• 충청수학회지
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• 제26권2호
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• pp.259-268
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• 2013

In this paper, we define the Banach-valued strong $M_{\alpha}$-integral and study the primitive of the strong $M_{\alpha}$-integral in terms of the $M_{\alpha}$-variational measures. We also prove that every function of bounded variation is a multiplier for the strong $M_{\alpha}$-integral.

• 충청수학회지
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• 제23권1호
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• pp.99-108
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• 2010

In this paper, we define the $M_{\alpha}$-integral and investigate properties of the $M_{\alpha}$-integral.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1997년도 봄 학술발표회 논문집
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• pp.35-42
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• 1997

The two-state or mutual M-integral which is derived from tile M-integral and is applicable for two elastic states, is applied for computing all intensity of a singular near-tip field around the vertex of a class of wedge, encountered in adhesive lap joints under mechanical loading. Numerically we verify that a simple auxiliary field associated with every eigenfunction for the composite wedge under consideration exists in the form of the conjugate solution in the sense of tile M-integral. The auxiliary field is then employed for superposition with the elastic field under consideration, and the associated two-state M-integral is computed via the domain integral technique. This enables us to extract the intensity for a singular field information for a singular elastic boundary layer is extracted form the domain integral representation without resort to singular finite element for the wedge vertex.

• Kyungpook Mathematical Journal
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• 제46권1호
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• pp.31-48
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• 2006

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

• 호남수학학술지
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• 제29권4호
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• pp.653-666
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• 2007

Let R be a commutative Noetherian ring (with a nonzero identity) and let M be an R-module. Further let I be an ideal of R. In this paper, by putting a suitable condition on $Ass_R$(M), we obtain some results concerning $I^{*(M)}$ and prove that the sequence of sets $Ass_R(R/(I^n)^{*(M)})$, $n\;\in\;N$, is increasing and ultimately constant. (Here $(I^n)^{*(M)}$ denotes the integral closure of $I^n$ relative to M.)

• 충청수학회지
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• 제24권2호
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• pp.383-391
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• 2011

In this paper, we investigate some properties of the $M_{\alpha}$-integral and prove convergence theorems for the $M_{\alpha}$-integral.

• 대한수학회지
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• 제44권6호
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• pp.1255-1266
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• 2007

We establish a weighted norm inequality for a class of rough parametric Marcinkiewicz integral operators $\mathcal{M}^{\rho}_{\Omega}$. As an application of this inequality, we obtain weighted $L^p$ inequalities for a class of parametric Marcinkiewicz integral operators $\mathcal{M}^{*,\rho}_{\Omega,\lambda}\;and\;\mathcal{M}^{\rho}_{\Omega,S}$ related to the Littlewood-Paley $g^*_{\lambda}-function$ and the area integral S, respectively.

• 충청수학회지
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• 제25권4호
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• pp.763-769
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• 2012

In this paper, we define the strong $M_{\alpha}$-integral of Banach-valued functions and investigate some properties of the strong $M_{\alpha}$-integral.

• 충청수학회지
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• 제25권1호
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• pp.115-125
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• 2012

In this paper, we define the $M_{\alpha}$-integral of Banach-valued functions and investigate some properties of the $M_{\alpha}$-integral.

• 충청수학회지
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• 제23권4호
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• pp.861-870
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• 2010

In this paper, we define the $M_{\alpha}$-integral and prove the integration by parts formula for the $M_{\alpha}$-integral.