Explicit F\"ollmer-Schweizer decomposition and discrete-time hedging in exponential L\'evy models

In a financial market driven by an exponential L\'evy process, an explicit representation is shown for the F\"ollmer-Schweizer decomposition of European type options, implying a closed-form expression of the corresponding local risk-minimizing strategies. Using a jump-adjusted approximation scheme, the error caused by discretising the local risk-minimizing strategies is investigated in dependence of properties of the L\'evy measure, the regularity of the pay-off function and the chosen random discretisation times. The rate of this error as the number of expected discretisation times increases is measured in weighted BMO spaces, implying also $L_p$-estimates. Moreover, the effect of a change of measure satisfying a reverse H\"older inequality is addressed.Comment: 28 page

Collaborative Consultation Doctors Model: Unifying CNN and ViT for COVID-19 Diagnostic

The COVID-19 pandemic presents significant challenges due to its high transmissibility and mortality risk. Traditional diagnostic methods, such as RT-PCR, have limitations that hinder timely and accurate screening. In response, AI-powered computer-aided imaging analysis techniques have emerged as a promising alternative for COVID-19 diagnosis. In this paper, we propose a novel approach that combines the strengths of Convolutional Neural Network (CNN) and Vision Transformer (ViT) to enhance the performance of COVID-19 diagnosis models. CNN excels at capturing spatial features in medical images, while ViT leverages self-attention mechanisms inspired by human radiologists. Additionally, our approach draws inspiration from subclinical diagnosis, a collaborative process involving attending physicians and specialists, which has proven effective in achieving accurate and comprehensive diagnoses. To this end, we employ an early fusion strategy integrating CNN and ViT, then fed into a residual neural network. By fusing these complementary features, our approach achieves state-of-the-art performance in accurately identifying COVID-19 cases on two benchmark datasets: Chest X-ray and Clean-CC-CCII. This research has the potential to enable timely and accurate screening, aiding in the early detection and management of COVID-19 cases. Our findings contribute to the growing knowledge of AI-powered diagnostic techniques and demonstrate the potential for advanced imaging analysis methods to support medical professionals in combating the ongoing pandemic

USING PRACTICAL CONTENT EXERCISES IN TEACHING 'MOMENTUM' - PHYSICS 10 TO DEVELOP STUDENTS' ABILITY TO APPLY KNOWLEDGE AND SKILLS

This study investigates the impact of integrating practical exercises into the teaching of "Momentum" in Physics 10, aiming to enhance students' ability to apply theoretical knowledge and skills. Recognizing the gap between theoretical physics education and its application, this research employs a comprehensive methodology, combining theoretical research, expert surveys, pedagogical experimentation, and statistical analysis to explore the efficacy of practical exercises. The pedagogical experiments, conducted in a controlled classroom setting, involved practical tasks that required students to apply concepts of momentum to solve real-world problems. The findings reveal a significant improvement in students' understanding and application of physics principles, particularly momentum, highlighting the value of experiential learning in physics education. Students demonstrated enhanced problem-solving abilities, deeper conceptual understanding, and increased engagement and interest in physics. Moreover, the study underscores the importance of practical exercises in bridging the gap between theoretical knowledge and real-world application, suggesting that such an approach not only facilitates a better grasp of scientific principles but also prepares students to tackle practical challenges effectively. The research advocates for the broader implementation of practical exercises in the physics curriculum, emphasizing their potential to transform traditional educational methodologies into more engaging and impactful learning experiences. Overall, this study contributes to the pedagogical discourse by affirming the critical role of practical exercises in developing competent and versatile learners capable of applying their knowledge and skills in diverse contexts, thus enhancing the quality of physics education and fostering a generation of problem-solvers equipped to navigate the complexities of the modern world

ẢNH HƯỞNG CỦA NGUỒN THỨC ĂN ĐẾN SỰ SINH TRƯỞNG CỦA GIUN ĐẤT Amynthas rodericensis (Grube, 1879) TRONG ĐIỀU KIỆN NUÔI THỬ NGHIỆM

Amynthas rodericensis is a common earthworm species in Vietnam. The feeding material and substrate affect the growth and reproduction of earthworms. The individual size, total number, weight, and gain weight of earthworms under laboratory conditions were investigated. The experiment was designed with four treatments (100% pig manure; 75% pig manure and 25% substrate; 50% pig manure and 50% substrate; 25% pig manure and 75% substrate) with six replicates in a completely randomized design; the experiments lasted ten weeks. The maximum growth and reproduction of A. rodericensis are observed with 75% pig manure and 25% substrate.Amynthas rodericensis là loài giun đất phổ biến ở Việt Nam. Nguồn thức ăn và cơ chất là những yếu tố ảnh hưởng đến sự sinh trưởng của giun đất nói chung và A. rodericensis nói riêng. Các yếu tố ảnh hưởng đến sự sinh trưởng bao gồm kích thước, khối lượng cơ thể, số lượng cá thể và tăng trọng cơ thể. Thí nghiệm có bốn nghiệm thức tương ứng với các tỷ lệ phối trộn phân lợn và chất nền khác nhau (NT1: 100% phân lợn; NT2: 75% phân lợn và 25% chất nền; NT3: 50% phân lợn và 50% chất nền; NT4: 25% phân lợn và 75% chất nền); mỗi nghiệm thức lặp lại sáu lần, bố trí theo phương pháp ngẫu nhiên hoàn toàn và được theo dõi đến 10 tuần. Kết quả cho thấy tỷ lệ phối trộn phân lợn với chất nền có ảnh hưởng khác nhau đến khả năng sinh trưởng của giun đất A. rodericensis. Sự sinh trưởng của giun cao nhất ở nghiệm thức NT2 (75% phân lợn và 25% chất nền)

Active fault-tolerance of the unmanned aerial vehicle automatic control systems

This paper presents an introductory overview of principles of the three-layer hierarchy of active fault-tolerance, providing, determination of the fault type with as many details as enough to get recoverable fault reason and failure toleration by flexible redundancy using; the conception of active fault-tolerant control in abnormal modes is described. Developed models and methods of a systematic approach to fault tolerance in the direction of the effective use of the signal, parametric and structural redundancies and selection of parrying tools. Performed experimental researches of the unmanned aerial vehicle (UAV) automatic control systems (ACS)