• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.189-193
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• 1996

In 1992. Boullion obtained the method of the calculus of the moments of discrete probability distributions using differential operator, and he published the method of calculus of the moments. The purpose of this paper is to introduce an idea that this method can be applied to calculate the moments of continuous probability distributions.

• Communications of the Korean Mathematical Society
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• v.8 no.2
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• pp.181-190
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• 1993

• Journal of the Korean Mathematical Society
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• v.23 no.2
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• pp.167-173
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• 1986

• Kyungpook Mathematical Journal
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• v.32 no.3_spc
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• pp.401-413
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• 1992

• Kyungpook Mathematical Journal
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• v.29 no.1
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• pp.87-103
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• 1989

• Kyungpook Mathematical Journal
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• v.30 no.1
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• pp.29-35
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• 1990

• Journal of Integrative Natural Science
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• v.7 no.4
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• pp.273-277
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• 2014

In this article, we consider a singular and a degenerate elliptic operators in a divergence form. The singularities exist on a part of boundary, and comparable to the logarithmic distance function or its inverse. If we assume that the operator can be treated in a pointwise sense than distribution sense, with this operator we obtain a priori Harnack continuity near the boundary. In the proof we transform the singular elliptic operator to uniformly bounded elliptic operator with unbounded first order terms. We study this type of estimations considering a De Giorgi conjecture. In his conjecture, he proposed a certain ellipticity condition to guarantee a continuity of a solution.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.455-460
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• 2007

In allelic model $X=(x_1,\;x_2,\;{\cdots},\;x_d)$, $$M_f(t)=f(p(t))-{\int}_0^t\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we try to apply diffusion processes for countable-allelic model in population genetic model and we can define a new diffusion operator $L^*$. Since the martingale problem for this operator $L^*$ is related to diffusion processes, we can define a integral which is combined with operator $L^*$ and a bilinar form $<{\cdot},{\cdot}>$. We can find properties for this integral using maximum principle.

• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.109-124
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• 2017

In this article the Srivastava-Owa-Ruscheweyh fractional derivative operator $\mathcal{L}^{\alpha}_{a,{\lambda}}$ is applied for defining and studying some new subclasses of analytic functions in the unit disk E. Inclusion results, radius problem and other results related to Bernardi integral operator are also discussed. Some applications related to conic domains are given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.1
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• pp.51-82
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• 2016

In view of ideas for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is generally included with existence and controllability (EaC) results for fractional neutral integro-differential systems (FNIDS) with state-dependent delay (SDD) in Banach spaces. Finally, an examples are also provided to illustrate the theoretical results.