• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.377-384
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• 1998

Let ${X_n,n \geq 1}$ be a sequence of stochatically dominated pairwise independent random variables. Let ${a_n, n \geq 1}$ and ${b_n, n \geq 1}$ be seqence of constants such that $a_n \neq 0$ and $0 < b_n \uparrow \infty$. A strong law large numbers of the form $\sum^{n}_{j=1}{a_j X_i//b_n \to 0$ almost surely is obtained.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.681-685
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• 2002

It is shown that, an immersion of n-dimensional compact manifold without boundary into (n + 1)-dimensional Euclidean space, hyperbolic space or the open half spheres, is a totally umbilic immersion if for some r, r =2, 3, …, n the r-th mean curvature Hr does not vanish and there are nonnegative constants $C_1$, $C_2$, …, $C_{r}$ such that (equation omitted)d)

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.275-282
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• 2004

Let {$a_{ni},\;u_n\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be an arry of constants. Let {X_{ni},\;u_n\;{\leq}\;i\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be {$a_{ni}$}-uniformly integrable random variables. Weak laws for the weighted sums ${{\Sigma}_{i=u_n}}^{{\upsilon}_n}\;a_{ni}X_{ni}$ are obtained.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.175-186
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• 2018

Let (M, J, ${\theta}$) be a complete pseudohermintian (2n+1)-manifold. In this paper, we derive the subgradient estimate for positive solutions to a nonlinear subelliptic equation ${\Delta}_bu+au{\log}u+bu=0$ on M, where $a{\leq}0$, b are two real constants.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.707-717
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• 2007

Arches are constrained with rotational resistance at both edges. An energy method is used to derive variational formulation which is used to prove the existence of equilibrium states of elastic circular arches for the torsional spring constants ${\rho}-\;{\geq}\;0,\;{\rho}+\;{\geq}\;0,\;and\;{\rho}-\;+\;{\rho}+\;>\;0$. The boundary conditions are searched using the existence of minimum potential energy.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.303-315
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• 1994

Let X be a real Banach space with norm ∥ㆍ∥. Let T > 0, r ≥a be fixed constants. We denote by L/sup p/ the usual L/sup p/( -r, 0; X) with norm ∥ㆍ∥/sub p/ for 1 ≤p < ∞. Our object is to study the existence of solutions of nonlinear functional evolution equations of the type (FDE) x'(t) ＋ A(t)x(t) = G(t, x/sub t/), 0 ≤t ≤T, x/sub 0/ = ø.(omitted)

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.63-79
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• 1997

Consider an oparator equation of the form : $$ (1.1) H[y](x) = \alpha(x)\delta^2 y(x) + \beta(x)\delta y(x) = \lambda_n y(x), $$ where $\alphs(x)$ and $\beta(x)$ are polynomials of degree at most two and one respectively, $\lambda_n$ is the eigenvalue parameter, and $\delta$ is Hahn's operator $$ (1.2) \delta f(x) = \frac{(q - 1)x + \omega}{f(qx + \omega) - f(x)}, $$ for real constants $q(\neq \pm 1)$ and $\omega$.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.411-422
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• 2017

Let {$X_{ni}$, $i{\geq}1$, $n{\geq}1$} be an array of rowwise asymptotically negatively associated random variables and {$a_{ni}$, $i{\geq}1$, $n{\geq}1$} an array of constants. Some results concerning complete convergence of weighted sums ${\sum}_{i=1}^{n}a_{ni}X_{ni}$ are obtained. They generalize some previous known results for arrays of rowwise negatively associated random variables to the asymptotically negative association case.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.335-337
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• 2015

We modify the normalizing constants of the functions in the orthonormal basis for the Bergman space and restate their consequences in the paper that was published in Honam Math. J. 36 (2014), no. 4, pp. 777-786.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.291-296
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• 2001

For randomly indexed sums of the form (Equation. See Full-text), where {X(sub)ni, i$\geq$1, n$\geq$1} are random variables, {N(sub)n, n$\geq$1} are suitable conditional expectations and {b(sub)n, n$\geq$1} are positive constants, we establish a general weak law of large numbers. Our result improves that of Hong [3].