Although classical computing has brought great convenience to mankind’s lives, classical computing is facing some problems. Combining computer science, information theory, and quantum mechanics, quantum information has been developed in many fields. Quantum gates can operate quantum bits, the carrier of quantum information, while quantum circuits are composed of quantum gates and quantum bits, showing the logic of operations. This study summarizes the fundamental concepts of quantum informatics: qubits, quantum circuits, and quantum gates where it is proved that single-bit quantum gates and CNOT gates are universal quantum gates. In addition, this research also demonstrates the current progress of quantum gates in the examination of fidelity of quantum gates, improvement of fidelity of quantum gates, and teleportation of quantum gates. Meanwhile, according to the current development status, the limits and prospects of quantum information are discussed. These results shed light on helping readers understand the basic concepts of quantum information, thus understand the future applications and developments in quantum information.

Quantum information is a cutting-edge technology that has numerous applications. It mainly makes usage of some quantum entanglement characteristics and uses the quantum entangled state as a carrier for information transfer. Therefore, compared to traditional information, quantum information has excellent features, e.g., stronger security and reduced susceptibility to interference. This article introduces the definition, concept, characteristics and history of quantum entanglement and quantum information. To be specific, this study lists the applications of quantum entanglement in communication and radar. In addition, it gives an outlook on the future function of quantum entanglement in quantum information based on the advantages and disadvantages of quantum entanglement. Contemporarily, the field of physics is rapidly advancing in both quantum entanglement and quantum information, and there have also been significant technological advancements. In experiments, scientists have been able to extend the transmission distance of quantum information to great distances. At the same time, scholars are looking for ways to minimise the interference of quantum information during transmission. In constant exploration and experimentation, the experimental results have inspired scientists to explore the deeper realms of quantum information.

With the rapid development of the digital age, information security, from personal data to national security, is becoming increasingly crucial. Information security primarily refers to the computation and processing of diverse information in computer systems and information exchange networks in order to safeguard information security. Cryptography is the technical foundation for achieving these objectives. In the early stages of education, advanced mathematics, linear algebra, probability theory, and other fundamental disciplines must be studied, although the practical application of modern algebra, cryptography, number theory, and mathematical knowledge will vary. This study explores the application of current algebra in cryptography, including both traditional and modern cryptographic applications, using a literature review approach. By comparing images from various eras, the researchers discovered that images were classed as "traditional" and "modern" at various times. Moreover, the likelihood of both traditional and modern images being identified throughout the modern era is comparatively higher.

This work investigates particle transportation Taylor-Couette Flow (TCF) experiments. We designed and built up the experimental set-up and then did two groups of experiments (S1 and S2). Small radius ratio (η) experiments (S1) focuses on the settling time t_set of a particle, which increases when Reynolds number (R) increases. The settling time within Taylor-Couette flow is larger than that in the still water due to horizontal motion of particle. To further understand the underlying flow mechanism of this increased t_set, we designed the large η experiments (S2), which identify Taylor vortices (TVF) and spiral vortices (SPI) that trap the particle and thus increase t_set. In addition, linear stability analysis also predicts the wavelength of flow structures in the same order of experimental observation, although some deviation exists.

Al. Last year, the Nobel Prize in Physics was awarded to Alain Aspect, John F. Clauser and Anton Zeilinger for their experimental verification of the violation of Bell's inequality by quantum mechanics using entangled photons, which pioneered the science of quantum information; in the same year, the 28th Solvay Conference on Physics, with the theme "Quantum Information In the same year, the 28th Solvay Conference on Physics, with the theme of "Quantum Information Physics", reviewed the development of quantum information in the last decade and the future direction. It is clear that the world of physics is now focused on the subsequent progress of quantum mechanics. In this paper, I will introduce the background of quantum information and explain in detail, clearly and thoroughly, the basic theory of quantum information and its specific applications. By describing the two fundamental and most important properties of quantum information, quantum entanglement and quantum unclonable, quantum information will give the reader a comprehensive understanding of the significance and usefulness of quantum information. This paper aims to help physics students to build up their basic knowledge of quantum information by explaining the basic theory of quantum information and helping them to expand their knowledge of quantum information.

Quantum mechanics is an important part of modern physics. It is a subject which aims at studying the motion law of microscopic particles. This represents the entry of human physics into the world of the micro. It also marks a fundamentally correct and revolutionary understanding of particle motion at the microscopic level. The study of quantum states is the definition of quantum systems. Quantum states and further processing are important blocks of quantum mechanics. This paper will focus on the definition of different quantum states and the application of quantum state operation will be introduced. To evaluate the application of quantum states from the advantages and limitations in order to achieve a comprehensive and objective display of the full picture of quantum states. This paper describes the specific classification of pure state and mixed state of quantum states, and explains their application and frontier applications as well as their current limitations and shortcomings from the perspective of different quantum states. Overall, these results shed light on guiding further exploration of applications for quantum techniques.

Nearly 30% of the components in the universe are dark matter, hitherto, astronomers are still uncertain about their properties. This project attempts to constrain whether dark matter is MACHOs or diffused particles via statistics of microlensing events observed toward quasars, which are the brightest objects in the Universe. The identification of isolated microlensing events enables us to study stellar and planetary objects in distant universes that would be otherwise unobservable. During the research two isolated microlensing events toward quasar J1821 is discovered in the first 25 quasars in our sample. The WISE light curves in W1 and W2 bands are almost identical in magnification, consistent with achromatic variability due to microlensing. The crossing times for the two events are about 2 days and 1.3 days, thus the lenses are probably a star or sub-stellar object. By assuming the lenses are in galaxies of the galactic cluster with a redshift of 0.81 lying in our sight of view to the quasar, calculations of the mass of the lenses as a function of its velocity can be made, yielding a planetary mass or less in the relative velocity dominated by the movements of galaxies. If the superluminous motion of jets in a quasar dominates the relative velocity, stellar masses are derived. The data analysis yielded from the microlensing light curves of J1821 suggests microlensing as a method for astronomers to further study stellar and sub-stellar objects in our Universe.

Perfectly symmetric curves always have a high degree of aesthetic value. While it is difficult to draw them by hand, Spirograph is an old and popular drawing toy that produces fascinating symmetric patterns. In playing with drawing software, the author explores types of Spirograph patterns, the type identification method, and the parametric equations to express Spirograph mathematically. This paper also discusses the key parameters of a Spirograph pattern and how they affect the pattern’ shape. Finally, Spirograph pattern design is carried out by analyzing the features of a random pattern and estimating its different parameters. These results to some extent demystify and predict the seemingly infinite Spirograph patterns, as the corresponding parameters of a given Spirograph pattern can be found so that the similar image can be drawn by hand through a physical Spirograph set.

The sun provides warmth and light essential to human life, making it important to investigate its formation, current state, and future evolution. This article includes information on the formation of the sun and an overview of its current state. The sun formed about 4.6 billion years ago from a giant nebula in one of the spiral arms of the Milky Way galaxy, after which the solar system formed from. As for its structure, the sun consists of six layers: core, radiative zone, convection zone, photosphere, chromosphere, and corona. The sun is a main sequence star and is situated at a considerable distance from the earth. This distance is calculated using the parallax method, which involves measuring the parallax angle and applying trigonometry. Another approach to determine the distance is by utilizing Kepler's Third Law. The sun continually undergoes fusion in its core due to specific conditions that allow for fusion reactions to occur, including extremely high temperatures, high density, and a suitable containment vessel. In the future, the sun will evolve into a red giant star before ultimately becoming a white dwarf star. Eventually, the earth will be engulfed by the sun as the sun evolves.

The logistics equation is the most classical model of population growth. Influenced by external environmental factors and growth inertia, the total population is in a state of periodic equilibrium. so, studying the stability of the periodic solution of the logistics equation is an important issue. If the logistics equation is considered as a function, the general method to judge the stability of the periodic point is to bring in the derivative of the function after iterating n times to take the value. The Lyapunov exponent is originally an important method used to judge the stability of dynamical systems. If the logistics map is considered as a discrete dynamical system, applying the Lyapunov exponent to the determination of the periodic solution will largely reduce the computational effort.

Calculus is the foundation of many natural sciences such as Physics. Calculus excels at calculating the area of irregularly shaped objects and thus it may be used in a vast array of domains. Because calculus is difficult to perform when combined with trigonometric and logarithmic functions, additional formulas are required to assist with calculations. By definition, limit of the sum of a function f(x) across given interval [a,b] is the definite integral. Notice the relationship between definite and indefinite integrals is as follow: result of a definite integral is a precise nice value, whereas an indefinite integral is expressed by a function. Their mathematical relationship is limited to computation regarding the Newton-Leibniz formula. This article describes only one of several methods for calculating definite integrals. Taylor expansion will also be used for auxiliary operations, while the relevant equations of Taylor expansion will also be presented in the text. It will also be learned through this paper that the result of the integral varies with π.

Limit is significant concept in mathematic analysis. Technically, limit’s definition in mathematics is that a variable in a function gradually approximates to a certain value in the changing process which cannot be ended. L’ Hôpital’s rule and Taylor expansion, together with other methods such as Stolz theorem, are usually used in measuring a limit’s value. In this paper, it will focus on some representative limits that are related to definite integrals. L’ Hôpital’s rule and Taylor's expansion are also jointed used so as to solve the problems. The main part of this work talks about the limit of the integration of trigonometric function, under which situation Taylor’s expansion is commonly utilized. This article talks about the polynomial’s integration as well, under which situation the approximation method is also employed. Trigonometric function and polynomial function are frequently appeared in evaluating limit. This means that this paper is summarizing the prime functions in integration-related limits.

The definite integral is a fundamental concept in calculus that has many applications in various fields such as physics, engineering, and economics. However, integration can be difficult and requires a variety of skills such as substitutions and partial integration. In this paper, Lobachevsky’s formula is explored, which provides a new way to evaluate definite integrals. It should be noted that Lobachevsky’s formula can only be applied in specific cases where the integrand is even and π-periodic. However, it is demonstrated to be an effective method in these cases. In this paper, the proof of the theorem is given, and a variety of examples are solved by virtue of this method. Hence, this paper may serve as a reference for relevant research in the field of calculus and provide insights into the applications of Lobachevsky’s formula.

Fourier analysis plays a central role in the modern physics, engineering, and mathematics itself. In the field of differential geometry, a Lie group G gives a symmetric structure, and one may apply the Fourier analysis by means of matrix-valued irreducible representations. Even though the entries of these irreducible representations are already shown to be the eigenfunctions of the Laplace-Beltrami operator, it is still desirable to consider a concrete example where both the operator and the irreducible representations can be computed explicitly. This study gives an explicit form of the Laplace-Beltrami operator on SO(3) using direct computations and show also that each entry of the irreducible representations o_n^ij is indeed an eigenfunction of this operator. Therefore, one can also find the application of the Fourier Analysis on differential equations, in this study Poisson’s equation as an example, using the Laplace-Beltrami operator as the corresponding differential operator. Overall, these results shed light on guiding further exploration of Fourier analysis.

A The Fourier transform has a wide range of applications in daily life, including physics, signal processing, acoustics etc. The topic of this article is to demonstrate the principle and applications of the Fourier transform in acoustics through theoretical derivation. The paper first derived the basic formula of the Fourier Transform and the related seven theorems. Then the paper detailed the research of Fourier Transform in underwater acoustic pulse signal detection technology. Finally, the application of Fourier Transform in the defect detection algorithm of MEMS acoustic films was detailed. According to the analysis, the paper demonstrated the primary application of Fourier Transform in underwater acoustic pulse signal detection and defect detection algorithm of MEMS acoustic film. Based on the evaluations, this study demonstrated the general application scenario of Fourier Transform and offered theoretical basis of its application in acoustic field, which promotes its developmental potential in the acoustic field. Overall, these results shed light on guiding further exploration of acoustic research.

Prevalent is the practical application of Elliptic Curve Cryptography (ECC) in the modern public-key cryptosystem, especially the implementation of ECC algorithm in Bitcoin source code. With the thorough introduction of discrete logarithm and Diffie-Hellman key exchange, ECC has gradually progressed to be sophisticated and efficient simultaneously. Therefore, it currently has been widely regarded as the successor of RSA algorithm in terms of inheritance for its shorter lengths of keys, faster speed and higher safety under the same encryption strength. Due to the potential safety and complexity of Elliptic Curve Cryptosystem, it is apparently noticed that there is included a large volume of Maths principles related to the establishment of ECC algorithm. As a consequence, this paper will mainly focus on qualitative research and exemplary analysis to specifically elucidate the general knowledge on essential mathematical principles of ECC, including the Law of Addition, the Elliptic Curve Discrete Logarithm Problems (ECDLP) and the Elliptic Curve ElGamal (EC ElGamal), together with the corresponding applications combined with their deprivation processes.

With the development of information technology and technology, more and more cutting-edge industries have come into view of the public, among which one of the most representative technologies is UAV. The emergence of UAVs has reduced the labor cost of some businesses, such as farming, forest fire prevention, maritime patrol and so on. In response to the common problems of long preparation time and poor maneuverability of unmanned aerial vehicles, this paper studies the aerodynamic layout of unmanned aerial vehicles and proposes a new layout. Firstly, the aerodynamic layout of typical UAVs is introduced and compared and analyzed. Then, a new type of compound wing UAV is designed by screening and analyzing the wing, flight analysis, main wing and UAV production process with Reynolds number. Subsequently, simulation experiments were conducted to analyze and optimize the aerodynamic layout performance of the designed UAVs, thereby verifying the reliability of the proposed method.. Finally, the entire content is summarized and analyzed.

This article introduces some basic methods that human usually uses nowadays to detect exoplanets, including transits method, radial velocity method, direct imaging method, gravitational microlensing method, and astrometry method. As we all know, none of these methods are perfect, each of them has its advantages: some of them are good at detecting planets with great mass, some are good at detecting planets with great radius, and some of the methods are good at detecting planets far away from their host star. But at the same time, each method has its own disadvantages. That is the reason why sometimes some of these methods are used together to get information about specific exoplanets. This chapter will introduce these methods by giving information on how these methods work, the equipment each of them requires, the advantages and limitations of these methods, and the history and development of these methods. Finally, there is a conclusion that states the characteristics of the planets each method is good at detecting.

As the discovery of exoplanets increased, their characteristics are becoming a main concern for new research. Amongst the many that are discovered, some have an atmosphere of their own just like planet Earth. The purpose of this paper is to examine these atmospheres and calculate the height of the atmosphere using escape velocity. Later in this paper, the issue of the total angular momentum of the planet is examined. This momentum is separated into two different sections whose momentum is added together. The angular momentum of the solid part of the planet is calculated by considering the planet as a rigid body and applying the formula for angular momentum. The second part of calculating the angular momentum is done by using integration to determine the momentum of the atmosphere and using the height of the atmosphere to act as a limit to the definite integral. By understanding the quantities of these exoplanets, further research can be done on how these exoplanets are formed.

The design of running shoes is mainly to reduce mechanical stress through the deformation of the viscoelastic midsole, which is usually made of ethylene vinyl acetate (EVA) foam. This study aims to analyze and compute the heel pad stresses through simulated strikes. For stresses and strains, a non-linear model and its differential equation (Eq.1) is reported. Through repeated measure ANOVAs, analyses and comparisons of the three methods for non-linear computation are made. Then detailed numerical approximations of a differential equation are derived using Euler’s method. In addition, Dinato reported biomechanical measures results for Air (Nike), Gel (Asics), and Adiprene (Adidas). The results are compared to simulated data correspondingly. The measured stresses (peak pressure, kPa) are 242.7 ± 40.8, 239.5 ± 420.0, and 246.5 ± 51.6 respectively. The computed boundary stress is 55 kPa. These show significant associations between the simulated and measured stress.