Innovation Transformation and Industry-Education Integration:A Study on the Integration Path of Guangxi Zhuang’s Intangible Cultural Heritage and Master of Arts Education in China

This study focuses on the master of arts education in higher education institutions in Guangxi Zhuang Autonomous Region of China,explores the path of integrating Guangxi Zhuang’s intangible cultural heritage with the teaching of master of arts,and puts forward the teaching mode of“thinking guidance-autonomous judgement-program construction.”A theoretical model of innovative transformation of intangible cultural heritage is also summarized.Through the development of this study,it is expected to further enrich the practical teaching mechanism of master of arts education in Chinese universities and form a master of arts teaching model with strong local cultural characteristics.At the same time,the teaching reform based on the integration of Guangxi Zhuang’s intangible cultural heritage and master of arts education also has strong practical significance for promoting the inheritance and innovation of Chinese intangible cultural heritage,promoting the development of cultural and creative industries,and serving the economic and social development of Guangxi.

Research on the Integration Path of Taihang Spirit and Music Education Major in Colleges and Universities

A key strategy for raising students’humanistic aptitude is through music education.Culture is the soul of music and the source of innovation in music education.Under the current social education concept,it is advocated to carry forward excellent traditional and red culture in teaching,hence this paper further explores the path of integrating red culture into music education.The incorporation of the Taihang spirit,the most representative cultural resource in Shanxi,into music education in colleges and universities will promote the concept of Lide Shuren,further enhance students’training,and enable students to fulfill the dual education requirements.

Feynman Path Integral Using Operator Integration in Banach Space

Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.

Path integral solutions for n-dimensional stochastic differential equations underα-stable Lévy excitation

In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic processes.Then,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov equation.Besides,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.

Path Integral Quantization of Non-Natural Lagrangian

Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.

PATH INTEGRAL SOLUTION OF NONLINEAR DYNAMIC BEHAVIOR OF STRUCTURE UNDER WIND EXCITATION

A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito＇ s stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted. Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and effectiveness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.

Integrated P-T Paths of the High-Pressure Rocks and Their Tectonic Implications for the Mountain-Building of the North Qilian, China

After the integration of petrographic study, geothermobarometry and Gibbs method, the synthetic P-T paths for the rocks from different geological profiles in the North Qilian, China, have been derived. The composite P-T paths from different methods indicate that all the high-pressure rocks in the Qilian area recorded P-T paths with clockwise loops starting at the blueschist facies, later reaching peak metamorphism at the blueschist facies, eclogite fades or epidote-amphibolite facies and ending up with the greenschist facies. The incremental Ar-Ar dating shows that the plateau ages for the high-pressure rocks range from 410 to 443 Ma. The plateau ages could be used as a minimum age constraint for the subduction that resulted in the formation of these high-pressure rocks in the Qilian area. It is proposed that the late-stage decompressional and cooling P-T paths with ends at the greenschist facies for these high-pressure rocks probably reflect the uplift process which could occur after shifting the arc-trench tectonic system to the system of continental orogenic belts. The retrograde paths for the high-pressure rocks in the North Qilian tectonic belt are characterized by dramatic decompression with slight cooling, which suggests very rapid exhumation. Petrography supports that the mountain-building for the Qilian mountain range could undergo a very fast process which caused rapid uplift and denudation.

Unified treatment of the bound states of the Schioberg and the Eckart potentials using Feynman path integral approach

We obtain analytical expressions for the energy eigenvalues of both the Schioberg and Eckart potentials using an approximation of the centrifugal term. In order to determine the l-states solutions, we use the Feynman path integral approach to quantum mechanics. We show that by performing nonlinear space-time transformations in the radial path integral, we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system. The explicit expression of bound state energy is obtained and the associated eigenfunctions are given in terms of hypergeometric functions. We show that the Eckart potential can be derived from the Schioberg potential. The obtained results are compared to those produced by other methods and are found to be consistent.

Generalized path-integral solution and coherent states of the harmonic oscillator in D-dimensions

We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.

Effect of a force-free end on the mechanical property of a biopolymer--A path integral approach

We study the effect of a force-free end on the mechanical property of a stretched biopolymer.The system can be divided into two parts.The first part consists of the segment counted from the fixed point（i.e.,the origin） to the forced point in the biopolymer,with arclength L_f.The second part consists of the segment counted from the forced point to the force-free end with arclength △L.We apply the path integral technique to find the relationship between these two parts.At finite temperature and without any constraint at the end,we show exactly that if we focus on the quantities related to the first part,then we can ignore the second part completely.Monte Carlo simulation confirms this conclusion.In contrast,the effect for the quantities related to the second part is dependent on what we want to observe.A force-free end has little effect on the relative extension,but it affects seriously the value of the end-to-end distance if △L is comparable to L_f.

Establishing path integral in the entangled state representation for Hamiltonians in quantum optics

Based on two mutually conjugate entangled state representations, we establish the path integral formalism for some Hamiltonians of quantum optics in entangled state representations. The Wigner operator in the entangled state representation is presented. Its advantages are explained.

Path integral approach to electron scattering in classical electromagnetic potential

As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential.

Thermodynamic Parameters of Central Spin Coupled to an Antiferromagnetic Bath: Path Integral Formalism

A path-integral representation of central spin system immersed in an antiferromagnetic environment was investigated. To carry out this study, we made use of the discrete-time propagator method associated with a basic set involving coherent states of Grassmann variables which made it possible to obtain the analytical propagator which is the centerpiece of the study. In this study, we considered that the environment was in the low-temperature and low-excitation limit and was split into 2 subnets that do not interact with each other. The evaluation of our system was made by considering the first neighbor approximation. From the formalism of the path integrals, it is easy to evaluate the partition function and thermodynamic properties followed from an appropriate tracing over Grassmann variables in the imaginary time domain. We show that the energy of the system depends on the number of sites n when β → 0.

Path Integral Molecular Dynamics Simulation on Atomic Distribution in Amorphized Ice Ic

We have investigated the effects of compression and quantization on atomic distribution in ice Ic and in its compressed states at 77 K and 10 K, using the path integral molecular dynamics (PIMD) simulations over wide range of volume. It has been found that the high density amorphous ice (HDA) is attained by compression but volume range to retain ice structure is wider at 10 K than 77 K. We have discovered that quantum dispersion of atoms in ice Ic at 10 K induces non-zero probability that hydrogen-bonded H2O molecular molecules are oriented nonlinearly in the crystal structure, which was believed to contain exclusively linear orientation of hydrogen-bonded molecular pairs in this ice. It has been found that for HDA there is each non-zero probability of orientational disorder of hydrogen-bonded H2O pairs, of such uniform distribution of H atoms as observed in supercritical fluids in general, and of H atoms located at the O-O midpoint. The present PIMD simulations have revealed that these observed anomalous characteristics of atomic distribution in HDA are caused by both quantization of atoms and compression of the system.

Fuzzification of Feynman Path Integral and Its Effect on Field Theory and Quantum Gravity—Reformation and Redevelopment of Quantum Theory

The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory reforms quantum mechanics, making the later become its special case. This theory breaks unitarity, gauge invariance, probability conservation and information conservation, making these principles become approximate ones under certain conditions. This new theory, which needs no renormalization and can naturally give meaningful results which are in accordance with the experiments, is the proper theory to describe microscopic high-speed phenomenon, whereas quantum mechanics is only a proper theory to describe microscopic low-speed phenomenon. This theory is not divergent under the condition of there being no renormalization and infinitely many offsetting terms, thereby it can become the theoretical framework required for the quantization of gravity.

Path integral Monte Carlo study of(H_2)_n@C_(70)(n = 1, 2, 3)

The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.

On the Verification of the Multiverse

We outline a proposal for an experimental test of Everett’s many-worlds interpretation of quantum mechanics that could potentially verify the existence of a multiverse. This proposal is based on a quantum field theory formulation of many-worlds through the path integral formalism and a careful choice of the vacuum state.

On the Exceedance Probabilities of Extreme Drift Motions of An Offshore Structure

The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method. The path integral solution is based on the Ganss-Legendre interpolation scheme, and the values of the response probability density are obtained at the Gauss quadrature points in sub-intervals. It is demonstrated that a distinct advantage of the path integral solution is that the joint probability density of the response displacement and velocity is one of the by products of the calculations. This makes it possible to calculate the mean level up-crossing rates, which provides estimates of the exceedance probabilities of specified response levels for given time periods.

Second-order interference of two independent and tunable single-mode continuous-wave lasers

The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by em- ploying two-photon interference in Feynman＇s path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra.

Cognitive Supervisor for an Autonomous Swarm of Robots

As a sequel to our recent work [1], in which a control framework was developed for large-scale joint swarms of unmanned ground (UGV) and aerial (UAV) vehicles, the present paper proposes cognitive and meta-cognitive supervisor models for this kind of distributed robotic system. The cognitive supervisor model is a formalization of the recently Nobel-awarded research in brain science on mammalian and human path integration and navigation, performed by the hippocampus. This is formalized here as an adaptive Hamiltonian path integral, and efficiently simulated for implementation on robotic vehicles as a pair of coupled nonlinear Schr?dinger equations. The meta-cognitive supervisor model is a modal logic of actions and plans that hinges on a weak causality relation that specifies when atoms may change their values without specifying that they must change. This relatively simple logic is decidable yet sufficiently expressive to support the level of inference needed in our application. The atoms and action primitives of the logic framework also provide a straight-forward way of connecting the meta-cognitive supervisor with the cognitive supervisor, with other modules, and to the meta-cognitive supervisors of other robotic platforms in the swarm.