Zirconium dioxide (ZrO2) possesses numerous advantages such as high mechanical strength, low friction coefficient, excellent optical properties, and extended lifespan. Consequently, ZrO2 has a broad research foundation and practical significance in functional films and wear-resistant coatings. However, it suffers from brittleness and low ductility when used as a bio-coating material. In this study, a Ta/ZrO2 film was fabricated on Si (100) and titanium alloy substrates using a magnetron sputtering system, with tantalum (Ta) serving solely as a transition layer. Subsequently, Zr and Nb ions were implanted into the film at varying doses but with consistent energy levels. The analysis focused on the film's microstructure, mechanical properties, hydrophilicity, and corrosion resistance. The results demonstrated a significant improvement in the hydrophilicity and corrosion resistance of the ZrO2 film following the implantation of Zr and Nb ions. First-principles calculations based on density functional theory (DFT) principles indicated that, with increasing doping concentrations of Zr and Nb in the ZrO2 model, the stability of the model increased gradually, thereby enhancing its corrosion resistance.

With the rapidly increasing of people’s purchasing power, the fast moving consumer goods (FMCG) industry is supposed to grow dramatically. In order to gain more market access and profile, it is important for the FMCG manufacturers and retailers to find the preferences and provincial characteristics of consumers, to develop more suitable goods distribution strategy. Based on retails marketing data with geographic characteristics, this paper proposes a new combination of geography methods to solve the problems in distribution of FMCG. Via multiple K-means clustering and cross validation of KNN half off, the mesoscopic sales features are extracted through the classification of retails, which can indirectly grasp the consumer behavior characteristics. Based on space division and Moran’ I spatial autocorrelation arithmetic, two strategies are developed to satisfy consumer’s needs and promote sales, including conservative and positive strategies. According to our analysis, the total sales volume of the regions will increase by 5.1% and 10.3%. This study can be applied to the provide purchase strategies for FMCG retails according to their locations. The research can explore the consumption potential of different areas, thus improving the profile of retails and the development of economy in more mesoscopic scale.

We primarily investigate the existence of solutions for fractional neutral integro-differential equations subjected to Neumann-type boundary conditions, which is crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by integrating fixed point theorems, we establish the existence of mild solutions under more relaxed conditions.

In recent years, there has been a growing interest in remote sensing image-text cross-modal retrieval due to the rapid development of space information technology and the significant increase in remote sensing image data volume. One approach that has shown promising results in cross-modal retrieval of natural images is the multimodal fusion encoding method. However, remote sensing images have unique characteristics that make the retrieval task challenging. Firstly, the semantic features of remote sensing images are fine-grained, meaning they can be divided into multiple basic units of semantic expression. Additionally, these images exhibit variations in resolution, color, and perspective. Different combinations of basic units of semantic expression can generate diverse text descriptions. These characteristics pose considerable challenges for cross-modal retrieval. To address these challenges, this paper proposes a multi-task guided fusion encoder (MTGFE) based on the multimodal fusion encoding method. The model incorporates three tasks: image-text matching (ITM), masked language modeling (MLM), and the newly introduced multi-view joint representations contrast (MVJRC) task. By jointly training the model with these tasks, we aim to enhance its capability to capture fine-grained correlations between remote sensing images and texts. Specifically, the MVJRC task is designed to improve the model’s consistency in feature expression and fine-grained correlation, particularly for remote sensing images with significant differences in resolution, color, and angle. Furthermore, to address the computational complexity associated with large-scale fusion models and improve retrieval efficiency, this paper proposes a retrieval filtering method. This method achieves higher retrieval efficiency while minimizing accuracy loss. Extensive experiments were conducted on four public datasets to evaluate the proposed method, and the results validate its effectiveness. Overall, this study focuses on remote sensing image-text cross-modal retrieval and introduces the MTGFE model, which combines multimodal fusion encoding with multiple tasks to enhance the model’s ability to capture fine-grained correlations. Additionally, a retrieval filtering method is proposed to improve retrieval efficiency. Experimental results demonstrate the effectiveness of the proposed method.