An elementary proof of the real version of the Riesz-Thorin theorem

2007 ◽  
pp. 179-182
Author(s):  
Natan Kruglyak
Keyword(s):  
Elementary Proof ◽  
The Real

scholarly journals MOTIVIC DOUBLE SHUFFLE

2010 ◽  
Vol 06 (02) ◽  
pp. 339-370 ◽  
Author(s):  
ISMAEL SOUDÈRES
Keyword(s):  
Moduli Spaces ◽  
Elementary Proof ◽  
Blow Up ◽  
Multiple Zeta Values ◽  
The Real ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Real Multiple

The goal of this paper is to give an elementary proof of the double shuffle relations directly for the Goncharov and Manin motivic multiple zeta values. The shuffle relation is straightforward, but for the stuffle, we use a modification of a method first introduced by Cartier for the purpose of proving stuffle for the real multiple zeta values. We will use both the representation of multiple zeta values on the moduli spaces of curve introduced by Goncharov and Manin and we will apply suitable blow-up sequences to the representation of multiple zeta values as integral over a cube.

On the arc-sine laws for Lévy processes

1994 ◽  
Vol 31 (01) ◽  
pp. 76-89 ◽  
Author(s):  
R. K. Getoor ◽  
M. J. Sharpe
Keyword(s):  
Random Walks ◽  
Real Line ◽  
Lévy Process ◽  
Elementary Proof ◽  
Levy Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Real ◽  
Necessary And Sufficient ◽  
Spitzer's Theorem

Let X be a Lévy process on the real line, and let Fc denote the generalized arcsine law on [0, 1] with parameter c. Then t −1 ⨍0 t P 0(X s > 0) ds → c as t → ∞ is a necessary and sufficient condition for t —1 ⨍0 t 1{Xs >0} ds to converge in P 0 law to Fc. Moreover, P 0(Xt > 0) = c for all t > 0 is a necessary and sufficient condition for t —1 ⨍0 t 1{Xs >0} ds under P 0 to have law Fc for all t > 0. We give an elementary proof of these results, and show how to derive Spitzer's theorem for random walks in a simple way from the Lévy process version.

On the arc-sine laws for Lévy processes

1994 ◽  
Vol 31 (1) ◽  
pp. 76-89 ◽  
Author(s):  
R. K. Getoor ◽  
M. J. Sharpe
Keyword(s):  
Random Walks ◽  
Real Line ◽  
Lévy Process ◽  
Elementary Proof ◽  
Levy Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Real ◽  
Necessary And Sufficient ◽  
Spitzer's Theorem

Let X be a Lévy process on the real line, and let Fc denote the generalized arcsine law on [0, 1] with parameter c. Then t−1 ⨍0tP0(Xs > 0) ds → c as t → ∞ is a necessary and sufficient condition for t—1 ⨍0t1{Xs>0}ds to converge in P0 law to Fc. Moreover, P0(Xt > 0) = c for all t > 0 is a necessary and sufficient condition for t—1 ⨍0t1{Xs>0}ds under P0 to have law Fc for all t > 0. We give an elementary proof of these results, and show how to derive Spitzer's theorem for random walks in a simple way from the Lévy process version.

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
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