Volume 12

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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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