• Journal of applied mathematics & informatics
• /
• v.41 no.3
• /
• pp.511-524
• /
• 2023

An L(p₁, p₂, p₃, . . . , p_m)-labeling of a graph G is an assignment of non-negative integers, called as labels, to the vertices such that the vertices at distance i should have at least pi as their label difference. If p₁ = 4, p₂ = 3, p₃ = 2, p₄ = 1, then it is called a L(4, 3, 2, 1)-labeling which is widely studied in the literature. A L(4, 3, 2, 1)-path coloring of graphs, is a labeling g : V (G) → Z⁺ such that there exists at least one path P between every pair of vertices in which the labeling restricted to this path is a L(4, 3, 2, 1)-labeling. This concept was defined and results for some simple graphs were obtained by the same authors in an earlier article. In this article, we study the concept of L(4, 3, 2, 1)-path coloring for complete bipartite graphs, 2-edge connected split graph, Cartesian product and join of two graphs and prove an existence theorem for the same.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.18 no.11
• /
• pp.1048-1055
• /
• 2005

The formula to calculate a variation of optical path length of single crystal by the electric field was derived by this study. The formula was applied to $Bi_{12}SiO_{20}$ single crystal. The results are as follows. In case of the applied electric field in the body diagonal direction and the passing light along the same direction, the variation of optical path length had the largest value. The symmetry of the space distribution of optical path length satisfied $E3C_2\;8C_3$, the set of elements of the symmetry of $Bi_{12}SiO_{20}$ single crystal. The property which gave the largest influence to the variation of optical path length is the strain of length by the Inverse piezoelectric effect. The second influence, is the variation of the refractive index by the electro-optic effect. The variation of optical path length by the inverse piezoelectric effect and by the electro-optic effect have a reverse sign each other.

• Communications of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.957-967
• /
• 2022

Recently, Brešar's Jordan {g, h}-derivations have been investigated on triangular algebras. As a first aim of this paper, we extend this study to an interesting general context. Namely, we introduce the notion of Jordan 𝒢_n-derivations, with n ≥ 2, which is a natural generalization of Jordan {g, h}-derivations. Then, we study this notion on path algebras. We prove that, when n > 2, every Jordan 𝒢_n-derivation on a path algebra is a {g, h}-derivation. However, when n = 2, we give an example showing that this implication does not hold true in general. So, we characterize when it holds. As a second aim, we give a positive answer to a variant of Lvov-Kaplansky conjecture on path algebras. Namely, we show that the set of values of a multi-linear polynomial on a path algebra KE is either {0}, KE or the space spanned by paths of a length greater than or equal to 1.

• Nuclear Engineering and Technology
• /
• v.54 no.10
• /
• pp.3604-3613
• /
• 2022

The Physical Protection System (PPS) plays an important role and must effectively deal with various adversary attacks in nuclear security. In specific single adversary path scenarios, we can calculate the PPS effectiveness by EASI (Estimated Adversary Sequence Interruption) through Probability of Interruption (P_I) calculation. EASI uses a single value of the probability of detection (P_D) and the probability of alarm communications (P_C) in the PPS. In this study, we develop a multi-path analysis code based on EASI to evaluate the effectiveness of PPS. Our quantification method for P_I considers the variability and uncertainty of P_D and P_C value by Monte Carlo simulation. We converted the 2-D scheme of the nuclear facility into an Adversary Sequence Diagram (ASD). We used ASD to find the adversary path with the lowest probability of interruption as the most vulnerable paths (MVP). We examined a hypothetical facility (Hypothetical National Nuclear Research Facility - HNNRF) to confirm our code compared with EASI. The results show that implementing the variability extension can estimate the P_I value and its associated uncertainty. The multi-path analysis code allows the analyst to make it easier to assess PPS with more extensive facilities with more complex adversary paths. However, the variability of the P_D value in each protection element allows a significant decrease in the PI value. The possibility of this decrease needs to be an important concern for PPS designers to determine the P_D value correctly or set a higher standard for PPS performance that remains reliable.

• Korean Journal of Mathematics
• /
• v.29 no.3
• /
• pp.577-580
• /
• 2021

For a finite simplicial graph 𝚪, let G(𝚪) denote the right-angled Artin group on the complement graph of 𝚪. For path graphs P_k, cycle graphs C_ℓ and complete bipartite graphs K_n,m, this article characterizes the embeddability of G(K_n,m) in G(P_k) and in G(C_ℓ).

• Korean Journal of Computational Design and Engineering
• /
• v.9 no.4
• /
• pp.286-293
• /
• 2004

Recently, hot processing using the heat source like laser machining and RFS was developed and spreaded gradually. In order to generate tool-path for the proper hot tool, a new tool-path linking algorithm is needed because tool-path linking algorithm for machining can't be applied. In this paper, zigzag tool-path liking algorithm was proposed to generate tool-path automatically for RFS. The algorithm is composed of three steps: 1) Generating valid tool-path element, 2) Storing tool-path elements and creating sub-groups, 3) linking sub-groups. Using the proposed algorithm, CAD/CAM software for the tool-path generation of hot tool was developed. The proposed algorithm was applied and verified for Venus's face and die of cellular phone case.

• Journal of IKEEE
• /
• v.27 no.4
• /
• pp.399-404
• /
• 2023

In this paper, we analyzed the current path in the O/N/O (Oxide/Nitride/Oxide) structure of 3D NAND Flash memory and in the O/N/F (Oxide/Nitride/Ferroelectric) structure where the blocking oxide is replaced by a ferroelectric. In the O/N/O structure, when V_read is applied, a current path is formed on the backside of the channel due to the E-fields of neighboring cells. In contrast, the O/N/F structure exhibits a current path formed on the front side due to the polarization of the ferroelectric material, causing electrons to move toward the channel front. Additionally, we performed an examination of device characteristics considering channel thickness and channel length. The analysis results showed that the front electron current density in the O/N/F structure increased by 2.8 times compared to the O/N/O structure, and the front electron current density ratio of the O/N/F structure was 17.7% higher. Therefore, the front current path is formed more effectively in the O/N/F structure than in the O/N/O structure.

• Bulletin of the Korean Chemical Society
• /
• v.31 no.6
• /
• pp.1665-1668
• /
• 2010

The spin exchange interactions of $(VO)_2(H_2O){O_3P-(CH_2)_3-PO_3}{\cdot}2H_2O$ were examined by spin dimer analysis based on extended Huckel tight binding method. The strongest spin exchange interaction occurs through the super-superexchange path $J_2$ and the second strongest spin exchange interaction occurs through the superexchange interaction path $J_1$. There are two strongly interacting spin exchange paths in $(VO)_2(H_2O){O_3P-(CH_2)_3-PO_3}{\cdot}2H_2O$. Therefore, magnetic susceptibility curve of $(VO)_2(H_2O){O_3P-(CH_2)_3-PO_3}{\cdot}2H_2O$ can be well reproduced by an alternating onedimensional antiferromagnetic chain model rather than an isolated spin dimer model.

• Journal of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.469-483
• /
• 2001

The configuration space and phase space oscillatory path integrals are computed in the case of the stochastic Schrodinger equation for the harmonic oscillator with a stochastic term of the form (K$\psi$(sub)t)(x) o dW(sub)t, where K is either the position operator or the momentum operator, and W(sub)t is the Wiener process. In this way formulae are derived for the stochastic analogues of the Mehler kernel.

• Journal of Multimedia Information System
• /
• v.8 no.4
• /
• pp.203-210
• /
• 2021

Deep leaning convolutional neural networks (CNN) have successfully been applied to image super-resolution (SR). Despite their great performances, SR techniques tend to focus on a certain upscale factor when training a particular model. Algorithms for single model multi-scale networks can easily be constructed if images are upscaled prior to input, but sub-pixel convolution upsampling works differently for each scale factor. Recent SR methods employ multi-scale and multi-path learning as a solution. However, this causes unshared parameters and unbalanced parameter distribution across various scale factors. We present a multi-scale single-path upsample module as a solution by exploiting the advantages of sub-pixel convolution and interpolation algorithms. The proposed model employs sub-pixel convolution for the highest scale factor among the learning upscale factors, and then utilize 1-dimension interpolation, compressing the learned features on the channel axis to match the desired output image size. Experiments are performed for the single-path upsample module, and compared to the multi-path upsample module. Based on the experimental results, the proposed algorithm reduces the upsample module's parameters by 24% and presents slightly to better performance compared to the previous algorithm.