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.

Syphilis remains a serious public health problem in mainland China that requires attention, modelling to describe and predict its prevalence patterns can help the government to develop more scientific interventions. The seasonal autoregressive integrated moving average (SARIMA) model, long short-term memory network (LSTM) model, hybrid SARIMA-LSTM model, and hybrid SARIMA-nonlinear auto-regressive models with exogenous inputs (SARIMA-NARX) model were used to simulate the time series data of the syphilis incidence from January 2004 to November 2023 respectively. Compared to the SARIMA, LSTM, and SARIMA-LSTM models, the median absolute deviation (MAD) value of the SARIMA-NARX model decreases by 352.69%, 4.98%, and 3.73%, respectively. The mean absolute percentage error (MAPE) value decreases by 73.7%, 23.46%, and 13.06%, respectively. The root mean square error (RMSE) value decreases by 68.02%, 26.68%, and 23.78%, respectively. The mean absolute error (MAE) value decreases by 70.90%, 23.00%, and 21.80%, respectively. The hybrid SARIMA-NARX and SARIMA-LSTM methods predict syphilis cases more accurately than the basic SARIMA and LSTM methods, so that can be used for governments to develop long-term syphilis prevention and control programs. In addition, the predicted cases still maintain a fairly high level of incidence, so there is an urgent need to develop more comprehensive prevention strategies.

We review the progress on the applications of the vortex-surface field (VSF). The VSF isosurface is a vortex surface consisting of vortex lines. Based on the generalized Helmholtz theorem, the VSF isosurfaces of the same threshold at different times have strong coherence. As a general flow diagnostic tool for studying vortex evolution, the numerical VSF solution is first constructed in a given flow field by solving a pseudo-transport equation driven by the instantaneous frozen vorticity, and then the VSF evolution is calculated by the two-time method. From the database of numerical simulations or experiments, the VSF can elucidate mechanisms in the flows with essential vortex dynamics, such as isotropic turbulence, wall flow transition, flow past a flapping plate and turbulence–flame interaction. The characterization of VSFs reveals the correlation between robust statistical features and the critical quantities needed to be predicted in engineering applications, such as the friction coefficient in transition, thrust in bio-propulsion and growth rate in interface instability. Since the VSF evolution captures the essential Lagrangian-based dynamics of vortical flows, it inspires novel numerical methods on cutting-edge hardware, e.g. graphic and quantum processors.

The discharged capillary plasma channel has been extensively studied as a high-gradient particle acceleration and transmission medium. A novel measurement method of plasma channel density profiles has been employed, where the role of plasma channels guiding the advantages of lasers has shown strong appeal. Here, we have studied the high-order transverse plasma density profile distribution using a channel-guided laser, and made detailed measurements of its evolution under various parameters. The paraxial wave equation in a plasma channel with high-order density profile components is analyzed, and the approximate propagation process based on the Gaussian profile laser is obtained on this basis, which agrees well with the simulation under phase conditions. In the experiments, by measuring the integrated transverse laser intensities at the outlet of the channels, the radial quartic density profiles of the plasma channels have been obtained. By precisely synchronizing the detection laser pulses and the plasma channels at various moments, the reconstructed density profile shows an evolution from the radial quartic profile to the quasi-parabolic profile, and the high-order component is indicated as an exponential decline tendency over time. Factors affecting the evolution rate were investigated by varying the incentive source and capillary parameters. It can be found that the discharge voltages and currents are positive factors quickening the evolution, while the electron-ion heating, capillary radii and pressures are negative ones. One plausible explanation is that quartic profile contributions may be linked to plasma heating. This work helps one to understand the mechanisms of the formation, the evolutions of the guiding channel electron-density profiles and their dependences on the external controllable parameters. It provides support and reflection for physical research on discharged capillary plasma and optimizing plasma channels in various applications.

The low maturation rate of oocytes is an important reason for female infertility and failure of assisted pregnancy. The germinal vesicle breakdown (GVBD) is a landmark event of oocyte maturation. In our previous studies, we found that zona pellucida 3 (ZP3) was strongly concentrated in the nuclear region of germinal vesicle (GV) oocytes and interacted with aryl hydrocarbon receptor-interacting protein-like 1 (AIPL1) and lamin A to promote GVBD. In the current study, we found that lamin A is mainly concentrated in the nuclear membrane. When ZP3 is knocked down, lamin A will be partially transferred to the nucleus of oocytes. The prelamin A is increased in both the nuclear membrane and nucleus, while phosphorylated lamin A (p-lamin A) is significantly reduced. AIPL1 was also proved to accumulate in the GV region of oocytes, and ZP3 deletion can significantly inhibit the aggregation of AIPL1 in the nuclear region. Similar to ZP3 knockdown, the absence of AIPL1 resulted in a decrease in the occurrence of GVBD, an increase in the amount of prelamin A, and a significant decrease in p-lamin A in oocytes developed in vitro. Finally, we propose the hypothesis that ZP3 can stabilize farnesylated prelamin A on the nuclear membrane of AIPL1, and promote its further processing into mature lamin A, therefore promoting the occurrence of GVBD. This study may be an important supplement for the mechanism of oocyte meiotic resumption and provide new diagnostic targets and treatment clues for infertility patients with oocyte maturation disorder.

We investigate the energy transport and heat transfer efficiency in turbulent Rayleigh–Bénard (RB) convection laden with radiatively heated inertial particles. Direct numerical simulations combined with the Lagrangian point-particle mode were carried out in the range of density ratio $854.7\le \rho _p/\rho _0 \le 8547$ and radiation intensity $1\le \phi /\phi _{solar}\le 100$ for both two-dimensional (2-D) and three-dimensional (3-D) simulations. The Rayleigh number ranges from $2\times 10^6$ to $10^8$ for 2-D cases, and is $10^7$ for 3-D cases for $Pr=0.71$. It is found that particles with small density ratio that encounter strong radiation significantly alter the flow momentum transport and fluid heat transfer, so the fluid temperature of bulk is remarkably heated. We then derived the theoretical relation of the Nusselt number for interphase heat transfer in the heated particle-laden RB convection, which reveals that the heat transfer difference between the top and bottom plates stems from the interphase heat transfer. We further found that both the interphase heat transfer and the interphase thermal energy transport exhibit universal properties. They are both increased linearly with the reciprocal of the normalized density ratio. Additionally, both the interphase heat transfer and the interphase thermal energy transport increase linearly with the increase of radiation intensity. The growth rates exhibit specific scaling relations versus Rayleigh number and density ratio. Two different regimes distinguished by the critical density ratio, i.e. the exothermic particle regime and the endothermic particle regime, are observed. We further derived the power-law relation of the critical density ratios versus Rayleigh number and radiation intensity, i.e. $\rho _p/\rho _c \sim (\phi /\phi _{solar})^{1/2}\,Ra^{1/3}$, which is in remarkable agreement with the 3-D simulations.

Electronic skin (e-skin) is playing an increasingly important role in health detection, robotic teleoperation, and human-machine interaction, but most e-skins currently lack the integration of on-site signal acquisition and transmission modules. In this paper, we develop a novel flexible wearable e-skin sensing system with 11 sensing channels for robotic teleoperation. The designed sensing system is mainly composed of three components: e-skin sensor, customized flexible printed circuit (FPC), and human-machine interface. The e-skin sensor has 10 stretchable resistors distributed at the proximal and metacarpal joints of each finger respectively and 1 stretchable resistor distributed at the purlicue. The e-skin sensor can be attached to the opisthenar, and thanks to its stretchability, the sensor can detect the bent angle of the finger. The customized FPC, with WiFi module, wirelessly transmits the signal to the terminal device with human-machine interface, and we design a graphical user interface based on the Qt framework for real-time signal acquisition, storage, and display. Based on this developed e-skin system and self-developed robotic multi-fingered hand, we conduct gesture recognition and robotic multi-fingered teleoperation experiments using deep learning techniques and obtain a recognition accuracy of 91.22%. The results demonstrate that the developed e-skin sensing system has great potential in human-machine interaction.

Due to the merits of high rigidity and good dynamics, hybrid machine tools have been gradually applied to efficient machining of thin-walled workpiece with complex geometries. However, the discontinuity of tangential component of toolpath in hybrid machine tools may cause velocity fluctuations, leading to poor surface quality of workpiece. In this paper, a novel 5-axis hybrid machine tool is taken as an example to demonstrate a smooth toolpath interpolation method. First, an adaptive acceleration and deceleration control algorithm is presented to realize the smooth transition between two constrained velocity points. Second, a spline curve-based interpolation algorithm is proposed to realize the smoothness of the trajectory. Meanwhile, a parameter synchronization method is proposed to ensure the synchronization of the interpolated tool-axis vector and the interpolated tool tip. Thirdly, an inverse kinematic analysis is conducted based on an inverse position solution model and a velocity mapping model. Finally, a set of machining tests on S-shape workpiece in line with the ISO standard is carried out to verify the effectiveness of the proposed smooth toolpath interpolation method.

Numerous animal models and epidemiological and observational studies have demonstrated that enterovirus (EV) infection could be involved in the development of clinical type 1 diabetes mellitus (T1DM), but its aetiology is not fully understood. Therefore, we reviewed the association between EV infection and clinical T1DM. We searched PubMed and Embase from inception to April 2021 and reference lists of included studies without any language restrictions in only human studies. The correlation between EV infection and clinical T1DM was calculated as the pooled odds ratio (OR) and 95% confidence intervals (CIs), analysed using random-effects models. Subgroup and sensitivity analyses were performed to evaluate the robustness of the associations. A total of 25 articles (22 case–control studies and three nested case–control studies) met the inclusion criterion including 4854 participants (2948 cases and 1906 controls) with a high level of statistical heterogeneity (I2 = 80%, P < 0.001) mainly attributable to methods of EV detection, study type, age distribution, source of EV sample and control subjects. Meta-analysis showed a significant association between EV infection and clinical T1DM (OR 5.75, 95% CI 3.61–9.61). There is a clinically significant association between clinical T1DM and EV infection.

Using near miss data detected from non-accident information to analyse marine traffic risk can alleviate some of the limitations of accident-based methods. A model based on an arena for detecting scenes of near miss is proposed to detect comprehensively those ship encounters with potential collision risk. To eliminate the influence of data sampling frequency on the detection of scenes of near miss, a single near miss is defined as the whole progress of traffic state from the time the target ship sails into the arena of the subject ship to the time it leaves the arena of the subject ship. To research the geographical distribution characteristics of marine traffic risk, first, a statistical model for the scenes of near miss based on the water grid method is proposed, and then a macroscopic collision risk model based on near miss is developed. The geographical distribution characteristics of marine traffic risk in the Bohai Sea are analysed, and the water areas of high marine traffic risk are obtained. The findings can provide theoretical support for marine safety management.

Dolostones are widely developed in the middle Permian rocks of East Yunnan, China, mainly in the shoal-facies Maokou Formation. The previously reported dolostone formation mechanisms cannot explain the distribution and geochemical characteristics of these dolostones, in particular their strontium, magnesium and oxygen isotope signatures. To help predict the distribution of dolostone reservoirs and reduce the exploration risk and cost, this study proposes a new model of dolomitization: open thermal convection dolomitization. In this new dolomitization model, Mg2+ in dolomitizing fluids originates mostly from seawater, with a minor component coming from deep hydrothermal fluids. Elevated heat flux (in this case due to the nearby Emei mantle plume) causes spatial temperature variations in the fluid along the circulation flow pathways, resulting in fast and pervasive dolomitization of limestone. The proposed model not only explains the characteristics and distribution of dolostones in the study area but also serves as a reference for predicting the distribution of dolostones in other areas subjected to thermal convection.

A solution to the problem of Gaussian beam scattering by a circular perfect electric conductor coated with eccentrically anisotropic media is presented. The incident Gaussian beam source is expanded as an approximate expression in the simple form with Taylor's series. The transmitted field in the anisotropically coated region is expressed as an infinite summation of Eigen plane waves with different polar angles. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions. The addition theorem for cylindrical functions is applied to transfer from the local coordinates to the global ones. The infinite series can be truncated under the prerequisite of achieving the solution convergence. Only the case of transverse-electric polarization is discussed. The similar formulation of transverse-magnetic polarization can be obtained by adopting a similar method. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the eccentric geometry comes to the concentric one.