Deformation theory of deformed Hermitian Yang-Mills connections and deformed Donaldson-Thomas connections

A deformed Hermitian Yang-Mills (dHYM) connection and a deformed Donaldson-Thomas (dDT) connection are Hermitian connections on a Hermitian vector bundle $L$ over a K\"ahler manifold and a $G_2$-manifold, which are believed to correspond to a special Lagrangian and a (co)associative cycle via mirror symmetry, respectively. In this paper, when $L$ is a line bundle, introducing a new balanced Hermitian structure from the initial Hermitian structure and a dHYM connection and a new coclosed $G_2$-structure from the initial $G_2$-structure and a dDT connection, we show that their deformations are controlled by a subcomplex of the canonical complex introduced by Reyes Carri\'on. The expected dimension is given by the first Betti number of a base manifold for both cases. In the case of dHYM connections, we show that there are no obstructions for their deformations, and hence, the moduli space is always a smooth manifold. As an application of this, we give another proof of the triviality of the deformations of dHYM metrics proved by Jacob and Yau. In the case of dDT connections, we show that the moduli space is smooth if we perturb the initial $G_2$-structure generically.Comment: 56 pages, 1 figure, 4 tables, v2: a few typos are corrected, a reference is adde

A Dilated Odontoma in the Second Molar Region of the Mandible

A case of dilated odontoma in the second molar region of the mandible was reported. The patient was a 14-year-old female. Panoramic X-ray and CT examination revealed an oval ring-shaped radiopaque lesion accompanying a radiolucent area in the center at the left second molar region of the mandible. The left second molar and all third molars were not found. The lesion was diagnosed as odontoma and extirpated under general anesthesia. The lesion was a spherical mass of 12x9mm. Histologically, the mass was composed of dentin arranged in an oval ring shape with dentinal tubules. Inside the dentin, immature enamel was present. The central area of the mass was filled with fibrous tissue with a small nest of bone and cementum. Bone tissue was also observed in contact with the immature enamel layer. These morphological and histological features are compatible with those of a dilated odontoma

A Case of Dominant Dystrophic Epidermolysis Bullosa with a G2043R Mutation in the Type VII Collagen Gene

Dystrophic epidermolysis bullosa (DEB) is a subepidermal bulla, characterized by severe itching, lichenoid or nodular prurigo-like lesions, skin erosion, scars, milia, and nail dystrophy, resulting from COL7A1 mutation. Herein, we report a case of dominant DEB with a G2043R mutation in COL7A1

A Lagrangian construction of rotating stars

We present a new formulation for numerically obtaining axisymmetric equilibrium structures of rotating stars in two spatial dimensions. With a view to apply it to the secular evolution of rotating stars, we base it on the Lagrangian description, i.e., we solve the force-balance equations to find the spatial positions of fluid elements endowed individually with a mass, specific entropy and angular momentum. The system of nonlinear equations obtained by finite-differencing the basic equations are solved with the W4 method, which is a new multi-dimensional root-finding scheme of our own devising. We augment it with a remapping scheme to avoid distortions of the Lagrangian coordinates. In this first one of a series of papers, we will give a detailed description of these methods initially. We then present the results of some test calculations, which include the construction of both rapidly rotating barotropic and baroclinic equilibrium states. We gauge their accuracies quantitatively with some diagnostic quantities as well as via comparisons with the counterparts obtained with an Eulerian code. For a demonstrative purpose, we apply the code to a toy-model cooling calculation of a rotating white dwarf.Comment: 15pages, 14 figures, submitted to MNRA