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数学（線形代数）の試験答案に見いだされる計算ミスのパターンを分析した。これらの計算ミスは、いくつかのパターンに分類することが出来る。計算ミスのパターンとして、内容が理解できていないということ以外に、計算規則の間違い、暗算ミス、文字・数字・式の読み間違いや転記ミス、前提条件の抜けなどが見受けられる。これらのミスがどのように起こるかを理解することは、教員が講義をするうえで非常に有用であると考えられる。, Miscalculations found in mathematics examination sheets for problems of linear algebra are categorized into several patterns. These miscalculations include calculation rule mistakes, giving incorrect sign and number, incorrect calculations, missing preconditions, and others. Understanding how these mistakes happen will help students to avoid these mistakes.

This research attempts to analyze literary expressions in Alice’s Adventures in Wonderland from numerical and mathematical aspects such a speed, mass, and tesseract movement. One of Carrol’s titles was mathematician, and he has worked as a mathematics lecturer at Oxford University. Because of this background, his literary works contain mathematical elements. This paper presents specific calculation formulas and processes for the events, and analyzes the events of the story from a mathematical viewpoint, including basic concepts and properties. This paper focuses on “Alice’s fall,” “the amount of Alice’s tears,” and “Alice’s existence from the viewpoint of the tesseract movement.”

本稿の目的は，算数・数学科における学習指導案の項目やその役割を振り返るとともに，年代別の特徴を明らかにすることによって，学習指導案の意義を検討することである。まず学習指導案の構成要素について概観した。次いで，『日本数学教育学会誌』に掲載された論文の中で，学習指導案が含まれている論文を分析対象とし，50年前，25年前，近年の3つの区分で比較を行った。その結果，学習指導案の項目では，50年前は「評価」に関する項目はなかったが，近年は増加傾向であり，「教師の活動」に関する項目は漸減傾向である。展開過程では，「練り上げ」や「導入」に重点が置かれるようになってきた。, The purpose of this paper is to investigate the meanings of lesson plans by reflecting items or roles of them in mathematics class at the age, and clarifying some their features. At first, we explore the component of lesson plans. Secondly, we analyze lesson plans involved in some papers in “Journal of Mathematical Education” with respect of three terms of today, 25years ago, and 50years ago. As a result, in items of lesson plan, the “evaluation” is not include in 50 years ago but is an increasing tendency recently. The “teacher's activity” is also a gradual decrease. The “introduction” or “discussion” is given priority in the lesson stage.

本稿では類推における写像内容の適応過程を明らかにすることを目的とした。そこで現代美術における類推的ずらしを用いた創造フロセスから,類推的ずらしを用いて問題解決過程を分析する研究枠組みを作成し,類題を解く際の適応の過程とその様子を探った。その結果,既存の問題の解法で問題を解決できないと判断すると抽象化した解法から新たな問題の解法を生成して適応すること,新しい問題の解法で問題を解決可能と判断すると抽象化した解法を変容させることも示唆された。, The purpose of this paper is to clarify the process of adaptation of mapped content in analogical displacement. We developed a research framework for analyzing the problem-solving process using analogical modification based on the creative process using analogical displacement in contemporary art, and explored the process and state of adaptation in solving analogous problems. The results suggest that when a problem cannot be solved by the existing solution method, a new solution method is generated from the abstraction of the solution method and adapted. It was also suggested that when they judged that the new solution method could solve the problem, they transformed the abstraction of the solution method..

In this paper, we deal with normal two-dimensional singularities with multiplicity two. We call such a singularity double point. The purpose of this paper is to give an estimate of the arithmetic genus for double points in terms of Horikawa's canonical resolution and a $p_{a}$-formula for some class of double points. It is known that, by using the data obtained from the canonical resolution, the geometric genus for double points is formulated, and rational double points and elliptic double points are characterized. We give a characterization of double points with the arithmetic genus two.

This paper deals with handling of a floating object by several space robots. Operational ability of a space robot depends on its scale, and the scale of a space robot is restricted by the capacity of a rocket, which is used to launch the space robot into space. For this reason, a cooperation of several smaller scale space robots is useful and necessary in space development. In this paper, system which consists of two space robots and a floating object is considered, and two partition methods of its kinematic relation equation is proposed. Moreover, Resolved Motion Rate Control schemes for the system are designed based on the partitioned kinematic relation equations, and computer simulations are carried out to verify the control law.

Lagrangian $H$-umbilical submanifolds introduced in $[1, 2]$ can be regarded as the simplest Lagrangian submanifolds in Kaehler manifolds next to totally geodesic ones. It was proved in [1] that Lagrangian $H$-umbilical submanifolds of dimension $\geq 3$ in complex Euclidean spaces are complex extensors, Lagrangian pseudo-spheres, and flat Lagrangian $H$-umbilical submanifolds. Lagrangian $H$-umbilical submanifolds of dimension $\geq 3$ in non-flat complex space forms are classified in [2]. In this paper we deal with the remaining case; namely, non-totally geodesic Lagrangian $H$-umbilical surfaces in complex space forms. Such Lagrangian surfaces are characterized by a very simple property; namely, $JH$ is an eigenvector of the shape operator $A_{H}, where $H$ is the mean curvature vector field. The main operator of this paper is to determine both the intrinsic and the extrinsic structures of Lagrangian $H$-umbilical surfaces.

We present a numerical analysis method for optimization problems of domains in which incompressible steady-state viscous flow field problems are defined. Reshaping was accomplished by the traction method that was proposed as a solution to domain optimization problems in which elliptic boundary value problems were defined. In the previous paper, to total dissipation energy minimization problems we applied the traction method to the Stokes flow field problems ignoring the convective terms. The present paper describes an application of the traction method to the viscous flow field problems including convective terms. For the numerical analyses we employ the finite-element method. The successful results to two-dimensional low-Reynolds-number problems of a bending channel and a channel in which an isolated body exists show the validity of the present method.

We prove a unique existence theorem of classical solutions to some Neumann problem oflinear hyperbolic-parabolic coupled systems with coefficientsin Sobolev spaces and energy estimates are also obtained. This paper gives a preparation for solving some nonlinear hyperbolic-parabolic coupled system with Neumann boundary condition. §0. Introduction. Let Q be a domain in an n-dimensional Euclidean space, its boundary F being a C°°and compact hypersurface. Let x=(xu ■■■, xn) and t denote a point of Rn and a time, respectively. For differentiations we use the symbols dt= d/dt and dj―d/dxj (j―1, ・■■ , n). In this paper, we consider the following problem: (N) JlH^lu^dnH^-diiAmdjUjm-AmdidtUnif) JlP(t)m=AmdtuP(t)-di(A^(t)djuP(t))-Ahn+i(t)diuP(t) A^j^didfu H(f)AP°H{t)didt u u{t)=fP(S) ^H(t)lu^viAU(t)djuH(t) + BnHP1mP(t) + B°H(t)dtuH(t) = $H(t) tBAtXu^^ViAWdjUp^+BpHiVdtUHit) + BPH{t)diuH{t)+ BPKt)uP{t)=gP(t) uH(O) = um, dtuH(O)= uHi, uP(o)=uPO in (0, T)XQ

「数学とは何か」という問いを文明史的観点から俯瞰する。・数学マジック・コピー用紙の縦横比とピタゴラス音律の関係・地図と暦をつくりだされた技が数学・円周率のミステリー・geo(地球)+ metry(測る)= geometry 幾何学 ・数学最大のマジック コンピューター ・Mathematics=人として学ぶべきこと(古代ギリシア語), An overview of the question "What is mathematics ?" from the perspective of civilization history.・Mathematics magic・Relationship between aspect ratio of copy paper and Pythagorean temperament・Mathematics is a technique that creates maps and calendars・Pi mystery・Geo + metry = geometry・The largest in mathematics magic is computer・Mathematics=Learning as a person (Ancient Greek), 講演記録

Let R be a complete discrete valuation ring with quotient field K and A a basic R-order in a separable /f-algebra,and let e be a primitive idempotent of A. In this paper we shall study tilting^-latticesin the form of T={l―e)A (BTr/X/e) where / is the Jacobson radical of A and Trz,is the transpose functor for yl-lattices. Tilting theory was initiated by Brenner and Butler [5] and its general theory over artin algebras was given in Happel and Ringel [6] and Bongartz [4] and has been used and developed by many authors not only in the study of representations of artin algebras but also in more general situations. Among them tilting modules arising from suitable simple modules are concrete and typical ones (see [2] and [5]). While almost all general results in [4] are reconstructed in the case of orders by Roggenkamp [8], it seems also to be desirable to provide an order version of such tilting modules and study its fundamental properties, which is the aim of this paper. In Section 1, we shall recall some definitions and notation which will be used throughout the paper. In Section 2, we shall show that T=(l―e)A 0 TrL(/e) is a tilting.//-lattice if and only if Je is not J-reflexive and Ae is not isomorphic to a direct summand of the projective cover of Je (Theorem 2.1). We call such a tilting.//-lattice Brenner-Butler type (BB-type for short). We shall also show that T is a tiltingJ-lattice of BB-type if and only if T is a tiltingleft /"-latticeof BB-type and J=Endr(T) where T=End^(T) (Theorem 2.4). As an application of Theorem 2.1 we shall show that a non-hereditary, basic tiled R-order of finite global dimension always has tiltinglattices of BBtype (Proposition 2.5). As a special class of BB-type, in Section 3, we shall introduce the notion of tiltinglattices of Auslander-Platzeck-Reiten type (APRtype for short), which arise from almost splitsequences starting from certain projective modules. It should be noted that in the case of orders we cannot consider simple projective modules. We shall replace simplicity by injectivity of its radical. (See Theorem 3.1.)In Section 4, we shall precisely describe the

This paper presents development of educational software materials for secondary school mathematics, especially functions and geometry subjects. We try to develop them by Mathematica and GeoGebra, a powerful computer algebra system and interactive geometry software, respectively. Developing these materials, we obtained various findings about programming technics on mathematical software and design directions on human interfaces of software materials. These tips are useful for other developers and teachers who arrange and use our materials.

紀要論文, Students who went to university not majoring in Science and Technology may not think that they need to study mathematics any more. However, for example, students who have advanced to the department of economics and management must have the minimum mathematical knowledge and the ability to adapt it to economic and management models. However, it is not effective to teach, by using chalk and blackboard only, mathematical approach and its application to economic and management models for students who are not good at or not interested in mathematics. Therefore, I developed learning materials for freshmen majoring in business administration at a university using the calculation and visualization function of Mathematica, which can be used for both lectures and self-study. This paper reports how the materials were used in class and discusses its implications and challenges.

For linear distributed parameter systems with a finite number of boundary inputs, we propose a framework to implement the method of weighted residuals using candidate trial functions without boundary homogenization. Proposed scheme utilizes inner product matrix, or Grammian, of the trial functions to separate appropriate homogenized basis functions and the other trial functions matching inhomogeneous boundary conditions. The finite-dimensional approximate model by using the proposed scheme is represented in descriptor form and it is proved to be straightforwardly transformed into state space form. Feasibility of the method is illustrated by a brief controller design example using the approximate model of a heat conduction rod with Dirichlet boundary input.

Bulletin, The knowledge of mathematics is often required in the lecture of the university.But for the student who makes the mathematics a weak point to exist a lot by the science, a trouble attends a lecture besides the mathematics. The target of this research is to consider how to advance it learning support for improvement of the student's mathematics power of the science. It was investigated together with its degree of acceptance because I'd like to use a web for picking and choosing of learning method, consciousness to mathematics and the case that the current state about the mathematics ability is grasped to student's mathematics as learning support later by this investigation. As a result, the difference was seen by the ability of the mathematics,but the positive posture which considers a promise and studies mathematics was seen. This posture can be maintained. It's necessary to introduce implementation of an exercise for settlement of knowledge,making of a problem by ability and learning by a group to the class end as well as YOU and passive tuition and advance a lecture.To use Web because low of the possession rate of the PC and a paper base had the strong liked tendency, I found out that it's necessary to guide procedures to do a manual and a workshop.

Ju. T. Lisica and the author have defined in [4] strong homology groups HP(X;G) of inverse systems of spaces X={XX, pxx-, A) over directed cofinite sets A (every element AeA has only finitelymany predecessors). It was shown in [5] that these groups are functors on the coherent prohomotopy category CPHTop, introduced in [2] and [3]. The notion of strong or Steenrod homology H£(X; G) of an arbitrary space X was then defined [1], [6] and shown to be a functor on the strong shape category SSh [2], [3]. The procedure consisted in choosing a cofiniteANR-resolution p:X->X of Z([7], [8], [9]) and of defining HSV{X; G) as HV{X;G). That the group HSP{X; G) does not depend on the choice of the resolution is a consequence of the following factorizationtheorem ([3], Theorem II.2.3). If p:X->Xi$ a resolution and f:X-*Y is a coherent map into a cofiniteANR-system, then there exists a unique coherent homotopy class of coherent maps g: X―> Y such that gp and / are coherently homotopic. The definition of composition in CPHTop and the proof of the factorization theorem essentiallyused the assumption that the index sets A be cofinite. On the other hand, the construction of the homology groups HP(X; G) did not require thisassumption. Therefore, it remained unclear whether one can use also non-cofmite ANR-resolutions to determine the homology groups Hp{X; G) of the space X. To prove that thisis indeed the case is the main purpose of this paper. Such an information can prove useful in situations where a non-cofmite ANR-resolution naturally arises. The main idea of the proof is to replace a given ANR-resolution p: X―>X by a cofinite ANR-resolution p*: X-*X* using the "trick" described in ([9], Theorem I, 1.2). What remains to be done is to exhibit a natural isomorphism m* : HP(X; G)-^HP(X*; G). The correct formula for u* is easily found. However, the formula for the inverse v* of u* is less obvious. Even more complicated is the verificationof the two equalities u^v^―1, v*u*=l. In order to simplify notations throughout the paper we omit the coefficient groups G, although all results hold for an arbitrary G.

Let k be an algebraically closed field. We understand by a Del Pezzo surface X over k a non-singular rational surface on which the anti-canonical sheaf ―wx is ample. We call the self-intersectionnumber d=a)x of wx the degree of X, then we get that 1^J^E9. It is well known that X is isomorphic to PlxP\ which has degree 8, or an image of P2 under a monoidal transformation with center the union of r―9―d points which satisfiesthe following conditions: (a) no three of them lie on a line; (b) no six of them lie on a conic; (c) there are no cubics which pass through seven of them and have a double point at the eighth point. Conversely any surface described above is a Del Pezzo surface of the corresponding degree ([8,in, Theorem 1]). It is also well known that ―o)x is very ample when d^3 and that ample divisors on X of degree 3, which is a cubic surface, are very ample too. In this paper we will get that ample divisorson X of degree d^3 are very ample and that ample divisors on X of degree 2 [resp. 1] other than ―o>x [resp. ―o)x nor ―2^x] ore very ample. A closed subscheme V in PN is said to be projectively Cohen-Macaulay if its affine cone is Cohen-Macaulay. It is equivalent to that H1(PN,Jv(m))=0 for every meZ and H\V, Ov(m))-0 for every meZ and 0

The characterization of the harmonic, Einstein and super-Einstein spaces bymeans of the firstor the second mean values (or the relations between them) for small geodesic spheres in a Riemannian manifold is recently studied by many authors ([3], [7], [10], [17], etc.). Among them, 0. Kowalski [10] characterized the three spaces by the degree of concordance of the two mean values in some sense, proposing new classes of spaces which should be located between the harmonic and the super-Einstein spaces. On the other hand M. Pinsky [12] verified that the stochastic mean values are also useful for the characterization of the Einstein spaces. In this paper, we study the above three mean values more in detail and fillthe blanks in the previous works (Theorem 2 below). The main tool for our proof is Schauder's estimate, which enables us to treat C°°manifolds even more easily than Cauchy-Kowalewski's method for C° manifolds used in most of the previous papers. We also introduce some other new conditions which also characterize the above three spaces, that is, the conditions (M2), (M4) and (L2)-(L4) (see section 2 for the definitions). The condition (M2) is a variation of (M3) given in [3]. But it seems to be more natural than (M3) in connection with (Ml). The conditions (M4) and (L4) are closely related to Helgason's expansion in [8: p. 435]. Indeed, the above three mean values coincide with Helgason's, if the manifold is an Euclidean space or a globally symmetric space of rank one, and we are interested in to what extent the Laplacian determines the mean values. Our results include the assertion; one of the operators induced by the three mean values is expanded by means of a sequence of polynomials of Laplacian if and only if the manifold is harmonic (Theorem 2 (1)). As a by-product, we also obtain some sufficientconditions for a C6 manifold to be analytic (Theorem 1). In the course of our proof, we partially answer for smooth manifolds to Kowalski's conjecture given in [10] (Theorem 3).

This paper is a continuation of my previous paper [13], and is concerned with generalizarions of the following two classicak theorems on a continuous map f of an n-sphere Sn to itself. ...

The purpose of this paper is to study a continuous spin system by introducing the relative free energy* which plays a role of the free energy in discrete spin systems. Although the usual free energy is a very important functional,it can be available to only identically distributed 2-spin lattice systems. About such systems, refer to Holley [1], [2]. On the other hand, our relative free energy enables us to deal with spin systems with state space not necessarily discrete nor identically distributed. In Section 3, we consider a 1-dimensional lattice spin system with continuous state space to show that the relative free energy does not increase with time and especiallyit strictly decreases if the initial state is not Gibbsian; this is one of the main results of this paper. From this fact, moreover we conclude that the time evolution of any shift invariant non-Gibbsian state converges to an equilibrium state. The precise definitions of the relative free eners-v et al are erivenin Section 2.

Let k be a field of characteristic zero. Let G be a connected &-split linear algebraic group, p: G^GL(X) with X=Affra a &-homomorphism. If there exists a Zariski-dense p(G)-orbit Y, we say that (G, p, X) is a prehomogeneous vector space (abbrev. P. V.). When each irreducible component is castling equivalent to a non-trivial reduced irreducible prehomogeneous vector space or each irreducible component is a regular prehomogeneous vector space, we have completed a classification of reductive prehomogeneous vector spaces over a complex number field C (see [4], [5]). Put G = p(G). Let / be the number of G(£)-orbits in Y(k), i. e., /= | G(k)\Y(k)\. We say that Y is a universally transitive open orbit if l=\G(k)\Y(k)\=l for all k satisfying H\k, Aut(SL2))=£0, i.e., there exists a nonsplit quaternion kalgebra. This condition is satisfied by every local field k other than C. Actually our classification depends on the transitivity of G(k) on Y(k) for just one k satisfying H\k, Aut(SL2))^0 (see Remarks 2.13 and 3.5). In [1] and [2], allirreducible regular prehomogeneous vector spaces with universally transitive open orbits are classified. In [10], we have classified simple or 2-simple prehomogeneous vector spaces with universally transitive open orbits. In this paper, we shall classify reductive prehomogeneous vector spaces with universally transitive open orbits when each irreducible component is castling equivalent to a non-trivial reduced irreducible prehomogeneous vector space or each irreducible component is a regular prehomogeneous vector space. This paper consists of the following three sections. §1. Preliminaries. §2, Reductive P.V.'s with universally transitive open orbits: the case I. §3. Reductive P.V.'s with universally transitive open orbits: the case II. The results are given in Theorems 2.11, 3.4 and Corollary 2.12.

In recent years, we have been developing a system we call QDB which helps teachers conduct quizzes (especially online ones）and allows students do exercises online. We describe our system as a practical one which has been developed so that it satisfies the needs of our classes. In this paper, we summarize the characteristics and our evaluations of the system developed so far, and discuss how it can be upgraded to the next stages.

P(論文), In a technical college, mathematics is a very important element of engnieering. In order to have a suitable class inmathematics for technical college student, teachers must know what level of mathematics the first year students have attained.This paper reports the results of the new achievement test which covers the mathematics which the first year students have tounderstand.

This paper is concerned with a gait generation framework for legged robots based on iterative learning control (ILC) of Hamiltonian systems. This method allows one to obtain solutions to a class of optimal control problems by iteration of laboratory experiments and, furthermore, precise knowledge of the plant model is not required for it by taking advantage of a symmetric property of Hamiltonian systems. Generally in walking motion, there are discontinuous state transitions caused by collision between the foot and the ground. The proposed framework can also deal with such state transitions without using the parameters of the transition model by combining ILC method and the least-squares. It is applied to a compass-like biped robot to generate optimal gait on the level ground. Some numerical examples demonstrate the effectiveness of the proposed method.

P(論文), In a technical college, mathematics is a very important element of engnieering. In order to have a suitable class inmathematics for technical college student, teachers must know what level of mathematics the first year students have attained.This paper reports the results of the achievement test since 1995 which covers the mathematics which the first year studentshave to understand.

The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study quasi-Einstein spacetimes. Some basic geometric properties of such a spacetime are obtained. The applications of quasi-Einstein spacetimes in general relativity and cosmology are investigated. Finally, the existence of such spacetimes are ensured by several interesting examples.

Let $M$ be an $n$-dimensional compact Willmore submanifold in an $(n + p)$-dimensional unit sphere $S^{n+p}$. Denote by $S$ and $H$ the square of the length of the second fundamental form and the mean curvature of $M$. Let $\rho$ be the non-negative function on $M$ defined by $\rho^{2} = S - nH^{2}$ and $K$ be the function which assigns to each point of $M$ the infimum of the sectional curvature at the point. In this paper, first of all, we prove that, if $K$, $H$ and $p$ satisfy $K \geq \frac{p-1}{2p-1} + (n - 2)\frac{H\rho}{\sqrt{n(n-1)}}+H^{2}$, then either $M$ is totally umbilic; or a Willmore torus $W_{1,n- l}$; or the Veronese surface in $S^4$; if the Ricci curvature $R_{ii}$, $H$ and $\rho$ satisfy $R_{ii} \geq (n - 2)+(n - 2)H{\rho} + H^{2}$, for $n \geq 5$, then either $M$ is totally umbilic or a Willmore torus $W_{m,m}$. Secondly, we consider the Willmore submanifold with flat normal connection, we obtain that, if $0 \leq \rho^{2} \leq n$ then eigher $M$ is totally umbilic or a Willmore torus $W_{m,n-m}$; if $K \geq (n-2)+ \frac{H\rho}{\sqrt{n(n-1)}}+ H^{2}$, then $M$ is totally umbilic or $n \leq \rho^{2} \leq np$.

In this paper, we classify a Hopf hypersurface in a nonflat complex space form whose Levi-form is parallel with respect to the generalized Tanaka-Webster connection.

The atomic surface $X_q$ from an unimodular Pisot substitution $\sigma$ usually has the fractal boundary and it generates a selfaffine tiling. In this paper, we study the boundary $\partial X_{q}$ as the graph directed self-affine fractal and estimate the Hausdorff dimension of the boundary.

Let $\ell_{2}(\tau)$ be the Hilbert space with weight $\tau$ and $\ell_{2}^{f}$ be the linear span of the canonical orthonormal basis of the separable Hilbert space $\ell_{2}$. In this paper, we prove that if a metric space $X$ ishomeomorphic to $\ell_{2}(\tau)$ or $\ell_{2](\tau) \times \ell_{2}^{f}$ then the hyperspace $Fin_{H}(X)$ of non-empty finite subsets of $X$ with the Hausdorff metric is homeomorphic to $\ell_{2}(\tau) \times \ell_{2}^{f}$.

An Einstein-Weyl structure is a natural generalization of an Einstein structure within the framework of conformal geometry. We are interested in considering an Einstein-Weyl structure on a CR manifold. A CR manifold has a conformal structure only on its hyperdistribution. In this paper, on a CR manifold we naturally define an Einstein-Weyl structure closely related to the conformal structure on the hyperdistribution.

In this paper, we treat piecewise Riemannian 2-polyhedra which are combinatorial 2-polyhedra such that each 2-simplex is isometric to a triangle bounded by three smooth curves on some Riemannian 2-manifold. We will introduce the total curvature $C(X)$ of a piecewise Riemannian 2-polyhedron $X$ not only in the compact case but also in the noncompact case, and obtain some generalizations of the Gauss-Bonnet theorem and the Cohn-Vossen theorem. Furthermore, we will show that the difference between $C(X)$ and some value concerning to the topology of $X$ coincides with some expanding growth rate of $X$.

This paper studies the simultaneous Diophantine phenomena of commuting systems of vector fields and diffeomorphisms. We consider how these conditions are related with the Diophantine phenomena of every element of the system.

In this paper, we will show that classical resultants-which are generalizations of Sylvester determinants-are closely related to Chow-forms of projective varieties. As a result, we will see that the maximal degree of the coefficients of a Chow-form in the coefficients of defining equations may be assumed to be bounded from above.

In this paper, we propose a new control method for two-wheeled non-holonomic mobile robots. Since the non-holonomic mobile robots has non-integrable constraint conditions, it is difficult to derive a control law so that the robots are convergent to the target state. The proposed method designs a nonlinear regulator carrying out asymptotic convergence of non-holonomic mobile robots to a given trajectory family. The trajectory family is chosen so that it passes through the origin and its gradient at the origin is equal to zero. As the result, the mobile robots are convergent to the origin as the target state while generating their path. We name this method Path-generating Regulator. Neither the coordinate transformation nor the input transformation is needed in this method unlike other methods. Global asymptotic regulation property of this method is proven by a Lyapunov-based stability analysis. By numerical simulations and experiments, we show the validity of the proposed method.

The hypergeometric series reduce to many elementary functions. Many of them are known to have the continued fraction expansions. Few of them for certain values, however, are known to have the simple continued fraction expansions which keep reg- ularities. In this paper we show more simple continued fraction expansions holding regularities.

A glued Riemannian space is obtained from Riemannian manifolds $M_1$ and $M_2$ by identifying their isometric submanifolds $B_{1}$ and $B_{2}$. A curve on a glued Riemannian space which is a geodesic on each Riemannian manifold and satisfies certain passage law on the identified submanifold $B \mathrel{:=} B_{1} \cong B_{2}$ is called a $B$-geodesic. Considering the variational problem with respect to arclength $L$ of piecewise smooth curves through $B$, a critical point of $L$ is a $B$-geodesic. A $B$-Jacobi field is a Jacobi field on each Riemannian manifold and satisfies certain passage condition on $B$. In this paper, we extend Rauch's theorem which gives a comparison of the lengths of Jacobi fields along geodesics in different Riemannian manifolds to $B$-Jacobi fields along $B$-geodesics in different glued Riemannian spaces.

A smooth surface $S$ in $\bf{R}^3$ is called parallel curved if there exists a plane in $\bf{R}^3$ such that at each point of $S$, there exists a principal direction parallel to the plane. For example, a plane, a cylinder and a round sphere are parallel curved. More generally, a surface of revolution is also parallel curved. The purposes of this paper are to study the behavior of the principal distributions on a real-analytic, parallel curved surface and to classify the connected, complete, real-analytic, embedded, parallel curved surfaces.

In this paper we show that periodic Takahashi 3-manifolds are cyclic coverings of the connected sum of two lens spaces (possibly cyclic coverings of the 3-sphere), branched over knots. When the base space is a 3-sphere, we prove that the associated branching set is a two-bridge knot of genus one, and we determine its type. Moreover, a geometric cyclic presentation for the fundamental groups of these manifolds is obtained in several interesting cases, including the ones corresponding to the branched cyclic coverings of the 3-sphere., 12 pages, 5 figures. To appear in Tsukuba Journal of Mathematics

In this paper, we examine a new method of implicit finite element analysis of soil/water coupling problems. It consists of two main schemes: One scheme is an implicit return mapping scheme and another is a scheme which employs the consistent tangential modulus. The implicit return mapping scheme is based on the notion of the elastic-plastic operator split that consists of the elastic predictor and the plastic corrector. A tangential modulus consisting with the integration algorithm is developed for a well-known Cam-clay model for soils. Some examples of the implicit method show the high accuracy and much reducing the total CPU time.

For any closed, oriented, simply connected spin 4-manifold $X$ with $b_{X}^{+}>1$ and even, by Fintushel and Stern [7], differential-topological polynomial invariants with its values in $Z_{2}$ are defined. These invariants are analogues of Donaldson polynomial invariants. In [7], it is proved that if $X=X^{\prime}\# S^{2}\times S^{2}$, then these invariants do not always vanish. But in this paper, it is proved that these invariants vanish for a large class of connected sums.