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In this research, we propose and study an online social network mathematical model with delay based on two innovative assumptions: (1) newcomers are entering community as either potential online network users or that who are never interested in online network at constant rates, respectively; and (2) it takes a certain time for the active online network users to start abandoning the network. The basic reproduction R0, the user-free equilibrium(UFE) P0, and the user-prevailing equilibrium(UPE) P∗ are identified. The analysis of local and global stability for those equilibria is carried out. For the UPE P∗, using the delay τ as the Hopf bifurcation parameter, the occurrence of Hopf bifurcation is investigated. The conditions are established that guarantee the Hopf bifurcation occurs as τ crosses the critical values. Numerical simulations are provided to illustrate the theoretical results.

In this research, we introduce and analyze a mathematical model for online social networks, incorporating two distinct delays. These delays represent the time it takes for active users within the network to begin disengaging, either with or without contacting non-users of online social platforms. We focus particularly on the user prevailing equilibrium (UPE), denoted as P*, and explore the role of delays as parameters in triggering Hopf bifurcations. In doing so, we find the conditions under which Hopf bifurcations occur, then establish stable regions based on the two delays. Furthermore, we delineate the boundaries of stability regions wherein bifurcations transpire as the delays cross these thresholds. We present numerical simulations to illustrate and validate our theoretical findings. Through this interdisciplinary approach, we aim to deepen our understanding of the dynamics inherent in online social networks.

We consider a second order boundary value problem with a parameter. A new upper bound for positive solutions and Green’s function of the problem is obtained.

H2 is regarded as an attractive green fuel and a promising energy carrier for the future. Here, the promotion functions of reverse spillover effects in the H2 generation reactions over bicomponent catalysts are revealed by performing in situ X ray absorption near edge structure characterization.

In the mining process of underground metal mines, the misjudgment of rock types by on-site technicians will have a serious negative impact on the stability evaluation of rock mass and the formulation of support schemes, which will result in the loss of economic benefits and potential safety hazards of mining enterprises. In order to realize the precise and intelligent identification of rock types, the image data of peridotite, basalt, marble, gneiss, conglomerate, limestone, granite, magnetite quartzite are amplified. Under the target detection framework of Faster R-CNN deep learning, the extraction network based on simplified VGG16 is used to extract and learn features of rock images, and finally the rock type identification system is successfully trained. The experimental verification shows that the system is correct for single-type rock image recognition and the accuracy is more than 96%. In order to realize accurate and intelligent identification of the surrounding rock surface under complex lithological conditions, the multi-type rocks hybrid images are also identified. The results show that the recognition effect is great and the accuracy rate is over 80%. Therefore, this system can accurately identify rock types with similar image features, which proves that the model has strong robustness and generalization ability. It has broad application prospects in rock mass stability evaluation and rock classification in underground mining.

Visible light communication (VLC) has attracted widespread attention for wireless communications. The popularity of GaN‐based light‐emitting diodes (LEDs) has also laid a solid foundation for the application of VLC. As the light source of VLC, LED's modulation bandwidth directly determines the speed of communication. Herein, reviewing progress on modulation bandwidth improvement schemes of GaN LEDs transmitter is reviewed, covering aspects from epitaxial to devices. Epitaxial approaches include c‐polar facet epitaxial optimization, non/semipolar facet epitaxial growth, and chip scheme such as micro‐LEDs, nano‐LEDs, resonant cavity‐LEDs (RC‐LEDs), plasmon, and metacavity LEDs. In terms of white LEDs, approaches to tackle the slow Stokes transfer and long carrier life for conventional phosphors including new color‐conversion materials (CCMs) and new energy transfer routes are reviewed. This review promotes the development of GaN‐based LEDs as the transmitter for high‐speed VLC.

An in-depth understanding of the gravity flow behaviour of broken ore is beneficial to improving the ore recovery in sublevel caving mines. In this study, granular dolomites were used as an analogue to experimentally explore the effect of the physical properties of fragments on the gravity flow behaviour of broken ore. Five groups of granular dolomites were prepared first. Then, the particle size, particle size distribution, and particle morphology (e.g., sphericity, circularity, and fractal dimension) in each group were measured following the standard particle morphology test. After that, the angle of repose and the isolated extraction zone (IEZ) of each group were determined by performing funnel and isolated draw experiments, respectively. The experimental results highlighted the insubstantial effect of particle size and the significant effect of particle morphology on the angle of repose and isolated extraction zone of granular dolomite. It was found that a wider particle size distribution yielded an isolated extraction zone with a nonuniform shape and a smaller mass drawn because of the percolation of finer particles and the jamming of larger particles. Further, a linear negative correlation was revealed between the repose angle and the IEZ mass. Establishing the relationship between the repose angle and the IEZ shape would be of great significance. In this regard, the findings of this study can aid a preliminary analysis.

To improve the performance of III-nitride compound semiconductor-based optoelectronic devices, highly reflective distributed Bragg reflectors (DBRs) are a requirement. In this report, AlN and Al1−xInxN layers were first sputtered and characterized concerning their optical, structural and morphological properties. Ellipsometry measurements were used to determine the optical constants (refractive index, n and coefficient of extinction, k, in dependence of the wavelengths of the layers. The indium content of the Al1−xInxN film was investigated by X-ray photoelectron spectroscopy analysis. Subsequently, AlN/Al1−xInxN DBRs with high reflectivity spectra operating in the UV A, B and C were designed and fabricated on Si (111) and SiO2 substrates by radio frequency (RF) magnetron sputtering. The DBRs consist of an eight-pair AlN/Al0.84In0.16N at 235 nm, 290 nm and 365 nm with reflectances of 86.5%, 97.7% and 97.5% with FWHM of 45 nm, 70 nm and 96 nm, respectively. Atomic force microscopy analysis yielded a Root Mean Square (RMS) of 2.95 nm, implying that the DBR samples can achieve reasonable smoothness over a wide area. Furthermore, the impact of an annealing phase, which is frequently required during device growth, was investigated. Our findings indicate that AlN and Al1−xInxN are suitable materials for the fabrication of deep UV DBRs.

In this paper, first a third degree transcendental polynomial is studied and the distribution of its zeros is established. Then the results are applied to study an SEIR model with a time delay. We show that, under some conditions, as the time delay increases, a stable endemic equilibrium will become unstable and periodic solution emerges by Hopf bifurcation. By finding the normal form of the system, the direction and the stability of the periodic solution are established. Numerical simulations are performed to demonstrate the theoretical results.

In this work, we report demonstration of optically-pumped single-mode deep-ultraviolet lasing actions operating at room temperature from ∼1-μm 150-nm-thick undercut microdisks with AlN/Al0.35Ga 0.65N (5.5 nm/2.5 nm) multiple quantum wells. These AlGaN-based microdisks are grown on Si substrate by metal-organic chemical vapor deposition. The lasing wavelength centers at ∼300.1 nm with the linewidth of ∼1.0 nm as the excitation exceeds the lasing threshold of ∼24.2 mJ/cm2. An emission coupling factor (β) of 9.2 × 10−2 is estimated based on the light output characteristics of the AlN/AlGaN microdisks with increasing the pumping densities. Concurrently, a 100 meV blue-shift in the mode energy has also been observed. The lasing spectral peak is attributed to fundamental-order transverse-electric whispering-gallery modes, confirmed by three-dimensional finite-difference time-domain simulations.

In this manuscript, we provide a framework for the double-Hopf singularity with 1:1 resonance for general delayed differential equations (DDEs). The corresponding normal form up to the third-order terms is derived. As an application of our framework, a double-Hopf singularity with 1:1 resonance for a van der Pol oscillator with delayed feedback is investigated to illustrate the theoretical results.

In this paper, we experimentally demonstrated a novel approach known as electroless silver plating (ESP) for the fabrication of Ag-only reflectors on vertical light-emitting diodes (VLEDs). The Ag reflector that was obtained through the ESP approach shows a higher reflectance of 83% and a lower contact resistivity of 6 * 10-3 Ω · cm2 with p-GaN, compared with that fabricated through the conventional electron beam (EB) approach, which shows a reflectance of 75% and a contact resistivity of 6.2 * 10-2 Ω · cm2, respectively. Improvements in the light output intensity-current (L-I) and current-voltage (I-V) results in VLEDs, which originated from the high reflectance and low-contact resistivity of the incorporated ESP-Ag reflector. Our result opens up an alternative and promising way to substitute the traditional EB approach for Ag-based reflector fabrication and, thus, is practically meaningful in real device fabrication, such as with VLEDs.

The analysis of crosscut stability is an indispensable task in underground mining activities. Crosscut instabilities usually cause geological disasters and delay of the project. On site, mining engineers analyze and predict the crosscut condition by monitoring its convergence and stress; however, stress monitoring is time-consuming and expensive. In this study, we propose an improved extreme learning machine (ELM) algorithm to predict crosscut’s stress based on convergence data, for the first time in literature. The performance of the proposed technique is validated using a crosscut response by means of the FLAC3D finite difference program. It is found that the improved ELM algorithm performs higher generalization performance compared to traditional ELM, as it eliminates the random selection for input weights. Furthermore, a crosscut construction project in an underground mine, Yanqianshan iron mine, located in Liaoning Province (China), is selected as the case study. The accuracy and efficiency of the improved ELM algorithm has been demonstrated by comparing predicted stress data to measured data on site. Additionally, a comparison is conducted between the improved ELM algorithm and other commonly used artificial neural network algorithms.

In this paper, we investigate a Kaldor-Kalecki model of business cycle with delay in both the gross product and the capital stock. Stability analysis for the equilibrium point is carried out. We show that Hopf bifurcation occurs and periodic solutions emerge as the delay crosses some critical values. By deriving the normal forms for the system, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Examples are presented to confirm our results.

Disabilities after neural injury, such as stroke, bring tremendous burden to patients, families and society. Besides the conventional constrained-induced training with a paretic arm, bilateral rehabilitation training involves both the ipsilateral and contralateral sides of the neural injury, fitting well with the fact that both arms are needed in common activities of daily living (ADLs), and can promote good functional recovery. In this work, the fusion of a gesture sensor and a haptic sensor with force feedback capabilities has enabled a bilateral rehabilitation training therapy. The Leap Motion gesture sensor detects the motion of the healthy hand, and the omega.7 device can detect and assist the paretic hand, according to the designed cooperative task paradigm, as much as needed, with active force feedback to accomplish the manipulation task. A virtual scenario has been built up, and the motion and force data facilitate instantaneous visual and audio feedback, as well as further analysis of the functional capabilities of the patient. This task-oriented bimanual training paradigm recruits the sensory, motor and cognitive aspects of the patient into one loop, encourages the active involvement of the patients into rehabilitation training, strengthens the cooperation of both the healthy and impaired hands, challenges the dexterous manipulation capability of the paretic hand, suits easy of use at home or centralized institutions and, thus, promises effective potentials for rehabilitation training.

Incorporating Ag nanowires with graphene resulted in improved electrical conductivity and enhanced contact properties between graphene and p-GaN. The graphene/AgNWs hybrid films exhibited high transmittance and lower sheet resistance compared to bare graphene. The specific contact resistance between graphene and p-GaN reduced nearly an order of magnitude with the introduction of AgNWs. As a result, light emitting diodes based on the hybrid films showed 44% lower forward voltage and 2-fold higher light output power. The enhanced performance was attributed to the bridging by AgNWs of cracks, grain boundaries in graphene and the reduction of Schottky barrier height at graphene/ p-GaN interface.