• 대한수학회지
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• 제44권1호
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• pp.199-210
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• 2007

Given a field K and a finite group G, it is a very interesting problem, although very difficult, to find all Galois extensions over K whose Galois group is isomorphic to G. In this paper, we prepare a theoretical background to study this type of problem when G is the Mathieu group $M_{24}$ and K is a field of characteristic two.

• 대한수학회지
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• 제38권3호
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• pp.633-644
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• 2001

Revenel computed the Adams spectral sequence converging to BP(Ω$^2$S(sup)2n+1) and got the E(sub)$\infty$-term. Then he gave the conjecture about the extension. Here we prove that there should be non-trivial extension. We also study the BP(sub)*BP comodule structures on the polynomial algebras which are related with BP(sub)*(Ω$^2$S(sup)2n+1).

• 대한수학회지
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• 제38권5호
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• pp.1061-1068
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• 2001

We write down explicity a recursive formula of one-pointed gravitational Gromov-Witten invariants and reduce the computation of them to a combinatoric problem which is not solved yet. The one-pointed invariants were played important role in Givental’s program in mirror symmetry. In section 3, we describe the combinatoric problem which can be read independently.

• 대한수학회지
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• 제38권6호
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• pp.1205-1234
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• 2001

We consider the time local well-posedness of the Benjamin equation. Like the result due to Keing-Ponce-Vega [10], [12], we show that the initial value problem is time locally well posed in the Sobolev space H$^{s}$ (R) for s>-3/4.

• 대한수학회지
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• 제38권6호
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• pp.1179-1190
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• 2001

Quadratic invariant curve is one of the simplest nonlinear invariant curves and was considered by C. T. Ng and the author in order to study the one-dimensional nonlinear dynamics displayed by a second order delay differential equation with piecewise constant argument. In this paper a functional equation derived from the problem of invariant curves is discussed. Using a different method from what C. T. Ng and the author once used, we define solutions piecewisely and give results in the remaining difficult case left in C. T. Ng and the authors work. A problem of analytic extension given in their work is also answered negatively.

• 호남수학학술지
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• 제19권1호
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• pp.157-164
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• 1997

We are concerned with three classes of matrices that are relevant to the linear complementary problem. We prove that within the class of $P_0$-matrices, the Q-matrices are precisely the regular matrices and we show that the same characterizations hold for an L-matrix as well, and that the symmetric copositive-plus Q-matrices are precisely those which are strictly copositive.

• 충청수학회지
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• 제20권4호
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• pp.551-560
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• 2007

We prove the existence of solutions for the system of the nonlinear biharmonic equations with Dirichlet boundary condition $$\{^{-{\Delta}^2u-c{\Delta}u+{\gamma}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega},\;}_{-{\Delta}^2u-c{\Delta}u+{\delta}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega}}$$, where $u^+$ = max{u, 0}, ${\Delta}^2$ denotes the biharmonic operator and ${\phi}_1$ is the positive eigenfunction of the eigenvalue problem $-{\Delta}$ with Dirichlet boundary condition.

• East Asian mathematical journal
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• 제34권1호
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• pp.1-16
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• 2018

We study an optimization problem for hyperbolic absolute risk aversion (HARA) utility function under two-factor Heston's stochastic volatility model. It is not possible to obtain an explicit solution because our financial market model is complicated. However, by using asymptotic analysis technique, we find the explicit forms of the approximations of the optimal value function and the optimal strategy for HARA utility function.

• 대한수학회논문집
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• 제32권2호
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• pp.447-456
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• 2017

The purpose of this paper is to introduce some strong convergence theorems for the problem of finding a common zero of a finite family of monotone operators and the problem of finding a common fixed point of a finite family of nonexpansive in Hilbert spaces by hybrid projection method.

• 대한수학회보
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• 제52권4호
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• pp.1225-1240
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• 2015

We provide a complete proof that there are no eigenvalues of the integral operator ${\mathcal{K}}_l$ outside the interval (0, 1/k). ${\mathcal{K}}_l$ arises naturally from the deflection problem of a beam with length 2l resting horizontally on an elastic foundation with spring constant k, while some vertical load is applied to the beam.