Dn-geometry and singularities of tangent surfaces

The geometric model for Dn-Dynkin diagram is explicitly constructed and associated generic singularities of tangent surfaces are classified up to local diffeomorphisms. We observe, as well as the triality in D4 case, the difference of the classification for D3;D4;D5 and Dn(n ・ 6), and a kind of stability of the classification in Dn for n ! 1. Also we present the classifications of singularities of tangent surfaces for the cases B3;A3 = D3;G2;C2 = B2 and A2 arising from D4 by the processes of foldings and removings

D_n-geometry and singularities of tangent surfaces

The geometric model for Dn-Dynkin diagram is explicitly constructed and associated generic singularities of tangent surfaces are classified up to local diffeomorphisms. We observe, as well as the triality in D4 case, the difference of the classification for D3,D4,D5 and Dn(n ≥ 6), and a kind of stability of the classification in Dn for n → ∞. Also we present the classifications of singularities of tangent surfaces for the cases B3,A3 = D3,G2,C2 = B2 and A2 arising from D4 by the processes of foldings and removings

Singularities of tangent surfaces in Cartan's split G2-geometry

In the split G2-geometry, we study the correspondence found by E. Cartan between the Cartan distribution and the contact distribution with Monge structure on spaces of five variables. Then the generic classification is given on singularities of tangent surfaces to Cartan curves and to Monge curves via the viewpoint of duality. The geometric singularity theory for simple Lie algebras of rank 2, namely, for A2,C2 = B2 and G2 is established

Geometry of D_4 conformal triality and singularities of tangent surfaces

It is well known that the projective duality can be understood in the context of geometry of An-type. In this paper, as D4-geometry, we construct explicitly a flag manifold, its triplefibration and differential systems which have D4-symmetry and conformal triality. Then we give the generic classification for singularities of the tangent surfaces to associated integral curves, which exhibits the triality. The classification is performed in terms of the classical theory on root systems combined with the singularity theory of mappings. The relations of D4-geometry with G2-geometry and B3-geometry are mentioned. The motivation of the tangent surface construction in D4-geometry is provided

Brain Imaging of Nicotinic Receptors in Alzheimer's Disease

Neuronal nicotinic acetylcholine receptors (nAChRs) are a family of ligand-gated ion channels which are widely distributed in the human brain. Several lines of evidence suggest that two major subtypes (α4β2 and α7) of nAChRs play an important role in the pathophysiology of Alzheimer's disease (AD). Postmortem studies demonstrated alterations in the density of these subtypes of nAChRs in the brain of patients with AD. Currently, nAChRs are one of the most attractive therapeutic targets for AD. Therefore, several researchers have made an effort to develop novel radioligands that can be used to study quantitatively the distribution of these two subtypes in the human brain with positron emission tomography (PET) and single-photon emission computed tomography (SPECT). In this paper, we discuss the current topics on in vivo imaging of two subtypes of nAChRs in the brain of patients with AD

Existence and uniqueness for Legendre curves

We give a moving frame of a Legendre curve (or, a frontal) in the unite tangent bundle and define a pair of smooth functions of a Legendre curve like as the curvature of a regular plane curve. The existence and uniqueness for Legendre curves are holded like as regular plane curves. It is quite useful to analyse the Legendre curves. As applications, we consider contact between Legendre curves and the arc-length parameter of Legendre immersions in the unite tangent bundle.

チョウ コウレイシャ ニ ハッセイ シタ トクハツセイ タハツ チョウジュウセキ ト カンガエラレタ イチレイ

A 94-year-old woman visited our hospital with chief complaints of abdominal pain, nausea, and vomiting by way of her local clinic. Abdominal MDCT revealed a target sign of the small intestine, and its frontal section showed invagination of the oral intestinal tract into the anal intestinal tract, which led to a diagnosis of adult small intestinal intussusception. The abdominal symptom was minor, and no ischemic and necrotic manifestations of the intestinal tract were observed. Conservative treatment was considered. However the patient was oldest-old with dementia, and her consent to the long-term conservative treatment seemed unlikely to be obtained, as well as the small intestine had intussusception extending more than at least１０cm, and its natural reduction was judged to be difficult. Therefore an urgent operation was selected. Two places in the small intestine showed intussusceptions, which could be relatively easily reduced. Because the entire intestinal tract had no abnormalities such as mass and necrotic lesions, the intestine was not resected. Postoperatively, the patient had dementia symptoms such as wandering and abnormal behavior, but her postoperative course was good, leading to hospital discharge on the seventh postoperative day. We report the case of idiopathic multiple intestinal invagination that has never been reported in the past, with some literature review

ボウコウ ガ カンニュウ シタ リョウガワ ヘイサコウ ヘルニア ノ イチレイ

An 80-year-old woman visited our hospital with chief complaints of nausea, vomiting, and anorexia. She was diagnosed with bilateral obturator hernia involving the urinary bladder by an abdominal CT scan and retrograde cystography. The symptoms resolved with cessation of anticholinergic drugs that she was being given for the treatment of nocturia, and administration of laxative drugs. The bladder as hernia content was considered to have repeated invagination into an obturator foramen and natural reduction. Because intestinal obstruction and peritonitis due to intestinal invagination were likely to occur, the necessity of an operation was explained to the patient, but her consent to the operation could not be obtained, which led to a follow-up of the symptom. This was the second case report of bilateral obturator hernia of the bladder as hernia content in Japan, and was the first case report of synchronous bilateral obturator hernia in the country

Inefficient double-strand DNA break repair is associated with increased fasciation in Arabidopsis BRCA2 mutants

BRCA2 is a breast tumour susceptibility factor with functions in maintaining genome stability through ensuring efficient double-strand DNA break (DSB) repair via homologous recombination. Although best known in vertebrates, fungi, and higher plants also possess BRCA2-like genes. To investigate the role of Arabidopsis BRCA2 genes in DNA repair in somatic cells, transposon insertion mutants of the AtBRCA2a and AtBRCA2b genes were identified and characterized. atbrca2a-1 and atbrca2b-1 mutant plants showed hypersensitivity to genotoxic stresses compared to wild-type plants. An atbrca2a-1/atbrca2b-1 double mutant showed an additive increase in sensitivity to genotoxic stresses compared to each single mutant. In addition, it was found that atbrca2 mutant plants displayed fasciation and abnormal phyllotaxy phenotypes with low incidence, and that the ratio of plants exhibiting these phenotypes is increased by γ-irradiation. Interestingly, these phenotypes were also induced by γ-irradiation in wild-type plants. Moreover, it was found that shoot apical meristems of the atbrca2a-1/atbrca2b-1 double mutant show altered cell cycle progression. These data suggest that inefficient DSB repair in the atbrca2a-1/atbrca2b-1 mutant leads to disorganization of the programmed cell cycle of apical meristems

Geometry of D_4 conformal triality and singularities of tangent surfaces

It is well known that the projective duality can be understood in the context of geometry of An-type. In this paper, as D4-geometry, we construct explicitly a flag manifold, its triplefibration and differential systems which have D4-symmetry and conformal triality. Then we give the generic classification for singularities of the tangent surfaces to associated integral curves, which exhibits the triality. The classification is performed in terms of the classical theory on root systems combined with the singularity theory of mappings. The relations of D4-geometry with G2-geometry and B3-geometry are mentioned. The motivation of the tangent surface construction in D4-geometry is provided