• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.343-352
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• 2013

In this paper, we give a formula of $(P+Q)^D$ under the conditions $P^2Q+QPQ=0$ and $P^3Q=0$. Then applying it to give some results of block matrix $M=(^A_C^B_D)$ (A and D are square matrices) with generalized Schur complement is zero under some conditions. Finally, numerical examples are given to illustrate our results.

• 대한수학회논문집
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• 제32권1호
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• pp.225-231
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• 2017

Baskoro et al. [1] provided some constructions of new super edge-magic graphs from some old ones by attaching 1, 2, or 3 pendant vertices and edges. In this paper, we introduce (q, m)-super edge-magic total labeling and we give a construction of new super edge-magic graphs by attaching n pendant vertices and edges under some conditions, for any positive integer n. Also, we give a constraint on our construction.

• 대한수학회보
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• 제54권6호
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• pp.1935-1950
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• 2017

Let R be a Ding-Chen ring. Yang [24] and Zhang [25] asked whether or not every R-module has finite Ding projective or Ding injective dimension. In this paper, we give a new characterization of that all modules have finite Ding projective and Ding injective dimension in terms of the relationship between Ding projective and Gorenstein flat modules. We also give an example to obtain negative answer to the above question.

• 대한수학회보
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• 제54권6호
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• pp.2053-2063
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• 2017

In this paper we prove a condition under which a hyperbolic starshaped set has a center of hyperbolic symmetry. We also give the definition of isometric diameters for a hyperbolic convex set, which behave similar to affine diameters for Euclidean convex sets. Using this concept, we give a definition of constant hyperbolic width and we prove that the only hyperbolic sets with constant hyperbolic width and with a hyperbolic center of symmetry are hyperbolic discs.

• Korean Journal of Mathematics
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• 제22권3호
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• pp.443-454
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• 2014

In this paper, we give linearization of generalized Fi-bonacci sequences {$g_n$} and {$q_n$}, respectively, defined by Eq.(5) and Eq.(6) below and use this result to give the matrix form of the nth power of a companion matrix of {$g_n$} and {$q_n$}, respectively. Then we re-prove the Cassini's identity for {$g_n$} and {$q_n$}, respectively.

• 한국경영과학회지
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• 제19권2호
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• pp.153-176
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• 1994

In this paper we introduce machine learning theory to business domains for business decisions. First, we review machine learning in general. We give a new look on a previous framework, version space approach, and we introduce PAC (probably approximately correct) learning paradigm which has been developed recently. We illustrate major results of PAC learning with business examples. And then, we give a theoretical analysis is decision tree induction algorithms by the frame work of PAC learning. Finally, we will discuss implications of learning theory toi business domains.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.733-738
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• 2008

Using an information of dimensions of divergence points, we give full information of dimensions of the completely decomposed class of the lower(upper) distribution sets of a self-similar Cantor set. Further using a relationship between the distribution sets and the subsets generated by the lower(upper) local dimensions of a self-similar measure, we give full information of dimensions of the subsets by the local dimensions.

• 대한수학회보
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• 제47권4호
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• pp.839-857
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• 2010

We give a set of continuous characterizations for the homogeneous Triebel-Lizorkin spaces and use them to study boundedness properties of Fourier multiplier operators whose symbols satisfy a generalization of H$\ddot{o}$rmander's condition. As an application, we give new direct proofs of the imbedding theorems of the Sobolev type.

• 대한수학회지
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• 제50권1호
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• pp.95-109
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• 2013

The aim of this paper is to establish variational principle on cone metric spaces and to give some existence theorems of solutions for equilibrium problems on cone metric spaces. We give some equivalences of an existence theorem of solutions for equilibrium problems on cone metric spaces.

• 대한수학회보
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• 제52권5호
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• pp.1721-1728
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• 2015

We give certain properties of elements in a coset group with hypercomplex numbers and research a monogenic function and a Clifford regular function with values in a coset group by defining differential operators. We give properties of those functions and a power of elements in a coset group with hypercomplex numbers.