutions for partially dissipative hyperbolic system of balance laws

This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a general theory on the well-posedness of classical solutions in the framework of Chemin-Lerner's spaces with critical regularity is established. To do this, we first explore the functional space theory and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous Chemin-Lerner's spaces. Then this fact allows to prove the local well-posedness for general data and global well-posedness for small data by using the Fourier frequency-localization argument. Finally, we apply the new existence theory to a specific fluid model-the compressible Euler equations with damping, and obtain the corresponding results in critical spaces.Comment: 39 page

心不全を合併した心房細動患者のカテーテルアブレーション後の長期予後 : 左室駆出率に基づいた心不全のサブタイプ間における比較

Aims: Heart failure (HF) prognosis has been reported similar in patients with preserved vs. reduced left ventricular ejection fraction (LVEF). This study compared the long-term prognosis of HF patients undergoing radiofrequency catheter ablation (RFCA) for atrial fibrillation (AF). Methods and results: Among 5010 patients undergoing RFCA in Kansai Plus AF registry, 656 patients (13.1%) with a documented history of HF were enrolled in the study before RFCA. The primary endpoint was a composite of all-cause death, HF hospitalization, and stroke or systemic embolism. Patients with reduced (<40%), mid-range (40-49%), and preserved (≥50%) LVEF were 98 (14.9%), 107 (16.3%), and 451 (68.8%) patients, respectively. The prevalence of ischaemic heart disease and cardiomyopathies was higher among patients with reduced as compared with preserved LVEF (27.6% vs. 10.0%, P < 0.05 and 36.7% vs. 15.3%, P < 0.05, respectively). The median follow-up period was 2.9 years. The 3-year cumulative risk for the primary endpoint was higher in patients with reduced LVEF (32.7%) compared to those with mid-range (11.7%) or preserved (11.6%) LVEF (P < 0.001). Reduced LVEF was the most significant independent risk factor for primary endpoint (hazard ratio, 2.83; 95% confidence interval 1.74-4.61, P < 0.001). The 3-year arrhythmia recurrence rate was similar among the groups (48.2%, 42.8%, and 47.3%, respectively, P = 0.75). Conclusion : This study raises hypothesis that patients with HFrEF and AF had approximately three times higher risk for a composite of all-cause death, HF hospitalization, and stroke or systemic embolism after AF ablation compared with patients with HFmrEF or HFpEF.博士（医学）・甲第802号・令和3年12月21日Copyright: © Published on behalf of the European Society of Cardiology. All rights reserved. © The Author(s) 2021.This is a pre-copyedited, author-produced version of an article accepted for publication in Europace following peer review. The version of record "Europace Online ahead of print (2021 Aug 31;euab201) is available online at: https://doi.org/10.1093/europace/euab201.発行元が定める登録猶予期間終了の後、本文を登録予定（2022.08

The Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org