Finite Laurent Developments and the Logarithmic Residue Theorem in the Real Non-analytic Case

2005 ◽  
Vol 51 (4) ◽  
pp. 519-552 ◽  
Author(s):  
Julián López-Gómez ◽  
Carlos Mora-Corral
Keyword(s):  
Residue Theorem ◽  
The Real ◽  
Analytic Case ◽  
Logarithmic Residue

scholarly journals From a differentiable to a real analytic perturbation theory, applications to the Kupka Smale theorems

1986 ◽  
Vol 6 (3) ◽  
pp. 345-362 ◽  
Author(s):  
H. W. Broer ◽  
F. M. Tangerman
Keyword(s):  
Perturbation Theory ◽  
Normal Form ◽  
Heat Operator ◽  
Analytic Perturbation Theory ◽  
The Real ◽  
Smooth Case ◽  
Analytic Perturbation ◽  
Topological Proof ◽  
Analytic Case ◽  
Real Analytic

AbstractKupka-Smale like theorems are proven in the real analytic case, using existing perturbation schemes for the smooth case and the heat operator. As a consequence, a topological proof is obtained of Siegel's theorem on the generic divergence of normal form transformations.

scholarly journals Errata Corrige. Decomposition of CR-manifolds and splitting of CR-maps

2009 ◽  
pp. 233-233
Author(s):  
Atsushi Hayashimoto ◽  
Sung-Yeon Kim ◽  
Dmitri Zaitsev
Keyword(s):  
Finite Type ◽  
Dense Subset ◽  
Direct Products ◽  
Cr Manifolds ◽  
Splitting Property ◽  
The Real ◽  
Cancellation Problem ◽  
Analytic Case ◽  
Real Analytic ◽  
Infinitesimal Automorphisms

We show the uniqueness of local and global decompositions of abstract CR-manifolds into direct products of irreducible factors, and a splitting property for their CR-diffeomorphisms into direct products with respect to these decompositions. The assumptions on the manifolds are finite non-degeneracy and finite-type on a dense subset. In the real-analytic case, these are the standard assumptions that appear in many other questions. In the smooth case, the assumptions cannot be weakened by replacing “dense” with “open” as is demonstrated by an example. An application to the cancellation problem is also given. The proof is based on the development of methods of [BER99b], [BRZ00], [KZ01] and the use of “approximate infinitesimal automorphisms” introduced in this paper.

scholarly journals On the Local Theory of Continuous Infinite Pseudo Groups II

1961 ◽  
Vol 19 ◽  
pp. 55-91 ◽  
Author(s):  
Masatake Kuranishi
Keyword(s):  
Local Theory ◽  
Differential Systems ◽  
Exterior Differential Systems ◽  
The Real ◽  
Exterior Differential ◽  
Detailed Proof ◽  
Analytic Case ◽  
Real Analytic

In this chapter, we shall formulate, without proof, the theorys of exterior differential systems and of their prolongations using the language in the theory of jets developed by C. Ehresman, because such formulation seems to be most convenient in order to apply the theory to the theory of continuous infinite pseudo-groups, which we shall discuss in the next chapter. Since important theorems in our theory hold only in the real analytic case, we shall exclusively consider the real analytic case. So, we shall omit the adjective “analytic”, unless explicitly stated otherwise. As for the fundamental notions in the theory of jets and of differential systems, we refer to [5] and [6], respectively. Detailed proof of the contents of this Chapter will be published in [7].

Scanning electron microscopy of human iliac bone by a simple preparation method

1990 ◽  
Vol 48 (3) ◽  
pp. 226-227
Author(s):  
Toshihiko Takita ◽  
Tomonori Naguro ◽  
Toshio Kameie ◽  
Akihiro Iino ◽  
Kichizo Yamamoto
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Preparation Method ◽  
Specimen Preparation ◽  
Real Surface ◽  
Public Attention ◽  
Preparation Methods ◽  
The Real ◽  
Simple Preparation ◽  
Scanning Electron

Recently with the increase in advanced age population, the osteoporosis becomes the object of public attention in the field of orthopedics. The surface topography of the bone by scanning electron microscopy (SEM) is one of the most useful means to study the bone metabolism, that is considered to make clear the mechanism of the osteoporosis. Until today many specimen preparation methods for SEM have been reported. They are roughly classified into two; the anorganic preparation and the simple preparation. The former is suitable for observing mineralization, but has the demerit that the real surface of the bone can not be observed and, moreover, the samples prepared by this method are extremely fragile especially in the case of osteoporosis. On the other hand, the latter has the merit that the real information of the bone surface can be obtained, though it is difficult to recognize the functional situation of the bone.

Personal Audio System: Hearing Symptoms, Habits, and Sound Pressure Levels Measured in Real Ear and a Manikin

2020 ◽  
Vol 63 (6) ◽  
pp. 2016-2026
Author(s):  
Tamara R. Almeida ◽  
Clayton H. Rocha ◽  
Camila M. Rabelo ◽  
Raquel F. Gomes ◽  
Ivone F. Neves-Lobo ◽  
...  
Keyword(s):  
Sound Pressure ◽  
Daily Basis ◽  
Cross Sectional Study ◽  
Normal Hearing ◽  
Chi Square ◽  
Cross Sectional ◽  
The Real ◽  
Significant Difference ◽  
Sound Pressure Levels ◽  
Audio System

Purpose The aims of this study were to characterize hearing symptoms, habits, and sound pressure levels (SPLs) of personal audio system (PAS) used by young adults; estimate the risk of developing hearing loss and assess whether instructions given to users led to behavioral changes; and propose recommendations for PAS users. Method A cross-sectional study was performed in 50 subjects with normal hearing. Procedures included questionnaire and measurement of PAS SPLs (real ear and manikin) through the users' own headphones and devices while they listened to four songs. After 1 year, 30 subjects answered questions about their usage habits. For the statistical analysis, one-way analysis of variance, Tukey's post hoc test, Lin and Spearman coefficients, the chi-square test, and logistic regression were used. Results Most subjects listened to music every day, usually in noisy environments. Sixty percent of the subjects reported hearing symptoms after using a PAS. Substantial variability in the equivalent music listening level (Leq) was noted ( M = 84.7 dBA; min = 65.1 dBA, max = 97.5 dBA). A significant difference was found only in the 4-kHz band when comparing the real-ear and manikin techniques. Based on the Leq, 38% of the individuals exceeded the maximum daily time allowance. Comparison of the subjects according to the maximum allowed daily exposure time revealed a higher number of hearing complaints from people with greater exposure. After 1 year, 43% of the subjects reduced their usage time, and 70% reduced the volume. A volume not exceeding 80% was recommended, and at this volume, the maximum usage time should be 160 min. Conclusions The habit of listening to music at high intensities on a daily basis seems to cause hearing symptoms, even in individuals with normal hearing. The real-ear and manikin techniques produced similar results. Providing instructions on this topic combined with measuring PAS SPLs may be an appropriate strategy for raising the awareness of people who are at risk. Supplemental Material https://doi.org/10.23641/asha.12431435

Current Issues: Evidence-Based Practice for the Real World: Thoughts on Clinical Education in Communication Disorders

2010 ◽  
Vol 20 (3) ◽  
pp. 100-105 ◽  
Author(s):  
Anne K. Bothe
Keyword(s):  
Clinical Education ◽  
Real World ◽  
Evidence Based Practice ◽  
Communication Disorders ◽  
University Faculty ◽  
Evidence Based ◽  
Speech Language Pathology ◽  
Basic Principles ◽  
The Real ◽  
Language Pathology

This article presents some streamlined and intentionally oversimplified ideas about educating future communication disorders professionals to use some of the most basic principles of evidence-based practice. Working from a popular five-step approach, modifications are suggested that may make the ideas more accessible, and therefore more useful, for university faculty, other supervisors, and future professionals in speech-language pathology, audiology, and related fields.

Preparing Future Professionals—What’s the Real Story?

ASHA Leader ◽  
2002 ◽  
Vol 7 (14) ◽  
pp. 1-12
Author(s):  
Ellen Uffen
Keyword(s):  
The Real
Sign in / Sign up

Export Citation Format

Share Document