In history, theta function identities have been studied extensively and deeply. In this paper, applying the residue theorem of an elliptic function, we obtain a parameterized theta function identity. Then, by selecting the appropriate parameter, we derive some famous Jacobi identities, as well as other relatively simple theta function identities.

Under the dual erosion conditions of the dry-wet cycle, which is caused by the high chloride salt concentrations in mine water and fluctuations in mine water level, cemented paste backfill (CPB) suffers serious damage and deterioration. To discuss the mechanical properties and permeability characteristics of CPB under erosion, this study designs an immersion experiment for CPB under chloride salt and dry-wet cycle conditions. Through a uniaxial compressive strength (UCS) test, the change law for the mechanical parameters of the CPB was explored, strength constitutive equation of the CPB was constructed, and the process of deterioration of the CPB was analyzed. Through the penetration test, the diffusion characteristics of packing under chloride salt and dry-wet cycle conditions were explored. The results demonstrated that the strength and elastic modulus of the CPB first increased and then decreased rapidly, with maximum decrease rates of 32.2% and 38.2%, respectively. The CPB structure presents an initial non-damage stage, initial damage stage, damage development stage, damage destruction, and residual damage stage. The chloride ion penetration depth gradually increased with an increase in the number of dry-wet cycles, with a maximum diffusion depth of 20.5 mm. The maximum apparent diffusion coefficient of chloride ion was 18.99×10-10m2/s, and the maximum concentration was 0.303 mol/L. Under the double erosion conditions due to chloride salt and dry-wet cycle, the CPB structure is seriously damaged.

Background Hokkaido is the northernmost, least populous, and coldest of the Japanese islands. It was the first prefecture to be affected by COVID-19, while Kanagawa is home to one of the most populous areas of Japan, namely the Tokyo metro area. The Japanese government responded early during the pandemic by identifying infected patients, contact tracing, and performing PCR analysis on anyone who was suspected of having been exposed to SARS-CoV-2. The government has also been publishing information about each individual who tested positive for the virus. Both Hokkaido and Kanagawa started recording COVID-19 cases in the winter of 2020 and have detailed records of thousands of patients, thus providing an invaluable resource for the transmission and behavior of the virus. Methods The current study analyzed the COVID-19 registry data from the Hokkaido and Kanagawa prefectures. The Hokkaido registry contained 1,269 cases (674 (53%) females and 595 (47%) males) recorded between February 14 and July 22, 2020. The Kanagawa registry had 3,123 cases (1,346 (43%) females and 1,777 (57%) males. The final data contained a total of 4,392 cases (2,020 (46%) females and 2,372 (54%) males). By leveraging the information on viral transmission paths available in the registry data, we performed exponential random graph model (ERGM) network analysis to examine demographic and symptomological homophilies of the SARS-CoV-2 viral transmission networks. Results We observed age, symptomatic, and asymptomatic homophilies in both prefectures. Furthermore, those patients who contracted the virus through secondary or tertiary contacts were more likely to be asymptomatic than those who contracted it from primary infection cases. The transmission networks showed that transmission occurred significantly in healthcare settings, as well as in families, although the size of the networks was small in the latter. Most of the transmissions stopped at the primary and secondary levels and no transmission beyond quaternary was observed. We also observed a higher level of asymptomatic transmission in Kanagawa than in Hokkaido. Conclusions Symptom homophilies are an important component of COVID-19 and suggest that nuanced genetic differences in the virus may affect its epithelial cell type range and can thus result in the diversity of symptoms seen in individuals infected by SARS-CoV-2. Moreover, environmental variables such as temperature and humidity may also be playing an important role in the overall pathogenesis of the virus.

Concrete is more stable than filler as a false roof in a downward approach type infill quarry, but the mechanical model of a concrete false roof is not clear. As a result, there has been limited application. Therefore, it is necessary to establish the mechanical model of a concrete artificial false roof to enhance the stability of the downward approach infill quarry. This paper combines theoretical analysis, model derivation, finite element analysis and field application methods. Firstly, the basic assumptions of thin plate theory and elasticity mechanics are used as the premise to establish the differential equations of the deflection curve of the concrete thin plate false roof. Then, the three types of bending moment generation of the concrete thin plate false roof are explored. Secondly, the relationship between the location of dangerous surface and dangerous point in hard-supported weak-slab structure and soft-supported weak-slab structure is analyzed, and the type of uniform load and calculation model of concrete thin-slab false roof are improved. Finally, according to the established mechanical model of thin slab false roof, finite element analysis and field application were carried out. The results show that there are three types of deflection curve differential equations in the concrete thin slab false roof perpendicular to the strike, and three extreme points exist in the middle section of the thin slab and on both sides of the surrounding rock. The hazardous surface of the hard-supported weak-slab structure is present at the intersection of the encircling rock and the thin-slab fake ceiling, with the perilous point situated on the top of this surface. The hazardous surface of the soft-supported weak-slab structure can be found in the centre section of the thin-slab fake ceiling, with the perilous point being located at the bottom of this surface. Moreover, the damage mode for both structures is that of maximum tensile stress damage. Upon conducting a finite element analysis, the results indicate that the concrete's maximum tensile stress is significantly high.

The study aims to analyze the characteristic parameters of rooftop photovoltaic (PV) power generation on industrial plant buildings in the Ningxia region of China, in order to evaluate the impact of passive design characteristic parameters on the benefits of PV power generation and determine the degree of impact of different passive design characteristic parameters. The methodology involves analyzing the characteristics of existing industrial plant buildings in Ningxia, China, and conducting a series of regional studies on the parameters of plant PV power generation influencing factors. The simulation results revealed that five features, including roof form, PV panel laying pattern, PV panel laying area, azimuth angle, and PV module material, have a significant impact on PV power generation benefits of industrial plant buildings.The study further uses MATLAB 2022b to build a backpropagation neural network model with 5 neurons in the implicit layer to predict the PV power generation benefits. The model calculates the whole-life cycle power generation benefits and the whole-life cycle reduction of carbon emissions as output data. Finally, the Mean Impact Value (MIV) method is employed to select the feature parameter values one by one within their range, and the passive design feature parameters that have the greatest influence on the prediction results are identified as the PV panel laying method, the PV panel tilt angle, and the PV material parameters, respectively.

In this work, magnetic CuFe₂O₄/Ag nanoparticles activated by porous covalent organic frameworks (COF) was fabricated to evaluate the heterogenous reduction of 4-nitrophenol (4-NP). The core-shell CuFe₂O₄/Ag@COF was successfully prepared by polydopamine reduction of silver ions on CuFe₂O₄ nanoparticles, followed by COF layer condensation. With integrating the intrinsic characteristics of the magnetic CuFe₂O₄/Ag core and COF layer, the obtained nanocomposite exhibited features of high specific surface area (464.21 m² g^-1), ordered mesoporous structure, strong environment stability, as well as fast magnetic response. Accordingly, the CuFe₂O₄/Ag@COF catalyst showed good affinity towards 4-NP via π-π stacking interactions and possessed enhanced catalytic activity compared with CuFe₂O₄/Ag and CuFe₂O₄@COF. The pseudo-first-order rate constant of CuFe₂O₄/Ag@COF (0.77 min^-1) is 3 and 5 times higher than CuFe₂O₄/Ag and CuFe₂O₄@COF, respectively. The characteristics of bi-catalytic CuFe₂O₄/Ag and the porous COF shell of CuFe₂O₄/Ag@COF made a contribution to improve the activity of 4-NP reduction. The present work demonstrated a facile strategy to fabricate COF activated nano-catalysts with enhanced performance in the fields of nitrophenolic wastewater treatment.

Currently, in some domestic and foreign mines, the backfill drilling pipeline experience a rupture phenomenon even when the wear degree is low. This results in a delay in production due to the filling becoming 'sick'. This paper presents, for the first time, the damage mechanism from a mechanical perspective and re-derives the anti-extrusion strength model of the backfill drilling pipeline. We investigate the influence of law on the anti-extrusion strength of pipelines from the perspective of stratum and cement ring. We then verify the theoretical and simulation results through engineering examples. The results demonstrate that the Mises stress criterion is a suitable modification principle for the anti-extrusion strength model of the backfill drilling pipeline. The anti-extrusion strength of the pipeline is related to the elastic modulus and Poisson's ratio of the stratum, and the thickness of the cement ring. It is negatively affected by the depth of the stratum. For hard strata, a cement ring with a smaller elastic modulus is suitable, while for soft stratum, a cement ring with a larger elastic modulus is recommended. When the missing angle of the cement ring is less than 60°, the stress concentration factor increases up to 2.2. The stress unloading capacity of the cement ring ranges from 32.7% to 37.8%, and optimal performance of the cement ring is achieved when it has high strength and low rigidity. The backfill filling pipeline of a copper mine abroad was destroyed due to external extrusion force exceeding its anti-extrusion strength value. The modified pipeline anti-extrusion strength model is 18.2% higher than the casing API strength value. This finding can inform the design of the backfill filling pipeline for China's kilometer-deep wells in the future.

To facilitate the computation of the uniaxial compressive strength value of the cemented paste backfill under the condition of high sand-cement ratio, and to analyze the size effect of the cemented paste backfill with high sand-cement ratio under varied aspect ratios, the cemented paste backfill specimens with sand-cement ratios of 8:1-24:1 and aspect ratios of 0.5, 1, and 2 were prepared. Through response surface experiments and finite element analysis, the influence of three aspect ratios on the cemented paste backfill strength was explored, and the failure characteristics and size effect mechanisms of cemented paste backfill with various aspect ratios were analyzed. The model of strength conversion between cemented paste backfill with different aspect ratios was established. The results show that the compressive strength of the cemented paste backfill decreases with the increase of the aspect ratio under the same mass concentration and sand-cement ratio. When the aspect ratio is 0.5 and 1, the splitting failure is the main factor; when the aspect ratio is 2, the shearing failure is the main factor. The three-dimensional stress caused by the end effect of the cemented paste backfill is the main reason for the high strength when the aspect ratio is 0.5. Due to the one-dimensional stress zone generated in the middle of the cemented paste backfill with an aspect ratio of 2 in the laboratory, its strength value is closer to the actual uniaxial compressive strength value of the cemented paste backfill. The strength values of the cemented paste backfill with aspect ratios of 0.5 and 1 were higher than the actual uniaxial compressive strength values in the laboratory. The rationality of the theoretical analysis was verified by the ABAQUS analysis results. According to the experimental results, a strength conversion model between different aspect ratios is established, which can provide a reference for the design of the uniaxial compressive strength of the cemented paste backfill.

China is rich in coal resources, but the complex hydrogeological conditions lead to difficulties in coal mining, such as coal mine collapse, roof and water damage, and other accidents that occur frequently, resulting in many casualties and property losses. The use of coal mine hole detection technology to detect and analyze the internal environment of the coal mine in advance helps to reduce safety hazards and prevent coal mine accidents, for the existing coal mine hole detection technology operation is cumbersome, not easy to control, and insufficient depth of jacking prob-lems, this paper designs a new type of mine hole detection small robot. Firstly, this paper ana-lyzes the function and structural design of the mine hole detection robot, designs the variable diameter function according to the characteristics of narrow and uneven mine holes in coal mines, and analyzes the mechanics of the critical parts through theoretical calculations; secondly, based on the three-dimensional modeling software, established the structural model of the small robot for mine hole detection; after that, designed the robot's hardware circuits and control pro-grams for the presence of water and gas inside the mine hole, highlighting the need to carry out a new type of mine hole detection small robot. After that, we designed the robot's hardware circuit and control program, giving particular emphasis to the safety design of the circuit for the pres-ence of water and gas inside the mine hole of the coal mine. Finally, to verify the feasibility of the design program, the basic parameters and function tests of the mine hole detection small robot are carried out. The experimental results show that the mine hole inspection small robot realized by this design can adapt to the working hole diameter from 65 mm to 100 mm, the maximum working power is only 12 W, and the maximum crawling speed is 3.96 m/min. The maximum crawling slope reaches 90°, which can meet the actual mine hole inspection needs. The research can provide theoretical and design guidance for developing the mine hole detection robot with substantial engineering practical reference value.

Evaluating of long-term satellite-derived ocean color products using in-situ measurements is essential to ensure data quality and integrity. In this study, the Visible Infrared Imaging Radiometer Suite (VIIRS) remote sensing reflectance (Rrs) products were evaluated and analyzed by using long-term OC-CCI in-situ data from 2012 to 2021. The results demonstrate that the root mean square difference of VIIRS Rrs product accuracy in most bands is better than 0.002 (sr-1) when considering its average life span of 12 years. However, the VIIRS Rrs products in shorter wavelength bands (e.g., at 412 nm) had significantly lower accuracy in general and a long-term bias over the recent years. The annual precision of VIIRS Rrs products showed a declining trend especially in coastal or eutrophic waters. This accuracy deterioration of the VIIRS Rrs products suggests a strong need for continuous monitoring of its performance and further efforts on improving the atmospheric correction algorithm to specifically deal with satellite records at high SZAs and OZAs.

Three dimension (3D) Multi-input-multi-output (MIMO) scheme, which exploits another dimension of the spatial resource, is one of the enabling technologies for the next generation mobile communication. As the elevation angle in 3D-MIMO channel model might varies against the height of the base station transmit antenna, it has to be taken into account carefully. In this paper, the impact of antenna height on the channel characteristics of 3D MIMO channel is investigated by using the intelligent ray launching algorithm (IRLA). Three typical street scenarios, i.e., the straight street, the fork road and the cross road, are selected as benchmarks. On the basis of simulations, joint and marginal probability density functions (PDFs) of both the elevation angle of departure (EAoD) and the elevation angle of arrival (EAoA) are obtained. The elevation angle spread (AS) and the delay spread (DS) under various antenna heights are also discussed. Simulation results indicate that the PDFs of EAoD and EAoA vary characteristics under different street scenarios. Moreover, the minimum value of the DS can be achieved when the antenna height is half of the building height.

The advent of graphene opens up the research into two-dimensional (2D) material, which is considered as a revolutionary material in the future. Due to its unique geometric structure, graphene exhibits a series of exotic physical and chemical properties. Besides, single-element-based 2D materials (Xenes) have garnered tremendous interest. At present, 16 kinds of Xenes (silicene, borophene, germanene, phosphorene, tellurene, etc.) have been explored, mainly distributed in the third, fourth, fifth and sixth main groups. The current methods to prepare monolayer or few-layer 2D materials include epitaxy growth, mechanical exfoliation, and liquid phase exfoliation. Although two Xenes (aluminene and indiene) have not been synthesized due to the limitations of synthetic methods or stability of Xenes, other Xenes have been successfully realized by elaborately artificial design and synthesis. Focusing on elemental 2D materials, this review mainly summarizes the recently reported work about tuning the electronic, optical, mechanical, or chemical properties of Xenes via surface modifications achieved by controllable approaches (doping, adsorption, strain, intercalation, phase transition, etc.) to broaden the applications in various fields, including spintronics, electronics, optoelectronics, superconducting, photovoltaics, sensors, catalysis, and biomedicines. These advances in surface modification of Xenes have laid a theoretical and experimental foundation for the development of 2D materials and their practical applications in diverse fields.

This study utilises NaOH to treat composite cementitious materials containing aeolian sand and zeolite powders, which were used to replace 50% of the cement in aeolian-sand concrete (ASC). The mechanical properties of treated ASC considerably improved, especially when the NaOH dosage was 4% by mass. After curing this sample (denoted as AAZC-4) for 28 d, its compressive strength improved by 17.2% and its split tensile was increased by 16.3%. Potassium feldspar and montmorillonite in zeolite powder and SiO2 in the sand were decomposed by OH− and combined with other elements to generate various silicate gels and A-type potassium zeolite crystals inside the concrete. Microscopic examination showed that the gels and crystals intertwined to fill the pores, decreasing (increasing) the percentage of large (small) pores, thus optimising the pore structure. This substantially improved the mechanical properties of ASC. Freeze–thaw salt-intrusion tests showed that the extent of mass loss, degree of damage and loss of compressive strength of AAZC-4 were similar to those of ordinary concrete but were reduced by 36.8%, 19% and 52.1%, respectively, compared with those of ASC. Therefore, AAZC-4 has sustainable working performance in the chloride ion permeable environment in cold and arid areas.