In this paper, we derive the a priori estimates for a class of more general (k, l)-Hessian quotient type equations involving u and Du on the right hand function. As an application we prove the Liouville theorem depend...In this paper, we derive the a priori estimates for a class of more general (k, l)-Hessian quotient type equations involving u and Du on the right hand function. As an application we prove the Liouville theorem depending on Pogorelov type estimates. On the other hand, we obtain the existence and uniqueness of the k-admissible solution for these general equations with the Neumann boundary condition, based on some growth conditions for the right hand function.展开更多
The high-resolution nonlinear simultaneous inversion of petrophysical parameters is based on Bayesian statistics and combines petrophysics with geostatistical a priori information. We used the fast Fourier transform–...The high-resolution nonlinear simultaneous inversion of petrophysical parameters is based on Bayesian statistics and combines petrophysics with geostatistical a priori information. We used the fast Fourier transform–moving average（FFT–MA） and gradual deformation method（GDM） to obtain a reasonable variogram by using structural analysis and geostatistical a priori information of petrophysical parameters. Subsequently, we constructed the likelihood function according to the statistical petrophysical model. Finally, we used the Metropolis algorithm to sample the posteriori probability density and complete the inversion of the petrophysical parameters. We used the proposed method to process data from an oil fi eld in China and found good match between inversion and real data with high-resolution. In addition, the direct inversion of petrophysical parameters avoids the error accumulation and decreases the uncertainty, and increases the computational effi ciency.展开更多
This study investigates the use of dynamic a priori error information according to atmospheric moistness and the use of quality controls in temperature and water vapor profile retrievals from hyperspectral infrared ...This study investigates the use of dynamic a priori error information according to atmospheric moistness and the use of quality controls in temperature and water vapor profile retrievals from hyperspectral infrared （IR） sounders. Temperature and water vapor profiles are retrieved from Atmospheric InfraRed Sounder （AIRS） radiance measurements by applying a physical iterative method using regression retrieval as the first guess. Based on the dependency of first-guess errors on the degree of atmospheric moistness, the a priori first-guess errors classified by total precipitable water （TPW） are applied in the AIRS physical retrieval procedure. Compared to the retrieval results from a fixed a priori error, boundary layer moisture retrievals appear to be improved via TPW classification of a priori first-guess errors. Six quality control （QC） tests, which check non-converged or bad retrievals, large residuals, high terrain and desert areas, and large temperature and moisture deviations from the first guess regression retrieval, are also applied in the AIRS physical retrievals. Significantly large errors are found for the retrievals rejected by these six QCs, and the retrieval errors are substantially reduced via QC over land, which suggest the usefulness and high impact of the QCs, especially over land. In conclusion, the use of dynamic a priori error information according to atmospheric moistness, and the use of appropriate QCs dealing with the geographical information and the deviation from the first-guess as well as the conventional inverse performance are suggested to improve temperature and moisture retrievals and their applications.展开更多
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc...In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.展开更多
The optocoupler is a weak link in the inertial navigation platform of a kind of guided munitions.It is necessary to use accelerated storage test to verify the storage life of long storage products.Especially for small...The optocoupler is a weak link in the inertial navigation platform of a kind of guided munitions.It is necessary to use accelerated storage test to verify the storage life of long storage products.Especially for small sample products,it is very important to obtain prior information for the design and implementation of accelerated degradation test.In this paper,the optocoupler failure mechanism verification test is designed and the experimental results are analyzed and the prior information is obtained.The results show that optocouplers have two failure modes,one is sudden failure and the other is degradation failure;the maximum temperature stress of optocoupler can’t exceed 140℃;the increase of leakage current of optocoupler is caused by movable ions contaminating the LED chip.The surface leakage current is proportional to the adsorption amount.The increase of leakage current makes p-n junction tunneling effect occur which LEDs the failure of the optocoupler.The lifetime distribution model of the optocoupler is determined by the failure physics.The lifetime of the optocoupler is subject to the lognormal distribution.The degeneracy orbit of the optocoupler leakage current is described by a power law model.The estimated values of the orbital parameters are initially calculated and the parameters of its life distribution function are deduced.The above information lays a good foundation for the optimization design and data processing of the accelerated degradation experiment.展开更多
Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not suppl...Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the A and B satisfy the following structural conditions展开更多
Computed tomography(CT) reconstruction with a well-registered priori magnetic resonance imaging(MRI) image can improve reconstruction results with low-dose CT, because well-registered CT and MRI images have similar st...Computed tomography(CT) reconstruction with a well-registered priori magnetic resonance imaging(MRI) image can improve reconstruction results with low-dose CT, because well-registered CT and MRI images have similar structures. However, in clinical settings, the CT image of patients does not always match the priori MRI image because of breathing and movement of patients during CT scanning. To improve the image quality in this case, multi-group datasets expansion is proposed in this paper. In our method, multi-group CT-MRI datasets are formed by expanding CT-MRI datasets. These expanded datasets can also be used by most existing CT-MRI algorithms and improve the reconstructed image quality when the CT image of a patient is not registered with the priori MRI image. In the experiments, we evaluate the performance of the algorithm by using multi-group CT-MRI datasets in several unregistered situations. Experiments show that when the CT and priori MRI images are not registered, the reconstruction results of using multi-group dataset expansion are better than those obtained without using the expansion.展开更多
In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2...In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2)^(q12)(x)+h_(1)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,(−Δ)_(a2)^(β/2)u2(x)=u_(1)^(q21)(x)+u_(2)^(q22)(x)+h_(2)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,u_(1)(x)=0,u_(2)(x)=0,x∈R^(n)∖Ω.Here(−Δ)_(a1)^(α/2) and(−Δ)_(a2)^(β/2) denote weighted fractional Laplacians andΩ⊂R^(n) is a C^(2) bounded domain.It is shown that under some assumptions on h_(i)(i=1,2),the problem admits at least one positive solution(u_(1)(x),u_(2)(x)).We first obtain the{a priori}bounds of solutions to the system by using the direct blow-up method of Chen,Li and Li.Then the proof of existence is based on a topological degree theory.展开更多
The <i>general purpose of the research</i>—systematical clarifying and explicating the too vague proper philosophical concepts of space, void, matter, motion, inertia, for making a logical harmony between...The <i>general purpose of the research</i>—systematical clarifying and explicating the too vague proper philosophical concepts of space, void, matter, motion, inertia, for making a logical harmony between them and the corresponding notions of proper physics. The <i>special purpose of the research</i>—invention (construction) of a <i>formal inference of the well-known Newton’s first law of mechanics</i> within a logically formalized axiomatic epistemology system from a set of precisely defined presumptions. For realizing this aim <i>the following work has been done</i>: a two-valued algebraic system of metaphysics as formal axiology has been applied to philosophical epistemology and philosophy of nature;a formal axiomatic theory called Sigma has been applied to physics for realizing the above-indicated special purpose of the research. Thus, constructing a discrete mathematical model of relationship between universal epistemology and philosophy of physics has been done. <i>Research results</i>: The main hitherto not published significantly new nontrivial scientific result of applied investigations presented in this article is a <i>formal inference of the well-known Newton’s first law of mechanics</i> within the formal axiomatic epistemology system Sigma from conjunction of the <i>formal-axiological analog</i> of the proper-law-of-mechanics (which <i>analog</i> is the <i>formal-axiological law</i> of two-valued algebra of metaphysics) and the assumption of a-priori-ness of knowledge. For obtaining this main research result, a set of accessory nontrivial novelties has been used, for instance;a precise algorithmic definition is given for the notion “<i>law of metaphysics</i>” in the algebraic system of metaphysics as formal axiology;a <i>formal-axiological equivalence</i> in the algebraic system is defined precisely. Precise tabular definitions are given for relevant evaluation-functions determined by evaluation-arguments, for example;“movement of (what, whom) <i>x</i>”;“speed of <i>x</i>”;“vector of <i>x</i>”;“velocity of <i>x</i>”;“magnitude of <i>x</i>”;“finiteness (definiteness) of <i>x</i>”;“dynamical closed-ness (isolated-ness) of <i>x</i>”;“constant-ness, immutability, conservation of <i>x</i>”.展开更多
The growing number of mobile users, as well as the diversification in types of services have resulted in increasing demands for wireless network bandwidth in recent years. Although evolving transmission techniques are...The growing number of mobile users, as well as the diversification in types of services have resulted in increasing demands for wireless network bandwidth in recent years. Although evolving transmission techniques are able to enlarge the network capacity to some degree, they still cannot satisfy the requirements of mobile users. Meanwhile, following Moore's Law, the data processing capabilities of mobile user terminals are continuously improving. In this paper, we explore possible methods of trading strong computational power at wireless terminals for transmission efficiency of communications. Taking the specific scenario of wireless video conversation, we propose a model-based video coding scheme by learning the structures in multimedia contents. Benefiting from both strong computing capability and pre-learned model priors, only low-dimensional parameters need to be transmitted; and the intact multimedia contents can also be reconstructed at the receivers in real-time. Experiment results indicate that, compared to conventional video codecs, the proposed scheme significantly reduces the data rate with the aid of computational capability at wireless terminals.展开更多
A new priori estimate of lower- solution is made for the following quasilinear elliptic equation : integral(G) {del v . A (x, u, del u) + vB (x, u, del u)} dx = 0, For All v is an element of (W) over circle(p)(1) (G)....A new priori estimate of lower- solution is made for the following quasilinear elliptic equation : integral(G) {del v . A (x, u, del u) + vB (x, u, del u)} dx = 0, For All v is an element of (W) over circle(p)(1) (G). The result presented in this paper enriches and extends the corresponding result of Gilbarg-Trudinger.展开更多
Recently,many data anonymization methods have been proposed to protect privacy in the applications of data mining.But few of them have considered the threats from user's priori knowledge of data patterns.To solve ...Recently,many data anonymization methods have been proposed to protect privacy in the applications of data mining.But few of them have considered the threats from user's priori knowledge of data patterns.To solve this problem,a flexible method was proposed to randomize the dataset,so that the user could hardly obtain the sensitive data even knowing data relationships in advance.The method also achieves a high level of accuracy in the mining process as demonstrated in the experiments.展开更多
We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to de...We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.展开更多
In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.
Finite Element Method (FEM), when applied to solve problems, has faced some challenges over the years, such as time consumption and the complexity of assumptions. In particular, the making of assumptions has had a sig...Finite Element Method (FEM), when applied to solve problems, has faced some challenges over the years, such as time consumption and the complexity of assumptions. In particular, the making of assumptions has had a significant influence on the accuracy of the method, making it mandatory to carry out sensitivity analysis. The sensitivity analysis helps to identify the level of impact the assumptions have on the method. However, sensitivity analysis via FEM can be very challenging. A priori error estimation, an integral part of FEM, is a basic mathematical tool for predicting the accuracy of numerical solutions. By understanding the relationship between the mesh size, the order of basis functions, and the resulting error, practitioners can effectively design and apply FEM to solve complex Partial Differential Equations (PDEs) with confidence in the reliability of their results. Thus, the coercive property and A priori error estimation based on the L1 formula on a mesh in time and the Mamadu-Njoseh basis functions in space are investigated for a linearly distributed time-order fractional telegraph equation with restricted initial conditions. For this purpose, we constructed a mathematical proof of the coercive property for the fully discretized scheme. Also, we stated and proved a cardinal theorem for a priori error estimation of the approximate solution for the fully discretized scheme. We noticed the role of the restricted initial conditions imposed on the solution in the analysis of a priori error estimation.展开更多
In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation o...In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H<sup>1</sup> and L<sup>2</sup> norms. Finally, some numerical experiments are carried out to support the theoretical results.展开更多
基金supported by the National Natural Science Foundation of China(No.11971157).
文摘In this paper, we derive the a priori estimates for a class of more general (k, l)-Hessian quotient type equations involving u and Du on the right hand function. As an application we prove the Liouville theorem depending on Pogorelov type estimates. On the other hand, we obtain the existence and uniqueness of the k-admissible solution for these general equations with the Neumann boundary condition, based on some growth conditions for the right hand function.
基金sponsored by the National Basic Research Program of China(No.2013CB228604)the Major National Science and Technology Projects(No.2011ZX05009)+1 种基金the Natural Science Foundation of Shandong Province(No.ZR2011DQ013)the National Science Foundation of China(No.41204085)
文摘The high-resolution nonlinear simultaneous inversion of petrophysical parameters is based on Bayesian statistics and combines petrophysics with geostatistical a priori information. We used the fast Fourier transform–moving average（FFT–MA） and gradual deformation method（GDM） to obtain a reasonable variogram by using structural analysis and geostatistical a priori information of petrophysical parameters. Subsequently, we constructed the likelihood function according to the statistical petrophysical model. Finally, we used the Metropolis algorithm to sample the posteriori probability density and complete the inversion of the petrophysical parameters. We used the proposed method to process data from an oil fi eld in China and found good match between inversion and real data with high-resolution. In addition, the direct inversion of petrophysical parameters avoids the error accumulation and decreases the uncertainty, and increases the computational effi ciency.
基金supported by GOES-R Algorithm Working Group Program and GOES-R High Impact Weather Project (Grant No NA10NES4400013)supported by the Korea Meteorological Administration Research and Development Program under Grant CATER 2006-2103the BK21 Project of the Korean Government
文摘This study investigates the use of dynamic a priori error information according to atmospheric moistness and the use of quality controls in temperature and water vapor profile retrievals from hyperspectral infrared （IR） sounders. Temperature and water vapor profiles are retrieved from Atmospheric InfraRed Sounder （AIRS） radiance measurements by applying a physical iterative method using regression retrieval as the first guess. Based on the dependency of first-guess errors on the degree of atmospheric moistness, the a priori first-guess errors classified by total precipitable water （TPW） are applied in the AIRS physical retrieval procedure. Compared to the retrieval results from a fixed a priori error, boundary layer moisture retrievals appear to be improved via TPW classification of a priori first-guess errors. Six quality control （QC） tests, which check non-converged or bad retrievals, large residuals, high terrain and desert areas, and large temperature and moisture deviations from the first guess regression retrieval, are also applied in the AIRS physical retrievals. Significantly large errors are found for the retrievals rejected by these six QCs, and the retrieval errors are substantially reduced via QC over land, which suggest the usefulness and high impact of the QCs, especially over land. In conclusion, the use of dynamic a priori error information according to atmospheric moistness, and the use of appropriate QCs dealing with the geographical information and the deviation from the first-guess as well as the conventional inverse performance are suggested to improve temperature and moisture retrievals and their applications.
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grants 60474027 and 10771211.
文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.
基金supported by the National Natural Science Foundation of China of China(No.61471385)。
文摘The optocoupler is a weak link in the inertial navigation platform of a kind of guided munitions.It is necessary to use accelerated storage test to verify the storage life of long storage products.Especially for small sample products,it is very important to obtain prior information for the design and implementation of accelerated degradation test.In this paper,the optocoupler failure mechanism verification test is designed and the experimental results are analyzed and the prior information is obtained.The results show that optocouplers have two failure modes,one is sudden failure and the other is degradation failure;the maximum temperature stress of optocoupler can’t exceed 140℃;the increase of leakage current of optocoupler is caused by movable ions contaminating the LED chip.The surface leakage current is proportional to the adsorption amount.The increase of leakage current makes p-n junction tunneling effect occur which LEDs the failure of the optocoupler.The lifetime distribution model of the optocoupler is determined by the failure physics.The lifetime of the optocoupler is subject to the lognormal distribution.The degeneracy orbit of the optocoupler leakage current is described by a power law model.The estimated values of the orbital parameters are initially calculated and the parameters of its life distribution function are deduced.The above information lays a good foundation for the optimization design and data processing of the accelerated degradation experiment.
文摘Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the A and B satisfy the following structural conditions
基金the National Natural Science Foundation of China(No.813716234)the National Basic Research Program(973)of China(No.2010CB834302)Shanghai Jiao Tong University Medical Engineering Cross Research Funds(Nos.YG2013MS30 and YG2014ZD05)
文摘Computed tomography(CT) reconstruction with a well-registered priori magnetic resonance imaging(MRI) image can improve reconstruction results with low-dose CT, because well-registered CT and MRI images have similar structures. However, in clinical settings, the CT image of patients does not always match the priori MRI image because of breathing and movement of patients during CT scanning. To improve the image quality in this case, multi-group datasets expansion is proposed in this paper. In our method, multi-group CT-MRI datasets are formed by expanding CT-MRI datasets. These expanded datasets can also be used by most existing CT-MRI algorithms and improve the reconstructed image quality when the CT image of a patient is not registered with the priori MRI image. In the experiments, we evaluate the performance of the algorithm by using multi-group CT-MRI datasets in several unregistered situations. Experiments show that when the CT and priori MRI images are not registered, the reconstruction results of using multi-group dataset expansion are better than those obtained without using the expansion.
文摘In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2)^(q12)(x)+h_(1)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,(−Δ)_(a2)^(β/2)u2(x)=u_(1)^(q21)(x)+u_(2)^(q22)(x)+h_(2)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,u_(1)(x)=0,u_(2)(x)=0,x∈R^(n)∖Ω.Here(−Δ)_(a1)^(α/2) and(−Δ)_(a2)^(β/2) denote weighted fractional Laplacians andΩ⊂R^(n) is a C^(2) bounded domain.It is shown that under some assumptions on h_(i)(i=1,2),the problem admits at least one positive solution(u_(1)(x),u_(2)(x)).We first obtain the{a priori}bounds of solutions to the system by using the direct blow-up method of Chen,Li and Li.Then the proof of existence is based on a topological degree theory.
文摘The <i>general purpose of the research</i>—systematical clarifying and explicating the too vague proper philosophical concepts of space, void, matter, motion, inertia, for making a logical harmony between them and the corresponding notions of proper physics. The <i>special purpose of the research</i>—invention (construction) of a <i>formal inference of the well-known Newton’s first law of mechanics</i> within a logically formalized axiomatic epistemology system from a set of precisely defined presumptions. For realizing this aim <i>the following work has been done</i>: a two-valued algebraic system of metaphysics as formal axiology has been applied to philosophical epistemology and philosophy of nature;a formal axiomatic theory called Sigma has been applied to physics for realizing the above-indicated special purpose of the research. Thus, constructing a discrete mathematical model of relationship between universal epistemology and philosophy of physics has been done. <i>Research results</i>: The main hitherto not published significantly new nontrivial scientific result of applied investigations presented in this article is a <i>formal inference of the well-known Newton’s first law of mechanics</i> within the formal axiomatic epistemology system Sigma from conjunction of the <i>formal-axiological analog</i> of the proper-law-of-mechanics (which <i>analog</i> is the <i>formal-axiological law</i> of two-valued algebra of metaphysics) and the assumption of a-priori-ness of knowledge. For obtaining this main research result, a set of accessory nontrivial novelties has been used, for instance;a precise algorithmic definition is given for the notion “<i>law of metaphysics</i>” in the algebraic system of metaphysics as formal axiology;a <i>formal-axiological equivalence</i> in the algebraic system is defined precisely. Precise tabular definitions are given for relevant evaluation-functions determined by evaluation-arguments, for example;“movement of (what, whom) <i>x</i>”;“speed of <i>x</i>”;“vector of <i>x</i>”;“velocity of <i>x</i>”;“magnitude of <i>x</i>”;“finiteness (definiteness) of <i>x</i>”;“dynamical closed-ness (isolated-ness) of <i>x</i>”;“constant-ness, immutability, conservation of <i>x</i>”.
基金supported by the National Basic Research Project of China (973) (2013CB329006)National Natural Science Foundation of China (NSFC, 61101071,61471220, 61021001)Tsinghua University Initiative Scientific Research Program
文摘The growing number of mobile users, as well as the diversification in types of services have resulted in increasing demands for wireless network bandwidth in recent years. Although evolving transmission techniques are able to enlarge the network capacity to some degree, they still cannot satisfy the requirements of mobile users. Meanwhile, following Moore's Law, the data processing capabilities of mobile user terminals are continuously improving. In this paper, we explore possible methods of trading strong computational power at wireless terminals for transmission efficiency of communications. Taking the specific scenario of wireless video conversation, we propose a model-based video coding scheme by learning the structures in multimedia contents. Benefiting from both strong computing capability and pre-learned model priors, only low-dimensional parameters need to be transmitted; and the intact multimedia contents can also be reconstructed at the receivers in real-time. Experiment results indicate that, compared to conventional video codecs, the proposed scheme significantly reduces the data rate with the aid of computational capability at wireless terminals.
文摘A new priori estimate of lower- solution is made for the following quasilinear elliptic equation : integral(G) {del v . A (x, u, del u) + vB (x, u, del u)} dx = 0, For All v is an element of (W) over circle(p)(1) (G). The result presented in this paper enriches and extends the corresponding result of Gilbarg-Trudinger.
文摘Recently,many data anonymization methods have been proposed to protect privacy in the applications of data mining.But few of them have considered the threats from user's priori knowledge of data patterns.To solve this problem,a flexible method was proposed to randomize the dataset,so that the user could hardly obtain the sensitive data even knowing data relationships in advance.The method also achieves a high level of accuracy in the mining process as demonstrated in the experiments.
文摘We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.
文摘In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.
文摘Finite Element Method (FEM), when applied to solve problems, has faced some challenges over the years, such as time consumption and the complexity of assumptions. In particular, the making of assumptions has had a significant influence on the accuracy of the method, making it mandatory to carry out sensitivity analysis. The sensitivity analysis helps to identify the level of impact the assumptions have on the method. However, sensitivity analysis via FEM can be very challenging. A priori error estimation, an integral part of FEM, is a basic mathematical tool for predicting the accuracy of numerical solutions. By understanding the relationship between the mesh size, the order of basis functions, and the resulting error, practitioners can effectively design and apply FEM to solve complex Partial Differential Equations (PDEs) with confidence in the reliability of their results. Thus, the coercive property and A priori error estimation based on the L1 formula on a mesh in time and the Mamadu-Njoseh basis functions in space are investigated for a linearly distributed time-order fractional telegraph equation with restricted initial conditions. For this purpose, we constructed a mathematical proof of the coercive property for the fully discretized scheme. Also, we stated and proved a cardinal theorem for a priori error estimation of the approximate solution for the fully discretized scheme. We noticed the role of the restricted initial conditions imposed on the solution in the analysis of a priori error estimation.
文摘In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H<sup>1</sup> and L<sup>2</sup> norms. Finally, some numerical experiments are carried out to support the theoretical results.
