The Stokes equation describes the flow velocity of a steady state fluid in relation to the pressure and the external source. The corresponding variational formulation of the Stokes equation is studied in the paper. In more detail, we delve into the analysis of the equivalence relations pertaining to the variational formulations of the Stokes equations. We found that the variational formulation of the Stokes equation can be approximated by a type of variational formulation with a coefficient but without the constraint on the divergence. Then we did a analysis on the approximation by the finite element method to the the variational formulation without the constraint on the divergence, and we find that we should use preconditioning techniques before using the iteration. More precisely, we give an error analysis of this numerical computation method through rigorous proofs, and from this we deduce the need to use preprocessing techniques to avoid long computation times.

Air suspension is a component that connects wheels and bodies and conducts force and moment by reaction force of air spring gas compression. The air suspension system exhibits notable merits in terms of enhanced driving comfort and stability, coupled with the ability to adjust multiple parameters. Consequently, examining the advantages of air suspension can serve as a theoretical foundation for the selection of automobile suspension systems. Furthermore, elucidating the benefits derived from the utilization of air suspension can facilitate subsequent studies by providing clarity and directness. In this paper, the advantages and disadvantages of air suspension are analyzed, and the semi-active control of air suspension is discussed, different parameters of air suspension can be controlled by the system. The limited adoption of air suspension systems can be predominantly ascribed to the substantial financial investment required for their installation and upkeep, including both higher initial costs and ongoing maintenance expenses. Accordingly, it has better driving comfort and stability than traditional mechanical suspension and can be controlled by the control system. Semi-active control of air suspension may make it closer to ideal performance in actual work by optimization and a combination of new technologies.

Wind tunnel test is widely used in aviation, automobile, construction and other fields to simulate the force and flow field distribution of objects in the wind field. However, due to the existence of complex flow phenomena such as turbulence, the accuracy of the wind tunnel test is affected to a certain extent. Therefore, it is of great significance to study the performance of various turbulence models in the wind tunnel to improve the accuracy of the wind tunnel test. This study compares and analyzes the performance of turbulence models in wind tunnel experiments. Based on various turbulence models, numerical simulation methods are employed to simulate and calculate the flow field in wind tunnel experiments, and the results are compared. Through the comparison and analysis, it is found that different turbulence models exhibit different performance in simulating wind tunnel experiments. Among them, the RSM model demonstrates better accuracy and stability, without the presence of boundary layer effects. The purpose of this research is to evaluate and analyze the applicability of various turbulence models in wind tunnel experiments, provide references and guidance for flow field simulations in wind tunnel testing. However, limitations of this study lie in the constraints of the models and computational methods used, and further research and exploration are needed to address these limitations.

As a desktop game with a long history, Chinese chess has been widely circulated. In recent years, Chinese chess championships have become increasingly popular. During the competition, in addition to the individual abilities of the participants, the use of different strategies in the competition also become another major factor affecting the outcome of the competition. Based on the fixed ability values of the contestants, this research focuses on discussing the selection of strategies. This paper will adopt points-based match rules in common competitions and quantify the player's ability values for making a data analysis about nine different strategies. Due to the use of a point system in the competition, this research could use zero-sum game for analysis. According to zero-sum game and Nash equilibrium, the payoff matrix could be obtained. Furthermore, a precise linear program model is built. After the calculation, this research presents a result about which strategies should be used in the competition and provide an analytical explanation.

Elliptic curves over Galois fields are widely used in modern cryptography. Cryptosystems based on elliptic curves are commonly deemed more secure than RSA for a given key size. However, with the rapid progress of quantum computing, the security of this traditional systems faces unprecedented challenge. To address this concern, this paper explores the resilience of a generalization of traditional elliptic curve cryptography. That is, we explore elliptic curves over non-prime rings (Zn), instead of fields. Elliptic curves over Zn for a composite integer n has been considered by researchers on information security. However, it is unclear how they stand against the unparalleled power of quantum computers. This article investigates quantum attacks on cryptosystems based on this new paradigm. The conclusion sheds light on the pressing and important task of searching for post-quantum cryptographic systems. In particular, the effectiveness of Shor’s algorithm (or its variation) on such systems is analyzed.

Game theory has been widely used in many fields including economics, politics and military for a long period of time. Game theory can be divided into two situations: zero-sum and non-zero-sum, since both situations can appear in the fields very often and should be of great importance to research, the objective is to maximize the finial net payoff or minimize the loss by linear programming. In zero-sum situations, this paper will create the payoff matrix and by the Max-min theorem, this paper can get the constraints to satisfy the condition of using python code, the calculation result of the code gives that strategy 3 and 4 should be the best input if the opponent is also choosing the best strategy. For non-zero-sum situation, this paper will discuss firm competition and American presidential Election, payoff matrix, linear formulation will be used to help get the result of best election result. The result shows that the resources should be put into the state with the most votes and net approval rating, python calculation will give these results.

The Scopus database, which includes many open-access items, conference papers, funding details, and patent linkages, has developed as a vital resource within the dynamic social and economic environment. Gaining popularity in several fields, systematic reviews synthesize the relevant research literature in order to guide deliberative judgments. However, researchers require assistance in keeping up with the ever-increasing multidisciplinary nature of work and the ever-changing nature of information. Researchers need efficient methods to navigate and leverage the wealth of available knowledge for their systematic review processes as the number of scholarly production grows tremendously. This study employs descriptive statistics to examine and graphically present the bibliography (the list of sources cited in the text). This study was conducted in Dr. Jodi Schneider's lab and aims to identify trends in scholarly publishing and evaluate the overall content of scholarly works. Publication dates, item types, author lists, titles, and keywords are examined in the analysis, which takes CSV(Comma Separated Values), BibTeX, or RIS formats as input. Emerging research fields and patterns of collaboration can be better understood with the help of the descriptive statistics generated. Word clouds also help readers evaluate the quality and topic focus of the papers by providing a visual assessment of the paper's composition.

Optical microscopy is an essential tool for biomedical discoveries and cell diagnosis at micro- to nano-scales. However, conventional microscopes rely on lenses to record 2-D images of samples, which limits in-depth inspection of large volumes of cells. This research project implements a novel 3-D lensless microscopic imaging system that achieves a wide field of view, high resolution, and an extremely compact, cost-effective design: the Digital Lensless Holographic Microscope (DLHM).A lensless holographic microscope is built with only a light source, a sample, and an imaging chip (with other non-essential supporting structures). The entire setup costs $500 to $600. A series of MATLAB-based algorithms were designed to reconstruct phase information of samples simultaneously from the recorded hologram with built-in high-resolution and phase unwrapping functions. This produces 3-D images of cell samples. The 3-D cell reconstruction of biological samples maintained a comparable resolution with conventional optical microscopes while covering a field of view of 36.2 mm2, which is 20-30 times larger. While most microscopes are extremely time-consuming and require professional expertise, the lensless holographic microscope is portable, low-cost, high-stability, and extremely simple. This makes it accessible for point-of-care testing (POCT) to a broader coverage, including developing regions with limited medical facilities.

In 1654, Pascal and Fermar discussed how two gamblers should fairly divide their winnings after a break in play, and they came up with the right answer for the first time. Many gamblers are convinced that luck is always on their side and the odds of victory are always in their hands because gambling that is based on random games does not require too many skills and strategies to gamble based on the gambler's luck and competitiveness. Can gambling activities that draw large numbers of gamblers actually result in a profit? Making a lot of money through sheer luck is a pipe dream, according to the principles of probability that govern random games like winning and losing in gambling. This paper employs a method based on literature reviews to first assess the core of gambling from a probability perspective, then discuss the previous contributions of gambling, and lastly discuss the significance of probability and the future development of gambling.

In this work, we investigated the phenomenon of spontaneous bidirectional sliding on a toppling rod under a frictional situation. We explained the reasons for sliding is the friction force from the table is not sufficient to support the horizontal acceleration of the mass center when toppling, so the rod itself has to obtain a horizontal acceleration and apply the inertia force to play the role of supporting the acceleration of the mass center. This phenomenon and converted the question into a mathematical model. We pick the contacting point between the rod and the horizontal surface as the reference point for our computing of physical quantity, therefore the torque caused by friction and normal force can be ignored. With this model, we finished the theoretical analysis of the effects of varying static friction and dynamic friction coefficients on the phenomenon, with computer simulations verified.

In recent years, the realization of quantum computation is a compelling research direction. To realize an error-tolerate quantum computer, topological quantum computation is considered as the most promising direction. Plenty of scholars have proved that non-abelian particles may play an important role on it. As a matter of fact, among particles obey non-abelian statistics, Majorana fermions is a typical example. On this basis, this study aims at introducing the development of Majorana-based quantum computation. To be specific, it will contain the conceptual framework of topological computation and introduce some recent research about Majorana-based quantum computation including the principles, configurations as well as the state-of-art analysis results. In addition, the current limitations for these studies will be demonstrated accordingly. Moreover, based on the summary the development of this field in recent years, this research will provide reference direction for future researchers. Overall, these results shed light on guiding further exploration of quantum computers.

The Neural Network is a well-known computational model that widely applied in machine learning (ML) inspired by human brains, which can perform the ML tasks including classification and feature extraction. Contemporarily it has been succeeded in all areas functioning as a powerful tool. Quantum computing is an emerging field based on quantum computers, which is a different calculation logic in the context of quantum dynamic theory providing an exponential computation power edge over traditional computers. Quantum Neural Network (QNN) is an intersection of the two areas, leveraging the advantage of quantum computing in the neural network, providing a strikingly powerful algorithm with promising potential. On this basis, this paper will demonstrate the state-of-art of QNN, which briefly explains the basic principle of QNN and an introduction of several typical QNN models. In addition, the current defects and drawbacks will also be discussed simultaneously. Overall, these results serve as a preliminary introduction to the topic, which shed light on guiding further exploration of quantum computing algorithms.

This research explores the relationship between the drag coefficient and front windscreen angles regarding to automobile engineering. The previous research indicates that the best angle for the front windscreen to reduce the drag coefficient was less than 45 degrees, and the tilt of the bonnet has a linear relationship with the drag coefficient. However, the ideal angle for the windshield to achieve the lowest possible drag coefficient is also governed by other factors such as road roughness and overall aerodynamic design. As 2D simulations can prove to be an invaluable resource for aerodynamic design, allowing designers to make sharp changes and test new ideas efficiently on the digital stage, this paper uses NURBS modelling techniques and ANSYS CFD-Post to predict liquid dynamics, further enhancing the prediction of the simulation. It can be concluded that reducing the drag coefficient will increase the range of electric vehicles, especially in severe weather conditions like winter. Overall, reducing air resistance has several positive effects on a vehicle, including stability, energy consumption, acceleration, and forward speed.

A time offset of 1 microsecond could lead to 300-meter positioning offset for a global navigational satellite system (GNSS). Therefore, appropriately evaluating and improving the clock performance onboard GNSS satellites are critical. The research methods and conclusions of papers written in distinct periods about their contemporary satellites clocks are chronologically synthesized. The satellites clocks among the same and different GNSSs are compared, with the time primarily centered around the launching and development of BeiDou-2 and BeiDou-3. It is found that passive hydrogen maser (PHM) and rubidium atomic frequency standard (RAFS) have a better performance than cesium (Cs) clocks, and PHM are among the best clock onboard satellites so more attention may be given to its development. Two major factors affecting timekeeping precision are the selection of clock manufacturers and clock types. The European manufacturing technique is pioneering, but the RAFS and PHM independently developed by China in recent years indicate a good performance. To improve navigation service, an accurate evaluation of satellites performance should be conducted, and the results can be used to assign the weight of satellite differently in computing navigation information.

This article is based on the fundamental thermodynamics theory to analyze the difference between the turbojet and turbofan engines. The result of this article is that the turbofan engine is suitable for commercial use since it consumes less fuel and has a higher bypass ratio than the turbojet engine. But low bypass ratio engines can serve the military since they have a smaller volume and higher speed, suitable for air combat. The turbojet engine can travel at a supersonic speed since it has extremely high jet flow from the nozzle and much higher fuel consumption, so it is for military use. This article also analyses two cases: i) How the number of fan blades and outlet guide vans affects the noise of the engine produced. ii) When airplanes fly through volcanic ash, how does the ash damage the airplane and the engine? The engineer found that 55 outlet guide vans are better than 37. To prevent airplanes from flying through volcanic ash, satellite weather photos start to show the volcanic ash area.

Nowadays, as traditional fossil energy sources are in decline, renewable energy sources are being actively sought, and the use of renewable energy is receiving widespread attention. The Dish engine solar power plant is vital in using solar energy. The Stirling engine is the fundamental element of the power plant, responsible for energy conversion. And the internal regenerator has an essential influence on the engine's performance. Hence, this paper focuses on the analysis and improvement of the regenerator. Heat transportation determines its efficiency, while the regenerator is the core component. An efficient Stirling engine cannot occur without a high-quality regenerator. This paper uses simulation experiments to explore the impact of various materials on the regenerator's performance. By comparing the regenerator performance of filled copper foam and stainless-steel mesh, it was found that the copper foam regenerator had a faster start time, while the stainless-steel mesh regenerator had a higher thermal capacity. After this conclusion, an optimized regenerator is designed, filled with different materials at each end according to the material properties. After simulations, it can be concluded that this enhancement improves the regenerator's performance, increasing the Stirling engine's overall efficiency.

With the rapid development of wireless communication technology, people have put forward higher requirements for the speed and quality of data transmission in wireless communication while enjoying a convenient life. Wireless communication systems are expected to be combined with artificial intelligence to meet these requirements. Machine learning (ML) can rely on different algorithms to process data without explicit programming. It can also optimize wireless systems by solving complex problems that traditional mathematics cannot solve. This paper briefly introduces wireless communication, machine learning, and the necessity of combining machine learning. The potential and applications of machine learning in various aspects of wireless communication, such as channel estimation, spectrum allocation, adaptive interference suppression, etc., are listed. The paper also introduces the various conveniences that machine learning in wireless communication brings to people in practical applications and the potential hazards that improper applications may bring.

The discovery of Hot Jupiter in 1995 marks the beginning of a new era in Astrophysics, and deep space observatory provides valuable data that helps us understand the evolution of the universe and extrasolar systems. This paper reports on the secondary eclipse depth and the geometric albedo of a hot Jupiter “Kepler-12 b” with a planet radius of 1.695±0.03R_J, and the use of Python programs helps derive the results. The Python programs also help draw the figures in this work with data from Spitzer IRAC, an infrared camera designed to detect near- and mid-infrared light. The conclusion drawn from the work is that the orbital period is 4.401 days and the geometric albedo A_g= 〖0.17〗_(-0.08)^(+0.08) . This work points out that the relatively low geometric albedo of Kepler-12b could imply that Kepler-12 b is a pM-class planet. The distinguishing factor between a hot Jupiter of pL-class and one of pM-class is the variation in their spectra and the temperature difference between their day and night sides.

In today's society, the application of integrated circuit technology can be seen everywhere, especially in the past two decades. This paper mainly studies the principle and design of CMOS devices in IC technology and discusses the research and analysis of the acceleration algorithm of IC design. This paper adopts the research method of literature review and analysis to summarize the existing research results. This paper first introduces the development background of integrated circuit technology and the importance of CMOS technology. Subsequently, the concept and interconnection principle of CMOS device, and the combined circuit design and sequential logic circuit design principle of dynamic and static CMOS are explained in detail. Then, the application principle of CMOS technology in GPU is analyzed, and its specific application in GPU acceleration algorithm is analyzed. Finally, the application of CMOS technology in integrated circuits and its application and acceleration effect are summarized.

In the milieu of promptly advancing technology and increasing demand for electronic devices, circuit defect detection has become crucial to warranting product quality. This study tackles the cons of traditional defect detection methods, proposing a mind-boggling approach based on AI deep learning. The study intends to establish and enhance deep learning algorithms for the exact and real-time detection of circuit defects. This research encompasses an in-depth review of existing literature on circuit defect detection and AI deep learning, underlining the existing gaps and pitfalls in the field. The study will primarily deploy convolutional neural networks (CNNs) and recurrent neural networks (RNNs) as the primary tools to process various data modalities. The results highlight that the proposed AI deep learning framework depicts grander performance, unlike in traditional manual inspection. The study sets precedence in AI applications in quality control as it contributes to improved manufacturing efficiency, reduced production costs, and delivery of utmost-quality electronic products to consumers.