Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

Study on Transformation of Ideas of Environmental Protection Administration and Construction of Ecological Civilization in China

The transformation process of ideas of environmental protection administration in China was introduced firstly,and then the connotation and construction of ecological civilization were analyzed.

New two-fold integration transformation for the Wigner operator in phase space quantum mechanics and its relation to operator ordering

Using the Weyl ordering of operators expansion formula （Hong-Yi Fan, J. Phys.A 25 （1992） 3443） this paper finds a kind of two-fold integration transformation about the Wigner operator △（ q＇,p） q-number transform） in phase space quantum mechanics,∫∫∞-∞dp＇dq＇/π △（q＇,p＇）e-2i（ p-p＇）（ q-q＇）=δ（ p-P）δ（ q-Q）,∫∫∞-∞dqdpδ（p-P）δ（q-Q）e2i（p-p＇）（q-q＇）=△（q＇,p＇）,whereQ,P are the coordinate and momentum operators, respectively. We apply it to study mutual converting formulae among Q-P ordering, P-Q ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched. The formula of the Weyl ordering of operators expansion and the technique of integration within the Weyl ordered product of operators are used in this discussion.

A New Kind of Two-Fold Integration Transformation in Phase Space and Its Uses in Weyl Ordering of Operators

We propose a new two-fold integration transformation in p-q phase space∫∫_(-∞)~∞ (dqdq/π) e^(2i(p-x)(q-y))f(p,q)2≡G(x,y),which possesses some well-behaved transformation properties.We apply this transformation to the Weyl ordering ofoperators,especially those Q-P ordered and P-Q ordered operators.

THE INTEGRAL TYPE GAUGE TRANSFORMATION AND THE ADDITIONAL SYMMETRY FOR THE CONSTRAINED KP HIERARCHY

In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.

A complementary integrated Transformer network for hyperspectral image classification

In the past,convolutional neural network(CNN)has become one of the most popular deep learning frameworks,and has been widely used in Hyperspectral image classification tasks.Convolution(Conv)in CNN uses filter weights to extract features in local receiving domain,and the weight parameters are shared globally,which more focus on the highfrequency information of the image.Different from Conv,Transformer can obtain the long‐term dependence between long‐distance features through modelling,and adaptively focus on different regions.In addition,Transformer is considered as a low‐pass filter,which more focuses on the low‐frequency information of the image.Considering the complementary characteristics of Conv and Transformer,the two modes can be integrated for full feature extraction.In addition,the most important image features correspond to the discrimination region,while the secondary image features represent important but easily ignored regions,which are also conducive to the classification of HSIs.In this study,a complementary integrated Transformer network(CITNet)for hyperspectral image classification is proposed.Firstly,three‐dimensional convolution(Conv3D)and two‐dimensional convolution(Conv2D)are utilised to extract the shallow semantic information of the image.In order to enhance the secondary features,a channel Gaussian modulation attention module is proposed,which is embedded between Conv3D and Conv2D.This module can not only enhance secondary features,but suppress the most important and least important features.Then,considering the different and complementary characteristics of Conv and Transformer,a complementary integrated Transformer module is designed.Finally,through a large number of experiments,this study evaluates the classification performance of CITNet and several state‐of‐the‐art networks on five common datasets.The experimental results show that compared with these classification networks,CITNet can provide better classification performance.

Radar fast long-time coherent integration via TR-SKT and robust sparse FRFT

Long-time coherent integration(LTCI)is an effective way for radar maneuvering target detection,but it faces the problem of a large number of search parameters and large amount of calculation.Realizing the simultaneous compensation of the range and Doppler migrations in complex clutter back-ground,and at the same time improving the calculation efficiency has become an urgent problem to be solved.The sparse transformation theory is introduced to LTCI in this paper,and a non-parametric searching sparse LTCI(SLTCI)based maneuvering target detection method is proposed.This method performs time reversal(TR)and second-order Keystone transform(SKT)in the range frequency&slow-time data to complete high-order range walk compensation,and achieves the coherent integra-tion of maneuvering target across range and Doppler units via the robust sparse fractional Fourier transform(RSFRFT).It can compensate for the nonlinear range migration caused by high-order motion.S-band and X-band radar data measured in sea clutter background are used to verify the detection performance of the proposed method,which can achieve better detection performance of maneuvering targets with less computational burden compared with several popular integration methods.

Thinking about Value Realization of Ecological Products under the Background of Urban-rural Integration in Chengdu“Western Control”Area

Chengdu's development strategy of“western control”has laid a solid ecological background for 8 western districts,cities and counties and cultivated good ecological resources.The integrated urban-rural development in the new era will realize the balanced development of urban and rural areas and give full play to the value of rural ecological resources through the“powerful combination”of urban and rural areas.To realize the urban-rural integration and high-quality rural development in Chengdu“western control”area,it is necessary to enhance the awareness of ecological resources and ecological products,and carry out unified planning of ecological infrastructure,ecological material products and ecological service products in the whole“western control”area.Meantime,ecological restoration must be carried out scientifically,and scene design for value transformation of ecological products should be implemented innovatively.

Practice and Exploration of Xijiang for the Deep Integration of Intangible Cultural Heritage and Tourism Development

The development of Intangible Cultural Heritage tourism in Xijiang Qianhu Miao Village has gone through a long process of exploration and innovation from scratch.By reinforcing the protection of the"Intangible Cultural Heritage"stilted building of the Miao Village,doing a good job with the"Intangible Cultural Heritage+"concept,and constantly innovating the inheritance and protection of Intangible Cultural Heritage,the rich Miao culture of Xijiang Qianhu Miao Village has been gradually transformed from a primitive traditional living custom to a productive tool for economic development,which has strongly promoted the high-quality development of the Miao cultural tourism industry.

FTransCNN:基于模糊融合的Transformer-CNN不确定性医学图像分割模型

准确的医学图像分割对于疾病的诊断和治疗至关重要,将多个模型提取的分割特征进行联合使用时存在异质性、不确定性等问题,针对这一问题,本文提出了一种基于模糊融合策略的Transformer-CNN模型(FTransCNN).首先以CNN和Transformer作为骨干网络,并行提取图片的特征信息;其次使用通道注意力促进Transformer全局关键信息,使用空间注意力增强CNN特征局部细节;接着应用Hadamard乘积对来自两个分支特征之间的细粒度交互进行建模,用Choquet模糊积分抑制融合特征的异质性以及融合特征的不确定性;然后使用Fuzzy Attention Fusion Module(FAFM)分级上采样,有效地捕获低级空间特征和高级语义上下文;最后反卷积得到最终的分割结果.在Chest X-ray数据集、Kvasir-SEG数据集和DRIVE数据集上的实验效果表明,FTransCNN与其它深度分割模型相比,在分割任务上有更好的效果.

A FAMILY OF INTEGRABLE SYSTEMS OF LIOUVILLE AND LAX REPRESENTATION, DARBOUX TRANSFORMATIONS FOR ITS CONSTRAINED FLOWS

A family of integrable systems of Liouville are obtained by, Tu pattern. Using higher-order potential-eigenfunction constraints, the integrable systems are factorized to two x- and t(n)-integrable Hamiltonian systems whose Lax representation and three kinds of Darboux transformations are presented.

MATHEMATICAL PROBLEMS IN THE INTEGRAL-TRANSFORMATION METHOD OF DYNAMIC CRACK

In the investigation on fracture mechanics,the potential function was introduced, and the moving differential equation was constructed. By making Laplace and Fourier transformation as well as sine and cosine transformation to moving differential equations and various responses, the dual equation which is constructed from boundary conditions lastly was solved. This method of investigating dynamic crack has become a more systematic one that is used widely. Some problems are encountered when the dynamic crack is studied. After the large investigation on the problems, it is discovered that during the process of mathematic derivation, the method is short of precision, and the derived results in this method are accidental and have no credibility.A model for example is taken to explain the problems existing in initial deriving process of the integral_transformation method of dynamic crack.

FOURIER TRANSFORMATION AND SINGULAR INTEGRALS ON SELF-SIMILAR MEASURE

This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to consider a singular integral operator on μ and show that this op- erator is of type (p,p)(1<p<∞).

Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series

The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed.By the use of fractional Occupation Times Formula,various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied,and the asymptotic distributions of the sample moments of such functions are obtained and analyzed.The transformations considered in this paper includes a variety of functions such as regular functions,integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis.It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is different from that of fractionally integrated processes,but is similar to the asymptotic theory of nonlinear transformations of integrated processes.

Optical complex integration-transform for deriving complex fractional squeezing operator

We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl–Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience.

Agrobacterium-Mediated Transformation of Rice: Constraints and Possible Solutions

Genetic transformation of rice(Oryza sativa L.) by introducing beneficial traits is now a central research instrument in plant physiology and a practical tool for plant improvement. Many approaches are verified for stable introduction of foreign genes into the plant genome. The review examined the different constraints that limit the success of rice genetic transformation via Agrobacterium-mediated approach and suggested possible solutions. Explant identification, gene transfer technique and construct to tailor the integration, transgene expression without collateral to genetic damage and transformant selection are among the technical challenges affecting the rice transformation. Despite the contests, Agrobacteriummediated transformation system has been a better option for producing transgenic rice varieties because of its exact T-DNA processing and simple integration of low copy-number transgene. This information is necessary for improving the transformation system for recalcitrant rice varieties.

REFINEMENTS OF TRANSFORMATION INEQUALITIES FOR ZERO-BALANCED HYPERGEOMETRIC FUNCTIONS

In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.

Dynamic response of axially moving Timoshenko beams: integral transform solution

The generalized integral transform technique （GITT） is used to find a semianalytical numerical solution for dynamic response of an axially moving Timoshenko beam with clamped-clamped and simply-supported boundary conditions, respectively. The implementation of GITT approach for analyzing the forced vibration equation eliminates the space variable and leads to systems of second-order ordinary differential equations （ODEs） in time. The MATHEMATICA built-in function, NDSolve, is used to numerically solve the resulting transformed ODE system. The good convergence behavior of the suggested eigenfunction expansions is demonstrated for calculating the transverse deflection and the angle of rotation of the beam cross-section. Moreover, parametric studies are performed to analyze the effects of the axially moving speed, the axial tension, and the amplitude of external distributed force on the vibration amplitude of axially moving Timoshenko beams.

High-order perturbed corrections with scaling transformation

The performance of the so-called superconvergent quantum perturbation theory （Wenhua Hal et al2000 Phys. Rev. A 61 052105） is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation τ → τ/Z applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge Z （in atomic units）. Using the improved Rayleigh-SchrSdinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems.