In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted co...In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted combination,the non-uniform rational B-spline(NURBS)functions are employed as basis functions.Moreover,the unbounded and artificial domains,defined in the PML method,are contained in a single patch domain.Based on the proposed scheme,the approximation of the geometry problem is set in a new scheme in which the PML’s absorbing and attenuation properties and the description of traveling waves can be represented.This includes a higher continuity and smoother approximation of the computed domain.As high-order NURBS basis functions are non-interpolatory,a penalty method is present to apply a time-dependent displacement load.The performance of the NURBS-based PML is analyzed through numerical examples for 1D and 2D domains,considering homogeneous and heterogeneous media.Further,we verify the long-time numerical stability of the present method.The developed method can be used to simulate hypothetical stratified domains commonly encountered in soil-structure interaction analyses.展开更多
When a vehicle moves over a flexible pavement structure,it generates loading and unloading cycles that produce recoverable(resilient)and permanent(plastic)deformations in the granular base and subbase layers,which are...When a vehicle moves over a flexible pavement structure,it generates loading and unloading cycles that produce recoverable(resilient)and permanent(plastic)deformations in the granular base and subbase layers,which are made of unbound granular materials(UGMs).The primary parameter used to evaluate the resilient response of UGMs in pavements is the resilient modulus(MR).The MR is widely used in calculating stress-strain states for flexible pavement design and as a control parameter during the construction process.It is also employed to understand the progression of distresses,such as fatigue cracking and rutting.The main objective of this study was to conduct a literature review on the resilient behavior of UGMs.This manuscript presents and describes the MR and the factors that influence it.It also outlines the evolution of the mathematical equations most commonly used to estimate and predict this physical parameter.Conclusions and recommendations for future research are provided at the end of the article.Despite the large amount of research done on the subject,the resilient behavior of UGM has not yet been fully understood.This is since these materials are highly heterogeneous and show nonlinear-anisotropic behavior under different cyclic loading paths and water contents.Likewise,these materials undergo different behaviors depending on their macro and microscopic properties(gradation,density,porosity,texture,mineralogy,particle geometry and orientation,temperature,among others).On the other hand,the main limitation of the mathematical equations is that their parameters are difficult to determine experimentally and are not constants of the material(they are state variables that can change with multiple factors).Additionally,these equations do not consider the boundary conditions to which UGM in pavements are exposed.Moreover,they are obtained from repeated load triaxial(RLT)tests,which cannot simulate the three cyclic stress components(vertical,horizontal,and shear)to which UGMs are subjected in a pavement.In recent years,there has been an increase in studies evaluating the use of recycled aggregates and the effect of temperature(particularly at subzero temperatures),but more research is still needed to reach definitive conclusions.展开更多
A rapid, sensitive, and robust reversed-phase liquid chromatography with tandem mass spectrometry method was developed and validated for the determination of total and unbound ceritinib, a secondgeneration ALK inhibit...A rapid, sensitive, and robust reversed-phase liquid chromatography with tandem mass spectrometry method was developed and validated for the determination of total and unbound ceritinib, a secondgeneration ALK inhibitor, in patient plasma and brain tumor tissue samples. Sample preparation involved simple protein precipitation with acetonitrile. Chromatographic separation was achieved on a Waters ACQUITY UPLC BEH C_(18) column using a 4-min gradient elution consisting of mobile phase A(0.1% formic acid in water) and mobile phase B(0.1% formic acid in acetonitrile), at a flow rate of 0.4 m L/min. Ceritinib and the internal standard([^(13)C_6]ceritinib) were monitored using multiple reaction monitoring mode under positive electrospray ionization. The lower limit of quantitation(LLOQ) was 1 n M of ceritinib in plasma. The calibration curve was linear over ceritinib concentration range of 1–2000 n M in plasma. The intra-and interday precision and accuracy were within the generally accepted criteria for bioanalytical method( o15%).The method was successfully applied to assess ceritinib brain tumor penetration, as assessed by the unbound drug brain concentration to unbound drug plasma concentration ratio, in patients with brain tumors.展开更多
Unbound granular material specifications for road pavements in Australia are primarily based on physical material specification rather than mechanical characterisation. This simplified approach does not reflect the ac...Unbound granular material specifications for road pavements in Australia are primarily based on physical material specification rather than mechanical characterisation. This simplified approach does not reflect the actual material performance under repeated dynamic traffic loads. There is a little information available on the influence of the local crushed rock properties and compacted layer properties on permanent deformation (PD). This study aims to characterise the local unbound granular materials in Victoria according to their PD behaviour under repeated loads and to develop a suitable shakedown criterion that could describe the PD of the tested materials to simplify the flexible pavement design. Repeated-load triaxial tests were conducted over several samples with a range of moisture contents, gradations, densities, and stress conditions. The laboratory test results showed that PD behaviour was influenced by several factors. In addition, the tested subbase-specified unbound granular materials reflect high PD resistance that is almost equivalent to basequality unbound granular materials. This may indicate that current requirements for the subbase-quality unbound granular materials are over-prescribe. Moreover, as the existing shakedown criterion was not applicable for the multi-stage repeated-load triaxial test and the local tested materials, a new shakedown criterion and new boundaries are proposed based on the PD behaviour. In the proposed criterion, the shakedown ranges are identified based on the curve angle of the PD vs. logarithm of the number of loading cycles, and this new criterion was validated using several materials from existing literature. The local tested base and subbase materials can be assigned as Range A when PD\1%, Range B when 1%\PD\3%, and Range C when PD[3%. The proposed criterion could provide a useful and quick approach to assess the PD of the unbound granular materials with both single and multistages of stresses.展开更多
Repeated load triaxial test is used to assess the deformation behaviour of unbound granular materials(UGMs) in flexible road pavements. Repeated load pulse characteristics(i.e. shape, loading period and rest period) a...Repeated load triaxial test is used to assess the deformation behaviour of unbound granular materials(UGMs) in flexible road pavements. Repeated load pulse characteristics(i.e. shape, loading period and rest period) are the stress configurations used in the experimental set-up to simulate the passing axle loads. Some researchers and standard testing protocols suggest a rest period of varying durations after a loading phase. A thorough review of existing literature and practises has revealed that there is no agreement about the effect of the rest period of vertical stress pulse on the deformation behaviour of the UGMs. Therefore,the main objective of this study is to investigate the effect of repeated stress rest period on the deformation behaviour of UGMs experimentally. Experiments are conducted, both with and without rest period, using basalt and granite crushed rocks from Victoria, Australia. Furthermore, in order to gain insight into the effect of the rest period, finite element modelling is also developed. Both the experimental and modelling results show that the rest period has a noticeable effect on both resilient and permanent deformation behaviours of UGMs. It is, therefore, recommended to take extra precautions while adopting a particular standard testing protocol and to supplement the results by additional tests with different loading configurations.展开更多
In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state...In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.展开更多
In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In additio...In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.展开更多
Several available mechanistic-empirical pavement design methods fail to include predictive model for permanent deformation(PD)of unbound granular materials(UGMs),which make these methods more conservative.In addition,...Several available mechanistic-empirical pavement design methods fail to include predictive model for permanent deformation(PD)of unbound granular materials(UGMs),which make these methods more conservative.In addition,there are limited regression models capable of predicting the PD under multistress levels,and these models have regression limitations and generally fail to cover the complexity of UGM behaviour.Recent researches are focused on using new methods of computational intelligence systems to address the problems,such as artificial neural network(ANN).In this context,we aim to develop an artificial neural model to predict the PD of UGMs exposed to repeated loads.Extensive repeated load triaxial tests(RLTTs)were conducted on base and subbase materials locally available in Victoria,Australia to investigate the PD properties of the tested materials and to prepare the database of the neural networks.Specimens were prepared over different moisture contents and gradations to cover a wide testing matrix.The ANN model consists of one input layer with five neurons,one hidden layer with twelve neurons,and one output layer with one neuron.The five inputs were the number of load cycles,deviatoric stress,moisture content,coefficient of uniformity,and coefficient of curvature.The sensitivity analysis showed that the most important indicator that impacts PD is the number of load cycles with influence factor of 41%.It shows that the ANN method is rapid and efficient to predict the PD,which could be implemented in the Austroads pavement design method.展开更多
By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, a...By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained.展开更多
The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite n...The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.展开更多
In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, ...In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.展开更多
The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of soluti...The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.展开更多
In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Dis...In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.展开更多
Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a...Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.展开更多
By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive...By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.展开更多
A standard assumption in the literature of learning theory is the samples which are drawn independently from an identical distribution with a uniform bounded output. This excludes the common case with Gaussian distrib...A standard assumption in the literature of learning theory is the samples which are drawn independently from an identical distribution with a uniform bounded output. This excludes the common case with Gaussian distribution. In this paper we extend these assumptions to a general case. To be precise, samples are drawn from a sequence of unbounded and non-identical probability distributions. By drift error analysis and Bennett inequality for the unbounded random variables, we derive a satisfactory learning rate for the ERM algorithm.展开更多
In this paper, we use the concentration-compactness principle together with the Mountain Pass Lemma to get the existence of nontrivial solutions and the existence of infinitely many solutions of the problem need not b...In this paper, we use the concentration-compactness principle together with the Mountain Pass Lemma to get the existence of nontrivial solutions and the existence of infinitely many solutions of the problem need not be compact operators from E to R~1.展开更多
The following nonlinear hyperbolic equation is discussed in this paper:where A= -? + Iandx∈Rn. The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local ...The following nonlinear hyperbolic equation is discussed in this paper:where A= -? + Iandx∈Rn. The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local solution of the above equation as M depends on x.展开更多
We consider fully nonlinear equations of the formF（z,u,Du,D<sup>2</sup>u） = F（x,y,u,u<sub>z</sub>,u<sub>y</sub>,u<sub>z</sub>z,u<sub>z</sub>y,u<sub>...We consider fully nonlinear equations of the formF（z,u,Du,D<sup>2</sup>u） = F（x,y,u,u<sub>z</sub>,u<sub>y</sub>,u<sub>z</sub>z,u<sub>z</sub>y,u<sub>y</sub>y） = 0 （1）in unbounded open subset G = R<sup>2</sup>\Ωof the plane R<sup>2</sup>,where F is a real continuous function on U = G×R×R<sup>2</sup>×R<sup>3</sup> and Ω= Ω<sub>i</sub>,Ω<sub>i</sub> is a simply connected region （i=1,2,"",N） . We assume the function F hascontinuous partial der ivatives F<sub>u<sub>z</sub>z</sub>, F<sub>u<sub>z</sub>y</sub>, F<sub>u<sub>y</sub>y</sub>. on U.For a real function r C（ G） a real function u（x,y） is called a solution of （1） satisfyingu = r on G,（2）if there exists a constant P0】2 such that u C<sup>1</sup> （ ） W<sup>2.p</sup><sub>Loc</sub>0 （G） satisfies （1） almost everywhere and （2）in the common sense.The method for treating the above exterior Dirichlet problem in a given unbounded region is as fol-展开更多
Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt[x(t)-P(t)x(h(t))]+Q(t)x(q(t))-R(t)x(r(t))=0, t≥t 0, where P(t)∈C([t 0, ∞), R), Q(t), R(t)∈C([t 0, ∞...Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt[x(t)-P(t)x(h(t))]+Q(t)x(q(t))-R(t)x(r(t))=0, t≥t 0, where P(t)∈C([t 0, ∞), R), Q(t), R(t)∈C([t 0, ∞), [WTHZ]R +), and h, q, r: [t 0, ∞)→R are continuously differentiable and strictly increasing, h(t)<t, q(t)<t, r(t)<t for all t≥t 0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable. [WTH1X]展开更多
文摘In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted combination,the non-uniform rational B-spline(NURBS)functions are employed as basis functions.Moreover,the unbounded and artificial domains,defined in the PML method,are contained in a single patch domain.Based on the proposed scheme,the approximation of the geometry problem is set in a new scheme in which the PML’s absorbing and attenuation properties and the description of traveling waves can be represented.This includes a higher continuity and smoother approximation of the computed domain.As high-order NURBS basis functions are non-interpolatory,a penalty method is present to apply a time-dependent displacement load.The performance of the NURBS-based PML is analyzed through numerical examples for 1D and 2D domains,considering homogeneous and heterogeneous media.Further,we verify the long-time numerical stability of the present method.The developed method can be used to simulate hypothetical stratified domains commonly encountered in soil-structure interaction analyses.
文摘When a vehicle moves over a flexible pavement structure,it generates loading and unloading cycles that produce recoverable(resilient)and permanent(plastic)deformations in the granular base and subbase layers,which are made of unbound granular materials(UGMs).The primary parameter used to evaluate the resilient response of UGMs in pavements is the resilient modulus(MR).The MR is widely used in calculating stress-strain states for flexible pavement design and as a control parameter during the construction process.It is also employed to understand the progression of distresses,such as fatigue cracking and rutting.The main objective of this study was to conduct a literature review on the resilient behavior of UGMs.This manuscript presents and describes the MR and the factors that influence it.It also outlines the evolution of the mathematical equations most commonly used to estimate and predict this physical parameter.Conclusions and recommendations for future research are provided at the end of the article.Despite the large amount of research done on the subject,the resilient behavior of UGM has not yet been fully understood.This is since these materials are highly heterogeneous and show nonlinear-anisotropic behavior under different cyclic loading paths and water contents.Likewise,these materials undergo different behaviors depending on their macro and microscopic properties(gradation,density,porosity,texture,mineralogy,particle geometry and orientation,temperature,among others).On the other hand,the main limitation of the mathematical equations is that their parameters are difficult to determine experimentally and are not constants of the material(they are state variables that can change with multiple factors).Additionally,these equations do not consider the boundary conditions to which UGM in pavements are exposed.Moreover,they are obtained from repeated load triaxial(RLT)tests,which cannot simulate the three cyclic stress components(vertical,horizontal,and shear)to which UGMs are subjected in a pavement.In recent years,there has been an increase in studies evaluating the use of recycled aggregates and the effect of temperature(particularly at subzero temperatures),but more research is still needed to reach definitive conclusions.
基金supported by the United States Public Health Service Cancer Center Support Grant P30 CA022453Novartis for providing the study drug and isotope-labeled internal standard and providing financial support for the clinical study
文摘A rapid, sensitive, and robust reversed-phase liquid chromatography with tandem mass spectrometry method was developed and validated for the determination of total and unbound ceritinib, a secondgeneration ALK inhibitor, in patient plasma and brain tumor tissue samples. Sample preparation involved simple protein precipitation with acetonitrile. Chromatographic separation was achieved on a Waters ACQUITY UPLC BEH C_(18) column using a 4-min gradient elution consisting of mobile phase A(0.1% formic acid in water) and mobile phase B(0.1% formic acid in acetonitrile), at a flow rate of 0.4 m L/min. Ceritinib and the internal standard([^(13)C_6]ceritinib) were monitored using multiple reaction monitoring mode under positive electrospray ionization. The lower limit of quantitation(LLOQ) was 1 n M of ceritinib in plasma. The calibration curve was linear over ceritinib concentration range of 1–2000 n M in plasma. The intra-and interday precision and accuracy were within the generally accepted criteria for bioanalytical method( o15%).The method was successfully applied to assess ceritinib brain tumor penetration, as assessed by the unbound drug brain concentration to unbound drug plasma concentration ratio, in patients with brain tumors.
文摘Unbound granular material specifications for road pavements in Australia are primarily based on physical material specification rather than mechanical characterisation. This simplified approach does not reflect the actual material performance under repeated dynamic traffic loads. There is a little information available on the influence of the local crushed rock properties and compacted layer properties on permanent deformation (PD). This study aims to characterise the local unbound granular materials in Victoria according to their PD behaviour under repeated loads and to develop a suitable shakedown criterion that could describe the PD of the tested materials to simplify the flexible pavement design. Repeated-load triaxial tests were conducted over several samples with a range of moisture contents, gradations, densities, and stress conditions. The laboratory test results showed that PD behaviour was influenced by several factors. In addition, the tested subbase-specified unbound granular materials reflect high PD resistance that is almost equivalent to basequality unbound granular materials. This may indicate that current requirements for the subbase-quality unbound granular materials are over-prescribe. Moreover, as the existing shakedown criterion was not applicable for the multi-stage repeated-load triaxial test and the local tested materials, a new shakedown criterion and new boundaries are proposed based on the PD behaviour. In the proposed criterion, the shakedown ranges are identified based on the curve angle of the PD vs. logarithm of the number of loading cycles, and this new criterion was validated using several materials from existing literature. The local tested base and subbase materials can be assigned as Range A when PD\1%, Range B when 1%\PD\3%, and Range C when PD[3%. The proposed criterion could provide a useful and quick approach to assess the PD of the unbound granular materials with both single and multistages of stresses.
文摘Repeated load triaxial test is used to assess the deformation behaviour of unbound granular materials(UGMs) in flexible road pavements. Repeated load pulse characteristics(i.e. shape, loading period and rest period) are the stress configurations used in the experimental set-up to simulate the passing axle loads. Some researchers and standard testing protocols suggest a rest period of varying durations after a loading phase. A thorough review of existing literature and practises has revealed that there is no agreement about the effect of the rest period of vertical stress pulse on the deformation behaviour of the UGMs. Therefore,the main objective of this study is to investigate the effect of repeated stress rest period on the deformation behaviour of UGMs experimentally. Experiments are conducted, both with and without rest period, using basalt and granite crushed rocks from Victoria, Australia. Furthermore, in order to gain insight into the effect of the rest period, finite element modelling is also developed. Both the experimental and modelling results show that the rest period has a noticeable effect on both resilient and permanent deformation behaviours of UGMs. It is, therefore, recommended to take extra precautions while adopting a particular standard testing protocol and to supplement the results by additional tests with different loading configurations.
文摘In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.
基金Supported by the National Natural Science Foundation of China(Grant No.11271092)the Natural Science Foundation of Guangdong Province(Grant No.S2011010005367)
文摘In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.
文摘Several available mechanistic-empirical pavement design methods fail to include predictive model for permanent deformation(PD)of unbound granular materials(UGMs),which make these methods more conservative.In addition,there are limited regression models capable of predicting the PD under multistress levels,and these models have regression limitations and generally fail to cover the complexity of UGM behaviour.Recent researches are focused on using new methods of computational intelligence systems to address the problems,such as artificial neural network(ANN).In this context,we aim to develop an artificial neural model to predict the PD of UGMs exposed to repeated loads.Extensive repeated load triaxial tests(RLTTs)were conducted on base and subbase materials locally available in Victoria,Australia to investigate the PD properties of the tested materials and to prepare the database of the neural networks.Specimens were prepared over different moisture contents and gradations to cover a wide testing matrix.The ANN model consists of one input layer with five neurons,one hidden layer with twelve neurons,and one output layer with one neuron.The five inputs were the number of load cycles,deviatoric stress,moisture content,coefficient of uniformity,and coefficient of curvature.The sensitivity analysis showed that the most important indicator that impacts PD is the number of load cycles with influence factor of 41%.It shows that the ANN method is rapid and efficient to predict the PD,which could be implemented in the Austroads pavement design method.
文摘By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained.
基金This work was supported by the China State Major Key Project for Basic Researches Science Fund of the Ministry of Education
文摘The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.
基金NSFC!( 1 9671 0 1 7) and NSF!( A970 1 2 ) of Fujian.
文摘In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.
文摘The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.
文摘In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.
文摘Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.
文摘By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
文摘A standard assumption in the literature of learning theory is the samples which are drawn independently from an identical distribution with a uniform bounded output. This excludes the common case with Gaussian distribution. In this paper we extend these assumptions to a general case. To be precise, samples are drawn from a sequence of unbounded and non-identical probability distributions. By drift error analysis and Bennett inequality for the unbounded random variables, we derive a satisfactory learning rate for the ERM algorithm.
文摘In this paper, we use the concentration-compactness principle together with the Mountain Pass Lemma to get the existence of nontrivial solutions and the existence of infinitely many solutions of the problem need not be compact operators from E to R~1.
文摘The following nonlinear hyperbolic equation is discussed in this paper:where A= -? + Iandx∈Rn. The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local solution of the above equation as M depends on x.
基金The project is supported by the Natural Science Foundation of Fujian,P.R.China.
文摘We consider fully nonlinear equations of the formF（z,u,Du,D<sup>2</sup>u） = F（x,y,u,u<sub>z</sub>,u<sub>y</sub>,u<sub>z</sub>z,u<sub>z</sub>y,u<sub>y</sub>y） = 0 （1）in unbounded open subset G = R<sup>2</sup>\Ωof the plane R<sup>2</sup>,where F is a real continuous function on U = G×R×R<sup>2</sup>×R<sup>3</sup> and Ω= Ω<sub>i</sub>,Ω<sub>i</sub> is a simply connected region （i=1,2,"",N） . We assume the function F hascontinuous partial der ivatives F<sub>u<sub>z</sub>z</sub>, F<sub>u<sub>z</sub>y</sub>, F<sub>u<sub>y</sub>y</sub>. on U.For a real function r C（ G） a real function u（x,y） is called a solution of （1） satisfyingu = r on G,（2）if there exists a constant P0】2 such that u C<sup>1</sup> （ ） W<sup>2.p</sup><sub>Loc</sub>0 （G） satisfies （1） almost everywhere and （2）in the common sense.The method for treating the above exterior Dirichlet problem in a given unbounded region is as fol-
文摘Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt[x(t)-P(t)x(h(t))]+Q(t)x(q(t))-R(t)x(r(t))=0, t≥t 0, where P(t)∈C([t 0, ∞), R), Q(t), R(t)∈C([t 0, ∞), [WTHZ]R +), and h, q, r: [t 0, ∞)→R are continuously differentiable and strictly increasing, h(t)<t, q(t)<t, r(t)<t for all t≥t 0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable. [WTH1X]
