Remarks on Krein-Kotani’s correspondence between strings and Herglotz functions

In the study of spectral functions of Strum-Liouville operators, S. Kotani found a one-to-one correspondence between the operators and Herglotz functions determining the spectral measures. In the present paper we give another correspondence to a class of Lévy processes obtained as a compensated integrals of Brownian local times. As an application the continuity theorem of Kotani’s correspondence is extended

Role of Bone Marrow-Derived Monocytes/Macrophages in the Repair of Mucosal Damage Caused by Irradiation and/or Anticancer Drugs in Colitis Model

Mucosal damage is a common side effect of many cancer treatments, especially radiotherapy and intensive chemotherapy, which often induce bone marrow (BM) suppression. We observed that acetic acid- (AA-) induced mucosal damage in the colon of mice was worsened by simultaneous treatment with irradiation or 5-FU. However, irradiation 14 days prior to the AA treatment augmented the recovery from mucosal damage, suggesting that the recovery from BM suppression had an advantageous effect on the mucosal repair. In addition, BM transplantation also augmented the recovery from AA-induced mucosal damage. We further confirmed that transplanted BM-derived cells, particularly F4/80+Gr1+ “inflammatory” monocytes (Subset 1), accumulated in the damaged mucosal area in the early healing phase, and both of Subset 1 and F4/80+Gr1− “resident” monocytes (Subset 2) accumulated in this area in later phases. Our results suggest that monocytes/macrophages contribute to the mucosal recovery and regeneration following mucosal damage by anticancer drug therapy

^{31}P and ^{75}As NMR evidence for a residual density of states at zero energy in superconducting BaFe_2(As_{0.67}P_{0.33})_2

^{31}P and ^{75}As NMR measurements were performed in superconducting BaFe_2(As_{0.67}P_{0.33})_2 with T_c = 30 K. The nuclear-spin-lattice relaxation rate T_1^{-1} and the Knight shift in the normal state indicate the development of antiferromagnetic fluctuations, and T_1^{-1} in the superconducting (SC) state decreases without a coherence peak just below T_c, as observed in (Ba_{1-x}K_{x})Fe_2As_2. In contrast to other iron arsenide superconductors, the T_1^{-1} \propto T behavior is observed below 4K, indicating the presence of a residual density of states at zero energy. Our results suggest that strikingly different SC gaps appear in BaFe_2(As_{1-x}P_{x})_2 despite a comparable T_c value, an analogous phase diagram, and similar Fermi surfaces to (Ba_{1-x}K_{x})Fe_2As_2.Comment: 4 pages, 5 figure