We study a correlation function for the one-dimensional isotropic XY model (XX0 model), which is called the Emptiness Formation Probability (EFP). It is the probability of the formation of a ferromagnetic string in the anti-ferromagnetic ground state. Using the expression of the EFP as a Toeplitz determinant, we discuss its asymptotic behaviors. We also compare the analytical results with numerical calculations as the density-matrix renormalization group and the quantum Monte-Carlo method.

L-type amino acid transporter 1 (LAT1) is a neutral amino acid transport system and is a major route for the transport of large neutral amino acids, including methionine, through the plasma membrane. LAT1 requires the heavy chain of 4F2 cell surface antigen (4F2hc) for its functional expression. Positron emission tomography (PET) with L-[methyl-(11)C] methionine (MET) provides information about amino acid metabolism in brain tumors. We conducted a clinicopathologic study to elucidate the correlation of LAT1 and 4F2hc expression with MET uptake in patients with newly diagnosed human gliomas. Thirty-three newly diagnosed glioma patients were enrolled in this study. Uptake of MET in the tumor was evaluated with the maximum standardized uptake value (SUVmax). Expression of the LAT1, 4F2hc, and CD34, and Ki-67 labeling index of the tumor were analyzed by immunohistochemical staining, and the correlation with the SUVmax in the tumors was examined. Expression of LAT1 and 4F2hc was higher in high-grade gliomas than in low-grade gliomas. The grade of LAT1 immunostaining increased with glioma grade. LAT1 was mainly expressed in the tumor cytoplasm and vascular endothelium and 4F2hc was mainly expressed in the tumor cytoplasm and plasma membrane. Expression of LAT1 but not 4F2hc was significantly correlated with MET SUVmax. Expression of LAT1 in the tumor vascular endothelium is significantly correlated with CD34 positive microvessel density. In conclusion, MET SUVmax correlates with LAT1 expression in the tumor in newly diagnosed gliomas. MET transport may be increased by an increased number of microvessels combined with a higher density or activity of LAT1 in the tumor endothelial cells in high-grade gliomas. Use of MET-PET as a molecular target combined with anti-angiogenesis in glioma therapy should be addressed in future studies.

PET studies using MET and FLT are useful for tumor detection in newly diagnosed gliomas. However, there is no complimentary information in tumor detection with simultaneous measurements of MET- and FLT-PET in low grade gliomas. FLT-PET seems to be superior than MET-PET in noninvasive tumor grading and assessment of proliferation activity in gliomas of different grades.

The results of this preliminary study suggest that, compared with FDG, FLT may be less sensitive for primary staging in patients with NSCLC. Although FLT uptake correlated significantly with proliferative activity in NSCLC, the correlation was not better than that for FDG uptake.

Isompic spin-l chains with band alternation are studied. Analytic (both varlational and pemrbative) results are presented A phase transition is found Lo separate the S = 1 Haldane phase and the dimer phase. The critical point is numerically determined using the Binder parameter. The univenaliry class is predicted to be given by the level-1 SU(2) Wess-Zuminc-Witten model, and this prediction is supported by the present exact diagonalization study. The dimer phase is found Lo be connected to the 'S = 2' Haldane phase in a special limit. The change of the excitation spectra and the suing order W t e r with bond alternation is discussed.