In this analysis, natural systems are posed to subsystemize in a manner facilitating both structured information/energy sharing and an entropy maximization process projecting a three-dimensional, spatial outcome. Nume...In this analysis, natural systems are posed to subsystemize in a manner facilitating both structured information/energy sharing and an entropy maximization process projecting a three-dimensional, spatial outcome. Numerical simulations were first carried out to determine whether n × n input-output matrices could, once entropy-maximized, project a three-dimensional Euclidean metric. Only 4 × 4 matrices could;a small proportion passed the test. Larger proportions passed when grouped random patterns on and within two- and three-dimensional forms were tested. The pattern of structural zonation within the earth was then tested in analogous fashion using spatial autocorrelation measures, and for three time periods: current, 95 million years b.p. and 200 million years b.p. All expected results were obtained;not only do the geometries of zonation project a three-dimensional structure as anticipated, but also do secondary statistical measures reveal levels of equilibrium among the zones in all three cases that are nearly total, distinguishing them from simulations that do not incorporate a varying-surface zone-width element.展开更多
Recently,a class of logarithmic-quadratic proximal(LQP)methods was intro- duced by Auslender,Teboulle and Ben-Tiba.The inexact versions of these methods solve the sub-problems in each iteration approximately.In this p...Recently,a class of logarithmic-quadratic proximal(LQP)methods was intro- duced by Auslender,Teboulle and Ben-Tiba.The inexact versions of these methods solve the sub-problems in each iteration approximately.In this paper,we present a practical inexactness criterion for the inexact version of these methods.展开更多
1 Introduction and preliminaries Let E be a real Banach space with the norm‖·‖and E~* denote the dual of E.Let KE be a cone,that is,a closed convex subset such that λKK for every λ】0 and {K}∩{-K}={0},wh...1 Introduction and preliminaries Let E be a real Banach space with the norm‖·‖and E~* denote the dual of E.Let KE be a cone,that is,a closed convex subset such that λKK for every λ】0 and {K}∩{-K}={0},where 0 is展开更多
文摘In this analysis, natural systems are posed to subsystemize in a manner facilitating both structured information/energy sharing and an entropy maximization process projecting a three-dimensional, spatial outcome. Numerical simulations were first carried out to determine whether n × n input-output matrices could, once entropy-maximized, project a three-dimensional Euclidean metric. Only 4 × 4 matrices could;a small proportion passed the test. Larger proportions passed when grouped random patterns on and within two- and three-dimensional forms were tested. The pattern of structural zonation within the earth was then tested in analogous fashion using spatial autocorrelation measures, and for three time periods: current, 95 million years b.p. and 200 million years b.p. All expected results were obtained;not only do the geometries of zonation project a three-dimensional structure as anticipated, but also do secondary statistical measures reveal levels of equilibrium among the zones in all three cases that are nearly total, distinguishing them from simulations that do not incorporate a varying-surface zone-width element.
基金The author was supported by NSFC grant 70371019.
文摘Recently,a class of logarithmic-quadratic proximal(LQP)methods was intro- duced by Auslender,Teboulle and Ben-Tiba.The inexact versions of these methods solve the sub-problems in each iteration approximately.In this paper,we present a practical inexactness criterion for the inexact version of these methods.
文摘1 Introduction and preliminaries Let E be a real Banach space with the norm‖·‖and E~* denote the dual of E.Let KE be a cone,that is,a closed convex subset such that λKK for every λ】0 and {K}∩{-K}={0},where 0 is
