An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group

We show the fundamental theorems of curves and surfaces in the 3-dimensional Heisenberg group and find a complete set of invariants for curves and surfaces respectively. The proofs are based on Cartan's method of moving frames and Lie group theory. As an application of the main theorems, a Crofton-type formula is proved in terms of p-area which naturally arises from the variation of volume. The application makes a connection between CR geometry and integral geometry

On invariants of constant pp-mean curvature surfaces in the Heisenberg group H1H_{1}

A fundamental goal of geometry of submanifolds is to find fascinating and significant classical examples. In this paper, depending on the theory we established in [5], along with the approach we provided for constructing constant $p$-mean curvature surfaces, we found some interesting examples of constant $p$-mean curvature surfaces. In particular, we give a complete description for rotationally invariant surfaces of constant $p$-mean curvature, including the geometric meaning of the energy $E$ (1.6}.Comment: 31 pages, 1 figure and 2 tables. Submitted. arXiv admin note: text overlap with arXiv:2101.1178

Modeling Online to Offline E-Business User Experience

Complex business patterns from providers and diverse needs of customers in E-commerce necessitate constant and rapid modifications of services for new business models. The online-to-offline (O2O) business model is one of newly developed models where smartphones, tablets, e-readers and digital signages provide mobility and entertainment that ordinary people have never experienced before. Business opportunities are brought forth by O2O from cyberspace into daily reality. User experience (UX) evaluation is thus getting more and more important for user-centered design. In the literature, UX evaluation methodologies were designed for usability and satisfaction of computers or consumer electronics. Their results, however, did not necessarily help design O2O smart business services in that UX constructs in O2O should differ from that in using computers or consumer electronics. Important constructs of UX in O2O such as usability, utility, adoptability and desirability should be considered in the design of service flows and activities. The current study proposed important UX constructs for assessing O2O design by analyzing O2O users. A rapid evaluation method for UX in O2O can be developed based on the constructs

Association of Chinese Herbal Medicines Use with Development of Chronic Obstructive Pulmonary Disease Among Patients with Rheumatoid Arthritis: A Population-Based Cohort Study

Purpose: Rheumatoid arthritis (RA) patients appear to report a higher risk of chronic obstructive pulmonary disease (COPD). While Chinese herbal medicine (CHMs) is proven to lower COPD risk, the scientific evidence regarding its effect in relation to COPD onset among them is limited. This longitudinal cohort study aimed to determine the relationship between CHMs use and the COPD risk in RA patients. Methods: Using the nationwide claim data, 8349 patients newly diagnosed with RA and simultaneously free of COPD between 1998 and 2010 were eligible for enrollment. From this sample, we enrolled 3360 CHMs users and 3360 non-CHMs users, randomly selected using propensity scores matching from the remaining cases. They were followed until the end of 2012 to record COPD incidence. The hazard ratio (HR) of COPD with regard to CHMs use was estimated by the Cox proportional hazards regression model. Results: In the follow-up period, 136 CHMs users and 202 non-CHMs users developed COPD, representing incidence rates of 5.16 and 7.66, respectively, per 1000 person-years. CHMs use was associated with a 32% lower subsequent risk of COPD (adjusted HR: 0.68, 95% Confidence Interval: 0.54–0.84). Eight commonly prescribed CHMs were discovered to be associated with lower COPD risk: Yan Hu Suo, Sānɡ Zhī, Dang Shen, Huang Qin, Jia-Wei-Xiao-Yao-San, Shu-Jing-Huo-Xue-Tang, Du-Huo-Ji-Sheng-Tang and Ge-Gen-Tang. Conclusion: A significant association of CHMs use with a lower risk of COPD onset in RA patients was found, suggesting that CHMs could be integrated into conventional therapy to reduce COPD risk

Bidirectional Associations Between Rheumatoid Arthritis and Depression: a Nationwide Longitudinal Study

Rheumatoid arthritis (RA) and depression may be associated with each other pathophysiologically, but few studies have been conducted on the interplay between these two diseases using longitudinal measurement. Therefore, we used the National Health Insurance Research Database of Taiwan to investigate the bidirectional associations between RA and depression. One cohort was included to analyze RA predicting the onset of depression and a second cohort for analysis of depression predicting RA. A sex- and age-matched control group was included for both. The incidence of depression in RA subjects was higher than in non-RA subjects [15.69 vs. 8.95 per 1,000 person-years (PYs)], with an adjusted hazard ratios (HRs) of 1.69 [95% confidence interval (CI), 1.51–1.87]. The incidence of RA was higher in depressed than non-depressed individuals (2.07 vs. 1.21 per 1,000 PYs), with an adjusted HRs of 1.65 (95%CI, 1.41–1.77). This population-based cohort study suggested strong bidirectional relationships between RA and depression. Healthcare providers are recommended to facilitate the implementation of more effective therapeutic interventions to achieve favorable prognosis, especially for those with new-onset or younger cases

Increased risk of depression in patients with rheumatoid arthritis: a seven-year population-based cohort study

OBJECTIVE: Rheumatoid arthritis (RA) is a costly and crippling autoimmune disease that can lead to the development of depression, contributing to suboptimal clinical outcomes. However, no longitudinal studies have identified an association between rheumatoid arthritis and subsequent depression. This study aimed to investigate the incidence and risk factors of depression among RA patients in Taiwan. METHODS: Using Taiwan's National Health Insurance Research Database, we identified 3,698 newly diagnosed RA patients aged 18 years or older, together with 7,396 subjects without RA matched by sex, age and index date, between 2000 and 2004. The incidence of depression and the risk factors among RA cases were evaluated using Cox proportional-hazard regression. RESULTS: The incidence of depression was 1.74-fold greater in the RA cohort than in the non-RA cohort (11.80 versus 6.89 per 1,000 person-years;