In this paper,we investigate the tensor similarity and propose the T-Jordan canonical form and its properties.The concepts of the T-minimal polynomial and the T-characteristic polynomial are proposed.As a special case...In this paper,we investigate the tensor similarity and propose the T-Jordan canonical form and its properties.The concepts of the T-minimal polynomial and the T-characteristic polynomial are proposed.As a special case,we present properties when two tensors commute based on the tensor T-product.We prove that the Cayley-Hamilton theorem also holds for tensor cases.Then,we focus on the tensor decompositions:T-polar,T-LU,T-QR and T-Schur decompositions of tensors are obtained.When an F-square tensor is not invertible with the T-product,we study the T-group inverse and the T-Drazin inverse which can be viewed as the extension of matrix cases.The expressions of the T-group and T-Drazin inverses are given by the T-Jordan canonical form.The polynomial form of the T-Drazin inverse is also proposed.In the last part,we give the T-core-nilpotent decomposition and show that the T-index and T-Drazin inverses can be given by a limit process.展开更多
Fish (mostly Tilapia zillii), (TZ), mass mortality in Lake Kinneret initiated a study of the biology of TZ in Lake Kinneret. The study included several aspects: spawning and nesting behavior, feeding habits, the statu...Fish (mostly Tilapia zillii), (TZ), mass mortality in Lake Kinneret initiated a study of the biology of TZ in Lake Kinneret. The study included several aspects: spawning and nesting behavior, feeding habits, the status of TZ in the Kinneret fishery and temperature tolerance. The merit of TZ to commercial landing fishery is negligible, but this specimen is one of the most common fishes in the lake. Several environmental factors are considered as promoters of the epilimnetic temperature decline: Jordan water inputs in winter season as a heat source parameter. ENSO (EL-NIÑO/Southern Oscillation) acts as a cooling enhancement factor. Supportive data on the impact of ENSO were found in two terrestrial agricultural monitors in the northern and southern parts of the drainage basin. Gut content analysis of young fingerlings and an adult TZ specimen, indicated the significant contribution of benthic sources which are common in the shallows. The great adaptive capabilities of breeding TZ with various bottom habitats are demonstrated.展开更多
End-Permian Gondwana siliciclastics (50 - 70 m) of the Um Irna F exposed along the NE Dead Sea, exhibit carbonate-free fining upward cycles (FUC) deposited during acid flash flood events under tropical climate. Severa...End-Permian Gondwana siliciclastics (50 - 70 m) of the Um Irna F exposed along the NE Dead Sea, exhibit carbonate-free fining upward cycles (FUC) deposited during acid flash flood events under tropical climate. Several ferruginous paleosol intercalations cover periods of drying upward formation (DUP) under semiarid/arid climates. Thin grey pelite beds interbedded between paleosol and overlying FUC, are interpreted as tephra deposits sourced in Siberian LIP- and Neo-Tethys (NT)-Degassing. The Wadi Bassat en Nimra-section exhibits the P-T transitional zone where flash flood deposits meet supra-/intertidal sediments of the southward-directed transgressive NT. Decreasing flash-flooding continued through the Lower Scythian (Ma’in F.) during transgression, reworking, and resedimentation. Two euryhaline foraminifera-bearing limestone beds are discussed as indicators for the end of mass extinction (recovery phase: ca. 250.8 - 250.4 Ma) possibly correlating with the Maximum Flooding Surface MFS Tr 10 (ca. 250.5 Ma) on the Arabian Shelf (Khuff cycles B;A). Comparable data from the Germanic Basin as FUC/DUP-cycles, tephrasuspicious “Grey Beds” with high concentrations of As, Co, Pb, Zn, and Cu as well as the U-Pb Age data of the Siberian LIP meet the PTB-Zone between the MFSs Intervals P 40 (ca. 254 Ma)/Tr 10 (ca 250.5 Ma) on the Arabian Shelf. MFS (Tr 10, 20, 30) and SBs resp. on the Arabian Plate, as well as Scythian Substage boundaries correlate with ∂<sup>13</sup> C-excursions recorded at Musandam, UAE. Thereby, the ratio of greenhouse gases (+climate forcing)/aerosols und tephra (-climate forcing) takes a significant influence on the ∂<sup>13</sup>C-Variation.展开更多
基金the National Natural Science Foundation of China(Grant No.11771099)the Hong Kong Research Grant Council(Grant Nos.PolyU 15302114,15300715,15301716 and 15300717)the Innovation Program of Shanghai Municipal Education Commission.
文摘In this paper,we investigate the tensor similarity and propose the T-Jordan canonical form and its properties.The concepts of the T-minimal polynomial and the T-characteristic polynomial are proposed.As a special case,we present properties when two tensors commute based on the tensor T-product.We prove that the Cayley-Hamilton theorem also holds for tensor cases.Then,we focus on the tensor decompositions:T-polar,T-LU,T-QR and T-Schur decompositions of tensors are obtained.When an F-square tensor is not invertible with the T-product,we study the T-group inverse and the T-Drazin inverse which can be viewed as the extension of matrix cases.The expressions of the T-group and T-Drazin inverses are given by the T-Jordan canonical form.The polynomial form of the T-Drazin inverse is also proposed.In the last part,we give the T-core-nilpotent decomposition and show that the T-index and T-Drazin inverses can be given by a limit process.
文摘Fish (mostly Tilapia zillii), (TZ), mass mortality in Lake Kinneret initiated a study of the biology of TZ in Lake Kinneret. The study included several aspects: spawning and nesting behavior, feeding habits, the status of TZ in the Kinneret fishery and temperature tolerance. The merit of TZ to commercial landing fishery is negligible, but this specimen is one of the most common fishes in the lake. Several environmental factors are considered as promoters of the epilimnetic temperature decline: Jordan water inputs in winter season as a heat source parameter. ENSO (EL-NIÑO/Southern Oscillation) acts as a cooling enhancement factor. Supportive data on the impact of ENSO were found in two terrestrial agricultural monitors in the northern and southern parts of the drainage basin. Gut content analysis of young fingerlings and an adult TZ specimen, indicated the significant contribution of benthic sources which are common in the shallows. The great adaptive capabilities of breeding TZ with various bottom habitats are demonstrated.
文摘End-Permian Gondwana siliciclastics (50 - 70 m) of the Um Irna F exposed along the NE Dead Sea, exhibit carbonate-free fining upward cycles (FUC) deposited during acid flash flood events under tropical climate. Several ferruginous paleosol intercalations cover periods of drying upward formation (DUP) under semiarid/arid climates. Thin grey pelite beds interbedded between paleosol and overlying FUC, are interpreted as tephra deposits sourced in Siberian LIP- and Neo-Tethys (NT)-Degassing. The Wadi Bassat en Nimra-section exhibits the P-T transitional zone where flash flood deposits meet supra-/intertidal sediments of the southward-directed transgressive NT. Decreasing flash-flooding continued through the Lower Scythian (Ma’in F.) during transgression, reworking, and resedimentation. Two euryhaline foraminifera-bearing limestone beds are discussed as indicators for the end of mass extinction (recovery phase: ca. 250.8 - 250.4 Ma) possibly correlating with the Maximum Flooding Surface MFS Tr 10 (ca. 250.5 Ma) on the Arabian Shelf (Khuff cycles B;A). Comparable data from the Germanic Basin as FUC/DUP-cycles, tephrasuspicious “Grey Beds” with high concentrations of As, Co, Pb, Zn, and Cu as well as the U-Pb Age data of the Siberian LIP meet the PTB-Zone between the MFSs Intervals P 40 (ca. 254 Ma)/Tr 10 (ca 250.5 Ma) on the Arabian Shelf. MFS (Tr 10, 20, 30) and SBs resp. on the Arabian Plate, as well as Scythian Substage boundaries correlate with ∂<sup>13</sup> C-excursions recorded at Musandam, UAE. Thereby, the ratio of greenhouse gases (+climate forcing)/aerosols und tephra (-climate forcing) takes a significant influence on the ∂<sup>13</sup>C-Variation.
