• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.123-129
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• 2023

For an ordered set W = {w₁, w₂, . . . , w_k} of vertices and a vertex v in a connected graph G, the k-vector r(v|W) = (d(v, w₁), d(v, w₂), . . . , d(v, w_k)) is called the metric representation of v with respect to W, where d(x, y) is the distance between the vertices x and y. A set W is called a resolving set for G if distinct vertices of G have distinct metric representations with respect to W. The minimum cardinality of a resolving set for G is its metric dimension dim(G), and a resolving set of minimum cardinality is a basis of G. The corona product, G ⊙ H of graphs G and H is obtained by taking one copy of G and n(G) copies of H, and by joining each vertex of the ith copy of H to the ith vertex of G. In this paper, we obtain bounds for dim(G ⊙ K₁), characterize all graphs G with dim(G ⊙ K₁) = dim(G), and prove that dim(G ⊙ K₁) = n - 1 if and only if G is the complete graph K_n or the star graph K_1,n-1.

• Bulletin of the Korean Chemical Society
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• v.31 no.8
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• pp.2228-2234
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• 2010

Theoretical studies have been performed to study the binding characteristics of the alkali metal iodides, M-I (M = Li, Na, K), to poly(ethylene oxide) (PEO, I), poly(ethylene amine) (PEA, II) and poly(ethylene N-methylamine) (PEMA, III) via the B3LYP method. In this study, two types of complexes, singly-coordinated systems (SCS) and doubly-coordinated systems (DCS), were considered, and dissociation energies (${\Delta}E_D$) were calculated both with and without basis set superposition error (BSSE). Two types of counterpoise (CP) approach were investigated in this work, but the ${\Delta}E_D$ values corrected by using the function CP (fCP) correction exhibited an unusual trend in some cases due to deformation of the sub-units. This problem was solved by including geometry relaxation in the CP-corrected (GCP) interaction energy. On the other hand, the effects of the BSSE on the structures were very small when the complexes were re-optimized on the CP-corrected (RCP) potential energy surface (PES), even if the bond lengths between X and $M^+$ ($d_{{X-M}^+}$) and between $M^+$ and $I^-$ ($d_{M^+-I^-}$) were slightly lengthened. Therefore, neither the GCP nor RCP corrections made much difference to the dissociation energies.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.869-874
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• 2001

In order that precision equipment using high precision industrial operate normally. vibration criteria of expected area that equipment be set up is micrometer level. that method is a trust design for apply to in field, when there attend to quantifiable method. Hence, semi -empirical method that using on the basis of experimental data about undefined information (properities of vibration source, dynamic properities of structure, etc.,) for prediction of vibration response make the use of dynamic structure design of semiconductor ＆ TFT-LCD in the inside and outside country. Like this, for doing an optimal design of dynamic about structure, it is best important to get trust data that apply to semi-empirical method that is method of prediction vibration level. In this paper, on the basis of experimental data which was offered by a manufacturing company Of precisin equipment that plan to set up in semiconductor factory, we predicted vibration response on expected area that equipment be set up.

• Bulletin of the Korean Chemical Society
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• v.31 no.10
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• pp.2806-2808
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• 2010

The structure of 3-aminophenol $(CO_2)_1$ cluster was computationally studied both in the ground and the lowest singlet excited electronic states. The ground state structure and binding energy of the cluster was investigated using the second-order M$\ddoot{o}$ller-Plesset perturbation theory (MP2) at the complete basis set (CBS) limit. The excited state geometry of the cluster was obtained at the second-order approximate coupled cluster (CC2) level with cc-pVDZ basis set, and the $S_0-S_1$ absorption spectrum was simulated by calculating Franck-Condon overlap integral. The ground state geometry of the global minimum with a very high binding energy of 4.3 kcal/mol was found for the cluster, due to the interaction between amino group and $CO_2$ in addition to the strong $\pi-\pi$ interaction between the aromatic ring and $CO_2$. The excited state geometry shows a very big shift in the position of $CO_2$ compared to the ground state geometry, which results in low intensity and broad envelope in the Franck-Condon simulation.

• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.487-494
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• 2012

This paper discusses a method for getting a basis set of estimable functions of model parameters in a two-way fixed effects model. Since the fixed effects model has more parameters than those that can be estimated, model parameters are not estimable. So it is not possible to make inferences for nonestimable functions of parameters. When the assumed model of matrix notation is reparameterized by the estimable functions in a basis set, it also discusses how to use projections for the estimation of estimable functions.

• Bulletin of the Korean Chemical Society
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• v.9 no.3
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• pp.153-156
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• 1988

Ab initio calculations are performed for $ArCO_2^+$ and $ArCO_2$. Between the two configurations of $ArCO_2^+$ the orbital interactions and the higher order correlation calculations favor the T-shape, and their interaction energies are calculated to be approximately half the experimental values using 6-31G$^{\ast}$ basis set. In $ArCO_2$, the calculations qualitatively favor the T-structure, which is compatible with the experiment. However, the true interaction energy is obscured since it is within the BSSE limit at this basis set size and the correlation level. Addition of sp type diffuse functions increase the interaction energies by a considerable amount, but the BSSE estimated by CP method are responsible for the significant portion of the difference. The possible equilibrium structure of the $Ar^+-CO_2$ complex, where the charge is localized on Ar, is suggested as having a linear structure. The potential energy surface and the amount of charge transfer are shown to be sensitive to the type and balancing of basis set.

• Bulletin of the Korean Chemical Society
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• v.23 no.9
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• pp.1267-1271
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• 2002

The conformation dependences of basis set superposition errors (BSSE) for 1,2-difluoroethane (DFE) and 1,2-dimethoxyethane (DME) molecules have been estimated using counterpoise method at the Moller-Plesset second order perturbation (MP2) level of theory with various basis sets, assuming that all BSSE dependences on conformations are due to the change in CC bond. The BSSE on the energy differences between eclipsed and gauche forms of DFE are in the range of 0.2-1.2 kcal/mol and those between local minima, gauche and anti forms, are less than 0.2 kcal/mol. For the larger DME molecule, the BSSE differences between local minima are still less than 0.4 kcal/mol, but may not be ignored compared to the energy differences of 0.2-3.0 kcal/mol between conformers.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.3
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• pp.239-245
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• 2008

A level set based topological shape optimization using extended B-spline basis functions is developed for steady-state heat conduction problems. The only inside of complicated domain identified by the level set functions is taken into account in computation, so we can remove the effects of domain outside parts in heat conduction problem. The solution of Hamilton-Jacobi equation leads to an optimal shape according to the normal velocity field determined from the sensitivity analysis, minimizing a thermal compliance while satisfying a volume constraint. To obtain exact shape sensitivity, the precise normal and curvature of geometry need to be determined using the level set and B-spline basis functions. Using topological derivative concept, the nucleation of holes for topological changes can be made whenever and wherever necessary during the optimization.

• Korean Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.243-250
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• 1998

In parametric surface interpolation, the choice of the parameter values to the set of scattered points makes a great deal of difference in the resulting surface. A new method is developed and tested for the parametrization in NURBS surface global interpolation. This method uses the parameter value at the maximal value of relevant rational basis function, to assign the parameter values to the arbitrary set of design data. This method gives us several important advantages in geometric modeling, the freedom of the selection of knot values, the feasible transformation of the data set to the matrix, the possibility of affinite transformation between the design data and generated surface, etc.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.957-960
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• 1995

A new method is introduced for the parametrization in B-spline surface interpolation. THis method uses the basis function to assign the parameter values to the arbitrary set of geometric data. This method gives us several important advantages in geometric modeling.