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Optimality Conditions for Strictly Efficient Solutions in Set-valued Optimization

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Acta Mathematicae Applicatae Sinica 2020年第4期36卷 891-901页

作者： yi-hong xu Department of Mathematics School of SciencesNanchang UniversityNanchang 330031China

A new kind of tangent derivative,M-derivative,for set-valued function is introduced with help of a modified Dubovitskij-Miljutin *** generalized pseudoconvex set-valued functions are *** both the objective function and constraint function are M-derivative,under the assumption of near conesubconvexlikeness,by applying properties of the set of strictly efficient points and a separation theorem for convex sets,Fritz John and Kuhn-Tucker necessary optimality conditions are obtained for a point pair to be a strictly efficient element of set-valued optimization *** the assumption of generalized pseudoconvexity,a Kuhn-Tucker sufficient optimality condition is obtained for a point pair to be a strictly efficient element of set-valued optimization problem.

关键词： strict efficiency near cone-subconvexlikeness set-valued optimization cone

A New Algorithm for Total Variation Based Image Denoising

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Acta Mathematicae Applicatae Sinica 2012年第4期28卷 721-730页

作者： yi-ping xu School of Science Southwest University of Science and Technology

We propose a new algorithm for the total variation based on image denoising problem. The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteration. An algebraic multi-grid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. Numerical experiments demonstrate that this algorithm is efficient even for images with large signal-to-noise ratio.

关键词： image denoising total variation split Bregman method algebraic multi-grid method,Krylov subspace acceleration

A stable staggered-grid finite-difference scheme for acoustic modeling beyond conventional stability limit

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Petroleum Science 2024年第1期21卷 182-194页

作者： Jing-yi xu Yang Liu National Key Laboratory of Petroleum Resources and Engineering China University of Petroleum(Beijing)Beijing 102249China China University of Petroleum(Beijing) Karamay CampusKaramay 834000XinjiangChina

Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical *** improved methods are proposed to enhance the accuracy of numerical ***,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid *** solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL ***,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL ***,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD *** addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed *** derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.

关键词： Acoustic wave Staggered-grid finite-difference(SGFD) modeling Courant-friedrichs-lewy(CFL)number Stability

A Combination Model for Image Denoising

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Acta Mathematicae Applicatae Sinica 2016年第3期32卷 781-792页

作者： yi-ping xu School of Science Southwest University of Science and Technology

In this paper, we propose an efficient combination model of the second-order ROF model and a simple fourth-order partial differential equation （PDE） for image denoising. The split Bregman method is used to convert the nonlinear combination model into a linear system in the outer iteration, and an algebraic multigrid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. At the same time, we prove that the model is strictly convex and exists a unique global minimizer. We have also conducted a variety of numerical experiments to analyze the parameter selection criteria and discuss the performance of ~he fourth-order PDE in the combination model. The results show that our model can reduce blocky effects and our algorithm is efficient and robust to solve the proposed model.

关键词： image denoising partial differential equations split Bregman method algebraic multi-grid method Krylov subspace acceleration

Volatiles in the mantle transition zone and their effects on big mantle wedge systems

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National Science Review 2024年第6期11卷 15-18页

作者： Yu Wang yi-Gang xu State Key Laboratory of Isotope Geochemistry Guangzhou Institute of Geochemistry Chinese Academy of Sciences Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou)

The mantle transition zone (MTZ), located between the upper and lower mantle, is characterized by sudden seismicvelocity discontinuities at depths of 410 and 660 km where significant change in mineralogical composition occurs. As a link between the upper and lower mantle,the MTZ is a layer of special significance in Earth’s deep structure, and a critical interface in geodynamics and material circulation.

关键词： systems effects mantle their transition volatiles wedge zone

Higher pressure differentiation of arc magmas under thicker crust

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National Science Review 2023年第3期10卷 100-101页

作者： yi-Gang xu State Key Laboratory of Isotope Geochemistry Guangzhou Institute of Geochemistry Chinese Academy of Sciences Southern Marine Science and Engineering Guangdong Laboratory(Guangzhou)

The formation of continental crust is pivotal to understanding the evolution of the earth and its *** average intermediate or’andesitic’bulk composition and characteristic depletion of niobium of the continental crust are strikingly matched by convergent margin magmas [1].This has led to the inference that most continental crust is derived from igneous,arc ***,continental crust has characteristically higher Mg#(>0.5) than most oceanic arc andesites (<0.5).

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A coupling VWM/CFD/CSD method for rotor airload prediction

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Chinese Journal of Aeronautics 2017年第1期30卷 204-215页

作者： Shi Yongjie xu yi xu Guohua Wei Peng National Laboratory of Science and Technology on Rotorcraft Aerodynamics Nanjing University of Aeronautics and Astronautics Pre-noncommissioned Officers Training Base Army Aviation Institute

A coupling fluid-structure method with a combination of viscous wake model（VWM）,computational fluid dynamics（CFD） and comprehensive structural dynamics（CSD） modules is developed in this paper for rotor unsteady airload prediction. The hybrid VWM/CFD solver is employed to model the nonlinear aerodynamic phenomena and complicated rotor wake dynamics;the moderate deflection beam theory is implemented to predict the blade structural deformation; the loose coupling strategy based on the ‘delt method＇ is used to couple the fluid and structure *** cases of Helishape 7A rotor are performed first to investigate the effect of elastic deformation on airloads. Then, two challenging forward flight conditions of UH-60 A helicopter rotor are investigated, and the simulated results of wake geometry, chordwise pressure distribution and sectional normal force show excellent agreement with available test data; a comparison with traditional CFD/CSD method is also presented to illustrate the efficiency of the developed method.

关键词： Airload CFD/CSD coupling Navier-Stokes equations Rotor Viscous wake model

Numerical study on flow control of ship airwake and rotor airload during helicopter shipboard landing

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Chinese Journal of Aeronautics 2019年第2期32卷 324-336页

作者： Yongjie SHI Xiang HE yi xu Guohua xu National Key Laboratory of Rotorcraft Aeromechanics Nanjing University of Aeronautics and Astronautics Shanghai Institute of Electro-Mechanical Engineering

A numerical study on flow control of ship airwake during shipboard landing is carried out to address the effect of flow control devices on helicopter rotor airload. The in-house Reynolds Averaged Navier-Stokes(RANS) based solver Rotorcraft AeroDynamics and Aeroacoustics Solver(RADAS), with combination of momentum source approach is employed to conduct the helicopter shipboard landing simulation. The control effects of three aerodynamic modifications of ship superstructure, i.e. ramp, notch and flap, in different Wind-Over-Deck(WOD) conditions are *** the steady simulation results, the effect of spatial variation of ship airwake on rotor airloads is concluded. The aerodynamic modifications reduce the strength of shedding vortex and increase rotor normal force through delaying and relieving flow separation, and therefore are beneficial to alleviate the limitation of control inputs. By contrast, the perturbation of unsteady ship airwake can cause the serious oscillation of rotor forces during shipboard landing. The unsteady simulations show that the turbulence intensity of ship airwake and oscillatory rotor airloading, represented by Root-Mean-Square(RMS) loading, can be remarkably reduced by the ramp and notch modifications, while the flap modification has adverse effect. It means that flow control devices have large potential benefits to alleviate the pilot's workload and improve the shipboard landing safety, but they should be well designed to avoid the introduction of more vortex, which leads to increase in disturbance of flow field.

关键词： Flow control Helicopter Rotor airload Ship airwake Shipboard landing

On rigidity of Clifford torus in a unit sphere

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Applied Mathematics(A Journal of Chinese Universities) 2011年第1期26卷 121-126页

作者： xu yi-wen xu Zhi-yuana Department of Mathematical Sciences Indiana University-Purdue University Indianapolis 402 N. Blackford St. Indianapolis IN 46202-3267 USA Department of Mathematics Zhejiang Sci-Tech University Hangzhou 310018 China Center of Mathematical Sciences Zhejiang University Hangzhou 310027 China

We extend the scalar curvature pinching theorems due to Peng-Terng, Wei-xu and Suh-Yang. Let M be an n-dimensional compact minimal hypersurface in S^n＋1 satisfying S f4 - f^2 3 ≤1/nS^3 where S is the squared norm of the second fundamental form of M, and fk = ∑λi^k and λi（1 ≤ i ≤ n） are the principal curvatures of M. We prove that there exists a positive constant δ（n）（≥ n/2） depending only on n such that if n ≤ S ≤ n ＋δ（n）, then S ≡ n, i.e., M is one of the Clifford torus S^K （√k/n） × S^n-k （V√n-k/n） for 1≤ k ≤ n - i. Moreover, we prove that if S is a constant, then there exists a positive constant T（n）（≥ n -2/3） depending only on n such that ifn ≤ S 〈 n ＋ τ（n）, then S ≡n, i.e.. M is a Clifford torus.

关键词： Minimal hypersurface rigidity scalar curvature second fundamental form Clifford torus.