In the paper an inverse problem for the heat equation is simulated directly and globaly. The bounding transform is used for avoiding unboundedness of the domain and the solution. A parameter is introduced for avoiding the difficulty in numerical computation which arise from the discontinuity. Moreover, it is useful for investigation of the growth rate. Numerical results are satisfactory.

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非線形の偏微分方程式に対して数値計算を行った.その偏微分方程式は,投資最適化問題におけるリスク選好の発展に関するものである.非有界な領域を数値計算するため,変数変換によるを行い,領域全体に対して解を求めた.数値計算の結果,リスク選好の偏微分方程式の解の振る舞いが明らかになった.

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熱伝導逆問題の大域解は非有界である． この大域解の数値計算は，時間と解の両方にをほどこせば行える可能性がある． しかし，こうすると解が不連続になってしまい，数値計算は困難を極める． そこで，複素数計算を行って，とりあえず数値計算を実行し， その結果から役立つ情報が得られないかと考えた．

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熱伝導方程式の逆問題に対して、時間変数に関する変数変換および解に関する変換を用いて無限領域を有限領域に変換させて数値計算を行う。いくつかの離散化手法に対する計算結果を紹介する。

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本文在以往相关研究的基础上，用“有界/无界”和“有标记/无标记”等理论解释了两类谓词性主语（指称性主语和陈述性主语）之间存在着的句法语义上的对立。本文认为，在无标记的指称性/陈述性主语句中，指称性主语通常由表示无界性动作或性状的谓词性成分来充当；陈述性主语通常由表示有界性动作或性状的谓词性成分来充当。而在有标记的情况下，则不限于此。本文最后试图用“连续统”的概念来说明这两类主语及其相关句式之间的关联。

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The calculated control input can diverge because of the saturation of plant input even if the control system is internally stable in the linear sense. In this paper a controller configuration that avoids this divergence is proposed.

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This paper points out a problem that the adaptive gain matrix of the conventional constant-trace algorithm may lose its positive definiteness when the signal in adaptive control system is not persistently exciting and proposes a remedy for this problem.

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本論は大きく2部にわかれる. 前半は, これまで体制としての地理学の中にあって伝統的地理学の非社会科学性を批判することに存在意義を見いだしてきた「批判的地理学」と呼ばれる立場がはらむパラドクシカルな論理の検討であり, 後半は, 筆者が前著『経済地理学』で提示した, 空間の経済・社会への包摂とそれをつうじた空間編成ならびに建造環境生産にかかわる経済・社会空間論の基本的枠組みの要約的な説明にあてられている. 非空間的な伝統的社会科学の導入による「社会科学としての地理学」を唱導して伝統的地理学を批判してきた地理学者は, 一方で地理学そのものを否定してこれを社会科学一般に解消することを導きながら, 他方では, その経済学・社会学修得の不十分さゆえ, 伝統的地理学への寄生的共存から抜け出しがたい, というパラドクスにおちいった. このため, 社会科学に学際的研究がすすんで学問の「仕切り」が開放的になり, また, 社会諸科学が空間論という新たなフロンティアに理論展開の方向を求めるようになったとき, 批判的地理学はこれに十分対応できる力量を持ち合わせていなかった. かくて批判的地理学の流れをくむ人々は, 自己の学問的アイデンティティーを求め, 一転して先祖返りし, 例外主義や機能・等質地域論, 立地論など伝統的地理学・経済地理学とおなじパラダイムを奉ずるようになった. このような逆説的な状況から抜け出すためには, 地理学を経済・社会空間編成の科学と位置付け, 空間が素材的にもつ物質性が社会に包摂されることによって, どのように社会・経済の諸過程ならびに諸関係の態様が変容するかを説明する, 経済・社会空間論の体系を構築しなくてはならない. この理論によりはじめて, 地理学は独自のdisciplineをもって他の社会科学と対等の学際的共同関係を築くことができる. 素材的空間を包摂した経済社会諸過程にかかわる論理体系は, 大要次のようなものである. 原初的空間は, 大きく絶対空間と相対空間の属性に分けられる. 絶対空間は, 空間の無限に広がる連続性であり, 空間のなかにある物質を相互に関係づけて均等化・同質化する性向をもつ. 他方相対空間は, 位置ごとの個別性と位置相互間の距離が生み出す隔離・分断の性向をもつ. 絶対空間を形式的に包摂した社会では, 主体・集団ないし行為の独立性が奪われないよう, 空間の連続性を仕切り, 「領域」が生産されなくてはならない. するとその中だけで同質化過程が作用し, 互いに異質なロカリティーができあがる. だが, 領域生産の他の一面の目的は社会関係をとり結ぶことだから, これらの異質的ロカリティーをもつ領域が集まってつくりだされた「集合的絶対空間」は, その上により広い領域を構成する社会関係の層を作りだす. こうして生産された複数の集合的絶対空間の層相互において, 空間的「連続性」と「分断」との間の関係という矛盾が発生する. 他方, 相対空間を形式的に包摂した社会は, その隔離の属性のために社会関係が破断しないよう, 集積をはかり, また交通網のネットワーク構築により「空間の絶滅」を行って, 領域内部の同質化を実際に達成しなくてはならない. しかし, 1次元の線のネットワークで2次元の面を絶滅するという交通路, ならびに点である集積が合わさってできた建造環境の編成は, その点や線と平面上の各位置との間の距離関係というあらたな空間的差異をつくりだし, 領域の同質化をめざすほどロカリティーの多様化が進む, という矛盾を生み出さざるを得ない. ここから, この2種類の生産された空間的に不均等な建造環境の編成が作り出す新たな素材的空間である「相関空間」をあらためて社会が実質的に包摂する, という課題が生じてくる. この相関空間の編成過程は, 集積とネットワークからなる空間と, さまざまな土地利用編成という集合的絶対空間の両面にわたって行われなくてはならない. これはいずれも, グローバルな空間の層のなかにあって個々のロカリティーが調整され, 新たな物質的空間としてまとめあげられてゆく過程である. ハーヴェイが語った, 「個別性や特定の場所と時間における経験と, 普遍的一般化との関係」という地理学的考察に取りついてきた「悪魔」(Harvey, 1985a, p. 61)は, こうした筋道だった空間的社会過程にかかわる考察によって解消することができる. そして同時にそのなかで, 地理学は, 経済・社会空間の編成論を究める分野として, 社会諸科学の分業のなかで自己の存在理由を主張することができるようになるのである.

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An economic or social body needs to place itself in its own spatial container, or territory, by bounding the contiguity of subsumed pristine absolute space. However, the boundary circumscribing the territory inevitably has physical and institutional porosity. In order to maintain the integrity of the economic or social body, the porosity has to be controlled by the body dominating the territory. It may allow or deny elements of society or economy passing through the boundary, in order to bring the configuration and functioning of its economy and society to the optimum. For an independent sovereign nation, the spatial container means its national territory; and the control of the institutional porosity of its international boundary is done through its immigration or customs regulations. Under contemporary globalism, the boundary becomes a contested terrain between the hegemonic nation and subservient sovereign nations, as well as between capital and labour. In order to exercise hegemony, the United States demands that other subservient nations give up control of their boundaries, and open up to the will of such international organisations as the IMF or the WTO, so that multinational industrial and speculative capital can freely move across the globe. As for labour migration, international boundaries are made strictly controlled; thus labour is normally confined within a national territory. High-income sovereign nations control the porosity of international boundaries so as to bring the inflow of labour from low-income nations to the optimum for the configuration of their labour markets. Multinational capital is glad to exploit differences in wage rates of various spatially confined labour markets thus created across the globe, under the principle of the new international division of labour and product cycles. Labour, on the contrary, tries to overcome this spatial confinement by attempting to permeate through the physical porosity and become 'illegal immigrants' in the country on the other side of the border. Many of them are then forced to work in sweatshops and are subjected to the worst kind of exploitation. A typical case demonstrating this spatial relation is found in the 'touch-base policy' engineered by the British Hong Kong government between 1974 and 1980. In the late 1960s and early 1970s, Hong Kong experienced frequent labour disputes with anti-British demands under the influence of the Cultural Revolution in the PRC. The 'touch-base policy' stipulated that it gave resident status and work permits to PRC Chinese who managed to reach the 'base'-Kowloon or Hong Kong Island- where most of the employment opportunities existed, while 'illegal' migrants found and arrested in the New Territories were repatriated. 70.1% of the successful 'illegal' migrants from the PRC were of the age between 15 and 24, which was the most appropriate for work in factories or on construction sites. Statistical evidence shows that while the 'touch-base policy' was in effect, a stunning parallel relationship existed between the inflow of both legal and 'illegal' migrants from the PRC and the number of days lost in labour disputes, and a negative relationship between the migrant inflow and the unemployment rates. This indicates that there was tacit government control over the in-migration of labour from the PRC in order to control the supply-demand situation of the labour market and concomitant labour disputes. A neo-liberalist Milton Friedman once praised that British Hong Kong was a typical case of successful laissez-faire policy and minimal government intervention; yet the evidence suggests that it was, in fact, subtle intervention to free competition that really brought success to the Hong Kong economy. The ideological nature of the neo-liberalist conception of globalism is thus obvious.

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This study investigates the structure and dynamic behavior of a linear system which describes the perturbation of a laminar pipe flow. In the preceding papers a numerical method for calculating the eigenvalues with sufficient accuracy was proposed, and the characteristic distribution pattern of eigenvalues for Poiseuille pipe flow and the classification of the modes of the perturbations were presented. This paper discusses the effects of the Reynolds number on the distribution pattern of eigenvalues. In the first place, for the Poiseuille pipe flow, it is shown how the distribution of eigenvalues in a complex phase velocity plane takes a tree like shape as the Reynolds number increases. Then the distributions of eigenvalues are calculated for the laminar developing pipe flow and the Poiseuille pipe flow with rigid rotation, which are known to be unstable for high Reynolds number. It is found that these distribution patterns take the same shape as that of Poiseuille pipe flow, and that the unstable eigenvalues belong to the specified modes of perturbations, as predicted in the former report.

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In this paper, we consider analytical formulation method of an impact oscillator system which is typical piecewise linear System, from a viewpoint of integrable system. First, global representation of general solution of the target system that is preveously proposed by present author can be regarded as rigourous discretization by means of unequally spaced difference scheme in relation to impact times. This means that dynamics of the impact oscillator as continous-time dynamical system is doublly prescribed by nonlinear difference equation governing impact times transcendentally and linear diference equation with regard to time evalution between impact states. Finaly, it is shown that piecewise linear system is exact solvable chaotic generating system that is included different important category, self reference system, hybrid system, and integrable system.

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This study aims to clarify the structure and dynamic behavior of the linear system which describes the small perturbation of a laminar pipe flow. In the preceding paper the eigenvalue problem was formulated for a Hilbert space, based on the spectrum theory. And a numerical method for calculating the eigenvalues was proposed, together with a measure of accuracy. Applying the proposed method, this paper discusses the distribution of eigenvalues and the mode of perturbations for the Poiseuille pipe flow. The wave perturbations for various azimuthal and axial wave numbers are investigated with a fixed Reynolds number. It is shown that the distribution of eigenvalues in a complex phase velocity plane has a tree like shape. The mode of perturbations is divided into three classes : slow, fast and mean modes by the axial phase velocity, or wall, center and neutral modes by the radial distribution of the magnitude of the eigenfunction. For each type of mode, the location of the corresponding eigenvalue in the complex phase velocity plane is clarified, and the dependence of the eigenvalue on the original linear dynamic system is also clarified by computer calculations.

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