A Class of Special Solutions for the Ultradiscrete Painlev\'e II Equation

A class of special solutions are constructed in an intuitive way for the ultradiscrete analog of $q$-Painlev\'e II ($q$-PII) equation. The solutions are classified into four groups depending on the function-type and the system parameter

Multiplicative equations related to the affine Weyl group E8_8

We derive integrable equations starting from autonomous mappings with a general form inspired by the multiplicative systems associated to the affine Weyl group E$_8^{(1)}$. Five such systems are obtained, three of which turn out to be linearisable and the remaining two are integrable in terms of elliptic functions. In the case of the linearisable mappings we derive nonautonomous forms which contain a free function of the dependent variable and we present the linearisation in each case. The two remaining systems are deautonomised to new discrete Painlev\'e equations. We show that these equations are in fact special forms of much richer systems associated to the affine Weyl groups E$_7^{(1)}$ and E$_8^{(1)}$ respectively.Comment: 9 pages, no figure

Casorati Determinant Solution for the Relativistic Toda Lattice Equation

The relativistic Toda lattice equation is decomposed into three Toda systems, the Toda lattice itself, B\"acklund transformation of Toda lattice and discrete time Toda lattice. It is shown that the solutions of the equation are given in terms of the Casorati determinant. By using the Casoratian technique, the bilinear equations of Toda systems are reduced to the Laplace expansion form for determinants. The $N$-soliton solution is explicitly constructed in the form of the Casorati determinant.Comment: 19 pages in plain Te

Casorati Determinant Solutions for the Discrete Painlev\'e III Equation

The discrete Painlev\'e III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel function. Moreover, based on the observation that these discrete Bessel functions are transformed to the $q$-Bessel functions by a simple variable transformation, we present a $q$-difference analogue of the Painlev\'e III equation.Comment: 16 pages in LaTe

精神障害者グループホームの課題 : 新潟県内調査からの考察

わが国では精神科病院において長期入院の問題が続いている。入院患者の特徴は統合失調症、長期入院、高齢者が多いことなどである。以前から、それらの人たちの受け入れ先としてグループホームの重要さが言われている。グループホームは単なる住居ではなく、自由でさまざまな支援と仲間がいることが特徴である。ここでは新潟県内の精神障害グループホーム調査から、そこでの障害者の特徴、支援の内容、課題などについて研究した。特に2005年から実施された障害者自立支援法後も、精神障害者の生活を支えるものとなっていないばかりか、むしろより困難な状況になっていることがわかった。今後の課題について考察する。The problem of long-term hospitalization continues in the psychiatry department hospital in our country. In-patient\u27s characteristic is that there are a lot of schizophrenia, long-term hospitalizations, and senior citizens. Importance at group home is said as those people\u27s receiver before. However, it is not a mere dwelling but it is free and there are various support and companions the feature in the group home. The content of handicapped person\u27s characteristic there and support and problems, etc. were researched from the mental disease group home survey of the Niigata prefecture here. It has been understood that it is not only the one after the law of the handicapped person independence support executed in especially 2005 to support life in the couch case but also a more difficult situation. Future tasks are considered