The theory of differential equations arises from the study of physical phenomena. This field has various applications in science and engineering. The study of qualitative properties for each mathematical model plays an important role, attracting the attention of both theoretical and applied researchers. Normally, the most significant qualitative property to be studied first is the existence and uniqueness of the solutions of each mathematical model. However, proving existence and uniqueness results for mathematical models where the source function has a singularity is a difficult problem and requires many different techniques. In this paper, we establish some new conditions suitable to achieve the unique solution criterion for ordinary first-order differential equations. To obtain the desired results, we have improved the methods that have been used to prove the results in the work of Krasnosel'skii and Krein (Krasnoselskii and Krein, 1956). In addition, we also provide an example to illustrate the theoretical results.

Full-duplex non-orthogonal multiple access wireless networks with energy harvesting have the potential to improve spectral efficiency and save energy. However, wireless signals are susceptible to eavesdropping by other devices within their coverage area. This paper studies the security performance of a full-duplex non-orthogonal multiple access wireless network with energy harvesting (FDNOMAWNwEH) over Nakagami-m fading channels. Results show that the total throughput increases as the power of the primary transmitter increases. Similarly, the total throughput also increases as the expected security level or the energy harvester efficiency increases. In addition, there exists a value of the NOMA power division factor that maximizes the total throughput. Furthermore, the results show that the total throughput decreases as the fading severity parameter increases.

In the early 21st century, China has increasingly recognized the critical importance of securing its national energy supply. As the demand for energy continues to rise, China has implemented an assertive and comprehensive energy diplomacy strategy on a global scale, with Southeast Asia emerging as a key focus. The region holds a geo-strategic significance, rich in vital natural resources such as oil, natural gas, and other minerals, making it a strategic partner in China’s broader energy security objectives. This policy, driven by China’s growing energy needs and its desire to diversify energy sources, has far-reaching impacts on Southeast Asia, influencing various sectors including economics, politics, and national security. China's energy diplomacy in Southeast Asia is not only an economic endeavor but also a means of strengthening political alliances and asserting its regional influence. This paper explores the nuances of China's energy diplomacy policy towards Southeast Asia in the early 21st century, highlighting its strategic objectives, the mechanisms employed, and the broader implications for regional and global security dynamics.

Digital transformation in education is an inevitable trend and has been increasingly promoted in Vietnam over the past few years. The application of digital games in mathematics instruction not only alleviates students’ stress and pressure but also fosters engagement and motivation in the learning process. This paper clarifies key concepts related to digital games as well as presents a set of principles and a design process for digital games using the web-based application Pink Cat Games. Based on a proposed four-step process, the paper illustrates the design of a digital game integrated with the mathematics curriculum for second grade. The findings of this research are to provide practical guidance for teachers in designing digital educational games, thereby augmenting the effectiveness of their pedagogical practices.

This paper explores the identity of Bình Dương Province through its place names, highlighting how these names reflect the region's historical, cultural, and economic transformation. Bình Dương, once a primarily agricultural province, has experienced rapid industrialization and urbanization; and how the evolution of place names mirrors these shifts, encapsulating themes of resilience, pride, and modernity in the province’s identity. Applying the Toponymic Analysis method to analyze the etymology, origin, and meaning of 3,462 toponymic words consisting of 4,155 subtypes of place names discovered in 91 communes and wards of Binh Duong province, the findings reveal that place names in Bình Dương not only serve as geographical markers but also function as symbols of Binh Duong identity. The place names are often closely tied to the region’s geography; reflect the rich cultural mix of its inhabitants; carry traces of colonial influence; have presented political and economic changes; serve to unify its population, invoking themes of strength, resilience, and local pride, equality. This research implies that toponymy is a powerful tool for understanding social and cultural identity of a place.

Fractional differential equations are an important branch of mathematics and have been considered under many different fractional derivatives. Among them, differential equations with Riesz-Caputo fractional derivatives have also attracted the attention of many researchers. Studying differential equations that may have singularity coefficients is more difficult than usual because they require several complex techniques. In the present paper, we consider a nonlinear pantograph differential equation where the source function may have a temporal singularity. Using the contraction principle, we prove that the problem has a unique solution under some appropriate conditions. Furthermore, we define a new type of Ulam-Hyers stability and show the main equation of the problem is stable in the mentioned sense. To obtain the main results, a new inequality is proposed and proved. Some examples are constructed to confirm the validity and feasibility of the theoretical results.

The paper analyzes the radial distribution power system with the series connection of FACTS devices, which is easily implemented using a formula from the power flow equation (PFE - power flow equation) with the voltage magnitude and power flow on the lines are treated as independent variables. When control variables such as the form of reactive power at nodes and lines are directly manipulated in the formulation, the application of FACTS device control operations in the power system is carried out quickly and directly. Using the ratio matrix at the nodes of a radial distribution system is primarily represented on the main diagonal to reduce computational procedures. All FACTS device models are unified under static stability conditions and can be easily integrated within the new framework through the process of "variable exchange". Using the IEEE standard system, the formulation of the formula is based on the trend on the line - Line Flow Based (LFB) by the author to provide easy implementation with multiple FACTS devices connected in the system and its efficiency.

We consider a boundary value problem involving a fractional differential equation with a g-Caputo fractional derivative. This paper establishes some new criteria for the existence of solutions to the problem, differing from those obtained by previous researchers. The method is based on the construction of a novel Green’s function and the application of the Schauder fixed point theorem. Examples are provided to illustrate the fundamental distinctions between our results and earlier work.

The rising demand for automation in agriculture and manufacturing necessitates efficient, cost-effective sorting systems to replace labor-intensive manual processes. This paper introduces an innovative system integrating a Siemens S7-1200 Programmable Logic Controller (PLC), LabVIEW-based image processing, and OPC (OLE for Process Control) communication for automated tomato sorting. Utilizing real-time vision analysis, the system classifies tomatoes by color and size, offering a low-cost, scalable solution tailored for small-scale industries. A high-resolution camera captures images, processed in LabVIEW using HSV color space and size thresholds, with results relayed via OPC to the PLC, which actuates a stepper motor-driven sorting mechanism. Experimental validation in a controlled setting achieved 92% sorting accuracy and a throughput of 60 tomatoes per minute, surpassing manual sorting in speed and consistency. The modular design supports scalability to other agricultural products, enhancing its practical utility.

In this paper, Mn-Fe bimetallic nanoparticles were synthesized by simultaneous reduction of a salt mixture of KMnO4 and FeCl3 with glucose as a reducing agent. Degradation of methyl orange in aqueous solution, using hydrogen peroxide as an oxidizing agent, was used to evaluate the catalytic activity of the material. The material was characterized using scanning electron microscopy, X-ray diffraction, and energy-dispersive X-ray spectroscopy. The results showed that cubic manganese oxide nanoparticles were formed at the molar ratio of KMnO4/C6H12O6·H2O = 5/5 and the hydrothermal temperature of 120-220°C, while the oval-shaped structure was formed at the molar ratio of KMnO4/C6H12O6·H2O = 5/40 and the hydrothermal temperature of 220 °C. The cubic Mn-Fe bimetallic nanoparticle was still formed at the molar ratio of Mn/Fe/C6H12O6 = 5/2/5 and the hydrothermal temperature of 120°C, and the methyl orange decomposition efficiency was found to be the highest value of 57% on this catalyst sample.

This study aims to determine and measure the influence of factors attracting domestic tourists to Binh Duong province through quantitative research with 129 domestic tourists, convenience sampling method, data collected from the period from March 1, 2022 to March 31, 2022. There are 5 selected sites: Hoi Khanh pagoda, Dai Nam tourist area, Thuy Chau eco-tourism area, Phu An bamboo village, Cau Mountain - Dau Tieng Lake relic complex. The results of EFA exploratory factor analysis using SPSS software show that there are 5 factors affecting the attraction of domestic tourists to Binh Duong province, including: (1) tourism resources; (2) travel services; (3) tourism products; (4) tourism infrastructure; (5) promotion of tourism. However, the results of the regression analysis show that only the factors "tourism infrastructure" and "tourism resources" affect the ability to attract domestic tourists to Binh Duong, while the other factors donˈt have enough grounds to conclude. On the basis of the research results, this paper proposes management implications to improve the ability to attract more tourists to visit.

Binh Duong Province is one of the regions with very significant population and labor force growth. The development and transformation of the labor structure have positively contributed to the province's labor productivity growth and economic growth, while at the same time contributing to the development of Vietnam in general. This paper combines descriptive statistics, comparisons, contrasts, and trend assessments to identify the characteristics, changes, and transitions in the labor structure of Binh Duong Province from 2015 to 2023. The results show a sustained increase in population and labor force; the labor structure has moved significantly away from the agricultural sector; demand for technical and assembly workers increased sharply; the number of service and sales workers steadily increased and became mainstream. The challenge for Binh Duong Province is that while the group of highly skilled workers is growing, the increase is not evenly distributed; the group of highly skilled professionals is growing rapidly while the group of intermediate-level professionals and secretaries is declining due to replacement by technology.

The excellent flexibility of graphene materials that allows them to adjust to the curvature of the substrate surface, chemical surface inertness, and impermeability have attracted considerable attention in the past decade as a blending material and an additive in anti-corrosion coatings. In this paper, we present the role of graphene in enhancing the protective properties of anti-corrosion coatings on metal surfaces with the aim of improving the anti-corrosion performance and extending the life of the coating on metal structures, comparing the anti-corrosion ability of graphene with some types of metal oxide materials such as zinc oxide, titanium dioxide. The methods of graphene fabrication and the method of blending graphene into the coating composition give results on mechanical properties, wettability, antibacterial properties, anti-corrosion properties, fire resistance and current research trends in graphene-based coating materials and explore optimal solutions for applications in the paint industry.

The objective of this paper is to describe the empty calories consumption using the application of some behavior change models (theories). The alarming rise in empty calories consumption, encompassing fast foods, junk foods, and ultra-processed foods, poses a significant threat to global public health. This review synthesizes existing literature on the prevalence, health implications, and determinants of empty calories consumption. Findings reveal a robust link between empty calories intake and various chronic diseases, including obesity, diabetes, cardiovascular disease, and certain cancers. The socio-ecological model (SEM) provides a framework for understanding the multifaceted influences on empty calories consumption, spanning individual, social, community, organizational, and policy levels. Other related theories are equally important in discerning empty calories consumption nowadays. This paper concludes by advocating for a multi-faceted approach to mitigate empty calories consumption, incorporating targeted interventions at individual, community, and policy levels

The paper presents the results of a study on the essential physical properties of armchair SiSn nanoribbon (SiSnNR) material, based on density functional theory (DFT) using the quantum simulation program VASP. Structural parameters are highlighted along with electronic and optical properties. The findings reveal that SiSnNR exhibits significant differences in bond lengths, bond angles, and buckling compared to SiNR and SnNR. SiSnNR demonstrates semiconducting properties, with a direct band gap width of approximately 0.3123Å calculated using GGA-PBE, increasing to 0.5892Å when using the hybrid HSE06 functional. The results indicate that Sn atoms primarily contribute to energy bands below the Fermi level, while Si atoms contribute more to higher energy levels. The study also highlights the overlap of py and pz orbitals, leading to sp2 and sp3 hybridization. In terms of optical properties, the energy range from 3 to 5eV is where SiSnNR exhibits the strongest light absorption. The largest number of electron-hole pairs is generated within the energy range of 8-10eV, resulting in intense optical absorption and transitions in this region.

This paper presents a method for liquid level stabilization using a fuzzy logic algorithm implemented on the PLC S7-1200. Maintaining liquid levels accurately is a critical requirement in various industrial processes to ensure safety, efficiency, and consistent product quality. The proposed approach employs fuzzy logic to manage the inherent nonlinearities and uncertainties in the system, providing robust control performance under varying operating conditions. The fuzzy controller is designed with rules and membership functions tailored to the dynamic characteristics of the liquid level system. The control logic is programmed and deployed on the Siemens PLC S7-1200, a widely used industrial automation device. Experimental results demonstrate that the fuzzy logic controller effectively stabilizes the liquid level, achieving better performance compared to traditional PID controllers in terms of response time, overshoot, and steady-state error. This study highlights the potential of integrating fuzzy logic with PLCs for advanced industrial automation applications.

This paper is devoted to guiding parents in organizing classrooms and bedrooms for their children, ensuring that they have the most reasonable position to rest and study. That is how to design, arrange, and select items in a room to serve two children of the same sex, aged from 6 to 18. Arrange the bed to suit the cramped housing situation. Install study tables and chairs so that children can sit and study comfortably. Choose to buy a bookshelf and hang it on the wall so that it is steady and within reach of your children's operation and use. Essential daily items are arranged neatly so that children can conveniently take them out, use them, and store them in the right place. Thanks to having an ideal room to rest, study, and conveniently use equipment, children will develop well in literature, physical skills, and aesthetics and will always love their family. Later, when the children grow up, no matter where they go, the image of the beautiful little room of their childhood will always be kept in their memories. The interior design of the classroom and bedroom for two small children in a family is fully and clearly shown in 3D images by us. We have presented how to arrange and install items in the room so that everyone can apply this design to their family situation.

As fossil fuel resources are gradually depleting, countries are increasingly focusing on developing renewable energy as a sustainable alternative. A trend is the shift of the energy market towards a decentralized model, where renewable energy can be traded flexibly. This is partly evidenced by the rise of blockchain-based solutions in the energy sector. Blockchain technology garners attention due to its outstanding advantages such as anonymity, decentralization, and transparency. Therefore, this study explores the application of blockchain in the energy sector. We shed light on four main areas: energy management, peer-to-peer (P2P) trading, applications related to electric vehicles, and carbon credit trading. This paper provides insights into how blockchain technology can act as a catalyst for revolutionizing the energy sector in both management and control

The Sokoto Caliphate, founded by Usmanu Danfodiyo in 1804, was a significant Islamic state in West Africa that spanned a vast region of present-day northern Nigeria and parts of neighboring countries. The Caliphate became a center of Islamic learning, governance, and military activity, with its capital at Sokoto. One of the key institutions that contributed to its strength and expansion was the Ribat. this paper aims to discuss the formation of Gwadabawa Ribat, and its values. The Gwadabawa Ribat successfully provided a food security hub, resettlement area, and security as well to the caliphate. the Gwadabawa Ribat served as a hub for Islamic learning and warfare, protecting the Sokoto Caliphate from enemies. It ensured food security through agriculture, with fertile land suitable for various crops. The establishment of the Ribat was based on Islamic principles, providing a secure environment for the Sokoto Caliphate. Gwadabawa Ribat provided protection for the Sokoto Caliphate; the Ribat promoted Islamic learning and warfare, and agriculture in Gwadabawa ensured food security for the Caliphate.

This paper focuses on the application of the two-step flow theory in university admission communication strategies, particularly in the context of university autonomy in Vietnam. The two-step flow theory, developed by Katz and Lazarsfeld (1955), emphasizes the role of opinion leaders in transmitting messages from the information source to the target audience. In addition to analyzing the core elements of the theory and the methods of identifying and utilizing influential individuals within the educational community, this study proposes solutions for applying digital tools to support communication processes. These solutions include optimizing content and search engine tools, organizing both online and offline communication events, and closely coordinating with opinion leaders to implement proactive, flexible, and creative admission communication campaigns that are sustained throughout the process. Consequently, the study aims to enhance the quality of university admissions in the context of digital transformation

In this paper, the structural properties of crystalline and polycrystalline Cr have been investigated using molecular dynamics simulations. The interaction between atoms is modeled via the MEAM potential. Periodic boundary conditions are applied in the x, y, and z directions. The structural characteristics are analyzed through the total energy function, heat capacity, radial distribution function, and angle distribution. Dynamics are evaluated through the analysis of mean squared displacement and diffusion coefficient. The results show that the melting temperature of crystalline Cr is higher than that of polycrystalline Cr, indicating that the polycrystal melts earlier. This information is important when considering material applications in high-temperature environments.

This paper studies the performance of a IoT-relaying node transmission with massive multiple-input multiple-output (MIMO) system network. The system is a simple schematic setup which includes one user, one IoT-relaying node and one base station (BS). The user and IoT-relaying node have a single antenna while the BS is equipped with a hundred and/or even a thousand of antennas array. The transmission protocol is performed based on a very simple amplify-and-forward (AF) relaying scheme. To decode the transmitted signal from the user, the BS applies maximum-ratio (MR) combining technique (the combined channel of the links from the user to BS and the IoT-relaying node to the BS) under assumption of perfect channel station (CSI). The exact closed-form of the throughput and the results for the signal-to-interference-plus-noise ratio (when the number of relay antennas goes to large) are analyzed.

Based on previous surveys, it is evident that Food Technology students at Thu Dau Mot University face challenges in learning English, such as limited vocabulary, weak grammar, inaccurate pronunciation, and poor listening and speaking skills. These can lead to declining academic performance and restricted career opportunities. The paper highlights the potential of Artificial Intelligence (AI) in overcoming these challenges. AI tools like Gemini Google can provide personalized learning experiences, improve interaction with the language, and offer immediate feedback. Gemini is specifically chosen due to its free access, Vietnamese interface, and support for over 40 languages. This study demonstrates that Gemini is an effective tool for undergraduate students, particularly those in Food Technology who have weak English backgrounds, to improve their English skills. Gemini improves vocabulary, grammar, speaking, listening, pronunciation, reading, and writing. It offers simple instructions and ideas in both English and Vietnamese, making it ideal for beginners, selflearners, and people with limited English proficiency. Unlike traditional learning, Gemini provides access at any time and from any location, as well as the ability to overcome shyness and blunders. Gemini's large, up-to-date database and user-friendly interface enable personalized learning paths and can be paired with other methods for best language learning. The study also proposes various strategies for utilizing Gemini Google to improve English learning effectiveness in areas like vocabulary, grammar, listening, speaking, reading, writing, and creating a positive learning environment. Furthermore, Gemini's value extends beyond languages, offering assistance in a variety of other areas.

This paper presents a comprehensive analysis of the wastewater management system implemented at a medical center located within the Bau Bang Industrial Park in Binh Duong province, Vietnam. With a staff of 166 and 60 beds, the facility operates in accordance with TCVN 4470:2012 General Hospital design standards, serving a diverse range of water demands including domestic, medical, and auxiliary requirements. The wastewater management system is meticulously designed to handle both rainwater and wastewater separately. Rainwater is efficiently collected through surface and roof drainage networks, while domestic and medical wastewater undergo discrete collection processes. The medical center's wastewater treatment facility, operating at a capacity of 100 m³/day, employs a multistage treatment process to ensure compliance with stringent regulatory standards (QCVN 28:2010/BTNMT, column B, K = 1). This process includes preliminary treatment, anaerobic and aerobic biological treatment, membrane filtration, and disinfection. The facility consistently meets quality parameters outlined in QCVN 28:2010/BTNMT, exhibiting effective removal rates for organic pollutants, suspended solids, ammonia, phosphates, and pathogens. Furthermore, the medical center demonstrates commendable environmental stewardship through its stormwater drainage infrastructure, which integrates seamlessly with the local drainage network, safeguarding against environmental contamination. Overall, the wastewater management practices at the medical center exemplify best practices in environmental management within the healthcare sector. This study provides valuable insights into the design, implementation, and performance evaluation of wastewater treatment systems in industrial settings, contributing to the global discourse on sustainable wastewater management practices.