• 대한수학회보
• /
• 제53권3호
• /
• pp.751-763
• /
• 2016

The properties of the nonabelian tensor products are interesting in different contexts of algebraic topology and group theory. We prove two theorems, dealing with the nonabelian tensor products of projective limits of finite groups. The first describes their topology. Then we show a result of embedding in the second homology group of a pro-p-group, via the notion of complete exterior centralizer. We end with some open questions, originating from these two results.

• Journal of Astronomy and Space Sciences
• /
• 제11권2호
• /
• pp.273-280
• /
• 1994

A linear method for determining three-dimensional motion of a rigid object is presented. In this method, two three-dimensional line correspondences are used. By using three-dimensional information of the features and observing that the rotation is unique regardless of the translation vector, the two components of motion parameters (rotation and translation) are computed separately. Also in this paper, the solution is given without a scale factor which is necessary in other methods that use only the two-dimensional projective constraints.

• 대한수학회보
• /
• 제32권2호
• /
• pp.321-328
• /
• 1995

In this note all are commutative rings with identity and all modules are unital. Let R be a ring. An R-module M is called a multiplication module if for every submodule N of M there esists an ideal I of R such that N = IM. Clearly the ring R is a multiplication module as a module over itself. Also, it is well known that invertible and more generally profective ideals of R are multiplication R-modules (see [11, Theorem 1]).

• 대한수학회논문집
• /
• 제11권2호
• /
• pp.385-390
• /
• 1996

Let X be a smooth projective threefold whose anticanonical division $-K_X$ is ample, i.e., Fano threefold. In this paper, we studied the linear system $$\mid$-nK_X$\mid$$ for a positive integer n. In Theorem 4, we studied the cases that $\-nK_X$\mid$$ has no base-points and the cases that $$\mid$-nK_X$\mid$$ generate the birational map. In Proposition 5, we studied the possible exceptional cases given in Theorem 4. Some results in this paper are already known, but we have gave brief proofs for those results.

• 대한수학회보
• /
• 제40권4호
• /
• pp.649-661
• /
• 2003

The ($\alpha,\;\beta$)-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-form $\beta$. In this paper, we discuss the projective flatness of Finsler spaces with certain ($\alpha,\;\beta$)-metrics ([5]) in a locally Minkowski space.

• 대한수학회보
• /
• 제52권5호
• /
• pp.1579-1586
• /
• 2015

In this paper we investigate the barrellednes of some spaces of X-valued measures, X being a barrelled normed space, and provide examples of non barrelled spaces of bounded linear operators from a Banach space X into a barrelled normed space Y, equipped with the uniform convergence topology.

• 대한수학회보
• /
• 제45권2호
• /
• pp.263-267
• /
• 2008

Kaplansky introduced the Baer rings as rings in which every left (or right) annihilator of each subset is generated by an idempotent. On the other hand, Hattori introduced the left (resp. right) P.P. rings as rings in which every principal left (resp. right) ideal is projective. The purpose of this paper is to introduce the near-rings with Baer like condition and near-rings with P.P. like condition which are somewhat different from ring case, and to extend the results of Arendariz and Jondrup.

• 대한수학회보
• /
• 제57권4호
• /
• pp.865-872
• /
• 2020

Let X ⊂ ℙ^r be an integral and non-degenerate variety. Set n := dim(X). Let 𝜌(X)" be the maximal integer such that every zero-dimensional scheme Z ⊂ X smoothable in X is linearly independent. We prove that X is linearly normal if 𝜌(X)" ≥ 2⌈(r + 2)/2⌉ and that 𝜌(X)" < 2⌈(r + 1)/(n + 1)⌉, unless either n = r or X is a rational normal curve.

• 대한수학회보
• /
• 제57권4호
• /
• pp.873-890
• /
• 2020

In this paper, for discrete groups G and K, we show that the cohomology of the complex of projective tensor product B*(G)⨶B*(K) is isomorphic to the bounded cohomology Ĥ*(G × K) of G × K, which is the cohomology of B*(G × K) as topological vector spaces, where B*(G) is a complex of bounded cochains of G with real coefficients ℝ. In fact, we construct an isomorphism between these two cohomology groups that carries the canonical seminorm in Ĥ*(G × K) to the seminorm in the cohomology of B*(G)⨶B*(K).

• 대한수학회논문집
• /
• 제11권3호
• /
• pp.743-756
• /
• 1996

The purpose of this paper is to compute the covariant derivative of a shape operator of a generic submanifold of a complex space form without using the Green-Stoke's theorem. In particular, we classify complete generic submanifolds of a complex number space $C^m$ with parallel mean curvature vector satisfying a certain condition.