• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.1-8
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• 2003

In this paper, we further develop the weak polygroup theory, we define quotient weak polygroup and then the fundamental homomorphism theorem of group theory is derived in the context of weak polygroups. Also, we consider the fundamental relation $\beta$$^{*}$ defined on a weak polygroup and define a functor from the category of all weak polygroups into the category of all fundamental groups.s.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.93-101
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• 2002

The $S^1$-Eule characteristics of X is defined by $\bar{\chi}_{S^1}(X)\;{\in}\;HH_1(ZG)$, where G is the fundamental group of connected finite $S^1$-compact manifold or connected finite $S^1$-finite complex X and $HH_1$ is the first Hochsch ild homology group functor. The purpose of this paper is to find several cases which the $S^1$-Euler characteristic has a homotopic invariant.

• The Journal of the Convergence on Culture Technology
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• v.4 no.1
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• pp.275-278
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• 2018

This study examines how poem and poetic ego of Cho Ji-Hoon form synapses. It is to clarify the synaptic structure of the healing, the contact point between the literary mechanism and the mechanism of the ego. Therefore, it aims to encode the active therapy by substituting the structure into the literary therapy program. Cho Ji-Hoon's poem "Bellflower Flower" is a mesh of poem, and a mesh of semantic arguments is set up for the 'Bellflower Flower' of functor. At this time, the longing that attracts depression to the net of the semantic argument is caught. This exists as a function of healing. If we embody a literary therapy program that utilizes the synaptic structure of this healing, it will be able to experience the function of literary therapy improved than before.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1365-1373
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• 2015

We find all ${\mathcal{F}}{\mathcal{M}}_m$-natural operators A transforming torsion free classical linear connections ${\nabla}$ on m-manifolds M into base preserving fibred maps $A({\nabla}):{\bar{J}}^rY{\rightarrow}J^rY$ for ${\mathcal{F}}{\mathcal{M}}_m$-objects Y with bases M, where ${\bar{J}}^r$, $J^r$ are the semiholonomic and holonomic jet functors of order r on the category ${\mathcal{F}}{\mathcal{M}}_m$ of fibred manifolds with m-dimensional bases and their fibred maps with embeddings as base maps.

• Language and Information
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• v.19 no.2
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• pp.1-18
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• 2015

This paper retraces the development of Database Semantics (DBS) from its beginnings in Montague grammar. It describes the changes over the course of four decades and explains why they were seen to be necessary. DBS was designed to answer the central theoretical question for building a talking robot: How does the mechanism of natural language communication work? For doing what is requested and reporting what is going on, a talking robot requires not only language but also non-language cognition. The contents of non-language cognition are re-used as the meanings of the language surfaces. Robot-externally, DBS handles the language-based transfer of content by using nothing but modality-dependent unanalyzed external surfaces such as sound shapes or dots on paper, produced in the speak mode and recognized n the hear mode. Robot-internally, DBS reconstructs cognition by integrating linguistic notions like functor-argument and coordination, philosophical notions like concept-, pointer-, and baptism-based reference, and notions of computer science like input-output, interface, data structure, algorithm, database schema, and functional flow.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.503-511
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• 1994

In this paper, the ring A will mean a commutative Noetherian ring with non-zero multiplicative identity, it is understood that the ring homomorphisms respect identity elements and M will denote an A-module. Throughout this paper A and B will denote rings, $f : A \to B$ a ring homomorphism. C(A) (resp. C(B)) presents the category of all A-modules (resp. B-modules) and A-homomorphisms (resp. B-homorphisms) between them. The following ideas will be used without further explanation. B can be regarded as an A-module by means of f and $M\otimesB$ can be regarded as a B-module in the natural way. Furthermore the restriction of scalars provides a functor from C(B) to C(A).

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.865-877
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• 2013

The disjoint union of mapping class groups of surfaces forms a braided monoidal category $\mathcal{M}$, as the disjoint union of the braid groups $\mathcal{B}$ does. We give a concrete and geometric meaning of the braidings ${\beta}_{r,s}$ in $\mathcal{M}$. Moreover, we find a set of elements in the mapping class groups which correspond to the standard generators of the braid groups. Using this, we can define an obvious map ${\phi}\;:\;B_g{\rightarrow}{\Gamma}_{g,1}$. We show that this map ${\phi}$ is injective and nongeometric in the sense of Wajnryb. Since this map extends to a braided monoidal functor ${\Phi}\;:\;\mathcal{B}{\rightarrow}\mathcal{M}$, the integral homology homomorphism induced by ${\phi}$ is trivial in the stable range.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.1-14
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• 1998

In this short note we study the torsion theories over a commutative ring R and discuss a relative dimension related to such theories for R-modules. Let ${\sigma}$ be a torsion functor and (T, F) be its corresponding partition of Spec(R). The concept of ${\sigma}$-Cohen Macaulay (abbr. ${\sigma}$-CM) module is defined and some of the main points concerning the usual Cohen-Macaulay modules are extended. In particular it is shown that if M is a non-zero ${\sigma}$-CM module over R and S is a multiplicatively closed subset of R such that, for all minimal element of T, $S{\cap}p={\emptyset}$, then $S^{-1}M$ is a $S^{-1}{\sigma}$-CM module over $S^{-1}$R, where $S^{-1}{\sigma}$ is the direct image of ${\sigma}$ under the natural ring homomorphism $R{\longrightarrow}S^{-1}R$.

• Korean Journal of English Language and Linguistics
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• v.4 no.2
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• pp.175-194
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• 2004

This paper provides computational algorithms for English Questions, by which we can effectively handle and implement Yes-No Questions and Wh-Questions. Those algorithms will be developed in Categorial Grammar. In this paper, we will modify and revise Steedman＇s Combinatory Categorial Grammar (CCG) so that we can computationally implement Questions effectively, which will be called a CCG-like system. In this system, semantic interpretations of Questions will be calculated compositionally based on the functor-arguments relations of the constituents. In sum, this paper provides analyses of Questions in Categorial Grammar, by which we can effectively implement Questions in English.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.187-198
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• 2021

This work presents an exposition of both the internal structure of derived category of an abelian category D^*(𝓐) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented between objects in D^*(𝓐) as elements in appropriate cohomology groups along with their compositions with the help of Yoneda construction under the assumption that the homological dimension of D^*(𝓐) is greater than or equal to 2. These computational settings will then be considered under sheaf cohomological context with a particular case from projective geometry.