The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-ho...The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-homogeneous rectangular plates of variable thickness having clamped boundary conditions on all the four edges is studied. For non–homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the method of separation of variables, the governing differential equation is solved. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Time period and deflection at different points for the first two modes of vibration are calculated for various values of temperature gradients, non- homogeneity constant, taper constant and aspect ratio. Comparison studies have been carried out with non-homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.展开更多
The effect of Pasternak foundation and non-homogenity on the axisymmetric vibrations of polar orthotropic parabolically varying tapered circular plates has been analyzed on the basis of classical plate theory. Ritz me...The effect of Pasternak foundation and non-homogenity on the axisymmetric vibrations of polar orthotropic parabolically varying tapered circular plates has been analyzed on the basis of classical plate theory. Ritz method has been used to find the numerical solution of the specified problem. The efficiency of the Ritz method depends on the choice of basis function based upon deflection of polar orthotropic plates. The effects of different plate parameters viz. elastic foundation, non-homogeneity, taper parameter and that of orthotropy on fundamental, second and third mode of vibration have been studied for clamped and simply-supported boundary conditions. Mode shapes for specified plates have been drawn for both the boundary conditions. Convergence and comparison studies have been carried out for specified plates.展开更多
The problem considered here is the response of a non-homogeneouscomposite material containing some cracks subjected to dynamicloading. It is assumed that the composite material is or- thotropicand all material propert...The problem considered here is the response of a non-homogeneouscomposite material containing some cracks subjected to dynamicloading. It is assumed that the composite material is or- thotropicand all material properties depend only on the coordinate y (alongthe thickness direcion). In the analysis, the elastic region isdivided into a number of plies of infinite length. The materialproperties are taken to be constants for each ply. By utilizing theLaplace transform and Fourier transform technique, the generalsolutions for plies are derived.展开更多
We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argum...We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.展开更多
In most practical engineering applications,the translating belt wraps around two fixed wheels.The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries.In this paper,...In most practical engineering applications,the translating belt wraps around two fixed wheels.The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries.In this paper,non-homogeneous boundaries are introduced by the support wheels.Utilizing the translating belt as the mechanical prototype,the vibration characteristics of translating Timoshenko beam models with nonhomogeneous boundaries are investigated for the first time.The governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's principle.The effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations,critical velocities,natural frequencies,and modes,are numerically calculated and analyzed.The numerical results indicate that the beam experiences deformation characterized by varying curvatures near the wheels.The radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam models.Comparing the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized wheels.When the two wheels are of equal size,the critical velocities of both beam models reach their respective minima.In addition,the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%.Furthermore,as the axial velocities increase,the impact of non-homogeneous boundaries on modal shape of translating beam becomes more significant.Although dealing with non-homogeneous boundaries is challenging,beam models with non-homogeneous boundaries are more sensitive to parameters,and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries.展开更多
The main goal of this paper is to establish the boundedness of bilinear strongly singular operator T^(-)and its commutator Tb_(1),b_(2)on generalized Morrey spaces M_(p)^(u)(μ)over non-homogeneous metric measure spac...The main goal of this paper is to establish the boundedness of bilinear strongly singular operator T^(-)and its commutator Tb_(1),b_(2)on generalized Morrey spaces M_(p)^(u)(μ)over non-homogeneous metric measure spaces.Under assumption that the Lebesgue measurable functions u,u1 and u2 belong to W_(τ)forτ∈(0,2),and u1u2=u.The authors prove that T_(-)is bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into spaces M_(p)^(u)(μ),where 1/p=1/p_(1)+1/p_(2)with 1<p1,p2<∞;and also bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into generalized weak Morrey spaces WM_(p)^(u)(μ).Furthermore,the author also show that commutator Tb1,b2 generated by b_(1),b_(2)∈RBMO(μ)and T is bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into spaces M_(p)^(u)(μ).展开更多
Let(X,d,μ)be a non-homogeneous metric measure space satisfying the geometrically doubling condition and the upper doubling condition.In this setting,the authors prove that the commutator M_(b)^(α)formed by b∈RBMO(...Let(X,d,μ)be a non-homogeneous metric measure space satisfying the geometrically doubling condition and the upper doubling condition.In this setting,the authors prove that the commutator M_(b)^(α)formed by b∈RBMO(μ)and the fractional maximal function M^((α))is bounded from Lebesgue spaces L^(p)(μ)into spaces L^(q)(μ),where 1/q=1/p-αforα∈(0,1)and p∈(1,1/α).Furthermore,the boundedness of the M_(b)^(α)on Orlicz spaces L^Φ(μ)is established.展开更多
Ge condensation process of a sandwiched structure of Si/SiGe/Si on silicon-on-insulator （SOI） to form SiGe-on- insulator （SGOI） substrate is investigated. The non-homogeneity of SiGe on insulator is observed after...Ge condensation process of a sandwiched structure of Si/SiGe/Si on silicon-on-insulator （SOI） to form SiGe-on- insulator （SGOI） substrate is investigated. The non-homogeneity of SiGe on insulator is observed after a long time oxidation and annealing due to an increased consumption of silicon at the inflection points of the corrugated SiGe film morphology, which happens in the case of the rough surface morphology, with lateral Si atoms diffusing to the inflection points of the corrugated SiGe film. The transmission electron microscopy measurements show that the non-homogeneous SiGe layer exhibits a single crystalline nature with perfect atom lattice. Possible formation mechanism of the non-homogeneity SiGe layer is presented by discussing the highly nonuniform oxidation rate that is spatially dependent in the Ge condensation process. The results are of guiding significance for fabricating the SGOI by Ge condensation process.展开更多
The present paper deals with the effect of linearly temperature on transverse vibration of non-homogeneous orthotropic trapezoidal plate of parabolically varying thickness. The deflection function is defined by the pr...The present paper deals with the effect of linearly temperature on transverse vibration of non-homogeneous orthotropic trapezoidal plate of parabolically varying thickness. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. The non homogeneity of the plate is characterized by taking linear variation of the Young's modulus and parabolically variation of the density of the material. The non homogeneity is assumed to arise due to the variation in the density of the plate material and it is taken as parabolically. Rayleigh Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the transverse vibrations of orthotropic trapezoidal plates, are derived with boundary condition clamped-simply supported-clamped-simply supported. Frequencies corresponding to first two modes of vibration are calculated for the trapezoidal plate for various combinations of the parameters of the non-homogeneity, thermal gradient, taper constant and for different values of the aspect ratios and shown by figures. All The results presented here are entirely new and are not found elsewhere. Comparison can only be made for homogeneous plates, and in that cases the results have been compared with those found in the existing literatures and are in excellent agreement.展开更多
Volcanic terrains exhibit a complex structure of pyroclastic deposits interspersed with sedimentary processes,resulting in irregular lithological sequences that lack lateral continuity and distinct stratigraphic patte...Volcanic terrains exhibit a complex structure of pyroclastic deposits interspersed with sedimentary processes,resulting in irregular lithological sequences that lack lateral continuity and distinct stratigraphic patterns.This complexity poses significant challenges for slope stability analysis,requiring the development of specialized techniques to address these issues.This research presents a numerical methodology that incorporates spatial variability,nonlinear material characterization,and probabilistic analysis using a Monte Carlo framework to address this issue.The heterogeneous structure is represented by randomly assigning different lithotypes across the slope,while maintaining predefined global proportions.This contrasts with the more common approach of applying probabilistic variability to mechanical parameters within a homogeneous slope model.The material behavior is defined using complex nonlinear failure criteria,such as the Hoek-Brown model and a parabolic model with collapse,both implemented through linearization techniques.The Discontinuity Layout Optimization(DLO)method,a novel numerical approach based on limit analysis,is employed to efficiently incorporate these advances and compute the factor of safety of the slope.Within this framework,the Monte Carlo procedure is used to assess slope stability by conducting a large number of simulations,each with a different lithotype distribution.Based on the results,a hybrid method is proposed that combines probabilistic modeling with deterministic design principles for the slope stability assessment.As a case study,the methodology is applied to a 20-m-high vertical slope composed of three lithotypes(altered scoria,welded scoria,and basalt)randomly distributed in proportions of 15%,60%,and 25%,respectively.The results show convergence of mean values after approximately 400 simulations and highlight the significant influence of spatial heterogeneity,with variations of the factor of safety between 5 and 12 in 85%of cases.They also reveal non-circular and mid-slope failure wedges not captured by traditional stability methods.Finally,an equivalent normal probability distribution is proposed as a reliable approximation of the factor of safety for use in risk analysis and engineering decision-making.展开更多
A drought is when reduced rainfall leads to a water crisis,impacting daily life.Over recent decades,droughts have affected various regions,including South Sulawesi,Indonesia.This study aims to map the probability of m...A drought is when reduced rainfall leads to a water crisis,impacting daily life.Over recent decades,droughts have affected various regions,including South Sulawesi,Indonesia.This study aims to map the probability of meteo-rological drought months using the 1-month Standardized Precipitation Index(SPI)in South Sulawesi.Based on SPI,meteorological drought characteristics are inversely proportional to drought event intensity,which can be modeled using a Non-Homogeneous Poisson Process,specifically the Power Law Process.The estimation method employs Maximum Likelihood Estimation(MLE),where drought event intensities are treated as random variables over a set time interval.Future drought months are estimated using the cumulative Power Law Process function,with theβandγparameters more significant than 0.The probability of drought months is determined using the Non-Homogeneous Poisson Process,which models event occurrence over time,considering varying intensities.The results indicate that,of the 24 districts/cities in South Sulawesi,14 experienced meteorological drought based on the SPI and Power Law Process model.The estimated number of months of drought occurrence in the next 12 months is one month of drought with an occurrence probability value of 0.37 occurring in November in the Selayar,Bulukumba,Bantaeng,Jeneponto,Takalar and Gowa areas,in October in the Sinjai,Barru,Bone,Soppeng,Pinrang and Pare-pare areas,as well as in December in the Maros and Makassar areas.展开更多
The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homoge- neous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young’s modulus and mas...The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homoge- neous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young’s modulus and mass density is the main cause for the occurrence of non-homogeneity in plate’s material. In this consideration, density varies linearly in one direction. The governing differential equations have been derived by Rayleigh-Ritz method in order to attain fundamental frequencies. With C-S-C-S boundary condition, a two term deflection function has been considered. The effect of structural parameters such as taper constants, thermal gradient, aspect ratio and non-homogeneity constant has been investigated for first two modes of vibration. The obtained numerical results have been presented in tabular and graphical form.展开更多
The main aim of the present work is to study the linear temperature behaviour of a non-homogeneous trapezoidal plate whose thickness varies linearly in both directions. The temperature behaviour considered linear alon...The main aim of the present work is to study the linear temperature behaviour of a non-homogeneous trapezoidal plate whose thickness varies linearly in both directions. The temperature behaviour considered linear along the length of the plate. Non-homogeneity in plate arises due to variation in density along the length of the plate. The two-term deflection function with clamped-simply supported-clamped-simply supported boundary condition is taken into consideration. The effect of structural parameters such as taper constants, thermal gradient, non-homogeneity constant and aspect ratio has been studied. Rayleigh-Ritz method is used to solve the governing differential equations and to obtain the fundamental frequencies for the first two modes of vibration. Results are presented in graphical form.展开更多
This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on th...This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.展开更多
Underground utility tunnels are the most fundamental and reliable lifeline network in urban cities,and are widely constructed throughout the world.In urban areas,most utility tunnels usually encounter the non-homogene...Underground utility tunnels are the most fundamental and reliable lifeline network in urban cities,and are widely constructed throughout the world.In urban areas,most utility tunnels usually encounter the non-homogeneity of subsoil condition due to various construction effects.Studies have shown that the damage mechanism of shallow underground structures mainly depends on the inhomogeneity of the subsoil conditions.This would become a considerable factor for the stability of the underground utility tunnel structures.However,this type of research still needs to establish the vulnerable seismic design.In this study,a series of shaking table tests were conducted on non-homogenous soils to investigate the performance of seismic interaction between utility tunnels,surrounding soils and interior pipelines.The dynamic responses measured from the test account for the boundary condition of non-homogeneous soils,the internal forces,displacement of tunnel joints,the dynamic characteristics on interior pipelines and the reasonable spring stiffness with damping in the seismically isolated gas pipeline model inside the tunnel.The vulnerability of underground utility tunnel in non-homogeneous soil zone and the mechanism of the stability of interior facilities are the main topics discussed in this paper.展开更多
In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body...In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.展开更多
This paper presents a new strategy of using the radial integration boundary element method （RIBEM） to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial ...This paper presents a new strategy of using the radial integration boundary element method （RIBEM） to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial in-tegral which is used to transform domain integrals to equivalent boundary integrals is carried out on the basis of elemental nodes. As a result, the computational time spent in evaluating domain integrals can be saved considerably in comparison with the conventional RIBEM. Three numerical examples are given to demonstrate the correctness and computational efficiency of the proposed approach.展开更多
In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β...In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β) and 1/q = 1/p-(α + β), and obtain their weak(L^1(μ), L^(1/(1-α-β))(μ))-type. Moreover, the authors also consider the boundedness in the case that 1/(α+β) < p < 1/α,1/α≤ p ≤∞ and the endpoint cases, namely, p = 1/(α + β).展开更多
The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_(γ)]which is generated by fractional integral I_(γ)and function b∈Lip_(β)(μ)...The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_(γ)]which is generated by fractional integral I_(γ)and function b∈Lip_(β)(μ)on Morrey space over non-homogeneous metric measure space,which satisfies the geometrically doubling and upper doubling conditions in the sense of Hytonen.Under assumption that the dominating functionλsatisfies weak reverse doubling condition,the author proves that the commutator[b,I_(γ)]is compact from Morrey space M_(q)^(p)(μ)into Morrey space M_(t)^(s)(μ)if and only if b∈Lip_(β)(μ).展开更多
A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the gove...A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure.展开更多
文摘The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-homogeneous rectangular plates of variable thickness having clamped boundary conditions on all the four edges is studied. For non–homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the method of separation of variables, the governing differential equation is solved. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Time period and deflection at different points for the first two modes of vibration are calculated for various values of temperature gradients, non- homogeneity constant, taper constant and aspect ratio. Comparison studies have been carried out with non-homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.
文摘The effect of Pasternak foundation and non-homogenity on the axisymmetric vibrations of polar orthotropic parabolically varying tapered circular plates has been analyzed on the basis of classical plate theory. Ritz method has been used to find the numerical solution of the specified problem. The efficiency of the Ritz method depends on the choice of basis function based upon deflection of polar orthotropic plates. The effects of different plate parameters viz. elastic foundation, non-homogeneity, taper parameter and that of orthotropy on fundamental, second and third mode of vibration have been studied for clamped and simply-supported boundary conditions. Mode shapes for specified plates have been drawn for both the boundary conditions. Convergence and comparison studies have been carried out for specified plates.
文摘The problem considered here is the response of a non-homogeneouscomposite material containing some cracks subjected to dynamicloading. It is assumed that the composite material is or- thotropicand all material properties depend only on the coordinate y (alongthe thickness direcion). In the analysis, the elastic region isdivided into a number of plies of infinite length. The materialproperties are taken to be constants for each ply. By utilizing theLaplace transform and Fourier transform technique, the generalsolutions for plies are derived.
基金Supported by National Natural Science Foundation of China(Grant No.62363005).
文摘We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.
基金Project supported by the YEQISUN Joint Funds of the National Natural Science Foundation of China(No.U2341231)the National Natural Science Foundation of China(No.12172186)。
文摘In most practical engineering applications,the translating belt wraps around two fixed wheels.The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries.In this paper,non-homogeneous boundaries are introduced by the support wheels.Utilizing the translating belt as the mechanical prototype,the vibration characteristics of translating Timoshenko beam models with nonhomogeneous boundaries are investigated for the first time.The governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's principle.The effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations,critical velocities,natural frequencies,and modes,are numerically calculated and analyzed.The numerical results indicate that the beam experiences deformation characterized by varying curvatures near the wheels.The radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam models.Comparing the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized wheels.When the two wheels are of equal size,the critical velocities of both beam models reach their respective minima.In addition,the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%.Furthermore,as the axial velocities increase,the impact of non-homogeneous boundaries on modal shape of translating beam becomes more significant.Although dealing with non-homogeneous boundaries is challenging,beam models with non-homogeneous boundaries are more sensitive to parameters,and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries.
基金Supported by the National Natural Science Foundation of China(Grant No.12201500)the Science Foundation for Youths of Gansu Province(Grant No.22JR5RA173)the Young Teachers’Scientific Research Ability Promotion Project of Northwest Normal University(Grant No.NWNU-LKQN2020-07)。
文摘The main goal of this paper is to establish the boundedness of bilinear strongly singular operator T^(-)and its commutator Tb_(1),b_(2)on generalized Morrey spaces M_(p)^(u)(μ)over non-homogeneous metric measure spaces.Under assumption that the Lebesgue measurable functions u,u1 and u2 belong to W_(τ)forτ∈(0,2),and u1u2=u.The authors prove that T_(-)is bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into spaces M_(p)^(u)(μ),where 1/p=1/p_(1)+1/p_(2)with 1<p1,p2<∞;and also bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into generalized weak Morrey spaces WM_(p)^(u)(μ).Furthermore,the author also show that commutator Tb1,b2 generated by b_(1),b_(2)∈RBMO(μ)and T is bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into spaces M_(p)^(u)(μ).
基金the Science Foundation for Youths of Gansu Province(Grant No.22JR5RA173)Master Foundation of Northwest Normal University(Grant No.2022KYZZ-S121).
文摘Let(X,d,μ)be a non-homogeneous metric measure space satisfying the geometrically doubling condition and the upper doubling condition.In this setting,the authors prove that the commutator M_(b)^(α)formed by b∈RBMO(μ)and the fractional maximal function M^((α))is bounded from Lebesgue spaces L^(p)(μ)into spaces L^(q)(μ),where 1/q=1/p-αforα∈(0,1)and p∈(1,1/α).Furthermore,the boundedness of the M_(b)^(α)on Orlicz spaces L^Φ(μ)is established.
基金Project supported by the National Key Basic Research Program of China(Grant Nos.2012CB933503 and 2013CB632103)the National Natural Science Foundation of China(Grant Nos.61176092,61036003,and 60837001)+1 种基金the Ph.D.Programs Foundation of Ministry of Education of China(Grant No.20110121110025)the Fundamental Research Funds for the Central Universities,China(Grant No.2010121056)
文摘Ge condensation process of a sandwiched structure of Si/SiGe/Si on silicon-on-insulator （SOI） to form SiGe-on- insulator （SGOI） substrate is investigated. The non-homogeneity of SiGe on insulator is observed after a long time oxidation and annealing due to an increased consumption of silicon at the inflection points of the corrugated SiGe film morphology, which happens in the case of the rough surface morphology, with lateral Si atoms diffusing to the inflection points of the corrugated SiGe film. The transmission electron microscopy measurements show that the non-homogeneous SiGe layer exhibits a single crystalline nature with perfect atom lattice. Possible formation mechanism of the non-homogeneity SiGe layer is presented by discussing the highly nonuniform oxidation rate that is spatially dependent in the Ge condensation process. The results are of guiding significance for fabricating the SGOI by Ge condensation process.
文摘The present paper deals with the effect of linearly temperature on transverse vibration of non-homogeneous orthotropic trapezoidal plate of parabolically varying thickness. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. The non homogeneity of the plate is characterized by taking linear variation of the Young's modulus and parabolically variation of the density of the material. The non homogeneity is assumed to arise due to the variation in the density of the plate material and it is taken as parabolically. Rayleigh Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the transverse vibrations of orthotropic trapezoidal plates, are derived with boundary condition clamped-simply supported-clamped-simply supported. Frequencies corresponding to first two modes of vibration are calculated for the trapezoidal plate for various combinations of the parameters of the non-homogeneity, thermal gradient, taper constant and for different values of the aspect ratios and shown by figures. All The results presented here are entirely new and are not found elsewhere. Comparison can only be made for homogeneous plates, and in that cases the results have been compared with those found in the existing literatures and are in excellent agreement.
基金the project PID2022-139202OB-I00Neural Networks and Optimization Techniques for the Design and Safe Maintenance of Transportation Infrastructures:Volcanic Rock Geotechnics and Slope Stability(IA-Pyroslope),funded by the Spanish State Research Agency of the Ministry of Science,Innovation and Universities of Spain and the European Regional Development Fund,MCIN/AEI/10.13039/501100011033/FEDER,EU。
文摘Volcanic terrains exhibit a complex structure of pyroclastic deposits interspersed with sedimentary processes,resulting in irregular lithological sequences that lack lateral continuity and distinct stratigraphic patterns.This complexity poses significant challenges for slope stability analysis,requiring the development of specialized techniques to address these issues.This research presents a numerical methodology that incorporates spatial variability,nonlinear material characterization,and probabilistic analysis using a Monte Carlo framework to address this issue.The heterogeneous structure is represented by randomly assigning different lithotypes across the slope,while maintaining predefined global proportions.This contrasts with the more common approach of applying probabilistic variability to mechanical parameters within a homogeneous slope model.The material behavior is defined using complex nonlinear failure criteria,such as the Hoek-Brown model and a parabolic model with collapse,both implemented through linearization techniques.The Discontinuity Layout Optimization(DLO)method,a novel numerical approach based on limit analysis,is employed to efficiently incorporate these advances and compute the factor of safety of the slope.Within this framework,the Monte Carlo procedure is used to assess slope stability by conducting a large number of simulations,each with a different lithotype distribution.Based on the results,a hybrid method is proposed that combines probabilistic modeling with deterministic design principles for the slope stability assessment.As a case study,the methodology is applied to a 20-m-high vertical slope composed of three lithotypes(altered scoria,welded scoria,and basalt)randomly distributed in proportions of 15%,60%,and 25%,respectively.The results show convergence of mean values after approximately 400 simulations and highlight the significant influence of spatial heterogeneity,with variations of the factor of safety between 5 and 12 in 85%of cases.They also reveal non-circular and mid-slope failure wedges not captured by traditional stability methods.Finally,an equivalent normal probability distribution is proposed as a reliable approximation of the factor of safety for use in risk analysis and engineering decision-making.
基金funded by Hasanuddin University,grant number 00309/UN4.22/PT.01.03/2024.
文摘A drought is when reduced rainfall leads to a water crisis,impacting daily life.Over recent decades,droughts have affected various regions,including South Sulawesi,Indonesia.This study aims to map the probability of meteo-rological drought months using the 1-month Standardized Precipitation Index(SPI)in South Sulawesi.Based on SPI,meteorological drought characteristics are inversely proportional to drought event intensity,which can be modeled using a Non-Homogeneous Poisson Process,specifically the Power Law Process.The estimation method employs Maximum Likelihood Estimation(MLE),where drought event intensities are treated as random variables over a set time interval.Future drought months are estimated using the cumulative Power Law Process function,with theβandγparameters more significant than 0.The probability of drought months is determined using the Non-Homogeneous Poisson Process,which models event occurrence over time,considering varying intensities.The results indicate that,of the 24 districts/cities in South Sulawesi,14 experienced meteorological drought based on the SPI and Power Law Process model.The estimated number of months of drought occurrence in the next 12 months is one month of drought with an occurrence probability value of 0.37 occurring in November in the Selayar,Bulukumba,Bantaeng,Jeneponto,Takalar and Gowa areas,in October in the Sinjai,Barru,Bone,Soppeng,Pinrang and Pare-pare areas,as well as in December in the Maros and Makassar areas.
文摘The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homoge- neous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young’s modulus and mass density is the main cause for the occurrence of non-homogeneity in plate’s material. In this consideration, density varies linearly in one direction. The governing differential equations have been derived by Rayleigh-Ritz method in order to attain fundamental frequencies. With C-S-C-S boundary condition, a two term deflection function has been considered. The effect of structural parameters such as taper constants, thermal gradient, aspect ratio and non-homogeneity constant has been investigated for first two modes of vibration. The obtained numerical results have been presented in tabular and graphical form.
文摘The main aim of the present work is to study the linear temperature behaviour of a non-homogeneous trapezoidal plate whose thickness varies linearly in both directions. The temperature behaviour considered linear along the length of the plate. Non-homogeneity in plate arises due to variation in density along the length of the plate. The two-term deflection function with clamped-simply supported-clamped-simply supported boundary condition is taken into consideration. The effect of structural parameters such as taper constants, thermal gradient, non-homogeneity constant and aspect ratio has been studied. Rayleigh-Ritz method is used to solve the governing differential equations and to obtain the fundamental frequencies for the first two modes of vibration. Results are presented in graphical form.
基金supported by the National Natural Science Foundation of China(7090104171171113)the Aeronautical Science Foundation of China(2014ZG52077)
文摘This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.
基金National Key Research and Invention Program of The Thirteenth under Grant Nos.2016YFC0802407,2018YFC0809605。
文摘Underground utility tunnels are the most fundamental and reliable lifeline network in urban cities,and are widely constructed throughout the world.In urban areas,most utility tunnels usually encounter the non-homogeneity of subsoil condition due to various construction effects.Studies have shown that the damage mechanism of shallow underground structures mainly depends on the inhomogeneity of the subsoil conditions.This would become a considerable factor for the stability of the underground utility tunnel structures.However,this type of research still needs to establish the vulnerable seismic design.In this study,a series of shaking table tests were conducted on non-homogenous soils to investigate the performance of seismic interaction between utility tunnels,surrounding soils and interior pipelines.The dynamic responses measured from the test account for the boundary condition of non-homogeneous soils,the internal forces,displacement of tunnel joints,the dynamic characteristics on interior pipelines and the reasonable spring stiffness with damping in the seismically isolated gas pipeline model inside the tunnel.The vulnerability of underground utility tunnel in non-homogeneous soil zone and the mechanism of the stability of interior facilities are the main topics discussed in this paper.
基金supported by the US ARO grants 49308-MA and 56349-MAthe US AFSOR grant FA9550-06-1-024+1 种基金he US NSF grant DMS-0911434the State Key Laboratory of Scientific and Engineering Computing of Chinese Academy of Sciences during a visit by Z.Li between July-August,2008.
文摘In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.
基金supported by the National Natural Science Foundation of China (10872050, 11172055)the Fundamental Research Funds for the Centred Universities (DUT11ZD(G)01)
文摘This paper presents a new strategy of using the radial integration boundary element method （RIBEM） to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial in-tegral which is used to transform domain integrals to equivalent boundary integrals is carried out on the basis of elemental nodes. As a result, the computational time spent in evaluating domain integrals can be saved considerably in comparison with the conventional RIBEM. Three numerical examples are given to demonstrate the correctness and computational efficiency of the proposed approach.
基金Supported by the National Natural Science Foundation of China(Grant No.11661075).
文摘In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β) and 1/q = 1/p-(α + β), and obtain their weak(L^1(μ), L^(1/(1-α-β))(μ))-type. Moreover, the authors also consider the boundedness in the case that 1/(α+β) < p < 1/α,1/α≤ p ≤∞ and the endpoint cases, namely, p = 1/(α + β).
基金Supported by the Scientific Startup Foundation for Doctors of Northwest Normal University(Grant No.0002020203)the Innovation Fund Project for Higher Education of Gansu Province(Grant No.2020A-010)。
文摘The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_(γ)]which is generated by fractional integral I_(γ)and function b∈Lip_(β)(μ)on Morrey space over non-homogeneous metric measure space,which satisfies the geometrically doubling and upper doubling conditions in the sense of Hytonen.Under assumption that the dominating functionλsatisfies weak reverse doubling condition,the author proves that the commutator[b,I_(γ)]is compact from Morrey space M_(q)^(p)(μ)into Morrey space M_(t)^(s)(μ)if and only if b∈Lip_(β)(μ).
基金The project supported by the National Natural Science Foundation of China (10172075 and 10002016)
文摘A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure.
