Uniform Cyclic Group Factorizations of Finite Groups

In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group $G$ is said to admit a uniform group factorization if there exist subgroups $H_1, H_2, \ldots, H_k$ such that $G = H_1 H_2 \cdots H_k$ and the number of ways to represent any element $g \in G$ as $g = h_1 h_2 \cdots h_k$ ($h_i \in H_i$) does not depend on the choice of $g$. Moreover, a uniform group factorization consisting of cyclic subgroups is called a uniform cyclic group factorization. First, we show that any finite solvable group admits a uniform cyclic group factorization. Second, we show that whether all finite groups admit uniform cyclic group factorizations or not is equivalent to whether all finite simple groups admit uniform group factorizations or not. Lastly, we give some concrete examples of such factorizations.Comment: 10 pages. To appear in Communications in Algebr

Significance of IgG4-positive cells in severe eosinophilic chronic rhinosinusitis

Background: IgG4 production is regulated by type 2 (IL-4 and IL-13) and regulatory (IL-10) cytokines involved in the pathophysiology of chronic rhinosinusitis (CRS). We sought to determine the pathophysiological characteristics of IgG4-positive cells in sinonasal tissues in CRS, especially eosinophilic CRS (ECRS). Methods: IgG4-positive cells in uncinate tissues (UT) and nasal polyps (NP) were examined by immunohistochemistry. Associations between the number of IgG4-positive cells and clinicopathological factors were analyzed. Receiver operating characteristics (ROC) analysis was performed to determine the cut-off value of IgG4-positive cells in tissue that can predict the post-operative course. Results: IgG4 was mainly expressed in infiltrating plasma and plasmacytoid cells, and the number of IgG4-positive cells was significantly higher in NP, especially those from severe ECRS patients, than in UT. In CRS patients, the number of IgG4-positive cells significantly and positively correlated with blood and tissue eosinophilia, radiological severity, and serum level of total IgE. The number of infiltrating IgG4-positive cells was significantly higher in patients with a poor post-operative course (sustained sinus shadow 6 months after surgery) than in those with a good one. The number of IgG4-positive cells in NP could discriminate patients with a good or a poor post-operative course (area under the curve: 0.769). Also, 73.3% sensitivity and 82.5% specificity were achieved when the cut-off value was set at 17 cells/high-power field. Conclusions: Our results suggest that the local expression of IgG4 on cells may be used as a biomarker that reflects the pathophysiology of CRS, including the post-operative course

An Adult Case of Nasal Chondromesenchymal Hamartoma: Imaging Characteristics Including Diffusion-Weighted Images

Nasal chondromesenchymal hamartoma (NCMH), a rare, benign, nasal cavity tumor, typically occurs in children. Differential diagnosis is difficult because NCMH often presents with non-specific findings, including cystic components and invasion of the surrounding area on T2-weighted magnetic resonance images. Here, we present a rare adult case of NCMH, with no clear hyperintensity on diffusion-weighted images (DWI), and bone remodeling on the tumor margins on computed tomography. To the best of our knowledge, this is the first report of DWI on NCMH, and these findings, which suggest benign disease, may be useful in diagnosing NCMH

Resonant-Like Field Enhancement by Nanoscale Grating-Coupled Propagating Surface Plasmons and Localized Surface Plasmons in the Mid-Infrared Range: Implications for Ultrafast Plasmonic Electron Sources

We investigated electron emission induced by an intense mid-infrared (MIR) field from a nanoscale aluminum-coated grating. The total photoelectron yields clearly show a resonant-like behavior when frustrated diffraction occurs near the Wood anomaly. This result indicates that a strong near field, which is formed by the localized surface plasmons (LSPs) at the ridge of the grating, can be enhanced by resonantly produced propagating surface plasmons (PSPs) owing to the phase matching between the diffracted light and PSPs. The observed photoelectron spectra can be reproduced well by a simple one-dimensional (1D) model of a near field that contains two parameters: the field enhancement factor, α, and the ridge radius, r0. In addition, we show that the resonant-like photoemission was attributed to the interference of the near fields produced by the LSPs and PSPs in the nanoscale grating structure. These results demonstrate that the nanoscale structure is useful for ultrafast plasmonic electron sources