Log-aesthetic Curves as Similarity Geometric Analogue of Euler's Elasticae

In this paper we consider the log-aesthetic curves and their generalization which are used in CAGD. We consider those curves under similarity geometry and characterize them as stationary integrable flow on plane curves which is governed by the Burgers equation. We propose a variational formulation of those curves whose Euler-Lagrange equation yields the stationary Burgers equation. Our result suggests that the log-aesthetic curves and their generalization can be regarded as the similarity geometric analogue of Euler's elasticae

Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the $\tau$ function are presented. B\"acklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation

Hamiltonian flows on null curves

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio

Discrete Integrable Systems and Hodograph Transformations Arising from Motions of Discrete Plane Curves

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation, and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.Comment: 19 page

Timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space

It is shown that timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL(2,R) via Bryant type representation formulae. These formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson correspondence, between timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space and timelike minimal surfaces in Minkowski 3-space. The hyperbolic Gauss map of timelike surfaces in anti-de Sitter 3-space, which is a close analogue of the classical Gauss map is considered. It is discussed that the hyperbolic Gauss map plays an important role in the study of timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space. In particular, the relationship between the Lorentz holomorphicity of the hyperbolic Gauss map and timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space is studied.Comment: 47 pages, 24 figures, references revised, Annals of Global Analysis and Geometr

High incidence of silent myocardial ischemia in elderly patients with non insulin-dependent diabetes mellitus

Celem badania była ocena częstości występowania niemego niedokrwienia mięśnia sercowego u bezobjawowych chorych na cukrzycę w podeszłym wieku (> 60 lat). Wstępnym etapem badania była maksymalna próba wysiłkowa na bieżni ruchomej. Spośród 140 chorych u 54 (38,6%) nie udało się osiągnąć diagnostycznego poziomu wysiłku podczas próby lub nie można jej było wykonać z innych przyczyn, u 39 z 86 chorych (45,3%) uzyskano pozytywny wynik próby wysiłkowej. W drugim etapie tej pracy u 93 chorych z dodatnią próbą wysiłkową, ale u których nie można było uzyskać maksymalnego wysiłku, wykonano scyntygrafię z użyciem talu w teście z dipirydamolem. U 39 z 93 chorych (41,9%), u których wystąpiły zaburzenia perfuzji, rozpoznano nieme niedokrwienie mięśnia sercowego. U 18 chorych z niemym niedokrwieniem mięśnia sercowego, którzy wyrazili zgodę, wykonano koronarografię. U 17 spośród 18 chorych (94,4%) stwierdzono znacznego stopnia zwężenia naczyń wieńcowych, co potwierdziło duże znaczenie predykcyjne tej metody. Podsumowując, stwierdzono, że częstość niemego niemego niedokrwienia mięśnia sercowego u chorych na cukrzycę typu 2 w podeszłym wieku jest bardzo wysoka (26,3%). Te wyniki sugerują, że wczesna intensywna diagnostyka zmian w naczyniach wieńcowych może się okazać niezbędna jako uzupełnienie rutynowego postępowania w tej grupie chorych.The present study was designed reveal the incidence of silent myocardial ischemia in asymptomatic elderly non-insulin-dependent diabetic (NIDDM) patients (aged over 60 years). As a first step screening, maximal treadmill exercise test was performed. Of 140 patients studied, 54 (38.6%) were unable or not expected to achieve diagnostic levels of exercise during treadmill testing. A positive exercise test was noted in 39 of 86 (45.3%) subjects. As a second step examination, dipyridamole thallium scintigraphy was performed for 93 subjects who exhibited a positive exercise test and could not perform a maximal exercise test. Abnormal perfusion pattern was found in 39 of 93 (41.9%), who were finally considered to have a silent myocardial ischemia. Coronary angiography was performed in 18 subjects with diagnosis of silent myocardial ischemia, who gave their consent. Significant coronary artery stenosis was in fact found in 17 of 18 (94.4%) subjects studied, confirming a very high positive predictive value of this diagnostic procedure. In conclusion, elderly NIDDM patients (aged over 60 years) had an extremely high prevalence (estimated 26.3%) of silent myocardial ischemia. This evidence suggests that early and intensive detection may be needed as a part of routine care for this grou

Explicit prognostic disclosure to Asian women with breast cancer: A randomized scripted video-vignette study

Health and self-regulatio

The relationship between trust in mass media and the healthcare system and individual health: evidence from the AsiaBarometer Survey

<p>Abstract</p> <p>Background</p> <p>Vertical and horizontal trust, as dimensions of social capital, may be important determinants of health. As mass media campaigns have been used extensively to promote healthy lifestyles and convey health-related information, high levels of individual trust in the media may facilitate the success of such campaigns and, hence, have a positive influence on health. However, few studies have investigated the relationship between trust levels in mass media, an aspect of vertical trust, and health.</p> <p>Methods</p> <p>Based on cross-sectional data of the general population from the AsiaBarometer Survey (2003–2006), we analyzed the relationship between self-rated health and trust in mass media, using a multilevel logistic model, adjusted for age, gender, marital status, income, education, occupation, horizontal trust, and trust in the healthcare system.</p> <p>Results</p> <p>In a total of 39082 participants (mean age 38; 49% male), 26808 (69%) were classified as in good health. By the levels of trust in mass media, there were 6399 (16%) who reported that they trust a lot, 16327 (42%) reporting trust to a degree, 9838 (25%) who do not really trust, 3307 (9%) who do not trust at all, and 191 (0.5%) who have not thought about it. In the multilevel model, trust in mass media was associated with good health (do not trust at all as the base group): the odds ratios (OR) of 1.16 (95% confidence interval (CI) = 1.05–1.27) for do not really trust; OR of 1.35 (95% CI = 1.23–1.49) for trust to a degree, and 1.57 (95% CI = 1.36–1.81) for trust a lot. Horizontal trust and trust in the healthcare system were also associated with health.</p> <p>Conclusion</p> <p>Vertical trust in mass media is associated with better health in Asian people. Since mass media is likely an important arena for public health, media trust should be enhanced to make people healthier.</p