Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in R^(n).In this paper,the authors are interested in the problem of identifying the type(local minimizer,maximizer or not ...Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in R^(n).In this paper,the authors are interested in the problem of identifying the type(local minimizer,maximizer or not extremum point)of a given isolated KKT point x^(*)of f over S.To this end,the authors investigate some properties of the tangency variety of f on S at x^(*),by which the authors introduce the definition of faithful radius of f over S at x^(*).Then,the authors show that the type of x^(*)can be determined by the global extrema of f over the intersection of S and the Euclidean ball centered at x^(*)with a faithful radius.Finally,the authors propose an algorithm involving algebraic computations to compute a faithful radius of x*and determine its type.展开更多
Galileo mission detected the magnetic anomalies originated from Galilean moons.These anomalies are likely generated in the moons' interiors,under the influence of a strong ambient Jovian field.Among various possib...Galileo mission detected the magnetic anomalies originated from Galilean moons.These anomalies are likely generated in the moons' interiors,under the influence of a strong ambient Jovian field.Among various possible generation mechanisms of the anomalies,we focus on magneto-convection and dynamos in the interiors via numerical simulation.To mimic the electromagnetic environment of the moons,we introduce in our numerical model an external uniform magnetic field B0 with a fixed orientation but varying field strength.Our results show that a finite B0 can substantially alter the dynamo processes inside the core.When the ambient field strength B0 increases to approximately 40% of the field generated by the pure dynamo action,the convective state in the core changes significantly:the convective flow decreases by 80% in magnitude,but the differential rotation becomes stronger in much of the fluid layer,leading to a stronger field generated in the core.The field morphologies inside the core tend to align with the ambient field,while the flow patterns show the symmetry-breaking effect under the influence of B0.Furthermore,the generated field tends to be temporally more stable.展开更多
基金supported by the Chinese National Natural Science Foundation under Grant No.11571350the Science and Technology Development Plan Project of Jilin Province,China under Grant No.YDZJ202201ZYTS302+1 种基金the National Research Foundation of Korea(NRF)Grant Funded by the Korean Government under Grand No.NRF-2019R1A2C1008672the International Centre for Research and Postgraduate Training in Mathematics(ICRTM)under Grant No.ICRTM012022.01。
文摘Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in R^(n).In this paper,the authors are interested in the problem of identifying the type(local minimizer,maximizer or not extremum point)of a given isolated KKT point x^(*)of f over S.To this end,the authors investigate some properties of the tangency variety of f on S at x^(*),by which the authors introduce the definition of faithful radius of f over S at x^(*).Then,the authors show that the type of x^(*)can be determined by the global extrema of f over the intersection of S and the Euclidean ball centered at x^(*)with a faithful radius.Finally,the authors propose an algorithm involving algebraic computations to compute a faithful radius of x*and determine its type.
基金supported by National Natural Science Foundation of China (Grant No. 40328006)
文摘Galileo mission detected the magnetic anomalies originated from Galilean moons.These anomalies are likely generated in the moons' interiors,under the influence of a strong ambient Jovian field.Among various possible generation mechanisms of the anomalies,we focus on magneto-convection and dynamos in the interiors via numerical simulation.To mimic the electromagnetic environment of the moons,we introduce in our numerical model an external uniform magnetic field B0 with a fixed orientation but varying field strength.Our results show that a finite B0 can substantially alter the dynamo processes inside the core.When the ambient field strength B0 increases to approximately 40% of the field generated by the pure dynamo action,the convective state in the core changes significantly:the convective flow decreases by 80% in magnitude,but the differential rotation becomes stronger in much of the fluid layer,leading to a stronger field generated in the core.The field morphologies inside the core tend to align with the ambient field,while the flow patterns show the symmetry-breaking effect under the influence of B0.Furthermore,the generated field tends to be temporally more stable.
