The utilization of gradient operators is prevalent in image processing,as they effectively detect edges and provide directional information.However,these operators only differentiate the horizontal and vertical direct...The utilization of gradient operators is prevalent in image processing,as they effectively detect edges and provide directional information.However,these operators only differentiate the horizontal and vertical directions,ignoring details and causing loss of information in other directions.This paper introduces the shear gradient operator to overcome this limitation by capturing details accurately in multiple directions.It investigates the properties of the shear gradient operator and proposes the shear total variation(STV)norm for image deblurring.By combining non-convex regularization to avoid excessive penalty and retain image details,a novel deblurring model integrating the STV norm and the L_(1)/L_(2) minimization is proposed.The alternating direction method of multipliers(ADMM)algorithm is employed to solve this computationally challenging model,demonstrating exceptional performance in non-blind image deblurring through experiments.展开更多
In this note, we obtain the elliptic estimate for diffusion operator L = △＋△Ф·△ on complete, noncompact Riemannian manifolds, under the curvature condition CD（K, m）, which generalizes B. L. Kotschwar＇s wo...In this note, we obtain the elliptic estimate for diffusion operator L = △＋△Ф·△ on complete, noncompact Riemannian manifolds, under the curvature condition CD（K, m）, which generalizes B. L. Kotschwar＇s work [5]. As an application, we get estimate on the heat kernel. The Bernstein-type gradient estimate for SchrSdinger-type gradient is also derived.展开更多
By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conser...By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under Gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed展开更多
In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=...In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=1,2.Under the appropriate conditions on gi and g2,our main results are obtained by using the monotone iterative method and the Arzela-Ascoli theorem.Furthermore,our main results also extend the previous existence results for both the single equation and systems.展开更多
The dynamic behavior of a viscoelastic high-order shear microbeam is studied based on a new constitutive model which incorporates size effects and viscoelasticity simultaneously.The size effects are modeled by the non...The dynamic behavior of a viscoelastic high-order shear microbeam is studied based on a new constitutive model which incorporates size effects and viscoelasticity simultaneously.The size effects are modeled by the nonlocal gradient elasticity,while viscoelastic effects are modeled by fractional-order derivatives.The constitutive relation and the equations of motion are both differential equations with fractional-order derivatives.Based on the Laplace transform and inverse transform,the analytical solution of the dynamic response under a step load is obtained in terms of the Mittag–Leffler function.In order to verify the reliability of the analytical solution,a comparison with the numerical solution is also provided.Based on the numerical results,the effects of the nonlocal parameter,strain gradient parameter,fractional-order parameter,and viscosity coefficient on the dynamic response of the viscoelastic microbeam are discussed.It is found that the influences of the fractional order and the coefficient of viscosity on the dynamic response of the microbeam are very different,although both are related to the viscoelastic behavior.展开更多
As stochastic gradient and Skorohod integral operators, is an adjoint pair of unbounded operators on Guichardet Spaces. In this paper, we define an adjoint pair of operator , where with being the conditional expectati...As stochastic gradient and Skorohod integral operators, is an adjoint pair of unbounded operators on Guichardet Spaces. In this paper, we define an adjoint pair of operator , where with being the conditional expectation operator. We show that (resp.) is essentially a kind of localization of the stochastic gradient operators (resp. Skorohod integral operators δ). We examine that and satisfy a local CAR (canonical ani-communication relation) and forms a mutually orthogonal operator sequence although each is not a projection operator. We find that is s-adapted operator if and only if is s-adapted operator. Finally we show application exponential vector formulation of QS calculus.展开更多
A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strai...A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length.The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic time.Numerical calculations are performed to analyze the effects of the nonlocal strain gradient parameters,the spatiotemporal fractional order,the nonlocal characteristic length,and the memory characteristic time on the natural frequencies,the vibration attenuation,and the phase shift between the temperature field and the displacement field.The numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.展开更多
Perfect anomalous reflections have been demonstrated in optical phase gradient metasurfaces(PGMs),but they suffer from single-frequency(narrow-band)response due to the intrinsic limitation of natural geometric periodi...Perfect anomalous reflections have been demonstrated in optical phase gradient metasurfaces(PGMs),but they suffer from single-frequency(narrow-band)response due to the intrinsic limitation of natural geometric periodicity.Here,we provide both numerical and analytical evidence that a depth gradient metasurface can achieve discrete ultra-broadband perfect anomalous reflection in the microwave range in the absence of geometric periodicity.Remarkably,by adjusting the operating frequency of the incident wave,the same effect can be steadily obtained via a physically equivalent phase periodicity in the PGM.Based on this mechanism,a perfect retroreflector with a broadband response ranging from 1 GHz to 40 GHz is realized.Our work has promising applications in communication,source tracking,and military satellites.展开更多
Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {An}n∈N be a family of monotone and Lipschitz continuos mappings of C into E＊. In this article, we consider th...Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {An}n∈N be a family of monotone and Lipschitz continuos mappings of C into E＊. In this article, we consider the improved gradient method by the hybrid method in mathematical programming [i0] for solving the variational inequality problem for {AN} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space.展开更多
On accomplishing an efficacious object tracking,the activity of an object concerned becomes notified in a forthright manner.An accurate form of object tracking task necessitates a robust object tracking procedures irr...On accomplishing an efficacious object tracking,the activity of an object concerned becomes notified in a forthright manner.An accurate form of object tracking task necessitates a robust object tracking procedures irrespective of hardware assistance.Such approaches inferred a vast computational complexity to track an object with high accuracy in a stipulated amount of processing time.On the other hand,the tracking gets affected owing to the existence of varied quality diminishing factors such as occlusion,illumination changes,shadows etc.,In order to rectify all these inadequacies in tracking an object,a novel background normalization procedure articulated on the basis of a textural pattern is proposed in this paper.After preprocessing an acquired image,employment of an Environmental Succession Prediction algorithm for discriminating disparate background environment by background clustering approach have been accomplished.Afterward,abstract textural characterizations through utilization of a Probability based Gradient Pattern(PGP)approach for recognizing the similarity between patterns obtained so far.Comparison between standardized frame obtained in prior and those processed patterns detects the motion exposed by an object and the object concerned gets identified within a blob.Hence,the system is resistant towards illumination variations.These illumination variation was interpreted in object tracking residing within a dynamic background.Devised approach certainly outperforms other object tracking methodologies like Group Target Tracking(GTT),Vi PER-GT,grabcut,snakes in terms of accuracy and average time.Proposed PGP-based pattern texture analysis is compared with Gamifying Video Object(GVO)approach and hence,it evidently outperforms in terms of precision,recall and F1 measure.展开更多
The effect of the Raman-pulse duration related to the magnetic field gradient, as a systematic error, is playing an important role on evaluating the performance of high-precision atomic gravimeters. We study this effe...The effect of the Raman-pulse duration related to the magnetic field gradient, as a systematic error, is playing an important role on evaluating the performance of high-precision atomic gravimeters. We study this effect with a simplified theoretical model of the time-propagation operator. According to the typical parameters, we find that this effect should be taken into account when the gravimeter reaches an accuracy of 10^-10g, and the larger the pulse duration is, the more obvious the systematic effect will be. Finally, we make a simple discussion on the possibility of testing this effect.展开更多
The aim of this paper is to study the notion of the gradient observability on a subregion w of the evolution domain W and also we consider the case where the subregion of interest is a boundary part of the system evol...The aim of this paper is to study the notion of the gradient observability on a subregion w of the evolution domain W and also we consider the case where the subregion of interest is a boundary part of the system evolution domain for the class of semilinear hyperbolic systems. We show, under some hypotheses, that the flux reconstruction is guaranteed by means of the sectorial approach combined with fixed point techniques. This leads to several interesting results which are performed through numerical examples and simulations.展开更多
In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogene...In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.展开更多
The aim of this work is to study the notion of the gradient observability on a subregion?ω of the evolution domain?Ω for a class of semilinear hyperbolic systems. We show, under some hypothesis, that the gradient re...The aim of this work is to study the notion of the gradient observability on a subregion?ω of the evolution domain?Ω for a class of semilinear hyperbolic systems. We show, under some hypothesis, that the gradient reconstruction is achieved following sectorial approach combined with fixed point techniques. The obtained results lead to an algorithm which can be implemented numerically.展开更多
基金Supported by the National Natural Science Foundation of China(61701004)。
文摘The utilization of gradient operators is prevalent in image processing,as they effectively detect edges and provide directional information.However,these operators only differentiate the horizontal and vertical directions,ignoring details and causing loss of information in other directions.This paper introduces the shear gradient operator to overcome this limitation by capturing details accurately in multiple directions.It investigates the properties of the shear gradient operator and proposes the shear total variation(STV)norm for image deblurring.By combining non-convex regularization to avoid excessive penalty and retain image details,a novel deblurring model integrating the STV norm and the L_(1)/L_(2) minimization is proposed.The alternating direction method of multipliers(ADMM)algorithm is employed to solve this computationally challenging model,demonstrating exceptional performance in non-blind image deblurring through experiments.
基金China Scholarship Council for financial support(2007U13020)
文摘In this note, we obtain the elliptic estimate for diffusion operator L = △＋△Ф·△ on complete, noncompact Riemannian manifolds, under the curvature condition CD（K, m）, which generalizes B. L. Kotschwar＇s work [5]. As an application, we get estimate on the heat kernel. The Bernstein-type gradient estimate for SchrSdinger-type gradient is also derived.
基金Project supported by the National Natural Science Foundation of China (No.10572076)
文摘By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under Gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed
基金supported by NSFC(12001344)the Graduate Education and Teaching Innovation Project of Shanxi,China(2021YJJG142)+1 种基金the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0123)the Technology Research Foundation of Chongqing Educational Committee(KJQN201900539 and KJQN202000528)。
文摘In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=1,2.Under the appropriate conditions on gi and g2,our main results are obtained by using the monotone iterative method and the Arzela-Ascoli theorem.Furthermore,our main results also extend the previous existence results for both the single equation and systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.12072022,11872105,and 11911530176)the Fundamental Research Funds for the Central Universities(FRF-BR-18-008B,FRF-TW-2018-005).
文摘The dynamic behavior of a viscoelastic high-order shear microbeam is studied based on a new constitutive model which incorporates size effects and viscoelasticity simultaneously.The size effects are modeled by the nonlocal gradient elasticity,while viscoelastic effects are modeled by fractional-order derivatives.The constitutive relation and the equations of motion are both differential equations with fractional-order derivatives.Based on the Laplace transform and inverse transform,the analytical solution of the dynamic response under a step load is obtained in terms of the Mittag–Leffler function.In order to verify the reliability of the analytical solution,a comparison with the numerical solution is also provided.Based on the numerical results,the effects of the nonlocal parameter,strain gradient parameter,fractional-order parameter,and viscosity coefficient on the dynamic response of the viscoelastic microbeam are discussed.It is found that the influences of the fractional order and the coefficient of viscosity on the dynamic response of the microbeam are very different,although both are related to the viscoelastic behavior.
文摘As stochastic gradient and Skorohod integral operators, is an adjoint pair of unbounded operators on Guichardet Spaces. In this paper, we define an adjoint pair of operator , where with being the conditional expectation operator. We show that (resp.) is essentially a kind of localization of the stochastic gradient operators (resp. Skorohod integral operators δ). We examine that and satisfy a local CAR (canonical ani-communication relation) and forms a mutually orthogonal operator sequence although each is not a projection operator. We find that is s-adapted operator if and only if is s-adapted operator. Finally we show application exponential vector formulation of QS calculus.
基金the National Natural Science Foundation of China(Nos.12072022 and 11872105)the Fundamental Research Funds for the Central Universities(Nos.FRF-TW-2018-005 and FRF-BR-18-008B)。
文摘A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length.The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic time.Numerical calculations are performed to analyze the effects of the nonlocal strain gradient parameters,the spatiotemporal fractional order,the nonlocal characteristic length,and the memory characteristic time on the natural frequencies,the vibration attenuation,and the phase shift between the temperature field and the displacement field.The numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.
基金supported by the National Natural Science Foundation of China(Grant Nos.12274313,62275184,and 62411540033)Collaborative Innovation Center of Suzhou Nano Science and Technology,Suzhou Basic Research Project(Grant No.SJC2023003)+1 种基金the Gusu Leading Talent Plan for Scientific and Technological Innovation and Entrepreneurship(Grant No.ZXL2024400)the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Perfect anomalous reflections have been demonstrated in optical phase gradient metasurfaces(PGMs),but they suffer from single-frequency(narrow-band)response due to the intrinsic limitation of natural geometric periodicity.Here,we provide both numerical and analytical evidence that a depth gradient metasurface can achieve discrete ultra-broadband perfect anomalous reflection in the microwave range in the absence of geometric periodicity.Remarkably,by adjusting the operating frequency of the incident wave,the same effect can be steadily obtained via a physically equivalent phase periodicity in the PGM.Based on this mechanism,a perfect retroreflector with a broadband response ranging from 1 GHz to 40 GHz is realized.Our work has promising applications in communication,source tracking,and military satellites.
文摘Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {An}n∈N be a family of monotone and Lipschitz continuos mappings of C into E＊. In this article, we consider the improved gradient method by the hybrid method in mathematical programming [i0] for solving the variational inequality problem for {AN} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space.
文摘On accomplishing an efficacious object tracking,the activity of an object concerned becomes notified in a forthright manner.An accurate form of object tracking task necessitates a robust object tracking procedures irrespective of hardware assistance.Such approaches inferred a vast computational complexity to track an object with high accuracy in a stipulated amount of processing time.On the other hand,the tracking gets affected owing to the existence of varied quality diminishing factors such as occlusion,illumination changes,shadows etc.,In order to rectify all these inadequacies in tracking an object,a novel background normalization procedure articulated on the basis of a textural pattern is proposed in this paper.After preprocessing an acquired image,employment of an Environmental Succession Prediction algorithm for discriminating disparate background environment by background clustering approach have been accomplished.Afterward,abstract textural characterizations through utilization of a Probability based Gradient Pattern(PGP)approach for recognizing the similarity between patterns obtained so far.Comparison between standardized frame obtained in prior and those processed patterns detects the motion exposed by an object and the object concerned gets identified within a blob.Hence,the system is resistant towards illumination variations.These illumination variation was interpreted in object tracking residing within a dynamic background.Devised approach certainly outperforms other object tracking methodologies like Group Target Tracking(GTT),Vi PER-GT,grabcut,snakes in terms of accuracy and average time.Proposed PGP-based pattern texture analysis is compared with Gamifying Video Object(GVO)approach and hence,it evidently outperforms in terms of precision,recall and F1 measure.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11625417,11727809,11474115,91636219,and 91636221)the Post-doctoral Science Foundation of China(Grant No.2017M620308)
文摘The effect of the Raman-pulse duration related to the magnetic field gradient, as a systematic error, is playing an important role on evaluating the performance of high-precision atomic gravimeters. We study this effect with a simplified theoretical model of the time-propagation operator. According to the typical parameters, we find that this effect should be taken into account when the gravimeter reaches an accuracy of 10^-10g, and the larger the pulse duration is, the more obvious the systematic effect will be. Finally, we make a simple discussion on the possibility of testing this effect.
文摘The aim of this paper is to study the notion of the gradient observability on a subregion w of the evolution domain W and also we consider the case where the subregion of interest is a boundary part of the system evolution domain for the class of semilinear hyperbolic systems. We show, under some hypotheses, that the flux reconstruction is guaranteed by means of the sectorial approach combined with fixed point techniques. This leads to several interesting results which are performed through numerical examples and simulations.
基金supported by Ministry of Education and Training(Vietnam),under grant number B2023-SPS-01。
文摘In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.
文摘The aim of this work is to study the notion of the gradient observability on a subregion?ω of the evolution domain?Ω for a class of semilinear hyperbolic systems. We show, under some hypothesis, that the gradient reconstruction is achieved following sectorial approach combined with fixed point techniques. The obtained results lead to an algorithm which can be implemented numerically.
