Structure-preserving algorithms for guiding center dynamics based on the slow manifold of classical Pauli particle

The classical Pauli particle(CPP) serves as a slow manifold, substituting the conventional guiding center dynamics. Based on the CPP, we utilize the averaged vector field(AVF) method in the computations of drift orbits. Demonstrating significantly higher efficiency, this advanced method is capable of accomplishing the simulation in less than one-third of the time of directly computing the guiding center motion. In contrast to the CPP-based Boris algorithm, this approach inherits the advantages of the AVF method, yielding stable trajectories even achieved with a tenfold time step and reducing the energy error by two orders of magnitude. By comparing these two CPP algorithms with the traditional RK4 method, the numerical results indicate a remarkable performance in terms of both the computational efficiency and error elimination. Moreover, we verify the properties of slow manifold integrators and successfully observe the bounce on both sides of the limiting slow manifold with deliberately chosen perturbed initial conditions. To evaluate the practical value of the methods, we conduct simulations in non-axisymmetric perturbation magnetic fields as part of the experiments,demonstrating that our CPP-based AVF method can handle simulations under complex magnetic field configurations with high accuracy, which the CPP-based Boris algorithm lacks. Through numerical experiments, we demonstrate that the CPP can replace guiding center dynamics in using energy-preserving algorithms for computations, providing a new, efficient, as well as stable approach for applying structure-preserving algorithms in plasma simulations.

Evaluation of the famous classic formula Sanhua decoction based on network pharmacology and multi-component quantitative analysis

Background:Sanhua decoction has significant effects in the treatment of stroke.The study of the Sanhua decoction material benchmark was carried out to analyze the value transfer relationship between the Chinese herbal pieces and the substance benchmark.Methods:Network pharmacology was employed to investigate the potential active components and molecular mechanisms of Sanhua decoction in the treatment of stroke.15 batches of Sanhua decoction lyophilized powder were prepared using traditional formulas and subjected to high-performance liquid chromatography analysis to generate fingerprints of the Sanhua decoction substance benchmarks.Then,a multi-component quantitative analysis method was established,allowing for the simultaneous determination of ten components,to study the transfer of quantity values between pieces and substance benchmarks.Results:60 active ingredients were screened from Sanhua decoction by network pharmacology,of which gallic acid,magnolol honokiol,physcion,and aloe-emodin may have a greater effect than other active components.63 key targets and 134 pathways were predicted as the potential mechanism of Sanhua decoction in treating stroke.The fingerprint similarity of the Sanhua decoction substance benchmarks was found to be good among the 15 batches,confirming the 19 common peaks.The content of the 10 components was basically consistent.The components’transfer rates were within 30%of their respective means.Conclusions:This study provided a comprehensive and reliable strategy for the quality evaluation of Sanhua decoction substance benchmarks and held significant importance in improving its application value.

Heuristic Estimation of the Vacuum Energy Density of the Universe: Part II-Analysis Based on Frequency Domain Electromagnetic Radiation

In Part I of this paper, an inequality satisfied by the vacuum energy density of the universe was derived using an indirect and heuristic procedure. The derivation is based on a proposed thought experiment, according to which an electron is accelerated to a constant and relativistic speed at a distance L from a perfectly conducting plane. The charge of the electron was represented by a spherical charge distribution located within the Compton wavelength of the electron. Subsequently, the electron is incident on the perfect conductor giving rise to transition radiation. The energy associated with the transition radiation depends on the parameter L. It was shown that an inequality satisfied by the vacuum energy density will emerge when the length L is pushed to cosmological dimensions and the product of the radiated energy, and the time duration of emission is constrained by Heisenberg’s uncertainty principle. In this paper, a similar analysis is conducted with a chain of electrons oscillating sinusoidally and located above a conducting plane. In the thought experiment presented in this paper, the behavior of the energy radiated by the chain of oscillating electrons is studied in the frequency domain as a function of the length L of the chain. It is shown that when the length L is pushed to cosmological dimensions and the energy radiated within a single burst of duration of half a period of oscillation is constrained by the fact that electromagnetic energy consists of photons, an inequality satisfied by the vacuum energy density emerges as a result. The derived inequality is given by where is the vacuum energy density. This result is consistent with the measured value of the vacuum energy density, which is 5.38 × 10-10 J/m. The result obtained here is in better agreement with experimental data than the one obtained in Part I of this paper with time domain radiation.

Beyond Equations:The Challenge of Mathematical Rigor in Economics

The mathematical approach is threatening the progress of economics,as it tends to disregard the complexity of economic behaviour and the unpredictability of human actions.——Friedrich Hayek The reliance on mathematical models in economics has long been debated,with critics arguing that this approach fails to capture the complexity of human behavior and the unpredictability of economic systems.While mathematics provides a structured method for analyzing economic processes,it often simplifies decision-making to a one-dimensional utility function,neglecting social,psychological,and political influences.This paper examines the limitations of classical and neoclassical economic theories that heavily depend on mathematical rigor,highlighting the pitfalls of models like the Rational Agent Model,General Equilibrium Theory,and Expected Utility Theory.Drawing on examples such as the 2008 financial crisis and the Terra/Luna cryptocurrency collapse,the paper demonstrates how over-reliance on equations has led to inaccurate predictions and ineffective policy decisions.It calls for a more interdisciplinary approach that integrates insights from psychology and sociology to address the gaps left by traditional mathematical economics.

Classic Translation and Humanistic Spirit in the Age of AI

This article hopes to explore a question:in the era of artificial intelligence,do we still need traditional translation of canonical texts,and how is such translation possible?Artificial intelligence has an all-round impact on the world’s productivity,and translation is the first area to be challenged.With the increasing accuracy and optimization of big data computing,daily translation,business translation,simultaneous interpretation and even general academic translation are gradually being replaced by machine translation.In this context,whether the canon translation by scholars is still meaningful has become a question that must be asked.This article believes that translation of canonical texts will never be out of date,and it is precisely in this era that the canon translation with academic standards and humanistic spirit are more needed by academia and society.The contemporary task of canon translation is not only translation and introduction,but more importantly,the inheritance and construction of its own academic history and humanistic thoughts,as well as the understanding and cultivation of human history,civilization and humanistic spirit.

Dynamic and electrical responses of a curved sandwich beam with glass reinforced laminate layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact

The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigated.The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity.For the layer analysis,the high-order shear deformation theory(HSDT)and Frostig's second model for the displacement fields of the core layer are used.The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time.In order to validate the analytical method,the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI.Finite element(FE)simulations are conducted by means of the ABAQUS software.The effects of the parameters such as foam modulus,layer material,fiber angle,impactor mass,and its velocity on the generated voltage are reviewed.

Chinese Culture,Classical Philosophy,and the Cultivation of Life

This paper explores the intricate relationship between Chinese culture and the nation’s rise,emphasizing the indispensable role of cultural education in fostering a robust national spirit and civilization.Drawing from classical Chinese texts and contemporary philosophical insights,the study examines how cultural virtues and educational practices can lead to societal harmony,national rejuvenation,and global contributions.The analysis highlights the enduring relevance of Confucian principles and their potential to address modern challenges,advocating for a renewed focus on cultural education to achieve a prosperous and peaceful world.Additionally,it underscores the necessity of integrating traditional values with modern educational practices to create a holistic approach that fosters ethical leadership and global cooperation.

Comparative Analysis of Differences among Northern,Jiangnan,and Lingnan Classical Private Gardens Using Principal Component Cluster Method

This paper investigates the design essence of Chinese classical private gardens,integrating their design elements and fundamental principles.It systematically analyzes the unique characteristics and differences among classical private gardens in the Northern,Jiangnan,and Lingnan regions.The study examines nine classical private gardens from Northern China,Jiangnan,and Lingnan by utilizing the advanced tool of principal component cluster analysis.Based on literature analysis and field research,273 variables were selected for principal component analysis,from which four components with higher contribution rates were chosen for further study.Subsequently,we employed clustering analysis techniques to compare the differences among the three types of gardens.The results reveal that the first principal component effectively highlights the differences between Jiangnan and Lingnan private gardens.The second principal component serves as the key to defining the types of Northern private gardens and distinguishing them from the other two types,and the third principal component indicates that Lingnan private gardens can be categorized into two distinct types as well.

Research on the Progress of Treating Gastroesophageal Reflux Disease with Modified Classic Traditional Chinese Medicine Prescription

Gastroesophageal reflux disease (GERD) is a high-incidence digestive system disease. Western medicine mainly uses drugs such as proton pump inhibitors to inhibit gastric acid secretion, but some patients are accompanied by symptoms such as non-acid reflux and gas reflux, which cannot effectively treat the disease. It is necessary to actively explore other treatment schemes. Traditional Chinese medicine (TCM) has a long history of research on gastroesophageal reflux disease, which emphasizes the treatment based on syndrome differentiation as a whole. Through the treatment of various and multi-component TCM prescriptions, the patient’s body condition can be adjusted, and the treatment effect on gastroesophageal reflux disease is reliable, which has obvious therapeutic advantages. To further clarify the treatment of gastroesophageal reflux disease, this study reviewed and analyzed the research progress of the treatment of liver disease with modified prescriptions, and the report is as follows.

Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

Deep Learning Applied to Computational Mechanics:A Comprehensive Review,State of the Art,and the Classics

Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.

Reflections on Studying Huang Di Nei Jing in the West

Huang Di Nei Jing(《黄帝内经》The Yellow Emperor’s Inner Classic) has been the source text of Chinese medicine knowledge and innovation for over two thousand years. Despite this key relevance, many of its ideas and practices have proven difficult to understand and implement fully into clinical practice. Cultural and language differences can be compounded with these challenges but may also present new opportunities for advancement and insight when studied by researchers outside of the originating culture. This article introduces the method of Classical-Text Archaeology and delves into the author’s two-decade journey of researching this text, with a discussion on cultural differences and issues of medical scholarship.

The Art of The Ages

Ethiopian artist presents the 64 characters of the ancient Chinese classic divination text the I Ching in a series of unique paintings Dawit Muluneh,50,found his calling for painting and sculpture at an early age.Born and raised in Ethiopia’s capital Addis Ababa,he abandoned the playground and became obsessed with watching his uncle paint.

The Silent Curriculum:Classical Aesthetics as a Catalyst for Emotional and Social Skills in Higher Vocational Education

This study examines the integration of classical aesthetics into the silent curriculum of higher vocational education,emphasizing its potential to significantly enhance emotional and social skills.Incorporating aesthetic principles into education emphasizes the importance of nurturing emotional intelligence,creativity,and cultural awareness in students-skills that go beyond the classroom and are essential for their growth,adaptability,and future careers.It explores theoretical foundations and practical implementations and addresses challenges such as the need for specialized educator training,overcoming institutional resistance,and securing adequate resources.Advocating for empirical research and strategic cultural partnerships,the paper proposes a transformative approach to vocational education,aligning it with contemporary societal and labor market demands,and underscores the vital role of classical aesthetics in enriching vocational training and enhancing student outcomes.

Global Existence of Smooth Solutions for the One-Dimensional Full Euler System for a Dusty Gas

We study the existence of global-in-time classical solutions for the one-dimensional nonisentropic compressible Euler system for a dusty gas with large initial data.Using the characteristic decomposition method proposed by Li et al.(Commun Math Phys 267:1–12,2006),we derive a group of characteristic decompositions for the system.Using these characteristic decompositions,we find a sufficient condition on the initial data to ensure the existence of global-in-time classical solutions.

Reception of Translated Classics of Traditional Chinese Medicine in the Spanish-speaking World:A Survey of Seven Spanish Versions of Huangdi Neijing(The Yellow Emperor’s Inner Classic)

Previous studies on translations of Huangdi Neijing(The Yellow Emperor’s Inner Classic)have focused on English versions;little attention has been given to non-English translations.The present study is the first investigation of the reception of the seven Spanish versions of Huangdi Neijing in terms of three parameters:collection records in libraries worldwide;book reviews and citation counts in international journals;and customer reviews on Amazon.The results revealed four features of Spanish translations and communication of Huangdi Neijing in terms of reception of academia,reception of general readers,the center of translation and communication,and the role of Chinese scholars.These factors demonstrate the marginal status of Spanish translations of traditional Chinese medicine(TCM)classics.The implications are summarized in hopes of promoting the translation and communication of TCM classics in the Spanish-speaking world and to provide insights into the communication of TCM culture in the non-English-speaking world.

GLOBAL CLASSICAL SOLUTIONS AND THE CLASSICAL LIMIT OF THE NON-RELATIVISTIC VLASOV-DARWIN SYSTEM WITH SMALL INITIAL DATA

We investigate the global classical solutions of the non-relativistic Vlasov-D arwin system with generalized variables(VDG)in three dimensions.We first prove the global existence and uniqueness for small initial data and derive the decay estimates of the Darwin potentials.Then,we show in this framework that the solutions converge in a pointwise sense to solutions of the classical Vlasov-Poisson system(VP)at the asymptotic rate of 1/c2 as the speed of light c tends to infinity for all time.Moreover,we obtain rigorously an asymptotic estimate of the difference between the two systems.

POSITIVE CLASSICAL SOLUTIONS OF DIRICHLET PROBLEM FOR THE STEADY RELATIVISTIC HEAT EQUATION

In this paper,for a bounded C2 domain,we prove the existence and uniqueness of positive classical solutions to the Dirichlet problem for the steady relativistic heat equation with a class of restricted positive C2 boundary data.We have a non-existence result,which is the justification for taking into account the restricted boundary data.There is a smooth positive boundary datum that precludes the existence of the positive classical solution.

Translation Principles of Chinese Ethnic Minority Classics:A Case Study on the English Translation of Yimakan Mandu Mergen

Different translation principles may result in different translation products Chinese and foreign scholars put forward a lot of insightful and perceptive views on translation principles based on their plentiful translation practice.Taken the Hezhe Peo ple’s oral tradition Yimakan Mandu Mergen as an example,the paper probes into the English translation principles and strategies of Chinese ethnic minority classics.

On the Mean Value of High-Powers of a Special Character Sum Modulo a Prime

In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.