• 한국전산유체공학회:학술대회논문집
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• 1999.05a
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• pp.79-84
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• 1999

The shock wave diffracted behind a finite wedge is partially scattered after interacting with a starting vortex originated from the sharp vertex of the wedge. The shock is divided into the accelerated and decelerated shocks. The decelerated shock then interacts with the small vortexlets brought about by the vortex instability, producing weak compression waves. The shock-shock interaction produces Mach stems. Through this successive process, the shock attenuated. In this study, these complicated shock phenomena are computed using Euler equations and compared with experimental results obtained by the authors.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.551-563
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• 2011

Let ${\kappa}$ be a positive integer and let G be a simple graph with vertex set V(G). A function f : V (G) ${\rightarrow}$ {-1, 1} is called a signed total ${\kappa}$-dominating function if ${\sum}_{u{\in}N({\upsilon})}f(u){\geq}{\kappa}$ for each vertex ${\upsilon}{\in}V(G)$. A set ${f_1,f_2,{\ldots},f_d}$ of signed total ${\kappa}$-dominating functions of G with the property that ${\sum}^d_{i=1}f_i({\upsilon}){\leq}1$ for each ${\upsilon}{\in}V(G)$, is called a signed total ${\kappa}$-dominating family (of functions) of G. The maximum number of functions in a signed total ${\kappa}$-dominating family of G is the signed total k-domatic number of G, denoted by $d^t_{kS}$(G). In this note we initiate the study of the signed total k-domatic numbers of graphs and present some sharp upper bounds for this parameter. We also determine the signed total signed total ${\kappa}$-domatic numbers of complete graphs and complete bipartite graphs.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.533-544
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• 2013

The multiplicative version of Wiener index (${\pi}$-index), proposed by Gutman et al. in 2000, is equal to the product of the distances between all pairs of vertices of a (molecular) graph G. In this paper, we first present some sharp bounds in terms of the order and other graph parameters including the diameter, degree sequence, Zagreb indices, Zagreb coindices, eccentric connectivity index and Merrifield-Simmons index for ${\pi}$-index of general connected graphs and trees, as well as a Nordhaus-Gaddum-type bound for ${\pi}$-index of connected triangle-free graphs. Then we study the behavior of ${\pi}$-index upon the case when removing a vertex or an edge from the underlying graph. Finally, we investigate the extremal properties of ${\pi}$-index within the set of trees and unicyclic graphs.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.631-638
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• 2018

Chellai et al. [3] gave an upper bound on the [1, 2]-domination number of tree and posed an open question "how to classify trees satisfying the sharp bound?". Yang and Wu [5] gave a partial solution for tree of order n with ${\ell}$-leaves such that every non-leaf vertex has degree at least 4. In this paper, we give a new upper bound on the [1, 2]-domination number of tree which extends the result of Yang and Wu. In addition, we design a polynomial time algorithm for solving the open question. By using this algorithm, we give a characterization on the [1, 2]-domination number for trees of order n with ${\ell}$ leaves satisfying $n-{\ell}$. Thereby, the open question posed by Chellai et al. is solved.

• Journal of computational fluids engineering
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• v.11 no.4 s.35
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• pp.39-47
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• 2006

In this paper, the authors developed a multidimensional interpolation method inside a finite volume cell in the computation of high-order accurate numerical flux such as the fifth order WEND (weighted essentially non-oscillatory) scheme. This numerical method starts from a simple Taylor series expansion in a proper spatial order of accuracy, and the WEND filter is used for the reconstruction of sharp nonlinear waves like shocks in the compressible flow. Two kinds of interpolations are developed: one is for the cell-averaged values of conservative variables divided in one mother cell (Type 1), and the other is for the vertex values in the individual cells (Type 2). The result of the present study can be directly used to the cell refinement as well as the convective flux between finer and coarser cells in the Cartesian adaptive grid system (Type 1) and to the post-processing as well as the viscous flux in the Navier-Stokes equations on any types of structured and unstructured grids (Type 2).

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.365-377
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• 2015

For a (molecular) graph, the first and second Zagreb indices (M₁ and M₂) are two well-known topological indices, first introduced in 1972 by Gutman and Trinajstić. The first Zagreb index M₁ is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M₂ is equal to the sum of the products of the degrees of pairs of adjacent vertices. Let $K_{n_1,n_2}^{P}$ with n₁ $\leq$ n₂, n₁ + n₂ = n and p < n₁ be the set of bipartite graphs obtained by deleting p edges from complete bipartite graph K_n1,n2. In this paper, we determine sharp upper and lower bounds on Zagreb indices of graphs from $K_{n_1,n_2}^{P}$ and characterize the corresponding extremal graphs at which the upper and lower bounds on Zagreb indices are attained. As a corollary, we determine the extremal graph from $K_{n_1,n_2}^{P}$ with respect to Zagreb coindices. Moreover a problem has been proposed on the first and second Zagreb indices.

• International Journal of Aeronautical and Space Sciences
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• v.3 no.1
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• pp.74-85
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• 2002

The numerical experiment has been conducted to investigate the unsteady shock wave reflecting phenomena. The cell-vertex finite-volume, Roe's upwind flux difference splitting method with unstructured grid is implemented to solve unsteady Euler equations. The $4^{th}$-order Runge-Kutta method is applied for time integration. A linear reconstruction of the flux vector using the least-square method is applied to obtain the $2^{nd}$-order accuracy for the spatial derivatives. For a better resolution of the shock wave and slipline, the dynamic grid adaptation technique is adopted. The new concept of grid adaptation technique, which is much simpler than that of conventional techniques, is introduced for the current study. Three error indicators (divergence and curl of velocity, and gradient of density) are used for the grid adaptation procedure. Considering the quality of the solution and the numerical efficiency, the grid adaptation procedure was updated up to $2^{nd}$ level at every 20 time steps. For the convenience of comparison with other experimental and analytical results, the case of interaction between the straight incoming shock wave and a sharp wedge is simulated for various flow conditions. The numerical results show good agreement with other experimental and analytical results, in the shock wave reflecting structure, slipline, and the trajectory of the triple points. Some critical cases show disagreement with the analytical results, but these cases also have been proven to show hysteresis phenomena.

• Clinical and Experimental Pediatrics
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• v.48 no.7
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• pp.753-759
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• 2005

Purpose : This study was performed to characterize clinical features of benign convulsions with gastroenteritis(CwG) in infants. Methods : We reviewed clinical features of 67 episodes in 64 patients with afebrile seizure accompanied gastroenteritis admitted to Dept. of Pediatrics Bundang CHA hospital from January 2001 to June 2004. Patients with meningitis, encephalitis/encephalopathy or apparent history of epilepsy were excluded. Results : There were 32 boys and 35 girls. The age of onset ranged from 1 to 42 months($18.5{\pm}6.1$ months). The number of children admitted to the hospital with acute gastroenteritis was 2,887 in the same period. The percentage of patients with CwG was 2.3. Seizure type was exclusively generalized tonic or tonic-clonic seizure. The average number of seizures during a single episode was 3.1 (range, 1-13). Two or more seizures occurred in 53(79.1%) of the 67 episodes. Antiepileptic drugs were administered for 42 episodes. Seizure did not cease after the administration of one kind of antiepileptic drug in 23 episodes(54.7%). The seizures were rather refractory to initial antiepileptic treatment. There were no abnormalities in serum biochemistry test including glucose and electrolytes. Cerebrospinal fluid was normal in all 54 episodes. Stool cultures were negative in 49 episodes. Rotavirus was positive in stools in 51(82.3%) of 62 episodes. Norovirus was positive in stools in 2 episodes and astrovirus in 1 of 18 episodes. CT and/or MRI were performed in 15 cases and demonstrated no neuroradiologic abnormalities. Of 73 Interictal EEG, initial 24 cases showed occasional spike or sharp wave discharges from the mid-line area during stage I-II sleep, which were apparently differentiated from vertex sharp transient or K-complexes. The mean follow-up period was 5.7 months(1-36 months). Three patients experienced a recurrence of CwG, but all patients exhibited normal psychomotor development at the last follow-up. Conclusion : Afebrile infantile convulsions with gastroenteritis are brief generalized seizure in cluster with normal laboratory findings and good prognosis. Therefore CwG is likely to be categorized as situation-related seizure of special syndrome. Recognition of this entity should lead to assurance of the parents and long-term anticonvulsant therapy is not usually warranted.

• Journal of the Korea Computer Graphics Society
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• v.17 no.2
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• pp.27-36
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• 2011

The Dual Contouring method has an advantage over the primal polygonization methods like the Marching Cube method in terms of better expression of sharp features. In this paper, the Dual Contouring method is implemented in Spherical coordinates, not the Cartesian ones to examine some characteristics. For this purpose, our octree is defined in Spherical coordinates, which is called "S-Octree". Among some characteristics, the proposed Dual Contouring method in the S-Octree tends to produce less vertices at the same octree level. In particular, for any surface models close to surface sphere, the generated mesh surfaces are smoother and more detailed than those of the Cartesian Dual Contouring approach for specific applications including mesh compression where available geometric information is quite limited.

• Sleep Medicine and Psychophysiology
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• v.17 no.2
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• pp.75-84
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• 2010

The cyclic alternating pattern (CAP) is a periodic EEG activity in NREM sleep, characterized by sequences of transient electrocortical events that are distinct from background EEG activities. A CAP cycle consists of two periodic EEG features, phase A and subsequent phase B whose durations are 2-60 s. At least two consecutive CAP cycles are required to define a CAP sequence. The CAP phase A is a phasic EEG event, such as delta bursts, vertex sharp transients, K-complex sequences, polyphasic bursts, K-alpha, intermittent alpha, and arousals. Phase B is repetitive periods of background EEG activity. The absence of CAP more than 60 seconds or an isolated phase A is classified as non-CAP. Phase A activities can be classified into three subtypes (A1, A2, and A3), based on the amounts of high-voltage slow waves (EEG synchrony) and low-amplitude fast rhythms (EEG desynchrony). CAP rate, the percentage of CAP durations in NREM sleep is considered to be a physiologic marker of the NREM sleep instability. In insomnia, the frequent discrepancy between self-reports and polysomnographic findings could be attributed to subtle abnormalities in the sleep tracing, which are overlooked by the conventional scoring methods. The conventional scoring scheme has superiority in analysis of macrostructure of sleep but shows limited power in finding arousals and transient EEG events that are major component of microstructure of sleep. But, it has recently been found that a significant correlation exists between CAP rate and the subjective estimates of the sleep quality in insomniacs and sleep-improving treatments often reduce the amount of CAP. Thus, the extension of conventional sleep measures with the new CAP variables, which appear to be the more sensitive to sleep disturbance, may improve our knowledge on the diagnosis and management of insomnia.