• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.67-80
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• 1998

In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

• The Mathematical Education
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• v.21 no.3
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• pp.25-28
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• 1983

In this paper we examine some properties of spectral measures and try to establish a fundamental theorem on the existence of the solution of a generalized Volterra equation in a Hilbert space as the results.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.349-361
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• 2017

By means of the Oberhettinger integral, certain generalized integral formulae involving product of generalized k-Bessel function $w^{{\gamma},{\alpha}}_{k,v,b,c}(z)$ and general class of polynomials $S^m_n[x]$ are derived, the results of which are expressed in terms of the generalized Wright hypergeometric functions. Several new results are also obtained from the integrals presented in this paper.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.601-617
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• 2017

We give a function associated with generalized Ostrowski type inequality and its integral representation for local fractional calculus. Then, using this function and its integral representation, we establish several inequalities of generalized Ostrowski type for twice local fractional differentiable functions. We also consider some special cases of the main results which are further applied to a concrete function to yield two interesting inequalities associated with two generalized means.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.477-499
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• 2020

In this paper, we introduce a new class of generalized Apostol-type Frobenius-Euler-Hermite polynomials and derive some explicit and implicit summation formulae and symmetric identities by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Frobenius-Euler type polynomials and Hermite-based Apostol-Euler and Apostol-Genocchi polynomials studied by Pathan and Khan, Kurt and Simsek.

• Korean Journal of Mathematics
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• v.8 no.1
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• pp.73-86
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• 2000

We study the Sobolev spaces to the generalized Sobolev spaces $H^s_{\mathcal{G}}$ of exponential type based on the Silva space $\mathcal{G}$ and investigate its properties such as imbedding theorem and structure theorem. In fact, the imbedding theorem says that for $s$ > 0 $u{\in}H^s_{\mathcal{G}}$ can be analytically continued to the set {$z{\in}\mathbb{C}^n{\mid}{\mid}Im\;z{\mid}$ < $s$}. Also, the structure theorem means that for $s$ > 0 $u{\in}H^{-s}_{\mathcal{G}}$ is of the form $$u={\sum_{\alpha}\frac{s^{{|\alpha|}}}{{\alpha}!}D^{\alpha}g{\alpha}$$ where $g{\alpha}$'s are square integrable functions for ${\alpha}{\in}\mathbb{N}^n_0$. Moreover, we introduce a classes of symbols of exponential type and its associated pseudo-differential operators of exponential type, which naturally act on the generalized Sobolev spaces of exponential type. Finally, a generalized Bessel potential is defined and its properties are investigated.

• Korean Management Science Review
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• v.31 no.3
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• pp.27-39
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• 2014

We derive a generalized statistic form of Q control chart, which is especially suitable for short run productions and start-up processes, for the detection of process mean shifts. The generalization means that the derived control chart statistic concurrently uses within lot variability and between lot variability to explain the process variability. The latter variability source is noticeably prevalent in lot type production processes including semiconductor wafer fabrications. We first obtain the generalized Q control chart statistic when both the process mean and process variance are unknown, which represents the case of implementing statistical process control charting for short run productions and start-up processes. Also, we provide the corresponding generalized Q control chart statistics for the rest of three cases of previous Q control chart statistics : (1) both the process mean and process variance are known (2) only the process mean is unknown and (3) only the process variance is unknown.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.405-408
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• 2003

This paper proposes a new algorithm for cloudy area detection using K-Means and GHA (Generalized Hebbian Algorithm). K-Means is one of simple classification algorithm, and GHA is unsupervised neural network for data compression and pattern classification. Proposed algorithm is based on block based image processing that size is l6$\times$l6. Experimental results shows good performance of cloudy area detection except blur cloudy areas.

• Kyungpook Mathematical Journal
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• v.22 no.2
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• pp.195-202
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• 1982

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.485-498
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• 2013

In this paper, the Schur convexity is generalized to Schur $f$-convexity, which contains the Schur geometrical convexity, harmonic convexity and so on. When $f$ : ${\mathbb{R}}_+{\rightarrow}{\mathbb{R}}$ is defined as $f(x)=(x^m-1)/m$ if $m{\neq}0$ and $f(x)$ = ln $x$ if $m=0$, the necessary and sufficient conditions for $f$-convexity (is called Schur $m$-power convexity) of Gini means are given, which generalize and unify certain known results.