On the Hecke Eigenvalues of Maass Forms

Let $\phi$ denote a primitive Hecke-Maass cusp form for $\Gamma_o(N)$ with the Laplacian eigenvalue $\lambda_\phi=1/4+t_{\phi}^2$. In this work we show that there exists a prime $p$ such that $p\nmid N$, $|\alpha_{p}|=|\beta_{p}| = 1$, and $p\ll(N(1+|t_{\phi}|))^c$, where $\alpha _{p},\;\beta _{p}$ are the Satake parameters of $\phi$ at $p$, and $c$ is an absolute constant with $0<c<1$. In fact, $c$ can be taken as $0.27332$. In addition, we prove that the natural density of such primes $p$ ($p\nmid N$ and $|\alpha_{p}|=|\beta_{p}| = 1$) is at least $34/35$.Comment: Version 2: typos corrected and a new section on natural density adde

Determination of modular elliptic curves by Heegner points

For every integer N ≥ 1, consider the set K(N) of imaginary quadratic fields such that, for each K in K(N), its discriminant D is an odd, square-free integer congruent to 1 modulo 4, which is prime to N and a square modulo 4N. For each K, let c = ([x]−[∞]) be the divisor class of a Heegner point x of discriminant D on the modular curve X = X(0)(N) as in [GZ]. (Concretely, such an x is the image of a point z in the upper half plane H such that both z and Nz are roots of integral, definite, binary quadratic forms of the same discriminant D ([B]).) Then c defines a point rational over the Hilbert class field H of K on the Jacobian J = J(0)(N) of X. Denote by cK the trace of c to K

Low lying zeros of families of L-functions

In Iwaniec-Sarnak [IS] the percentages of nonvanishing of central values of families of GL_2 automorphic L-functions was investigated. In this paper we examine the distribution of zeros which are at or neat s=1/2 (that is the central point) for such families of L-functions. Unlike [IS], most of the results in this paper are conditional, depending on the Generalized Riemann Hypothesis (GRH). It is by no means obvious, but on the other hand not surprising, that this allows us to obtain sharper results on nonvanishing.Comment: Abstract added in migration (from introduction

Big data analysis of water quality monitoring results from the Xiang River and an impact analysis of pollution management policies

Water pollution prevention and control of the Xiang River has become an issue of great concern to China's central and local governments. To further analyze the effects of central and local governmental policies on water pollution prevention and control for the Xiang River, this study performs a big data analysis of 16 water quality parameters from 42 sections of the mainstream and major tributaries of the Xiang River, Hunan Province, China from 2005 to 2016. This study uses an evidential reasoning-based integrated assessment of water quality and principal component analysis, identifying the spatiotemporal changes in the primary pollutants of the Xiang River and exploring the correlations between potentially relevant factors. The analysis showed that a series of environmental protection policies implemented by Hunan Province since 2008 have had a significant and targeted impact on annual water quality pollutants in the mainstream and tributaries. In addition, regional industrial structures and management policies also have had a significant impact on regional water quality. The results showed that, when examining the changes in water quality and the effects of pollution control policies, a big data analysis of water quality monitoring results can accurately reveal the detailed relationships between management policies and water quality changes in the Xiang River. Compared with policy impact evaluation methods primarily based on econometric models, such a big data analysis has its own advantages and disadvantages, effectively complementing the traditional methods of policy impact evaluations. Policy impact evaluations based on big data analysis can further improve the level of refined management by governments and provide a more specific and targeted reference for improving water pollution management policies for the Xiang River

Perceptions, behaviours and attitudes towards smoking held by the male partners of Chinese pregnant women:a qualitative study

Abstract Background Direct associations of tobacco exposure during pregnancy with pregnancy complications and adverse birth outcomes have been proven. Previous studies suggest that expecting a child provides a valuable opportunity to promote behavioural changes, such as smoking cessation, among the male partners of pregnant women. Thorough understandings of Chinese expectant fathers’ smoking behaviour during the transition to fatherhood is a prerequisite to the development of appropriate interventions to facilitate smoking cessation. This study aimed to explore the perceptions, behaviours and attitudes related to smoking among male partners of pregnant women in China. Methods A descriptive phenomenological approach was adopted. A purposive sample of expectant fathers aged 18 years or older who had a tobacco use history within the past year were recruited at obstetrics and gynaecology clinics and invited to participate in one-to-one, 20–30-min semi-structured interviews. The data analysis followed Colaizzi’s descriptive phenomenological method. Results Twenty-five expectant fathers were interviewed. Four themes were generated: 1) the benefits of smoking and respondents’ misperceptions of the impact of smoking and SHS and neglectful attitude of the impact of smoking, which were given as the major reasons for continuing to smoke; 2) factors contributing to smoking cessation, including concern for the potential health impact of continued smoking on the pregnant partner and baby, the role of being father, and the encouragement to quit from family members; and 3) perceived barriers to smoking cessation, including withdrawal symptoms or cigarette cravings, absence of smoking cessation support, and increasing stress. Conclusion This study provides a comprehensive understanding of the perception, behaviours, and attitudes related to smoking among Chinese expectant fathers. The findings of this study can guide healthcare professionals and policymakers in combining the distribution of educational information about the hazards of SHS for maternal and neonatal health with smoking cessation assistance for expectant fathers through policy initiatives and other types of incentives and programmes targeted to enhance smoking cessation among this population. Trial registration Prospectively registered at clinicaltrial.org ( NCT03401021 ) on 8 Jan 2018

The Gaps Between Current Management of Intracerebral Hemorrhage and Evidence-Based Practice Guidelines in Beijing, China

Background: The leading cause of death in China is stroke, a condition that also contributes heavily to the disease burden. Nontraumatic intracerebral hemorrhage (ICH) is the second most common cause of stroke. Compared to Western countries, in China the proportion of ICH is significantly higher. Standardized treatment based on evidence-based medicine can help reduce ICH's burden. In the present study we aimed to explore the agreement between the management strategies during ICH's acute phase and Class I recommendations in current international practice guidelines in Beijing (China), and to elucidate the reasons underlying any inconsistencies found.Method: We retrospectively collected in-hospital data from 1,355 ICH patients from 15 hospitals in Beijing between January and December 2012. Furthermore, a total of 75 standardized questionnaires focusing on ICH's clinical management were distributed to 15 cooperative hospitals. Each hospital randomly selected five doctors responsible for treating ICH patients to complete the questionnaires.Results: Numerous approaches were in line with Class I recommendations, as follows: upon admission, all patients underwent radiographic examination, about 93% of the survivors received health education and 84.5% of those diagnosed with hypertension were prescribed antihypertensive treatment at discharge, in-hospital antiepileptic drugs were administered to 91.8% of the patients presenting with seizures, and continuous monitoring was performed for 88% of the patients with hyperglycemia on admission. However, several aspects were inconsistent with the guidelines, as follows: only 14.2% of the patients were initially managed in the neurological intensive care unit and 22.3% of the bedridden patients received preventive treatment for deep vein thrombosis (DVT) within 48 h after onset. The questionnaire results showed that imaging examination, blood glucose monitoring, and secondary prevention of ICH were useful to more clinicians. However, the opposite occurred for the neurological intensive care unit requirement. Regarding the guidelines' recognition, no significant differences among the 3 education subgroups were observed (p &gt; 0.05).Conclusions: Doctors have recognized most of ICH's evidence-based practice guidelines. However, there are still large gaps between the management of ICH and the evidence-based practice guidelines in Beijing (China). Retraining doctors is required, including focusing on preventing DVT providing a value from the National Institutes of Health Stroke Scale and Glasgow Coma Scalescores at the time of admission

Ring roads and urban biodiversity: distribution of butterflies in urban parks in Beijing city and correlations with other indicator species

The capital of China, Beijing, has a history of more than 800 years of urbanization, representing a unique site for studies of urban ecology. Urbanization can severely impact butterfly communities, yet there have been no reports of the species richness and distribution of butterflies in urban parks in Beijing. Here, we conducted the first butterfly survey in ten urban parks in Beijing and estimated butterfly species richness. Subsequently, we examined the distribution pattern of butterfly species and analyzed correlations between butterfly species richness with park variables (age, area and distance to city center), and richness of other bioindicator groups (birds and plants). We collected 587 individual butterflies belonging to 31 species from five families; 74% of the species were considered cosmopolitan. The highest butterfly species richness and abundance was recorded at parks located at the edge of city and species richness was significantly positively correlated with distance from city center (p  0.05). Our study provides the first data of butterfly species in urban Beijing, and serves as a baseline for further surveys and conservation efforts