For $r\in(0,1)$, let $\mu \left( r\right) $ be the modulus of the plane Grötzsch ring $\mathbb{B}^2\setminus[0,r]$, where $\mathbb{B}^2$ is the unit disk. In this paper, we prove that

\begin{equation*}\mu \left( r\right) =\ln \frac{4}{r}-\sum_{n=1}^{\infty }\frac{\theta _{n}}{2n}r^{2n},\end{equation*}

with $\theta _{n}\in \left( 0,1\right)$. Employing this series expansion, we obtain several absolutely monotonic and (logarithmically) completely monotonic functions involving $\mu \left( r\right) $, which yields some new results and extend certain known ones. Moreover, we give an affirmative answer to the conjecture proposed by Alzer and Richards in H. Alzer and K. Richards, On the modulus of the Grötzsch ring, J. Math. Anal. Appl. 432(1): (2015), 134–141, DOI 10.1016/j.jmaa.2015.06.057. As applications, several new sharp bounds and functional inequalities for $\mu \left( r\right) $ are established.

All-fiber coherent beam combiners based on the self-imaging effect can achieve a near-perfect single laser beam, which can provide a promising way to overcome the power limitation of a single-fiber laser. One of the key points is combining efficiency, which is determined by various mismatches during fabrication. A theoretical model has been built, and the mismatch error is analyzed numerically for the first time. The mismatch errors have been numerically studied with the beam quality and combining efficiency being chosen as the evaluation criteria. The tolerance of each mismatch error for causing 1% loss is calculated to guide the design of the beam combiners. The simulation results are consistent with the experimental results, which show that the mismatch error of the square-core fiber is the main cause of the efficiency loss. The results can provide useful guidance for the fabrication of all-fiber coherent beam combiners.

The three-child policy constitutes a hotly debated socio-political issue in China. Upon its announcement, many Chinese citizens have ridiculed the move on social media. Adopting the cognitive mediation model and the influence of presumed influence theory, this study examines how social media exposure to three-child policy-related news and discussions could affect the Chinese public’s attitudes toward the policy. The online survey results show that social media exposure negatively predicts supportive opinion via cognitive elaboration and three types of perceived negative effects of the policy (i.e., perceived negative effects on self, on the public, and on females) in serial. It also finds that institutional trust moderates the relationship between cognitive elaboration and policy support. Only among people with high institutional trust, there is a positive effect of social media exposure on supportive opinion through cognitive elaboration.

We explored the transmission mechanisms of corporate fraud and its punishments within social network communities. Using fraud triangle theory and trust triangle theory, we hypothesize four transmitting channels of how fraud commission and detection are affected by peers’ fraud and punishment. Based on Chinese listed corporations from 2008 to 2018, we first construct and detect interlocked social network communities with a community-detecting algorithm, and then examine hypotheses using a bivariate probit model with partial observability. Our findings indicate that peer-concealing and -hinting effects exist within social network communities. The peer-concealing effect decreases the likelihood of being detected when committing fraud, for those with more and closer fraudulent peers. The peer-hinting effect increases the likelihood of being detected when committing fraud, for those with more and closer punished peers. There is no evidence to support peer-contagion and vicarious-punishment effects. Thus, an improved understanding of the transmission mechanism of corporate fraud commission and detection within communities is provided to prevent and detect corporate fraud. In addition, stakeholders and regulators should be aware of the deviant subculture and social distancing in social network communities.

Although ethanol treatment is widely used to activate oocytes, the underlying mechanisms are largely unclear. Roles of intracellular calcium stores and extracellular calcium in ethanol-induced activation (EIA) of oocytes remain to be verified, and whether calcium-sensing receptor (CaSR) is involved in EIA is unknown. This study showed that calcium-free ageing (CFA) in vitro significantly decreased intracellular stored calcium (sCa) and CaSR expression, and impaired EIA, spindle/chromosome morphology and developmental potential of mouse oocytes. Although EIA in oocytes with full sCa after ageing with calcium does not require calcium influx, calcium influx is essential for EIA of oocytes with reduced sCa after CFA. Furthermore, the extremely low EIA rate in oocytes with CFA-downregulated CaSR expression and the fact that inhibiting CaSR significantly decreased the EIA of oocytes with a full complement of CaSR suggest that CaSR played a significant role in the EIA of ageing oocytes. In conclusion, CFA impaired EIA and the developmental potential of mouse oocytes by decreasing sCa and downregulating CaSR expression. Because mouse oocytes routinely treated for activation (18 h post hCG) are equipped with a full sCa complement and CaSR, the present results suggest that, while calcium influx is not essential, CaSR is required for the EIA of oocytes.

Hepatitis B virus-related acute-on-chronic liver failure (HBV-ACLF) is a severe and life-threatening complication, characterised by multi-organ failure and high short-term mortality. However, there is limited information on the impact of various comorbidities on HBV-ACLF in a large population. This study aimed to investigate the relationship between comorbidities, complications and mortality. In this retrospective observational study, we identified 2166 cases of HBV-ACLF hospitalised from January 2010 to March 2018. Demographic data from the patients, medical history, treatment, laboratory indices, comorbidities and complications were collected. The mortality rate in our study group was 47.37%. Type 2 diabetes mellitus was the most common comorbidity, followed by alcoholic liver disease. Spontaneous bacterial peritonitis, pneumonia and hepatic encephalopathy (HE) were common in these patients. Diabetes mellitus and hyperthyroidism are risk factors for death within 90 days, together with gastrointestinal bleeding and HE at admission, HE and hepatorenal syndrome during hospitalisation. Knowledge of risk factors can help identify HBV-ACLF patients with a poor prognosis for HBV-ACLF with comorbidities and complications.

Wealth management products have been popular investment vehicles in China, and they are governed by standard form contracts. Existing studies mainly focus on the risk of such products and suggest having special laws to provide more protection for customers. Little is known about the actual contents of wealth management product contracts. Based on 66 hand-collected wealth management product contracts from major Chinese commercial banks, this article tries to explore the contractual relationship between giant banks and individual customers. It also tests the exploitation theory in a Chinese context by analysing whether the wealth management product contracts are more pro-seller or pro-buyer relative to the laws and regulations in China. Our findings reinforce the argument that standard form contracts are designed in favour of the sellers. The wealth management product contracts are tilted toward the commercial banks relative to the default rules. These contracts contain massive clauses that limit banks’ liabilities and restrict customers’ choice of conflict resolution mechanisms. However, a counter-intuitive finding is that national commercial banks provide less pro-seller terms than the local ones. We argue that the explanations for such variation in contract practices among Chinese commercial banks lie in the enforcement of relevant laws and regulations and the unique nature of national commercial banks.

We present a theoretical study of mode evolution in high-power distributed side-coupled cladding-pumped (DSCCP) fiber amplifiers. A semi-analytical model taking the side-pumping schemes, transverse mode competition, and stimulated thermal Rayleigh scattering into consideration has been built, which can model the static and dynamic mode evolution in high-power DSCCP fiber amplifiers. The mode evolution behavior has been investigated with variation of the fiber amplifier parameters, such as the pump power distribution, the length of the DSCCP fiber, the averaged coupling coefficient, the number of the pump cores and the arrangement of the pump cores. Interestingly, it revealed that static mode evolution induced by transverse mode competition is different from the dynamic evolution induced by stimulated thermal Rayleigh scattering. This shows that the high-order mode experiences a slightly higher gain in DSCCP fiber amplifiers, but the mode instability thresholds for DSCCP fiber amplifiers are higher than those for their end-coupled counterparts. By increasing the pump core number and reducing the averaged coupling coefficient, the mode instability threshold can be increased, which indicates that DSCCP fibers can provide additional mitigation strategies of dynamic mode instability.

A 1178 J near diffraction limited 527 nm laser is realized in a complete closed-loop adaptive optics (AO) controlled off-axis multi-pass amplification laser system. Generated from a fiber laser and amplified by the pre-amplifier and the main amplifier, a 1053 nm laser beam with the energy of 1900 J is obtained and converted into a 527 nm laser beam by a KDP crystal with 62% conversion efficiency, 1178 J and beam quality of 7.93 times the diffraction limit (DL). By using a complete closed-loop AO configuration, the static and dynamic wavefront distortions of the laser system are measured and compensated. After correction, the diameter of the circle enclosing 80% energy is improved remarkably from 7.93DL to 1.29DL. The focal spot is highly concentrated and the 1178 J, 527 nm near diffraction limited laser is achieved.

Frozen embryo transfer (FET) has been adopted by growing number of reproductive medicine centers due to the improved outcome compared with fresh embryo transfer. However, few studies have focused on the impact of embryo cryopreservation duration on pregnancy-related complications and neonatal birthweight. Thus, a retrospective cohort study including all FET cycles with livebirth deliveries in a university affiliated hospital from May 2010 to September 2017 was conducted. These deliveries were grouped by the cryopreservation duration of the transferred embryo (≤3 months, 4–6 months, 7–12 months, and >12 months). The associations between embryo cryopreservation duration and pregnancy-related complications were evaluated among the groups using multinomial logistic regression. Neonatal birthweight was compared according to the stratification of singletons and multiples using multinomial and multilevel logistic regression, respectively. Among all 12,158 FET cycles, a total of 3864 livebirth deliveries comprising 2995 singletons and 1739 multiples were included. Compared with those within 3 months, women undergoing FET after a cryopreservation time longer than 3 months did not show any increased risk of gestational diabetes mellitus, gestational hypertension, preeclampsia, meconium staining of the amniotic fluid, or preterm birth. Furthermore, the risk of lower birthweight, macrosomia, small-for-gestational-age, or large-for-gestational-age for either singletons or multiples was not affected by long-term cryopreservation. In summary, embryo cryopreservation duration does not have negative effects on pregnancy-related complications or birthweight after FET.

While procedural justice has been regarded as a distinct and essential factor shaping litigants' views on civil justice, few studies have focused on China, a country with a unique legal tradition and frequent legal reforms. Drawing on surveys and interviews with litigants in a basic-level court in Southern China, this study examines attitudes toward the civil justice system. Echoing several existing studies from China, our mixed methods analysis confirms that their views are dominated by outcomes—litigants with favorable outcomes are more likely to be satisfied, while those with unfavorable outcomes are more likely to be dissatisfied. Their unfamiliarity with the operation of the system constitutes a major reason for the dominance of substantive outcomes in their evaluations of the system. Many cannot distinguish between process and outcomes, nor do they feel control over the process. Moreover, they are dissatisfied with the process because it fails to meet their often-erroneous expectations. Our results do not necessarily challenge the importance of procedural justice, but they do suggest that China may be different. Litigants' perceptions of justice and fairness are situated and shaped by specific contexts.