A unified intrinsic functional expansion theory for solitary waves

A new theory is developed here for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120 down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokess formula, F2= tan , relating the wave speed (the Froude number F) and the logarithmic decrement of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokess basic term (singular in ), such that 2M is just somewhat beyond unity, i.e. 2M1. This fundamental criterion is fully validated by solutions for waves of various amplitude-to-water depth ratio =a/h, especially about 0.01, at which M=10 by the criterion. In this pursuit, the class of dwarf solitary waves, defined for waves with 0.01, is discovered as a group of problems more challenging than even the highest wave. For the highest wave, a new solution is determined here to give the maximum height hst=0.8331990, and speed Fhst=1.290890, accurate to the last significant figure, which seems to be a new record.

A Study of Planetary Theory in the Great Expansion System(Dayan li大衍历,727 CE):The Case of Mars

The planetary theory in the Great Expansion System(Dayan li大衍历,727 CE)is investigated,with a detailed example of Mars.In ancient Chinese astrology,the position of one planet and the relative positions of different planets had important astrological significance.Thus,planetary theory is an important part of Chinese mathematical astronomy.The Great Expansion System,which was compiled by Yixing一行of the Tang唐dynasty(618–907 CE),provided many innovations in planetary theory.Based on the extant Treatises on Mathematical Harmonics and Astronomy(Lüli zhi律历志)in Chinese official histories,the Great Expansion System was the first Chinese astronomical system to include tables of the planetary equation of center and procedures for correcting the influence of the planetary equation of center on the position of a planet.It was also the first Chinese system to design a table of the planetary phases of motion for calculating the mean position of a planet,which was the basis for calculating the true position of the planet.In addition,Yixing proposed the concept of the precession of planetary perihelion and gave the values of the precession of planetary perihelion for the first time in ancient China.The innovations of the Great Expansion System regarding planetary theory established its important position in the history of Chinese astronomical systems.Mars is taken as a case study to investigate the planetary theory in the Great Expansion System,including the astronomical constants related to Mars,two important astronomical tables,namely the table of the equation of center and the table of the phase motion of Mars in one synodic period,and the procedures for calculating the position of Mars on any given day using the planetary and solar equations of center.Two questions are addressed.First,how did Yixing correct the influence of the equation of center of Mars on the time of mean conjunction and the mean position of Mars?Second,how did Yixing calculate the true position of Mars on any given day?The original text of the Great Expansion System is analyzed to show how Yixing developed the planetary theory in the Sui and early Tang periods and constructed a complete method for predicting the true positions of planets using the planetary and solar equations of center.

Anisotropy of Thermal-expansion for β-Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine： Quantum Chemistry Calculation and Molecular Dynamics Simulation

Molecular dynamics simulations on octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine （HMX） at 303-383 K and atmospheric pressure are carried out under NPT ensemble and COMPASS force field, the equilibrium structures at elevated temperatures were obtained and showed that the stacking style of molecules don＇t change. The coefficient of thermal expansion （CTE） values were calculated by linear fitting method. The results show that the CTE values are close to the experimental results and show anisotropy. The total energies of HMX cells with separately increasing expansion rates （100%-105%） along each crystallographic axis was calculated by periodic density functional theory method, the results of the energy change rates are anisotropic, and the correlation equations of energy change-CTE values are established. Thus the hypostasis of the anisotropy of HMX crystal＇s thermal expansion, the determinate molecular packing style, is elucidated.

Application of Multi-agent Models to Urban Expansion in Medium and Small Cities: A Case Study in Fuyang City,Zhejiang Province,China

In this study, three-phase satellite images were used to define rules for the allocation of time and space in construction land resources based on a complex adaptive system and game theory. The decision behavior and rules of government agent, enterprise agent and resident agent in construction land growth were explored. A distinctive and dynamic simulation model of construction land growth was built, which integrated multi-agent, GIS technology and RS data and described the interaction among influencing agents, Taking Fuyang City in the Changjiang River Delta as an example, an assessment process for the remote sensing data in construction land and scenario planning was constructed. Repast and ArcGIS were used as simulation platforms. A simulation of the spatial pattern in land-use planning and the setting of scenario planning were conducted by using the incomplete active game, which was based on different natural, social and economic levels. Through this model, a simulation of urban planning space and decision-making for Fuyang City was created. Relevant non-structured problems arising from urban planning management could be identified, and the process and logic of urban planning spatial decision-making could thus be improved. Cell-by-cell comparison showed that the simulation accuracy was over 72%. This model has great potential for use by government and town planners in decision support and technique support in the policy-making process.

Thermal Expansion Coefficients of Thin Crystal Films

The formulas for atomic displacements and Hamiltonian of a thin crystal film in phonon occupation number representation are obtained with the aid of Green's function theory. On the basis of these results, the formulas for thermal expansion coefficients of the thin crystal film are derived with the perturbation theory, and the numerical calculations are carried out. The results show that the thinner films have larger thermal expansion coefficients.

Mean-field and high temperature series expansion calculations of some magnetic properties of Ising and XY antiferromagnetic thin-films

In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers （n = 2, 3, 4, 5, 6, and bulk （∞） by means of a mean-field and high temperature series expansion （HTSE） combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff （mean）, ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk （∞）.

Expansion of spherical cavity of strain-softening materials with different elastic moduli of tension and compression

An expansion theory of spherical cavities in strain-softening materials with different moduli of tension and com-pression was presented. For geomaterials,two controlling parameters were introduced to take into account the different moduli and strain-softening properties. By means of elastic theory with different moduli and stress-softening models,general solutions cal-culating Tresca and Mohr-Coulomb materials' stress and displacement fields of expansion of spherical cavity were derived. The effects caused by different elastic moduli in tensile and compression and strain-softening rates on stress and displacement fields and development of plastic zone of expansion of cavity were analyzed. The results show that the ultimate expansion pressure,stress and displacement fields and development of plastic zone vary with the different elastic moduli and strain-softening prop-erties. If classical elastic theory is adopted and strain-softening properties are neglected,rather large errors may be the result.

On a Quantum Gravity Fractal Spacetime Equation: QRG ≃HD + FG and Its Application to Dark Energy—Accelerated Cosmic Expansion

The paper suggests that quantum relativistic gravity (QRG) is basically a higher dimensionality (HD) simulating relativity and non-classical effects plus a fractal Cantorian spacetime geometry (FG) simulating quantum mechanics. This more than just a conceptual equation is illustrated by integer approximation and an exact solution of the dark energy density behind cosmic expansion.

From Witten’s 462 Supercharges of 5-D Branes in Eleven Dimensions to the 95.5 Percent Cosmic Dark Energy Density behind the Accelerated Expansion of the Universe

The measured 95.5% dark energy density of the cosmos presumed to be behind the observed accelerated cosmic expansion is determined theoretically based upon Witten’s five branes in eleven dimensions theory. We show that the said dark energy density is easily found from the ratio of the 462 states of the five dimensional Branes to the total number of states, namely 528 minus the 44 degrees of freedom of the vacuum, i.e. , almost exactly as found in WMAP and Type 1a supernova measurements.

Accelerating Expansion in a Closed Universe

In this paper, I suggest a possible explanation for the accelerating expansion of the universe. This model does not require any dark energy or quintessence. Rather, the idea is to suggest a different view on the origin of general relativity. Since it is very difficult to say something in general, I will mainly restrict myself to the case of very low curvature. The question about the underlying reasons for the acceleration is also closely related to the question whether the universe is a finite or infinite. It is part of the purpose of this paper to argue that a phase of accelerating expansion may be very well compatible with the idea of a closed universe.

Cosmological Inconstant, Supernovae 1a and Decelerating Expansion

In 1998, two groups of astronomers, one led by Saul Perlmutter and the other by Brian Schmidt, set out to determine the deceleration—and hence the total mass/energy—of the universe by measuring the recession speeds of type la supernovae (SN1a), came to an unexpected conclusion: ever since the universe was about 7 billion years old, its expansion rate has not been decelerating. Instead, the expansion rate has been speeding up. To justify this acceleration, they suggested that the universe does have a mysterious dark energy and they have emerged from oblivion the cosmological constant, positive this time, which is consistent with the image of an inflationary universe. To explain the observed dimming of high-redshift SN1a they have bet essentially on their distance revised upwards. We consider that an accelerated expansion leads right to a “dark energy catastrophe” (i.e., the chasm between the current cosmological vacuum density value of 10 GeV/m3 and the vacuum energy density proposed by quantum field theory of ~10122 GeV/m3). We suppose rather that the universe knows a slowdown expansion under the positive pressure of a dark energy, otherwise called a variable cosmological constant. The dark luminosity of the latter would be that of a “tired light” which has lost energy with distance. As for the low brilliance of SN1a, it is explained by two physical processes: The first relates to their intrinsic brightness—supposedly do not vary over time—which would depend on the chemical conditions which change with the temporal evolution;the second would concern their apparent luminosity. Besides the serious arguments already known, we strongly propose that their luminosity continually fades by interactions with cosmic magnetic fields, like the earthly PVLAS experiment which loses much more laser photons than expected by crossing a magnetic field. It goes in the sense of a “tired light” which has lost energy with distance, and therefore, a decelerated expansion of the universe. Moreover, we propose the “centrist” principle to complete the hypothesis of the cosmological principle of homogeneity and isotropy considered verified. Without denying the Copernican principle, he is opposed to a “spatial” theoretical construction which accelerates the world towards infinity. The centrist principle gives a “temporal” and privileged vision which tends to demonstrate the deceleration of expansion.

Assessing the range of blasting-induced cracks in the surrounding rock of deeply buried tunnels based on the unified strength theory

Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-induced cracks often ignore the impact of the in-situ stress,especially that of the intermediate principal stress.The particle displacement−crack radius relationship was established in this paper by utilizing the blasthole cavity expansion equation,and theoretical analytical formulas of the stress−displacement relationship and the crack radius were derived with unified strength theory to accurately assess the range of cracks in deep surrounding rock under a blasting load.Parameter analysis showed that the crushing zone size was positively correlated with in-situ stress,intermediate principal stress,and detonation pressure,whereas negatively correlated with Poisson ratio and decoupling coefficient.The dilatancy angle-crushing zone size relationship exhibited nonmonotonic behavior.The relationships in the crushing zone and the fracture zone exhibited opposite trends under the influence of only in-situ stress or intermediate principal stress.As the in-situ stress increased from 0 to 70 MPa,the rate of change in the crack range and the attenuation rate of the peak vibration velocity gradually slowed.

The “Dead Universe” Theory: Natural Separation of Galaxies Driven by the Remnants of a Supermassive Dead Universe

This article explores the dead universe theory as a novel interpretation for the origin and evolution of the universe, suggesting that our cosmos may have originated from the remnants of a preceding universe. This perspective challenges the conventional Big Bang theory, particularly concerning dark matter, the expansion of the universe, and the interpretation of phenomena such as gravitational waves.

协同理论视域下应用型高校产教融合拓展机理研究

分析产教融合的拓展机理,对于破解产教融合存在的问题,构建产教融合发展的长效机制具有重要意义。协同理论和产教融合具有较高的适切性,可以明确产教融合实施主体的主要责任和义务,可以规定产教融合实施过程中的利益分配情况,可以描绘产教融合的运行状态。文章分析了产教融合的现实困境,并以人才培养交流为产教融合的耦合点,详细说明了产教融合的纵向拓展机理及发展对策。在此基础上,文章分析了从人才培养交流向产教融合研发的横向拓展机理及策略,最终构建了一点深入、由点到线、由线到面的产教融合发展新机制,研究成果可为产教融合的进一步深化提供借鉴。

汉语网络语言“特种兵式XX”构式的构式语法分析

“特种兵式旅游”是2023年“十大流行语”和“十大网络用语”之一。Goldberg的认知构式语法理论被用作探究分析由“特种兵式旅游”发展而成的“特种兵式XX”构式的形式语义特征及其形成扩展机制。研究发现:(1)“特种兵式XX”组成成分包含常量“特种兵式”和变量“XX”,主要是借用特种兵执行特殊任务、超强体力等特征标榜出变量“XX”的一种新型形式。(2)此构式呈现以“特种兵式+双音节动词”为主的习语化特征。(3)此构式的中心意义为紧凑高效地完成“XX”行为,具有低成本、高效率、高强度的典型特征。(4)此构式的形成和扩展主要依赖大脑的记忆机制以及次范畴化和隐喻机制。

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

On a Fractal Version of Witten’s M-Theory

Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine the measured ordinary energy density of the cosmos which turns out to be intimately linked to the new theory’s fractal dimension via non-integer irrational Lorentzian-like factor: where is Hardy’s probability of quantum entanglement. Consequently, the energy density is found from a limiting classical kinetic energy to be Here, is ‘tHooft’s renormalon of dimensional regularization. The immediate logical, mathematical and physical implication of this result is that the dark energy density of the cosmos must be in astounding agreement with cosmic measurements and observations.

On the Ettringito Form of Sulfate Attack: Part 2. The Expansive Mechanism of Concrete Caused by Secondary Ettringite

In part 1 of this two-part series, the formation mechanism of secondary ettringite has been discussed. In this part, the expansive mechanisms of secondary ettringite due to the ettringite form of sulfate attack were reviewed and analyzed. Three theories have been proposed for explaining the expansive mechanism of secondary ettringite, that is, the crystallization pressure theory (or the crystal growth theory), the theory increasing in solid volume and the swelling theory. According to the analysis, swelling theory should be responsible for the expansion of secondary ettringite. The experimental results also verified that the expansion, subsequent the cracking and spalling of concrete can be caused by the swelling of fine ettringite particles formed at the interface zone of coarse aggregate particles.

The Theory of Relativity on the Finsler Spacetime

According to some local properties of Lorentz transformation, Einstein stated: 'Vetheitiss greater than that of light have no possibility of existence.' He neglected to point out the applicable range of the special theory of relativity. In fact, it could only be applied to the subluminal-speeds. This paper shows that if ones think of the possibility of the existence of the superluminal-speeds and redescribe the special theory of relativity following Einstein's way, it could be supposed that the physical spacetime is a Finsler spacetime, characterized by the metric ds4=gijkldxidxidxkdxl. If so, a new spactime transformation could be found by invariant ds4 and the theory of relativity is discussed on this transformation it is possible that the Finsler spacetime F(x,y) may be endowed with a catastrophic nature. Based on the different properties between the ds2 and ds4, it is discussed that the flat spacetime will also have the catastrophic nature on the Finsler metric ds4. The spacetime transformations and the Physical quantities will suddenly change at the catastrophe set of the spacetime, the light cone. It will be supposed that only the dual velocity of the superluminal-speeds could be observed. If so, a particle with the superluminal-speed v> c could be regarded as its anti-particle with the dual velocity v1=c2/ v< c. On the other hand, it could be assumed that the horizon of the field of the general relativity is also a catastrophic set. If so, a particle with the superluminal-speeds could be projected near the horizon of these fields, and the particle will move on the sauce-like curves. It is very interesting that, in the Schwarzschild fields, the theoretical calculation for the sauce-like curves should be in agreement with tie data of the superluminal expansion of extragalactic radio sources observed year after year. (see Gao, 1992b).The ca- tastrophe of spacetime has some deep cosmological means. According to the some interested subjects in the Process of evolution of the universe the catastrophe nature of the Finsler spacetime and its cosmological impli= cations are discussed. It is shown that the nature of the universal evolution could be attributed to the geometric features of the Finsler spacetime. (see Cao, 1993)

Cosmological applications in Kaluza-Klein theory

The field equations of Kaluz-Klein （KK） theory have been applied in the domain of cosmology. These equations are solved for a fiat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor＇s expansion of cosmological function, A（t）, up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.