Currently, the relatively popular public key encryption is RSA. It was officially launched in 1978 and given their initials as a name. Different encryption and decryption keys are used in the RSA public-key cryptosystem. Deriving decryption keys from known encryption keys is computationally difficult. Rsa has emerged in various forms since its development. Since the development of RSA, there have been various forms, which means there are various loopholes. Next, we will summarize several interesting attack methods of rsa. It will involve continued fractions and CRT and so on. Through this paper, one can learn a series of knowledge about rsa. As a classic asymmetric password, the value of rsa's existence is relatively high, and exploring its value is something that every password learner should experience. Through this article, one will learn about the most basic attack methods of rsa.

In many industries, there is a need to model the flow of air over structural components. With sufficient information from these models, engineers can better implement these parts into a complete design. The purpose of this paper is to provide a model of specific airfoils using computational fluid dynamics (CFD). With computational fluid dynamics, the characteristics of air around an airfoil can be modeled, providing useful data to engineers who could be designing an airfoil or airplane. The CFD calculations are performed using Python, along with the two packages Numpy and Matplotlib. The governing equations of CFD, including Newton's Second Law, small disturbance equation (SDE), wave propagation, etc. are discretized and transformed into partial differentiation equations (PDE). Using the second order derivative of the wave propagation PDE, the SDE can be solved in iterations and plotted on a graph showing the velocity distributions for a particular airfoil. The results from the CFD calculations show general trends in velocity distributions, regardless of airfoil shape. These include a decrease in x-direction velocity at the ends of an airfoil with an increase at the midsection of the airfoil. Also, y-direction velocity is generally positive and increasing at the front of the airfoil, but negative and decreasing at the end of the airfoil. What is important to understand is how different airfoil shapes can change velocity distributions, moving to using 3D CFD calculations, and the possibility of using CFD for modeling airflow over a multitude of objects.[ Henry Bao, the first author, participated in the Illinois junior academy of science state fair, and abstracts of the regional winners' presentations were posted online. (ilacadofsci.com)]

In recent years, the origination and formation of the black holes remains an unsolved issue. On this basis, a large number of scholars have suggested the possible relationship between primordial black holes and dark matter. To be specific, if one can confirm the existence of PBHs, it’s much more likely for researchers to determine the origin and nature of dark matter, and thus come to the solution to one of the most important problems in modern astrophysics. The search missions for PBHs have been on for decades, and amounts of money and time had been put in, yet no direct evidence has come in. In this paper, it is hoped to map out the dark matter distribution in early universe with THESAN simulations. According to the analysis, this study provides the most valuable and worthwhile observation goals for the search of PBHs. Overall, these results shed light on guiding further exploration of black holes.

The appearance and generation of O2 has long been discussed by the scientists. It is a fundamental topic as it can not only help us get to know the origin of lives, but can also give us the inspirations of discovering the possibilities of lives on other planets as O2 is vital to most creatures. And the GOE is the most important discovery in the O2-producing period.The appearance of the GOE was marvelous and is a great turning point in the earth’s developing history. Of course, the GOE cannot be simply explained as a coincidence, it is an inevitable development in the earth’s developing history. In this paper, we are going to focus on the mighty causes including photosynthesis in the early stage of earth and O2 storage. Also we are hunting the influences of the GOE and a relating experiment in search of the probabilities of mighty lives in the outer space.

For Disneyland visitors, a well-designed route is often necessary to experience the maximum number of preferred entertainment facilities within a limited time. To construct the best way that optimizes visitors’ satisfaction, a survey is first conducted to estimate the attraction value of each facility, followed by the collection of data that record the traveling time among each facility and the waiting line time. Using collected data and listed constraints, a possible route is listed as an example. To solve the problem, a model is constructed based on integer linear programming. The original, incomplete, and modified formulations are listed in the last part of this paper.

Although several discoveries have proved the gravitational effects of dark matter (DM) on various astrophysical objects, its origin remains one of the main puzzles in physics. These observations can be explained by adding a new particle to the Standard Model that is weakly interacting, massive, stable, and non-baryonic. One of the main characteristics of DM in question, beyond its exact particle nature, is its density in the Universe. In this paper, we use the latest data for the local DM density, total DM mass, and rotation curves in the Milky Way to estimate the density profile of these elusive particles in our Galaxy. We find the density profile parameters that match the current data and analyze the density of the stellar bulge and gas and star in the disk. We show that the stellar bulge dominates the Galactic dynamic for distances below a few kiloparsecs (kpc), the disk plays the most important role at intermediate distances, and DM explains rotation data beyond a few tens of kpc. Finally, we settle on a local DM density of about 0.5-0.7 GeV/ to fit the data well, regardless of the exact function we use to model the density profile.

The waterjet propulsion system is a marine propulsion device prevalently used on contemporary high-speed vessels. The performance of a waterjet propulsion system is considerably affected by the nozzle. In this study, the influences of the shape and the outlet area of a waterjet propulsion system on the efficiency of the propulsion system is investigated using the computational fluid dynamics method. A total of 10 different nozzle designs, including cylindrical and conical nozzles with 5 different outlet areas, are analyzed in terms of nozzle efficiency and overall efficiency, and the possible reasons and explanations behind the variations of the nozzle efficiency and the overall efficiency are proposed in this study. The simulated results indicate that the conical nozzles consistently have higher nozzle efficiency than the cylindrical nozzles, and the maximum nozzle efficiency occurs in the conical nozzle with an outlet area of 60% of the inlet duct area. The abrupt change in the flow direction at the transition between the guide vane section and the nozzle, as well as the skin friction on the nozzle wall, are predominant factors affecting the nozzle efficiency. The waterjet propulsion units equipped with conical nozzles generally have higher overall efficiency than their counterparts equipped with cylindrical nozzles, while the maximum overall efficiency occurs in both the cylindrical nozzle with an outlet area of 50% of the inlet duct area and the conical nozzle with an outlet area of 60% of the inlet duct area. The loss of mechanical energy due to viscosity and turbulence in a propulsion unit is the major source of energy loss, while the kinetic energy carried by the exit flow is also a considerable factor affecting the overall efficiencies of the propulsion units equipped with conical nozzles with relatively large outlet areas.

Galaxies as the most important structures in the universe and Galaxy formation is a sequential redistribution process.The basic picture of galaxy formation was first proposed by White and Rees.The physical processes involved in galaxy formation are very numerous and complex. We know very little about most of these processes. Therefore, we can only describe them with a few empirical formulas. In this article the popular simulation techniques for galaxy formation are discussed in detail, based on the most recently observed cosmic star formation history. This study will focus mostly on the goals of galaxy development by describing the processes of star formation, gas dispersion, dark matter, and galaxy correlation. In this paper, we do not study the formation process of a specific galaxy, but focus on the formation process of a large sample of galaxies in the framework of the whole cosmology We are also concerned not with the specific properties of a particular galaxy, but with the statistical properties of the whole sample of galaxies.Therefore the paper will next explore hydrodynamic techniques such as N-body simulation, other modified f (R) gravity models, smoothed-particle hydrodynamic simulation, and semi-analytic models to mimic the process of galaxy formation. This article finishes with a summary of galaxy formation.

Motivated by results in the literature that use representations and group actions to produce nice geometric results about algebraic varieties, this article studies projective equivalence relations between closures of orbits for several complex algebraic group actions on , where is a complex representation of . In particular, we study the cases when is one of the following:, , , and . On the way, we also obtain some interesting geometric results from studying these orbits.

When the wind blows against a building, the resulting force acting on the building at a particular elevation is called the “wind load”. Measuring and minimizing the wind load is crucial to ensure the safety of buildings. Therefore, the objective of this study is to investigate the effect of a building’s roof design on the wind load by evaluating and comparing the wind pressure differences ∆p that different building models experience by leveraging Computational Fluid Dynamics (CFD) simulations. The 3D CAD (Computer-Aided Design) software SolidWorks was used to construct building models of identical dimensions with the exception of roofs harboring different shapes and angles. By exerting a wind velocity through flow simulation, flow trajectories and cut plot graphs of wind velocity and pressure surrounding the building models are generated. Wind pressure differences ∆p for each situation were calculated and compared based on the CFD results. Wind tunnel experimentation with building models will also executed to test the computed data and prove its reliability and applicability. The data shows that, among all tested roof designs, the barrel-vaulted roof exhibits the minimum pressure difference (of 171.15 Pa) between the windward and the leeward surface and experiences the least wind load and resists strong wind most effectively. It reduces up to roughly 15% of wind load compared to the worst case tested. For symmetric triangular gable roof designs, the greater base angle leads to greater wind load. Overall, this study provides the theoretical basis and scientific evidence for the building designs of the next generation.

This study utilizes a time series ARIMA seasonal multiplicative model to predict the incidence trend of influenza in China, providing valuable early warning references for influenza prevention and control. Monthly incidence data of influenza cases nationwide were collected from January 2014 to August 2022. The data from January 2014 to December 2020 were used as the training set to fit the time series model of influenza incidence. The data from January 2021 to August 2022 were utilized as the testing set to predict the influenza incidence from January 2021 to August 2022 using the fitted model. The predicted values were then compared with the testing set. Through residual white noise testing, significance testing of parameters, and examination of model fit, the final model was determined as , which demonstrated a good fit. The majority of actual data fell within the 95% confidence interval of the predicted values, and the predicted incidence trend aligned closely with the actual trend. The constructed model holds significant application value in early warning systems for influenza prevention and control, providing crucial insights for public health strategies. In practical applications, this model can be integrated with various factors such as social, natural, and geographic environments to formulate targeted prevention and control strategies, thus enhancing the efficiency and effectiveness of influenza prevention and control measures.

Energy shortage is one of nonnegligible problems nowadays. Even since the twenty centuries, the achievement of fission reactor has proved that nuclear energy is a powerful source. However, fission reaction could cause radiation hazard if operation error happens. Nuclear fusion can provide more clean energy. This paper discusses nuclear fusion and two typical models of fusion reactor, inertial confinement fusion reactor and tokamak, and their properties. Fusion reactors use deuterium and tritium to fuse heavier nucleus and release energy. With -distribution, deuterium-tritium fusion reactivity can be boosted at relatively low temperature. Furthermore, fusion reactor has initial success. The more energy can be created than energy used to ignition. To solve nuclear fuel problem, continue ignition progress problem, possibly achieving controllable fusion reaction. The improvements which this paper mentioned perhaps allow to extend the application context of fusion reactor.

With the continuous development and widespread use of quantum mechanics, solving the Schrödinger equation has become a hot research topic. The finite difference method has the advantages of simple calculation and high accuracy, which means that it has high potential in solving the numerical solutions of the Schrödinger equation. In this paper, we deeply explore the problem of using the finite difference method to solve the numerical solution of the time-independent Schrödinger equation, propose a solution method based on the finite difference method, and evaluate its performance under different conditions. Firstly, by analyzing the principles and characteristics of the finite difference method, we construct a difference format for the time-independent Schrödinger equation. Then, by converting the difference format of the numerical solutions of the equation into a matrix, the numerical calculation problem is transformed into a matrix eigenvalue and eigenvector problem. Finally, for different physical scenarios, the established model is numerically solved and its performance is analyzed. This study found that the constructed numerical solution method exhibits high accuracy and stability in solving the numerical solutions of the time-independent Schrödinger equation. In different physical scenarios, this method can provide satisfactory results, thus verifying the feasibility of applying the finite difference method to this problem.

This report aims to determine the probability range of the number of collisions under the optimum collision condition. The optimum condition was obtained by determining the average values of the given variables in the Glauber Model. Graphs of against eccentricity 1, 2, and 3 (Ecc1, 2, and 3) were plotted respectively according to the data generated from the Glauber Model Simulation in CERN ROOT. Then, the optimum average value was plotted as a vertical line on the graph to determine the range of . The probability ratio of an optimum collision versus maximum probability in an event was concluded to fall in a certain range of 0.30 ± 0.07, and this range is verified to be a stable range that could be used for prediction of optimum collision numbers in future nuclei collision experiment. This probability ratio can be used to predict the optimum collision with only provided.

As the world of commercial aviation recovers from the global recession after the pandemic, demands for faster and more reliable air transportation are on the rise. Research in Hypersonic Transports, led by both government and private sectors, aims to revolutionize the industry with its high time efficiency and customizability for various needs. This paper reviews the design principle and challenges of HST from a technical standpoint, while overviewing high-speed gas dynamics, analyzing the waverider configurations, and addressing the technical intricacies of designing a hypersonic vehicle. It shows that the waverider configuration is a suitable HST candidate for its large fuel storage and high inlet compatibility for an airframe-propulsion integrated design. This paper aims to provide holistic context for the advantages and challenges associated with HST, while providing insights into the compatibility of a waverider configuration that can be optimized for civilian transport applications.

Unified field theory is a physical theory that describes and reveals the common nature and intrinsic connections of fundamental interactions in a unified way, starting from the idea that interactions are transmitted by fields. This paper will start from the past of the unified field theory and use the literature research method to describe the problems encountered in completing the unified field theory and the possible solutions for the future. The result shows that unified field theory is a dynamic theory that is still being studied and has significant implications for the development of physics. This article argues that many of the shortcomings of this theory are due to the lack of mathematical theory. It is also pointed out that the creation of a new mathematical system is a feasible way. Finally, it is concluded that unified field theory is still a very difficult problem to explore.

Since the definition of matrices in 1855, matrix multiplication has played a crucial role in a wide range of fields. Over the years, numerous researchers have dedicated their efforts to improving the time complexity of this fundamental operation. This paper aims to delve into the historical development of matrix multiplication algorithms and methodologies employed to achieve these significant advancements in time complexity. By employing various approaches, researchers have been able to improve the time complexity of matrix multiplication, leading to a significant reduction from O () to O (). Across nearly two centuries, this progress is contributed by a lot of extraordinary scientists and researchers. This paper explores the practical implications of these improvements across various domains, such as computer science, physics, economics, and more. The development of more efficient matrix multiplication algorithms has enabled researchers and practitioners to tackle complex problems and explore new frontiers. In the future, with the rapid growth of machine learning techniques, matrix multiplication will continue to evolve and improve.

In modern times, mathematicians are often troubled by new approaches to deducing the outcomes of certain events. The introduction of Markov models eliminated queries across different sectors. In 1907, Russian mathematician Andrey Markov proposed the concept of Markov chains. It has been widely used in many aspects, such as weather prediction, deep learning, biological information, and so on. Therefore, this paper examines how the Markov chain model can be applied in a variety of situations. This study uses Python as a supporting tool to simulate states and possible outcomes. It can be concluded that Python is able to simulate the state transitions of the Markov chain. The paper also identifies the differences between Markov models, their application in common scenarios such as medical, finance, weather forecasting, machine learning and others in our everyday life and why they are so popularly used, including the simplicity of the model and more.

In daily life, we can transmit and obtain information through mechanical waves and electromagnetic waves. For example, judging where the fish swims from the flooded water waves, and learns from the wonderful music to know what kind of instrument the musicians are playing and communicating through the radio waves. Gravitational waves, a fundamental prediction of Einstein's theory of general relativity, have revolutionized our understanding of the universe. This essay explores the background of research on gravitational waves, tracing their theoretical origins to the early 20th century and highlighting their recent detection in 2015. The research technique employed involves highly sensitive interferometers, such as LIGO and Virgo, which can detect the minuscule distortions in space-time caused by these elusive waves. By observing the gravitational waves emitted during cataclysmic cosmic events, scientists can now delve deeper into the nature of black holes, neutron stars, and the origin of our universe. In conclusion, the discovery of gravitational waves opens up new avenues for exploring the cosmos, providing unprecedented insights into the fabric of space-time itself.

Angle of attack (A.O.A.) is defined as the angle at which the chord of an aircraft’s wing meets the relative wind. At low angles of attack, the wing could just create a small amount of lift, and it also experience a small amount of drag. As the A.O.A. increases, both lift and drag will increase. However, when the wing reaches a critical angle of attack, the lift it could produce will quickly decrease, since the separation of the air flow and the wing surface. The objective of this study is to find the relationship between the angle of attack and the lift coefficient(which is proportional to the lift it could produce) of the wing. And as a conclusion, we find that the A.O.A. increase, the lift coefficient will also increase, and if the inlet velocity, the wing’s surface area and the velocity remains constant, when the lift coefficient increase, the lift will also increase.