On a discrete nonlinear boundary value problem

AbstractThe nonlinear eigenvalue problem Δ2uk−1+λ|uk|γ=0,k=1,2,…,n under the Dirichlet boundary conditions u0=0=un+1 is studied. An existence and uniqueness theorem is proved. Qualitative properties of solutions are also given

Complexity Analysis of Balloon Drawing for Rooted Trees

In a balloon drawing of a tree, all the children under the same parent are placed on the circumference of the circle centered at their parent, and the radius of the circle centered at each node along any path from the root reflects the number of descendants associated with the node. Among various styles of tree drawings reported in the literature, the balloon drawing enjoys a desirable feature of displaying tree structures in a rather balanced fashion. For each internal node in a balloon drawing, the ray from the node to each of its children divides the wedge accommodating the subtree rooted at the child into two sub-wedges. Depending on whether the two sub-wedge angles are required to be identical or not, a balloon drawing can further be divided into two types: even sub-wedge and uneven sub-wedge types. In the most general case, for any internal node in the tree there are two dimensions of freedom that affect the quality of a balloon drawing: (1) altering the order in which the children of the node appear in the drawing, and (2) for the subtree rooted at each child of the node, flipping the two sub-wedges of the subtree. In this paper, we give a comprehensive complexity analysis for optimizing balloon drawings of rooted trees with respect to angular resolution, aspect ratio and standard deviation of angles under various drawing cases depending on whether the tree is of even or uneven sub-wedge type and whether (1) and (2) above are allowed. It turns out that some are NP-complete while others can be solved in polynomial time. We also derive approximation algorithms for those that are intractable in general

The association between problematic cellular phone use and risky behaviors and low self-esteem among Taiwanese adolescents

<p>Abstract</p> <p>Background</p> <p>Cellular phone use (CPU) is an important part of life for many adolescents. However, problematic CPU may complicate physiological and psychological problems. The aim of our study was to examine the associations between problematic CPU and a series of risky behaviors and low self-esteem in Taiwanese adolescents.</p> <p>Methods</p> <p>A total of 11,111 adolescent students in Southern Taiwan were randomly selected into this study. We used the Problematic Cellular Phone Use Questionnaire to identify the adolescents with problematic CPU. Meanwhile, a series of risky behaviors and self-esteem were evaluated. Multilevel logistic regression analyses were employed to examine the associations between problematic CPU and risky behaviors and low self-esteem regarding gender and age.</p> <p>Results</p> <p>The results indicated that positive associations were found between problematic CPU and aggression, insomnia, smoking cigarettes, suicidal tendencies, and low self-esteem in all groups with different sexes and ages. However, gender and age differences existed in the associations between problematic CPU and suspension from school, criminal records, tattooing, short nocturnal sleep duration, unprotected sex, illicit drugs use, drinking alcohol and chewing betel nuts.</p> <p>Conclusions</p> <p>There were positive associations between problematic CPU and a series of risky behaviors and low self-esteem in Taiwanese adolescents. It is worthy for parents and mental health professionals to pay attention to adolescents' problematic CPU.</p

Traditional Chinese Medicine Diagnosis “ Yang-Xu Zheng

Pathogenesis of sepsis includes complex interaction between pathogen activities and host response, manifesting highly variable signs and symptoms, possibly delaying diagnosis and timely life-saving interventions. This study applies traditional Chinese medicine (TCM) Zheng diagnosis in patients with severe sepsis and septic shock to evaluate its adaptability and use as an early predictor of sepsis mortality. Three-year prospective observational study enrolled 126 septic patients. TCM Zheng diagnosis, Acute Physiology and Chronic Health Evaluation (APACHE) II score, and blood samples for host response cytokines measurement (tumor necrosis factor-α, Interleukin-6, Interleukin-8, Interleukin-10, Interleukin-18) were collected within 24 hours after admission to Intensive Care Unit. Main outcome was 28-day mortality; multivariate logistic regression analysis served to determine predictive variables of the sepsis mortality. APACHE II score, frequency of Nutrient-phase heat, and Qi-Xu and Yang-Xu Zhengs were significantly higher in nonsurvivors. The multivariate logistic regression analysis identified Yang-Xu Zheng as the outcome predictor. APACHE II score and levels of five host response cytokines between patients with and without Yang-Xu Zheng revealed significant differences. Furthermore, cool extremities and weak pulse, both diagnostic signs of Yang-Xu Zheng, were also proven independent predictors of sepsis mortality. TCM diagnosis “Yang-Xu Zheng” may provide a new mortality predictor for septic patients

Comparison of the Prevalence of Metabolic Syndrome Between the Criteria for Taiwanese and Japanese and the Projected Probability of Stroke in Elderly Hypertensive Taiwanese

SummaryBackgroundThe cutoff of abdominal circumference for metabolic syndrome (MS) defined by the Bureau of Health Promotion (BHP) of Taiwan for Taiwanese (men, 90cm; women, 80cm) and by the International Diabetes Federation (IDF) for Japanese (men, 85cm; women, 90cm) differs. This study aimed to examine the impact of this difference on the prevalence of MS and the impact of an MS diagnosis on the projected risk of stroke in hypertensive Taiwanese.MethodsMS was examined in a sample of 3,472 hypertensive patients (aged 55–80 years; 1,709 women) across Taiwan. The 10-year probability of stroke estimated from the Framingham equation was compared between MS and non-MS patients.ResultsThe prevalence of MS using the BHP criteria was 59.2% using the BHP criteria (95% confidence interval, CI, 57.6–60.8%; men, 52.5%; women, 66.1%) and 48.9% by the IDF criteria (95% CI, 47.2–50.5%; men, 61.3%; women, 36.1%). Both criteria showed that, compared with non-MS, MS has higher predicted 10-year probability of stroke (BHP, 0.153 ± 0.115 vs. 0.133 ± 0.105; IDF, 0.159 ± 0.109 vs. 0.132 ± 0.112; both p < 0.001) because of the difference in women (BHP, 0.143 ± 0.124 vs. 0.102 ± 0.091; IDF, 0.147 ± 0.121 vs. 0.118 ± 0.110; both p < 0.001) rather than men (BHP, p = 0.21; IDF, p = 0.29).ConclusionBoth criteria demonstrate that MS is highly prevalent in elderly hypertensive patients in Taiwan. Additionally in women, but not men, the predicted probability of stroke is higher in MS than in non-MS patients. The diagnosis of MS is potentially useful for identifying elderly hypertensive females with an elevated risk of stroke in Taiwan

Numerical investigation on noise reduction for an in-line fan equipped with Helmholtz resonator

This research intends to analyze and improve the flow-induced noise of an in-line fan with Helmholtz resonator by the numerical simulation. At first, the flow and acoustic fields associated with the fan are simulated and analyzed via the CFD simulation. Subsequently, a thorough understanding on the aerodynamic and acoustic features of this mixed-flow fan is achieved. Later, to reduce the fan noise, a set of Helmholtz resonators for this inline-fan is designed and installed onto the critical regions inside the fan. Also, the flow-induced-noise reduction due to the resonator is examined and discussed in details. As a result, the maximum noise reductions on the 1st and the 2nd characteristic frequencies are obtained at 6.9 dBA and 9.8 dBA, respectively. Moreover, there is a minor noise-elimination effect found on the other harmonic frequency while the significant result appears on the designed characteristic frequency. However, all resonators used yield a significant noise reduction at the second BFF. In conclusions, a comprehensive parametric study on Helmholtz resonator is carried out and summarized for attaining a design guideline for its application on the in-line fan. The accomplishment of this study provides a systematic scheme of noise reduction for an inline-fan with the addition of Helmholtz resonator design