• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.165-167
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• 2005

Let M = (R, +, $\cdot$, <, ... ) be an o-minimal expansion of the standard structure R = (R, +, $\cdot$, >) of the field of real numbers. We prove that if 2 $\le$ r < $\infty$, then every n-dimensional definable $C^r$ manifold is definably $C^r$ imbeddable into $R^{2n+l}$. Moreover we prove that if 1 < s < r < $\infty$, then every definable $C^s$ manifold admits a unique definable $C^r$ manifold structure up to definable $C^r$ diffeomorphism.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.7
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• pp.1411-1417
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• 2009

In this paper, we consider the design of $H_{\infty}$ control of linear discrete-time systems having no mathematical model. The basic approach is to use Q-learning which is a reinforcement learning method based on actor-critic structure. The model-free control design is to use not the mathematical model of the system but the informations on states and inputs. As a result, the derived iterative algorithm is expressed as linear matrix inequalities(LMI) of measured data from system states and inputs. It is shown that, for a sufficiently rich enough disturbance, this algorithm converges to the standard $H_{\infty}$ control solution obtained using the exact system model. A simple numerical example is given to show the usefulness of our result on practical application.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.139-156
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• 2014

In this paper, we investigate the error estimates of a quadratic elliptic control problem with pointwise control constraints. The state and the co-state variables are approximated by the order k = 1 Raviart-Thomas mixed finite element and the control variable is discretized by piecewise linear but discontinuous functions. Approximations of order $h^{\frac{3}{2}}$ in the $L^2$-norm and order h in the $L^{\infty}$-norm for the control variable are proved.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.209-218
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• 2007

In this paper we investigate the ${\ell}^p$ space structure of the Banach envelope of $WeakL_1$. In particular, the Banach envelope of $WeakL_1$ contains a complemented Banach sublattice that is isometrically isomorphic to the nonseparable Banach lattice ${\ell}^p$, ($1{\leq}p<\infty$) as well as the separable case.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.2C
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• pp.61-68
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• 2012

In general, verticality error necessarily occurs in marine pile foundation due to construction error or marine environmental effects. In marine structure, design by vertical load rather than horizontal load is dominant, but in the offshore wind turbine foundation, horizontal load is dominant. As the structure type that has dynamic movement by blade rotation, verticality error may have structurally significant effects. In this study, structural response feature of foundation and ground were analyzed according to verticality error of monopile foundation of 5MW offshore wind turbine. Marine environmental load was calculated per ISO standard and the margin of verticality error was calculated to be $L/{\infty}$(=0), L/300, L/200 and L/100. As a result of analysis, it was found that the maximum value of member force of the foundation with L/100 error increased about 7.2% compared to the monopile without verticality error.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1655-1687
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• 2019

In this paper we define a new type of cohomology for multiplicative Hom-associative algebras, which generalizes Hom-type Hochschild cohomology and fits with deformations of Hom-associative algebras including the deformation of the structure map ${\alpha}$. Moreover, we provide various observations and similarly a new type cohomology of Hom-bialgebras extending the Gerstenhaber-Schack cohomology for Hom-bialgebras and fitting with formal deformations including deformations of the structure map.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.36 no.6
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• pp.646-653
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• 2003

Investigations were made on the population structure, sex ratio, growth, and recruitment patterns of Leptochela sydniensis in the southwestern coastal areas of Korea, between May 2000 and December 2001. Spawning period, fecundity, brood loss, reproductive output, and size at sexual maturity also were examined. The results of the sex ratio showed that females were more numerous than males during the overall study period. Parameters of growth were estimated using the modified von Bertalanffy growth function (VBGF) model incorporating seasonal variation into growth. Females grew somewhat faster and reached a larger size than males $(L\infty=12.80\;mm\;CL\;and\;K=0.70\;yr^{-1}\;or\;females,\and\;L\infty=12.08\;mm\;CL\;and\;K=0.69\;yr^{-1}$ for males). The structure of recruitment patterns obtained by the FiSAT program indicated one normally distributed group. Based on the occurrence of ovigerous females and the gonadosomatic index (GSI), the main spawning season was from June to August. Analysis of covariance indicated that brood loss was not observed during the incubation period. The size at which $50\%$ of females are mature is estimated as 5.48 mm CL.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.2
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• pp.49-58
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• 2003

The linear motor has not only no backlash and less friction, resulting in very high accuracy, but also mechanical simplicity, higher reliability, and longer lifetime. In this study, a large-capacity hybrid mass damper using linear motor principle has been developed to suppress vibration of large structures. It is designated linear motor damper in this paper. The LMD has been designed to be able to move the auxiliary damper mass of 155kg up to $\pm$250mm stroke. A series of performance tests for LMD control system with $H_{winfty}$ robust controller have been carried out on the full-scale steel frame structure. Through the performance tests, it is confirmed that vibration response levels are reduced down 10dB for the first and second modes of the test structure.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.859-869
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• 1997

It is shown that for $A_{k, m}$ a k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1$ such that no non-trivial matrix algebra can be factored out of $A_{k, m}$ and $A_{k, m} \otimes M_l(C)$ has a non-trivial bundle structure for any positive integer l, we construct an $A_{k, m^-} C(S^{2n - 1} \times S^1) \otimes M_k(C)$-equivalence bimodule to show that every k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1)$. Moreover, we prove that the tensor product of the k-homogeneous $C^*$-algebra $A_{k, m}$ with a UHF-algebra of type $p^\infty$ has the tribial bundle structure if and only if the set of prime factors of k is a subset of the set of prime factors of pp.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.44 no.4
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• pp.312-322
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• 2008

The age and growth of the sandfish, Arctoscopus japonicus were investigated from samples of the eastern sea danish seine and gill net fishery in the East Sea of Korea from February, 2004 to December, 2007. Ages were determined from annuli in otoliths and annuli were formed between December and February once a year. Also, the main spawning period was estimated to be between December and January, thus rings were considered to be annual marks. For the relationship between fork length and total weight, a multiplicative error structure was assumed because variability in growth increased as a function of the length. The relationship between fork length and total weight were $TW=0.0083FL^{3.01}(R^2=0.966)$ for female and $TW=0.0079FL^{3.04}(R^2=0.969)$ for male. The variability in growth was constant as a function of age, revealing an additive error structure. The von Bertalanffy growth parameters estimated by a non-linear method were $L_{\infty}=31.6cm$, K=0.266/year, $t_0=-0.835$ years for female and $L_{\infty}=27.7cm$, K=0.273/year, $t_0=-0.806$ years for male. Growth at age between male and female had a significant difference(P<0.001).