Classifying torsion pairs of Noetherian algebras

For a commutative Noetherian ring $R$ and a module-finite $R$-algebra $\Lambda$, we study the set $\mathsf{tors} \Lambda$ (respectively, $\mathsf{torf}\Lambda$) of torsion (respectively, torsionfree) classes of the category of finitely generated $\Lambda$-modules. We construct a bijection from $\mathsf{torf}\Lambda$ to $\prod_{\mathfrak{p}} \mathsf{torf}(\Lambda\otimes_R \kappa(\mathfrak{p}))$, and an embedding $\Phi$ from $\mathsf{tors} \Lambda$ to $\mathbb{T}_R(\Lambda):=\prod_{\mathfrak{p}} \mathsf{tors}(\Lambda\otimes_R \kappa(\mathfrak{p}))$, where $\mathfrak{p}$ runs all prime ideals of $R$. When $\Lambda=R$, these give classifications of torsionfree classes, torsion classes and Serre subcategories of $\mathsf{mod} R$ due to Takahashi, Stanley-Wang and Gabriel. To give a description of $\mathrm{Im} \Phi$, we introduce the notion of compatible elements in $\mathbb{T}_R(\Lambda)$, and prove that all elements in $\mathrm{Im} \Phi$ are compatible. We give a sufficient condition on $(R, \Lambda)$ such that all compatible elements belong to $\mathrm{Im} \Phi$ (we call $(R, \Lambda)$ compatible in this case). For example, if $R$ is semi-local and $\dim R \leq 1$, then $(R, \Lambda)$ is compatible. We also give a sufficient condition in terms of silting $\Lambda$-modules. As an application, for a Dynkin quiver $Q$, $(R, RQ)$ is compatible and we have a poset isomorphism $\mathsf{tors} RQ \simeq \mathsf{Hom}_{\rm poset}(\mathsf{Spec} R, \mathfrak{C}_Q)$ for the Cambrian lattice $\mathfrak{C}_Q$ of $Q$.Comment: 33 pages, one subsection was moved to Appendix, some propositions were added in Section

Optical Evidence of Itinerant-Localized Crossover of 4f4f Electrons in Cerium Compounds

Cerium (Ce)-based heavy-fermion materials have a characteristic double-peak structure (mid-IR peak) in the optical conductivity [$\sigma(\omega)$] spectra originating from the strong conduction ($c$)--$f$ electron hybridization. To clarify the behavior of the mid-IR peak at a low $c$-$f$ hybridization strength, we compared the $\sigma(\omega)$ spectra of the isostructural antiferromagnetic and heavy-fermion Ce compounds with the calculated unoccupied density of states and the spectra obtained from the impurity Anderson model. With decreasing $c$-$f$ hybridization intensity, the mid-IR peak shifts to the low-energy side owing to the renormalization of the unoccupied $4f$ state, but suddenly shifts to the high-energy side owing to the $f$-$f$ on-site Coulomb interaction at a slight localized side from the quantum critical point (QCP). This finding gives us information on the change in the electronic structure across QCP.Comment: 6 pages, 4 figures. To appear in JPSJ (Letters

Risk factor analysis of thoracic endovascular repair using the Matsui-Kitamura stent graft for acute aortic emergencies in the descending thoracic aorta

ObjectiveIn recent years, thoracic endovascular aneurysm repair (TEVAR) has been attempted for acute aortic emergencies (AAEs). However, the risk factors for achieving good results have not been identified. Besides focusing on Acute Physiology and Chronic Health Evaluation (APACHE) II score as a general indicator of patient condition, we analyzed both preoperative factors and intraoperative/postoperative factors. The purpose of this study was to identify those factors affecting the results of TEVAR using our Matsui-Kitamura stent graft (MKSG) for AAEs involving descending thoracic aortic aneurysm.MethodsBetween July 2000 and June 2008, a total of 32 patients (23 men, 9 women) with AAEs underwent endovascular repair. AAE was a result of aortic aneurysm rupture in 16 cases, rupture of penetrating atherosclerotic ulcer in 2 cases, traumatic aortic injury in 9 cases, complicated type B dissection in 4 cases, and aortic infiltration of sarcoma in 1 case. Low blood pressure in 6 patients, acute renal failure in 7 patients, anemia due to bleeding in 12 patients were found at the time of operation. Urgent TEVAR using the MKSG was performed. Perioperative and long-term results for these patients were investigated.ResultsThe delivery and technical success rate for TEVAR using the MKSG, was 100%. Perioperative mortality was 12.5%, and 5-year survival rate was 71%. In both univariate and multivariate analysis, the APACHE II score clarified a risk factor. Among the various elements of an APACHE II score, age, hematocrit, and total score were identified as significant factors. The mean of an APACHE II score was 9.5. Patients with an APACHE II score ≥10 showed significantly lower 5-year survival rates than patients with an APACHE II score ≤9.ConclusionsGood results were obtained using TEVAR to treat AAEs with MKSGs, both perioperatively and during medium-term follow-up. Evaluation of risk factors for TEVAR of AAEs showed the utility of APACHE II score (particularly age, hematocrit, and total score) with a score ≥10 indicating high risk

公的支援が技術の実用化・普及に及ぼす影響 : エネルギー技術開発プログラムに関する事例研究

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 馬場 靖憲, 東京大学教授 坂田 一郎, 東京大学教授 堤 敦司, 東京大学教授 松本 三和夫, 東京大学准教授 鎗目 雅University of Tokyo(東京大学

Early Stage of Pilomatricoma with an Empty Cyst Cavity and Unusual Clinical Appearance

We present an unusual case of cystic pilomatricoma. A 13-year-old Japanese boy was referred to our department for evaluation of a 10-day history of a small reddish nodule on his right cheek. Histopathological examination showed a well-circumscribed cystic structure showing a central empty cavity in the dermis. The wall of the cyst was composed of basophilic cells. Inner layers of the wall were covered with flattened epithelial cells having trichohyalin granules. Based on these findings, a diagnosis of cystic pilomatricoma was made. To our knowledge, there has been no report of cystic pilomatricoma with an empty cavity. Dermatologists should be aware of pilomatricoma in the early stage showing a central empty cavity

Squamous Cell Carcinoma Manifested as a Cutaneous Horn : A Key to Early Detection

We report a case of squamous cell carcinoma manifested as a cutaneous horn. A 92-year-old man was referred to our department for evaluation of a 3-month history of a keratotic cutaneous horn on the left side of his neck. The height of the cutaneous horn was larger than the diameter of erythema at the base. Histopathological examination showed a hyperkeratotic horn developing over a mass of large atypical keratinocytes with large hyperchromatic and pleomorphic nuclei. Based on these findings, a diagnosis of squamous cell carcinoma was made. A recent study showed that cutaneous horns in association with invasive squamous cell carcinoma had a tendency to have less height than the diameter of the base. In our case, however, the height of the cutaneous horn was larger than the diameter of the base, indicating that invasive squamous cell carcinoma sometimes shows a cutaneous horn that is higher than the diameter of the base. Thus, clinical finding of erythema at the base of the cutaneous horn would be a reliable feature for early detection of squamous cell carcinoma

ITERATION DYNAMICAL SYSTEMS OF DISCRETE LAPLACIANS ON THE PLANE LATTICE (II) (THE VISUAL IMPRESSIONS GIVEN BY DESIGN-PATTERNS)

The present study was designed to investigate the underlying factors determining the visual impressions of design-patterns that have complex textures. Design-patterns produced by "the dynamical system defined by iterations of discrete Laplacians on the plane lattice" were adopted as stimuli because they were not only complex, but also defined mathematically. In the experiment, 21 graduate and undergraduate students sorted 102 design-patterns into several groups by visual impressions. Those 102 patterns were classified into 12 categories by the cluster analysis. The results showed that the regularity of pattern was a most efficient factor for determining visual impressions of design-pattern, and there were some correspondence between visual impressions and mathematical variables of design-pattern. Especially, the visual impressions were influenced greatly by the neighborhood, and less influenced by steps of iterations

Measurements of neutron total and capture cross sections of 139^{139}La and evaluation of resonance parameters

Neutron total and capture cross sections of Lanthanum(La)-139 were measured at the Accurate Ne-utron-Nucleus Reaction measurement Instrument (ANNRI) of the Materials and Life Science Experimental Facility (MLF) in the Japan Proton Accelerator Research Complex (J-PARC). The total cross section was largely different from that in evaluated libraries, such as JENDL-5, in the energy range from 80 to 900~eV. Resonance parameters for four resonances including one negative resonance were obtained using a resonance analysis code, REFIT. The resonance analysis revealed discrepancies in several resonance parameters with the evaluated libraries. Furthermore, the information about the scattering radius was also extracted from the results of the total cross section. The obtained scattering radius was larger than that recorded in the evaluated libraries.Comment: 12 pages, 16 figure