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.

The study investigates the challenges faced by Food Technology students at Thu Dau Mot University in mastering English reading and writing skills. The findings reveal that limited vocabulary and grammar knowledge significantly hinder students' proficiency in these areas. For reading, students struggle with insufficient vocabulary, poor comprehension strategies, and a lack of background knowledge, making it difficult to understand texts, identify main ideas, and interpret references. Similarly, writing is affected by challenges such as improper grammar usage, insufficient vocabulary, awkward phrasing, and issues with sentence construction. Mistakes in punctuation, spelling, and word order further reduce the quality of written work, limiting students’ ability to express ideas clearly and cohesively. These difficulties stem from a combination of linguistic limitations, lack of exposure to English, and insufficient support in structured learning strategies. The study highlights the urgent need for targeted interventions to address these challenges. Proposed solutions include vocabulary enhancement exercises, grammar-focused sessions, structured reading techniques, and writing workshops. Additionally, integrating modern tools like AI-powered learning applications can provide personalized feedback and improve overall proficiency. By adopting these strategies, students can gradually overcome their difficulties, enhancing their reading and writing skills to meet both academic and professional demands. The findings emphasize the importance of consistent practice and tailored learning approaches in language development.

The application of Artificial Intelligence (AI) in education is rapidly transforming the teaching and learning landscape in Vietnam. AI technology is being integrated into various educational platforms to provide personalized learning experiences, support educators, and enhance the overall efficiency of the education system. In Vietnam, AI is utilized to develop adaptive learning programs, intelligent tutoring systems, and automated administrative processes. AI-powered tools such as virtual teaching assistants and chatbots are also being employed to offer real-time support and feedback to students. Furthermore, AI-driven data analytics is used to monitor and improve student performance and engagement levels. AI assists teachers in automating grading, reducing assessment time, and enabling speech recognition systems to evaluate students’ English-speaking skills. These innovations contribute to a more dynamic, interactive, and inclusive educational environment. However, challenges such as data privacy concerns, the digital divide, and the demand for a skilled workforce remain significant. Addressing these issues is crucial for the sustainable integration of AI into Vietnam’s education sector.

Enzyme immobilization offers an innovative approach for reuse, preservation, and optimization of production efficiency and costs in the food and biofuel industries. In this study, amylase enzymes immobilized in Ca-alginate membranes were utilized in the fermentation of traditional sticky rice wine. The morphology and activity of immobilized amylase beads were maintained effectively at a 2% concentration of both carrier material and enzyme solution. After seven days of fermentation, fermentation efficiency reached an ethanol concentration of 55% v/v. The activity of immobilized amylase retained 60% of its activity after four consecutive fermentation cycles. These results suggest that immobilized amylase beads have promising applications in sticky rice wine production, replacing free amylase, which is difficult to recover and reuse.

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.

In recent years, asymmetric gold nanoparticles have attracted a lot of attention from researchers owing to their unique properties and varied applications in many fields. In this study, gold nanobranches were prepared using a one-step, green reducing method, with the HEPES buffer acting as both a reducing agent and surfactant. The formation of gold nanoparticles was evaluated using UV-Vis spectroscopy by controlling several practical factors, including the volume of gold salt precursor, the concentration of HEPES buffer, and the solution pH. The morphologies and crystallization of the gold nanobranches were characterized by Scanning electron microscopy (SEM) and X-ray diffraction (XRD). The results indicated that under the optimal synthesis conditions, namely 250 µL of 5 mM HAuCl₄, 0.10 M HEPES, and a pH of 7.5, most of the gold particles in the colloidal solution exhibited multiple branches, with an average size ranging from 20 to 35 nm and high crystal density. This study presented a simple synthesis method utilizing eco-friendly substances to replace conventional reducing agents, contributing to the sustainable development of nanotechnology.

Resistant starch (RS) is an insoluble fibre stable under various food processing conditions, including high temperatures and pH levels. RS has many beneficial effects on human health, such as positive effects on digestive tract activity, microflora, blood cholesterol levels, glycemic index, diabetes control, increased satiety and effective weight loss. Recently, RS has emerged as a comprehensive health improvement solution. This report helps to clarify the basis of the effects and applications of this type of starch.

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.

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

Improving and exploring the photocatalytic performance of composites for new models continues to pose a challenge. Here, a straightforward thermal dispersion method is achieved by incorporating nitrogen (N) into TiO2 at different weights (1%, 3%, and 5%) to enhance photocatalytic activity. The material properties are analyzed through ultraviolet-visible diffuse reflectance spectroscopy (UV-VIS DRS), and X-ray diffraction (XRD). The results indicate that the NO gas removal efficiency of N-TiO2 photocatalytic materials is higher than that of pure TiO2 after 30 minutes of exposure to visible light. The highest NO gas treatment efficiency of N-TiO2 -1% is 40.4%, with a reaction rate following a first-order kinetic equation of 0.0688 min-1. Successfully fabricating N-TiO2 photocatalytic materials using the thermal dispersion method, with significantly enhanced photocatalytic performance under visible light activation, will benefit practical applications, particularly in the environmental sector.

The cold gas dynamic spraying (CGDS) method enables the application of coatings with various functional properties to nearly any substrate material, facilitates the restoration of geometric dimensions of parts damaged during use, and allows for the renewal of protective anticorrosive coatings without the need for complex structural dismantling. This review describes the latest developments in the processes and applications of CGDS technology.The ease and manufacturability of the process, along with the mobility of CGDS coating systems, make it suitable for use both in industrial settings with robotic systems and in "field" environments.

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.

Advanced materials have been of interest in recent years because of their outstanding properties that bring many useful applications to humans, they can be highly compatible with alternative materials. In particular, coating materials on HAp base increase the biocompatibility of HAp. In this study, we synthesize TiO2/HAp composite materials using the sol - gel method. Samples were made under different synthesis conditions in terms of HAp/TTIP ratios: (1:1); (1:1.5); (1:2); (1:2.5); (1:3). Factors affecting the synthesis process, such as the incubation time and pH of the solution, were also investigated. The optimal conditions for the synthesis process are the ratio HAp/TTIP: 1 gram HAp with 2 ml TTIP; stirring time: 16 hours; pH of the gel solution: pH = 0.5, as determined from the analysis of the X-ray diffraction spectrum and SEM surface morphology. The research results are the basis for research on biomedical materials.

Currently, to make human life more convenient and easier, many utility services have been provided. Among them, online food ordering applications with high coverage and diverse forms become prominent. This research aims to examine the factors influencing the intention of using online food ordering applications among students in Ho Chi Minh City. Using a multivariate linear regression model and the Ordinary Least Squares method (OLS), the research team analyzed primary data based on 120 valid survey sheets collected from students studying in HCMC. The research results indicate that there are seven factors influencing the intention to use (ITU) online food ordering applications, including: (1) Ease of use (EOU), (2) Convenience (CV), (3) Aesthetic appeal (AA), (4) Price expectations (PE), (5) Social influence (SI), (6) Perceived risk (PR), and (7) Habits (HB). Among them, the three factors with the greatest impact on the students’ intention are ease of use, aesthetic appeal, and social influence. Based on the test results, the study proposes a management implication to help food delivery service providers enhance service quality, suggest development directions, and make suitable strategies for potential target customers. Keywords: food delivery service providers, food ordering applications, management implication, students’ intention

In recent times, there has been a rapid surge in the advancement of technologies associated with Unmanned Aerial Vehicles (UAVs), particularly in the domains of sensors, networking, and processing. Consequently, substantial investments from both governments and industries have been directed towards the exploration of UAVs, aiming to enhance their performance for secure and dependable deployments. The evolution of design methodologies and the exploration of UAV systems have transitioned from single UAV applications to encompass multi-UAVs and cooperative UAV systems. These systems necessitate a heightened level of coordination and collaboration to execute tasks, demanding innovative networking models, approaches, and mechanisms tailored for highly mobile nodes, encompassing numerous intricate parameters and constraints. The present paper provides comprehensive insights and conducts a meticulous examination of UAV communication protocols, networking systems, architectures, and applications. Furthermore, it delves into UAV solutions while underscoring critical technical challenges and unresolved research issues that warrant further investigation and dedicated research and development endeavors. In this paper, we study some problems and solutions for The Command and Control (C2) aspect of UAV communication systems. We also give some directions for research in near future.

In engineering and science problems, the data being considered are often known in the form of sets of discrete points, not as a continuous function. In applications, the values of the discrete data at specific points may be required to estimate. To solve these problems, a common mathematical approach is to use the interpolation method. In this paper, we use the cubic natural spline interpolation method to build approximate functions for some real data in Vietnam such as data on rice output and rice area of cultivation, data on expenditure and income per capita. The data used in this paper are extracted from the General Statistics Office of Vietnam. We develop some Matlab programs to find the coefficients of splines and calculate the values of the interpolation functions at specific points. Using the obtained interpolation function, some missing values in the data on income and expenditure per capita in the Southeast region of Vietnam in 2019 and 2021 are estimated. Furthermore, some unknown data on rice productivity and cultivation area are obtained in a similar manner. A good agreement between the calculated values and actual values are found.

In this paper, we restate some applications of logarithms in Richter scale, pH scale and sound intensity level (Decibel scale).

Enzymes are biodegradable catalysts naturally present in living organisms. Enzymes can accelerate biochemical reactions by reducing the activation energy, and they are not consumed during reaction processes. Numerous applications of enzymes have been developed in biotechnology, industry, medicine, pharmaceuticals, food processing, biofuels, and so on. In this study, we develop a mathematical model describing enzymatic reactions with a Ping-Pong mechanism and competitive substrate inhibition. In order to obtain insights into the model behaviors, we use Python software to obtain numerical solutions for the model. Some discussions on the numerical results is provided. Finally, we briefly discuss a potential application of the model and some future work.

It is very common to stabilize the preset value (Wanted value) of analog signals such as temperature, pressure, weight, flow, speed in automatic control. However, these control objects often have some problems such as overshooting, taking a long time to bring the system to a steady value, and large errors. One of the most used systems to overcome these problems is the PID, which is a preset stabilizing system with a quick function that returns the system to the set value in a short time without overshooting. error is close to zero. However, determining the scale parameters Ki, integral Kp, and differential Kd for the system to work optimally is a problem that needs to be studied. This paper presents how to accurately determine differential, integral, and scale coefficients according to 3D virtual reality model. Used a lot in simulation modeling for training and practical applications.

Traditional fossil energy sources are increasingly exhausted, leading to the need for mankind to exploit alternative energy sources; and solar energy can be viewed as infinite. Solar photovoltaic and its applications are increasingly widely studied. However, due to its nonlinearity and unstable nature, high technology is required to achieve good conversion efficiency. One of the techniques to optimize solar cell efficiency is to use the Maximum Power Point Tracking algorithm (MPPT) and P&O is a relatively easy algorithm to implement. This article will present some problems about photovoltaic cells, power converters in solar power systems and using PSIM software to simulate an independent solar system with several harvesting solutions for solar power and compare the efficiency of them.

Indigofera aspalathoides Vahl ex DC. belongs to the Fabaceae family. I. aspalathoides is applied to heal tumors, inflammations, diabetes, leprosy, and kidney illnesses in traditional medicines. Compounds including kaempferol, kaempferol 5-O-β-D-glucopyranoside, 5,4'-dihydroxy 6,8-dimethoxy 7-O-rhamnosyl flavone, indigocarpan, and mucronulatol have isolated from this plant species. Hitherto, there is no comprehensive review available regarding the reported bioactivities of I. aspalathoides. Thus, this article goals to analyze, summarize and document the published bioactivities-related publications. Electronic databases the Web of Science, Scopus, ScienceDirect, and PubMed used to find relevant publications from 1900 to December 2020. Thus far, only in vivo and in vitro scientific evidence levels of bioactivities are available. I. aspalathoides holds such as anti-inflammatory, anticancer, antihepatotoxic, anti-arthritic, immunomodulatory, and antidiabetic properties. Overall, immunomodulatory, anti-inflammatory, and anticancer compounds have been isolated from this plant species Therefore, additional bioactivity and phytochemical-related researches would need to perform to generate more scientific evidence for other applications. This work will be useful for further bioactivity and phytochemical studies using this plant species.

With the development of information technology, many applications of robots are increasingly being applied to support research, learning, and teaching. This paper mainly investigates the modeling and simulation of a robotic arm with 3 degrees of freedom (dofs) for different applications. First, Kinematics and dynamics model of the robot based on the standard Denavit Hartenberg (D-H) modeling method, where the forward kinematics of robot is analyzed and computed to obtain by using the inverse kinematics, and then the solution of the robot dynamics is derived. Second, a CAD model of the robot is designed on CATIA software to convert to MapleSim software to simulation and control. Final, numerical simulation is presented to display results. This work provides a potential basis for the realization of the robotic arm in the industrial, education, and research field, which is of great significance for improving manufacturing efficiency and support teaching and research in the robot field.

Macadamia shells were used to prepare modified carbon by chemical agent H2O2 (25%) in 48 hours with coke ratio: H2O2 = 1:10. Modified carbon from Macadamia shells with chemical agent H2O2 has capable of adsorption heavy metal copper (Cu 2+ ) at an assumption concentration is 30ppm in the optimum conditions such as pH = 4, dose is 1.8 g/l, and the processing time is 30 minutes. The result showed that the adsorption ability of the material reached the highest efficiency is 78.33%. This result showed that modified carbon from shells Macadamia by chemical agent H2O2 capable of removing applications on heavy metal copper (Cu2+) in wastewater.