A coupled Legendre-Laguerre polynomial method with analytical integration for the Rayleigh waves in a quasicrystal layered half-space with an imperfect interface

The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.

Spatial pattern of urban-rural integration in China and the impact of geography

Urban-rural integration (URI) is a global challenge that is highly related to inequalities, poverty, economic growth, and other Sustainable Development Goals (SDGs). Existing research has evaluated the extent of URI and explored its influencing factors, but urban-rural linkages are seldom incorporated in evaluation systems, and geographical factors are rarely recognized as the influencing factors. We construct a URI framework including regional economy, rural development, urban-rural linkage, and urban-rural gap. Based on a dataset consisting of 1,669 counties in China in 2020, we reveal the spatial pattern of URI and find a high correlation between the spatial pattern of URI and the relief degree of land surface (RDLS). Using structural equation modeling, we discover that topography has direct ( − 0.18, p < 0.001) and indirect ( − 0.17, p < 0.001) effects on URI. The indirect negative effects are mediated through the infrastructure, and the combination of localized advantages and modern technical conditions could mitigate the negative impact of topography. Finally, we identify 742 counties as lagging regions in URI, which can be clustered into eight types. Our findings could facilitate policy designing for those countries striving for integrated and sustainable development of urban and rural areas.

Analytical solution based on the wavenumber integration method for the acoustic field in a Pekeris waveguide

An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide.

An Integration Depending on Parameter Ф for Analytical Solution of the Compression of Thin Workpiece

An integration depending on the parameter Ф has been applied to the function Фdx so that an explicit formula of specific pressure calculation and an analytical solution are obtained.It has been found that the analytical solution is basically the same as the prevailing numerical one which is from the formula There- fore,it is justified theoretically that for the slip line field in the compression of a thin workpiece a parametric integra- tion is perfectly possible for satisfactory analytical solution.

Analytical solution for stress and deformation of the mining floor based on integral transform

Following exploitation of a coal seam, the final stress field is the sum of in situ stress field and an excavation stress field. Based on this feature, we firstly established a mechanics analytical model of the mining floor strata. Then the study applied Fourier integral transform to solve a biharmonic equation,obtaining the analytical solution of the stress and displacement of the mining floor. Additionally, this investigation used the Mohr–Coulomb yield criterion to determine the plastic failure depth of the floor strata. The calculation process showed that the plastic failure depth of the floor and floor heave are related to the mining width, burial depth and physical–mechanical properties. The results from an example show that the curve of the plastic failure depth of the mining floor is characterized by a funnel shape and the maximum failure depth generates in the middle of mining floor; and that the maximum and minimum principal stresses change distinctly in the shallow layer and tend to a fixed value with an increase in depth. Based on the displacement results, the maximum floor heave appears in the middle of the stope and its value is 0.107 m. This will provide a basis for floor control. Lastly, we have verified the analytical results using FLAC3 Dto simulate floor excavation and find that there is some deviation between the two results, but their overall tendency is consistent which illustrates that the analysis method can well solve the stress and displacement of the floor.

Dosimetric Comparison of Integral Radiation Dose: Anisotropic Analytical Algorithm and Acuros XB in Breast Radiotherapy

The impact of the difference between Anisotropic Analytical Algorithm (AAA) and Acuros XB (AXB) in breast radiotherapy is not clearly due to different uses and further research is required to explain this effect. The aim of this study is to investigate the contribution of calculation differences between AAA and AXB to the integral radiation dose (ID) on critical organs. Seven field intensity modulated radiotherapy (IMRT) plans were generated using with AAA and AXB algorithms for twenty patients with early stage left breast cancer after breast conserving surgery. Volumetric and dosimetric differences, as well as, the Dmean, V5, V20 doses of the left and right-sided lung, the Dmean, V10, V20, V30 doses of heart and the Dmean, V5, V10 doses of the contralateral breast were investigated. The mean dose (Dmean), V5, V20 doses of the left-sided lung, the Dmean, V5, V10 doses of right-sided lung, the Dmean, V10, V20, V30 doses of heart and the Dmean, V5, V10 doses of the contralateral breast were found to be significantly higher with AAA. In this research integral dose was also higher in the AAA recalculated plan and the AXB plan with the average dose as follows left lung 2%, heart 2%, contralateral breast 8%, contralateral lung 4% respectively. Our study revealed that the calculation differences between Acuros XB (AXB) and Anisotropic Analytical Algorithm (AAA) in breast radiotherapy caused serious differences on the stored integral doses on critical organs. In addition, AXB plans showed significantly dosimetric improvements in multiple dosimetric parameters.

Derivation of lattice Boltzmann equation via analytical characteristic integral

A lattice Boltzmann(LB) theory, the analytical characteristic integral(ACI) LB theory, is proposed in this paper.ACI LB theory takes the Bhatnagar–Gross–Krook(BGK)-Boltzmann equation as the exact kinetic equation behind Navier–Stokes continuum and momentum equations and constructs an LB equation by rigorously integrating the BGK-Boltzmann equation along characteristics. It is a general theory, supporting most existing LB equations including the standard lattice BGK(LBGK) equation inherited from lattice-gas automata, whose theoretical foundation had been questioned. ACI LB theory also indicates that the characteristic parameter of an LB equation is collision number, depicting the particle-interaction intensity in the time span of the LB equation, instead of the traditionally assumed relaxation time, and the over-relaxation time problem is merely a manifestation of the temporal evolution of equilibrium distribution along characteristics under high collision number, irrelevant to particle kinetics. In ACI LB theory, the temporal evolution of equilibrium distribution along characteristics is the determinant of LB method accuracy and we numerically prove this.

Characterization of transgene integration pattern in F4 hGH-transgenic common carp (Cyprinus carpio L.)

The integration pattern and adjacent host sequences of the inserted pMThGH-transgene in the F4 hGH-transgeniccommon carp were extensively studied. Here we show that each F4 transgenic fish contained about 200 copies of thepMThGH-transgene and the transgenes were integrated into the host genome generally with concatemers in a head-to-tail arrangement at 4-5 insertion sites. By using a method of plasmid rescue, four hundred copies of transgenes fromtwo individuals of F4 transgenic fish, A and B, were recovered and clarified into 6 classes. All classes of recoveredtransgenes contained either complete or partial pMThGH sequences. The class I, which comprised 83% and 84.5%respectively of the recovered transgene copies from fish A and B, had maintained the original configuration, indicatingthat most transgenes were faithfully inherited during the four generations of reproduction. The other five classes weredifferent from the original configuration in both molecular weight and restriction map, indicating that a few transgeneshad undergone mutation, rearrangement or deletion during integration and germline transmission. In the five types ofaberrant transgenes, three flanking sequences of the host genome were analyzed. These sequences were common carpβ-actin gene, common carp DNA sequences homologous to mouse phosphoglycerate kinase-1 and human epidermalkeratin 14, respectively.

Optimization of integrated geological-engineering design of volume fracturing with fan-shaped well pattern

According to the variable toe-to-heel well spacing, combined with the dislocation theory, discrete lattice method, and finite-element-method(FEM) based fluid-solid coupling, an integrated geological-engineering method of volume fracturing for fan-shaped well pattern is proposed considering the geomechanical modeling, induced stress calculation, hydraulic fracturing simulation, and post-frac productivity evaluation. Besides, we propose the differential fracturing design for the conventional productivity-area and the potential production area for fan-shaped horizontal wells. After the fracturing of the conventional production area for H1 fan-shaped well platform, the research shows that the maximum reduction of the horizontal principal stress difference in the potential productivity-area is 0.2 MPa, which cannot cause the stress reversal, but this reduction is still conducive to the lateral propagation of hydraulic fractures. According to the optimized fracturing design, in zone-Ⅰ of the potential production area, only Well 2 is fractured, with a cluster spacing of 30 m and an injection rate of 12 m^(3)/min per stage;in zone-Ⅱ, Well 2 is fractured before Well 3, with a cluster spacing of 30 m and an injection rate of 12 m^(3)/min per stage. The swept area of the pore pressure drop in the potential production area is small, showing that the reservoir is not well developed. The hydraulic fracturing in the toe area can be improved by, for example, properly densifying the fractures and adjusting the fracture distribution, in order to enhance the swept volume and increase the reservoir utilization.

On Analytical Treatment of all Boundary and Volume Integrals in BEM

In this paper, the integrals appeared in BEM model for Poisson equation are all implemented analytically. Wherein, the boundary and the domain are discretized by linear boundary elements and linear internal triangle cells respectively. The closed formulations for all integrals are presented so that the computer effort for numerical solution is reduced considerably with higher accuray. The numerical example shows that the results are more accurate in comparision with Gaussian integration in the same discrezition. The basic idea of this paper could be extended to BEM model for Helmholtz equation and/or the time-dependent second other differential equations.

ANALYTICAL－GENERALIZED VARIATIONAL METHOD ABOUT SOLUTION OF SIF AND CONSERVATIVE INTEGRAL FOR DELAMINATlONS OF LAMINATE BEAM

AbstractIn this paper,first of all,the eigen expansions of stress and displacement fields satis-fying all governing equations, boundary conditions along crack surfaces and conditions ofcontinuity along hgament of two dissimilar media are derived.Next, the formula of con-servative integral J1 for the above media with interface crack is established and applied tothe case of detamination of composite laminate beam stacked orthogonally.Furtbermore,the coefficients of the above expansions are determined by generalized variational method,then the values of J1 can be obtained.The stress intensity factor Kn found directly fromthe leading term of the above expansions agrees with that indirectly from J1 satisfactorily,the convergency of results with increase of number of terms in the above expansions is verynice and values of J1 obtained from different paths of integration keep constantaccurately.

Pattern of Opening Up,Integration and Reshaping Economic Geography——A New Economic Geography Analysis of the Belt and Road Initiative and the Yangtze River Economic Belt

Since the 18 th National Congress of the Communist Party of China,the central government has implemented several regional development plans,including the Belt and Road Initiative and the Yangtze River Economic Belt,aiming to reshape the economic geography of China.This paper is based on the Belt and Road Initiative and the Yangtze River Economic Belt and outlines the pattern of opening up.To analyze the impact of the pattern of opening up on the regional integration of China's economic geography,this paper has developed a new economic geography model comprised of four regions and two countries.From this,it draws some conclusions.First,the change of pattern of opening up will lead to shifting centripetal and centrifugal forces from the international market.The greater the scale of neighboring markets,the stronger the agglomeration force will be; the more product varieties made in neighboring countries,the more potent its dispersion force.Second,developing an inland international trade corridor will decentralize industry distribution and reduce the impact of external market integration on home countries.Third,the inland international trade corridor could alter the effect of domestic market integration on the economic geography.When domestic integration occurs prior to international integration,further integration of a domestic market leads to greater industrial distribution along a bell-shaped curve,which describes economic activities from dispersion to agglomeration to decentralization.Therefore,developing an integrated market system of major countries and opening a corridor between China and Europe is not only the key to reshaping China's economic geography but also the path to solving the problems of the Heihe-Tengchong Line.

Application of Choquet Integral-Importance-Performance Analysis and TOPSIS Methods in Approaching the Preference Factors of Calligraphy and Seal Engraving Imagery

Classical Chinese characters,presented through calligraphy,seal engraving,or painting,can exhibit different aesthetics and essences of Chinese characters,making them the most important asset of the Chinese people.Calligraphy and seal engraving,as two closely related systems in traditional Chinese art,have developed through the ages.Due to changes in lifestyle and advancements in modern technology,their original functions of daily writing and verification have gradually diminished.Instead,they have increasingly played a significant role in commercial art.This study utilizes the Evaluation Grid Method(EGM)and the Analytic Hierarchy Process(AHP)to research the key preference factors in the application of calligraphy and seal engraving imagery.Different from the traditional 5-point equal interval semantic questionnaire,this study employs a non-equal interval semantic questionnaire with a golden ratio scale,distinguishing the importance ratio of adjacent semantic meanings and highlighting the weighted emphasis on visual aesthetics.Additionally,the study uses Importance-Performance Analysis(IPA)and Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)to obtain the key preference sequence of calligraphy and seal engraving culture.Plus,the Choquet integral comprehensive evaluation is used as a reference for IPA comparison.It is hoped that this study can provide cultural imagery references and research methods,injecting further creativity into industrial design.

Analysis on Development Trend of the D omestic Interior Design Pattern based on the Regional Characteristics and Cultural Integration

Interior is the main space of human activities, which is an important part of human life and design activities, and is the link between spiritual civilization and material civilization. Interior design originates from life, and needs to solve the problem of the material world and spiritual world. People improve the living environment and life quality through interior designs. The style of design depends on the geographical features and various cultures, which refi ects the artistic features and personality. The development history of modern architecture and interior design shows that the style of interior design is an important part of the whole architectural style, which reffects the design features of the whole building. Therefore, interior design and outdoor design should be in harmony. The orientation and characteristics of interior design determine the necessity of the style reforms. The future development trend of interior development may have the following characteristics humanism, green design, nationalization, intelligence and regionalization.

THE INTEGRAL AS A FUNCTION OF THE UPPER LIMIT AND AN ANALYTICAL SOLUTION TO PLANE STRAIN DRAWING AND EXTRUSION

A kinematically admissible velocity field which is different from Avitzur's is established in Cartesian Coordinates. An upper-bound analytical solution to strip drawing andextrusion is obtained by using the integral as a function of the upper limit in this paper.

An inverse problem in analytical dynamics

This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the time derivative of the integrals. Secondly, the differential equations can be written in the Lagrange equations under certain conditions and the Lagrangian can be obtained. Finally, two examples are given to illustrate the application of the result.

General Integral Formulasof （0, q）（q 〉 0）Differential Forms on the Analytic Varieties

In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of （0, q）（q 〉 0） differential forms for the twotypes of the bounded domains in complex submanifolds with codimension-m. Secondly weobtain the unified integral representation formulas of （0, q）（q 〉 0） differential forms for thegeneral bounded domain in complex submanifold with codimension-m, which include Hatzi-afratis formula, i.e. Koppelman type integral formula for the bounded domain with smoothboundary in analytic varieties. In particular, when m -- 0, we obtain the unified integralrepresentation formulas of （0, q）（q 〉 0） differential forms for general bounded domain in Cn,which are the generalization and the embodiment of Koppelman-Leray formula.

Analytical design of dies for the extrusion of sheets and annular parison

Based on the method of representative values and the flow pattern, that is, the position of the isobars parallel to the die orifice （PIPDO）, the design of dies for the sheet and annular parisons was improved in the present paper. Since this pattern includes the effects of the sloped manifold and the equations for designing the circular manifold are independent of operating conditions and the material, the distribution system of a die gives better uniformity of flow. In the previous study by Winter a defect was found, that is, the calculated position of the path of the island area lagged behind actual position. This defect was eliminated, and the modified equation was obtained. Another flow pattern, in which the pressure loss on all flow path is equal （PLFPE）, was introduced. The equivalency of the above two flow patterns was proved theoretically in this paper.

Research and application of sidewall stability predic-tion method based on analytic hierarchy process and fuzzy integrative evaluation method

As a difficult problem, sidewall instability has been beset drilling workers all the time. Not only does it cause huge economic losses, but also it determines the success or failure of drilling engineering. Due to complex relationship between various factors which influence sidewall stability, it hasn’t been found a widely applied method to predicate sidewall stability so far. Therefore, in order to formulate corresponding measures to ensure successful drilling, searching for a kind of better method to forecast sidewall stability before drilling becomes an imperative and significant topic for drilling engineering. On the basis of traditional sidewall stability analytical method, we have put forward the Fuzzy Comprehensive Evaluation Method to forecast sidewall stability regulation using physico-chemical performance parameters of the clay mineral. This method has been improved by introducing the Analytic Hierarchy Process (AHP) and the Maximum Subjection Principle in the application process. After introducing Analytic Hierarchy Process to identify weight, and Maximum Subjection Principle to obtain evaluation results, it has reduced the influence of human factors and enhanced the accuracy of the fuzzy evaluation results. The application in Hailaer Area indicates that this method can predict sidewall stability of gas-oil well with high credibility and strong practicability.

The Leray-Stokes Type Integral Representation Formulas on the Analytic Varieties

The closure of the bounded domains D in Cnconsists of a chain of the slit spaces,and may be divided into two types. Based on the two types of bounded domains in C^n, firstly using different method and technique we derive the corresponding integral representation formulas of differentiable functions for complex n-m(0 ≤ m < n) dimensional analytic varieties in the two types of the bounded domains. Secondly we obtain the unified integral representation formulas of differentiable functions for complex n-m(0 ≤ m < n) dimensional analytic varieties in the general bounded domains. When functions are holomorphic, the integral formulas in this paper include formulas of Stout^([1]), Hatziafratis^([2]) and the author^([3]),and are the extension of all the integral representations for holomorphic functions in the existing papers to analytic varieties. In particular, when m = 0, firstly we gave the integral representation formulas of differentiable functions for the two types of bounded domains in C^n. Therefore they can make the concretion of Leray-Stokes formula. Secondly we obtain the unified integral representation formulas of differentiable functions for general bounded domains in C^n. So they can make the Leray-Stokes formula generalizations.