In this paper, finite determination of bifurcation problems is discussed with respect to two equivalences-right and right-left. Some necessory and sufficient conditions are given.
The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v ...The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v = |z|k, local automorphisms are always determined by their 1-jets. Using this result, the second part describes special normal forms which by an additional normalization eliminate the nonlinear symmetries of the model and allows to decide effectively about local equivalence of two hypersurfaces given in this normal form.展开更多
The strong contact finite determinacy of relative map germs is studied by means of classical singularity theory. We first give the definition of a strong relative contact equivalence （or KS,T equivalence） and then p...The strong contact finite determinacy of relative map germs is studied by means of classical singularity theory. We first give the definition of a strong relative contact equivalence （or KS,T equivalence） and then prove two theorems which can be used to distinguish the contact finite determinacy of relative map germs, that is, f is finite determined relative to KS,T if and only if there exists a positive integer k, such that M^5（n）ε（S;n）p ∩→ TKs,T（f）.展开更多
The calcite mylonites in the Xar Moron-Changchun shear zone show a significance dextral shearing characteristics. The asymmetric(σ-structure) calcite/quartz grains or aggregates, asymmetry of calcite c-axes fabric di...The calcite mylonites in the Xar Moron-Changchun shear zone show a significance dextral shearing characteristics. The asymmetric(σ-structure) calcite/quartz grains or aggregates, asymmetry of calcite c-axes fabric diagrams and the oblique foliation of recrystallized calcite grains correspond to a top-to-E shearing. Mineral deformation behaviors, twin morphology, C-axis EBSD fabrics, and quartz grain size-frequency diagrams demonstrate that the ductile shear zone was developed under conditions of greenschist facies, with the range of deformation temperatures from 200 to 300°C. These subgrains of host grains and surrounding recrystallized grains, strong undulose extinction, and slightly curved grain boundaries are probably results of intracrystalline deformation and dynamic recrystallization implying that the deformation took place within the dislocation-creep regime at shallow crustal levels. The calculated paleo-strain rates are between 10-7.87s-1 and 10-11.49s-1 with differential stresses of 32.63-63.94 MPa lying at the higher bound of typical strain rates in shear zones at crustal levels, and may indicate a relatively rapid deformation. The S-L-calcite tectonites have undergone a component of uplift which led to subhorizontal lifting in an already non-coaxial compressional deformation regime with a bulk pure shear-dominated general shear. This E-W large-scale dextral strike-slip movement is a consequence of the eastward extrusion of the Xing’an-Mongolian Orogenic Belt, and results from far-field forces associated with Late Triassic convergence domains after the final closure of the Paleo-Asian Ocean.展开更多
文摘In this paper, finite determination of bifurcation problems is discussed with respect to two equivalences-right and right-left. Some necessory and sufficient conditions are given.
文摘The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v = |z|k, local automorphisms are always determined by their 1-jets. Using this result, the second part describes special normal forms which by an additional normalization eliminate the nonlinear symmetries of the model and allows to decide effectively about local equivalence of two hypersurfaces given in this normal form.
基金Science Foundation (20070105) for Young Teachers of Northeast Normal University
文摘The strong contact finite determinacy of relative map germs is studied by means of classical singularity theory. We first give the definition of a strong relative contact equivalence （or KS,T equivalence） and then prove two theorems which can be used to distinguish the contact finite determinacy of relative map germs, that is, f is finite determined relative to KS,T if and only if there exists a positive integer k, such that M^5（n）ε（S;n）p ∩→ TKs,T（f）.
基金financially co-supported by the National Key R&D Program of China (Grant No.2017YFC0601401 and 2017YFC0601300-01)the National Natural Science Foundation of China (Grant no. 41602211 and 41230206)
文摘The calcite mylonites in the Xar Moron-Changchun shear zone show a significance dextral shearing characteristics. The asymmetric(σ-structure) calcite/quartz grains or aggregates, asymmetry of calcite c-axes fabric diagrams and the oblique foliation of recrystallized calcite grains correspond to a top-to-E shearing. Mineral deformation behaviors, twin morphology, C-axis EBSD fabrics, and quartz grain size-frequency diagrams demonstrate that the ductile shear zone was developed under conditions of greenschist facies, with the range of deformation temperatures from 200 to 300°C. These subgrains of host grains and surrounding recrystallized grains, strong undulose extinction, and slightly curved grain boundaries are probably results of intracrystalline deformation and dynamic recrystallization implying that the deformation took place within the dislocation-creep regime at shallow crustal levels. The calculated paleo-strain rates are between 10-7.87s-1 and 10-11.49s-1 with differential stresses of 32.63-63.94 MPa lying at the higher bound of typical strain rates in shear zones at crustal levels, and may indicate a relatively rapid deformation. The S-L-calcite tectonites have undergone a component of uplift which led to subhorizontal lifting in an already non-coaxial compressional deformation regime with a bulk pure shear-dominated general shear. This E-W large-scale dextral strike-slip movement is a consequence of the eastward extrusion of the Xing’an-Mongolian Orogenic Belt, and results from far-field forces associated with Late Triassic convergence domains after the final closure of the Paleo-Asian Ocean.
