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

Disposition Kinetics of Taxanes in Peritoneal Dissemination

Treatment of cancers in the abdominal cavity, such as peritoneal dissemination, is difficult, but in principle intraperitoneal administration of anticancer drugs is expected to be preferable to systemic administration. Taxane anticancer drugs are used to treat gastric cancer patients with peritoneal dissemination. They are administered as micellar preparations, Taxol and Taxotere, which consist of paclitaxel in Cremophor EL (crEL) and docetaxel in Polysorbate-80 (PS-80), respectively. In this paper we review the disposition kinetics of taxane anticancer drugs after intraperitoneal administration in peritoneal dissemination patients and animal models and also discuss the effect of the surfactant vehicle on the behavior of taxanes

Highly porous melamine-formaldehyde monoliths with controlled hierarchical porosity toward application as a metal scavenger

We report a new synthetic strategy for melamine-formaldehyde (MF) monoliths with controlled hierarchical porosity toward metal-ion scavengers. The obtained MF monoliths possessed micro-, meso- and macroporosity, which allowed efficient adsorption performance of precious metal ions in water. Applications such as recovery/removal of metal ions are expected

カガワケン ニ ブンプ スル テシマイシセイ セキゾウ ブンカザイ ノ フウカ テイド ノ ヒョウカ

Weathering grade of Teshima stone, Miocene lapilli tuff, used in lithic cultural heritage in Kagawa Prefecture, Japan was evaluated by using colorimeter, magnetic susceptibility meter, moisture meter and schmidt rock hammer. The stone pagodas have been exposed to weathering for 200 - 600 years, and have developed surface erosion due to weathering. Basaltic rock fragments in Teshima stone are slightly weathered based on necked-eye observation with increasing weathering period. L*-value of color index increased with increasing weathering period, however a*- and b*-values of color index and magnetic susceptibility are constant with increasing weathering period. Increasing of L* value is derived from weathering of basaltic rock fragments in Teshima stone. The results of measurement of a*-, b*- values and magnetic susceptibility suggest that mineralogical weathering such as iron mineral concentration has not occurred. The hardness of excavated cave wall surface on quarry of Teshima stone using schmidt rock hammer decreases in the entrance of the cave. Weathering properties of Teshima stone are characterized by surface erosion and rapid decreasing of rock surface hardness