It is shown that for any two n x n complex valued matrices A, B the inequality ｜perA-perB｜≤n｜｜A-B｜｜Fmax（｜｜A｜｜F,｜｜B｜｜F）^n-1 or ｜perA-perB｜≤｜｜A｜｜F^n＋｜｜B｜｜F^n holds for ｜｜A｜｜F =（∑i=1^n...It is shown that for any two n x n complex valued matrices A, B the inequality ｜perA-perB｜≤n｜｜A-B｜｜Fmax（｜｜A｜｜F,｜｜B｜｜F）^n-1 or ｜perA-perB｜≤｜｜A｜｜F^n＋｜｜B｜｜F^n holds for ｜｜A｜｜F =（∑i=1^n∑j=1^n｜αij｜^2）^1/2 where A^H denotes the conjuagte transpose of the matrix A = （αij）n×n.展开更多
Gastric cancer (GC) remains a leading cause of cancer death worldwide. Radical gastrectomy is the only potentially curative treatment, and perioperative adjuvant therapies may improve the prognosis after curative rese...Gastric cancer (GC) remains a leading cause of cancer death worldwide. Radical gastrectomy is the only potentially curative treatment, and perioperative adjuvant therapies may improve the prognosis after curative resection. Prognosis largely depends on the tumour stage and histology, but the host systemic inflammatory response (SIR) to GC may contribute as well, as has been determined for other malignancies. In GC patients, the potential utility of positron emission tomography/computed tomography (PET/CT) with the imaging radiopharmaceutical <sup>18</sup>F-fluorodeoxyglucose (FDG) is still debated, due to its lower sensitivity in diagnosing and staging GC compared to other imaging modalities. There is, however, growing evidence that FDG uptake in the primary tumour and regional lymph nodes may be efficient for predicting prognosis of resected patients and for monitoring tumour response to perioperative treatments, having prognostic value in that it can change therapeutic strategies. Moreover, FDG uptake in bone marrow seems to be significantly associated with SIR to GC and to represent an efficient prognostic factor after curative surgery. In conclusion, PET/CT technology is efficient in GC patients, since it is useful to integrate other imaging modalities in staging tumours and may have prognostic value that can change therapeutic strategies. With ongoing improvements, PET/CT imaging may gain further importance in the management of GC patients.展开更多
Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity prop...Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity property and the set of all McDuff sub/actors of t are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2. We also consider the connection of perturbation of operator algebras under d2 with the fundamental group and the generator problem of type II1 factors. When M is a finite yon Neumann algebra with a normal faithful trace, the set of all von Neumann subalgebras B of M such that B ∪→ M is rigid is closed in the Hausdorff metric d2.展开更多
基金Supported by the Natural Science Foundation of Hubei Province(2004X157).
文摘It is shown that for any two n x n complex valued matrices A, B the inequality ｜perA-perB｜≤n｜｜A-B｜｜Fmax（｜｜A｜｜F,｜｜B｜｜F）^n-1 or ｜perA-perB｜≤｜｜A｜｜F^n＋｜｜B｜｜F^n holds for ｜｜A｜｜F =（∑i=1^n∑j=1^n｜αij｜^2）^1/2 where A^H denotes the conjuagte transpose of the matrix A = （αij）n×n.
文摘Gastric cancer (GC) remains a leading cause of cancer death worldwide. Radical gastrectomy is the only potentially curative treatment, and perioperative adjuvant therapies may improve the prognosis after curative resection. Prognosis largely depends on the tumour stage and histology, but the host systemic inflammatory response (SIR) to GC may contribute as well, as has been determined for other malignancies. In GC patients, the potential utility of positron emission tomography/computed tomography (PET/CT) with the imaging radiopharmaceutical <sup>18</sup>F-fluorodeoxyglucose (FDG) is still debated, due to its lower sensitivity in diagnosing and staging GC compared to other imaging modalities. There is, however, growing evidence that FDG uptake in the primary tumour and regional lymph nodes may be efficient for predicting prognosis of resected patients and for monitoring tumour response to perioperative treatments, having prognostic value in that it can change therapeutic strategies. Moreover, FDG uptake in bone marrow seems to be significantly associated with SIR to GC and to represent an efficient prognostic factor after curative surgery. In conclusion, PET/CT technology is efficient in GC patients, since it is useful to integrate other imaging modalities in staging tumours and may have prognostic value that can change therapeutic strategies. With ongoing improvements, PET/CT imaging may gain further importance in the management of GC patients.
基金supported by National Natural Science Foundation of China(Grant No.11371222)Natural Science Foundation of Shandong Province(Grant No.ZR2012AM024)
文摘Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity property and the set of all McDuff sub/actors of t are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2. We also consider the connection of perturbation of operator algebras under d2 with the fundamental group and the generator problem of type II1 factors. When M is a finite yon Neumann algebra with a normal faithful trace, the set of all von Neumann subalgebras B of M such that B ∪→ M is rigid is closed in the Hausdorff metric d2.
