• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.3
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• pp.39-49
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• 2003

The delta operator approach and the singular perturbation technique are introduced. The former reduces the round-off error in the numerical computation. The latter reduces computing time by decoupling the original system into the fast and slow sub-systems. The aircraft dynamics consists of the Phugoid and short-period motions whether its model is longitudinal or lateral. In this paper, an approximated solutions of lateral dynamic model of Beaver obtained by using those two methods in compared with the exact solution. For open-loop system and closed-loop system, and approximated solution gets identical to the exact solution with only one iteration and without iteration, respectively. Therefore, it is shown that implementing those approaches is very effective in the flight dynamic and control.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.10
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• pp.90-99
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• 1992

In this paper, we propose a neural network model for speech recognition. The model consists of feature extraction parts and recognition parts. The interconnection model based on ${\Delta}^2$G operator was used for frequency analysis. Two features, global feature and local feature, were extracted from this model. Recognition parts consist of global grouping stage and local grouping stage. When the input pattern was coded by slope method, the recognition rate of speakers, A and B, was 100%. When the test was performed with the data of 9 speakers, the recognition rate of 91.4% was obtained.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.289-304
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• 2021

In this paper, we establish several geometric characterizations focusing on the relationship between the squared norm of the second fundamental form and the warping function of SCR-lightlike warped product submanifolds in an indefinite Kaehler manifold. In particular, we find an estimate for the squared norm of the second fundamental form h in terms of the Hessian of the warping function λ for SCR-lightlike warped product submanifolds of an indefinite complex space form. Consequently, we derive an optimal inequality, namely $${\parallel}h{\parallel}^2{\geq}2q\{{\Delta}(ln{\lambda})+{\parallel}{\nabla}(ln{\lambda}){\parallel}^2+\frac{c}{2}p\}$$, for SCR-lightlike warped product submanifolds in an indefinite complex space form. We also provide one non-trivial example for this class of warped products in an indefinite Kaehler manifold.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.967-986
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• 2017

We give the necessary condition for an operator defined on a cartesian product of $c_0(\mathcal{X})$ spaces to be summing or dominated and we show that for the multiplication operators this condition is also sufficient. By using these results, we show that ${\Pi}_s(c_0,{\ldots},c_0;c_0)$ contains a copy of $l_s(l^m_2{\mid}m{\in}\mathbb{N})$ for s > 2 or a copy of $1_s(l^m_1{\mid}{\in}\mathbb{N})$, for any $l{\leq}S$ < ${\infty}$. Also ${\Delta}_{s_1,{\ldots},s_n}(c_0,{\ldots},c_0;c_0)$ contains a copy of $l_{{\upsilon}_n(s_1,{\ldots},s_n)}$ if ${\upsilon}_n(s_1,{\ldots},s_n){\leq}2$ or a copy of $l_{{\upsilon}_n(s_1,{\ldots},s_n)}(l^m_2{\mid}m{\in}\mathbb{N})$ if 2 < ${\upsilon}_n(s_1,{\ldots},s_n)$, where ${\frac{1}{{\upsilon}_n(s_1,{\ldots},s_n})}={\frac{1}{s_1}}+{\cdots}+{\frac{1}{s_n}}$. We find also the necessary and sufficient conditions for bilinear operators induced by some method of summability to be 1-summing or 2-dominated.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.117-121
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• 2009

For $1{\leq}p$, $q{\leq}{\infty}$ and $s{\in}\mathbb{R}$, it is proved that there exists a constant C > 0 such that for any $f{\in}B^{s+2}_{p,q}(\mathbb{R}^n)$ $${\parallel}f{\parallel}_{B^{s+2}_{p,q}(\mathbb{R}^n)}{\leq}C{\parallel}f\;-\;{\Delta}f{\parallel}_{B^{s}_{p,q}(\mathbb{R}^n)}$$, which tells us that the operator $I-\Delta$ is $B^{s+2}_{p,q}$-coercive on the Besov space $B^s_{p,q}$.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.833-842
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• 2000

Consider the even-order neutral difference equation (*) ${\delta}^m(x_n{-}p_ng(x_{n-k}))-q_nh(x_{n-1})=0$, n=0,1,2,... where $\Delta$ is the forward difference operator, m is even, ${-p_n},{q_n}$ are sequences of nonnegative real numbers, k, l are nonnegative integers, g(x), h(x) ${\in}$ C(R, R) with xg(x) > 0 for $x\;{\neq}\;0$. In this paper, we obtain some linearized oscillation theorems of (*) for $p_n\;{\in}\;(-{\infty},0)$ which are discrete results of the open problem by Gyori and Ladas.

• Journal of the Korean Chemical Society
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• v.14 no.1
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• pp.127-131
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• 1970

The variational approach for the direct evaluation of the energy difference ${\Delta}$E is studied. The method is based on the differential equation corresponding to the integral Hellmann-Feynman formula. The ${\Delta}$E is given by the expectation value of the Hermitian operator which does not involve the 1/$r_{ij}$ term. Because of its variational nature of the method, the coupling problem of the differential equations which are encountered in perturbation treatment does not occur. The method is applied to the evaluation of the electric polarizabilities of the Helium isoelectronic series atoms. The result is in good agreement with the experiment. The method is compared with the recent works of Karplus et al.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1529-1560
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• 2019

We are concerned with the following elliptic equations: $$(-{\Delta})^s_pu+V (x){\mid}u{\mid}^{p-2}u={\lambda}g(x,u){\text{ in }}{\mathbb{R}}^N$$, where $(-{\Delta})_p^s$ is the fractional p-Laplacian operator with 0 < s < 1 < p < $+{\infty}$, sp < N, the potential function $V:{\mathbb{R}}^N{\rightarrow}(0,{\infty})$ is a continuous potential function, and $g:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ satisfies a $Carath{\acute{e}}odory$ condition. We show the existence of at least one weak solution for the problem above without the Ambrosetti and Rabinowitz condition. Moreover, we give a positive interval of the parameter ${\lambda}$ for which the problem admits at least one nontrivial weak solution when the nonlinearity g has the subcritical growth condition.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.657-668
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• 2022

In the present paper we introduce and study Euler sequence spaces of fractional difference and backward difference operators. We make an effort to prove that these spaces are BK-spaces and linearly isomorphic. Further, Schauder basis for Euler fractional difference sequence spaces $e^{\varsigma}_{0,p}({\Delta}^{(\tilde{\beta})},\;{\nabla}^m)$ and $e^{\varsigma}_{c,p}({\Delta}^{(\tilde{\beta})},\;{\nabla}^m)$ are also elaborate. In addition to this, we determine the 𝛼-, 𝛽- and 𝛾- duals of these spaces.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.741-754
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• 2023

In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth $$\left{\array{-{\Delta}_{\lambda}u-{\mu}v={\mid}v{\mid}^{p-1}v&&\text{in }{\Omega},\\-{\Delta}_{\lambda}v-{\mu}u={\mid}u{\mid}^{q-1}u&&\text{in }{\Omega},\\u=v=0&&\text{ on }{\partial}{\Omega},}$$ where p, q > 1 and Ω is a smooth bounded domain in ℝ^N, N ≥ 3. Here Δ_λ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.