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L(4, 3, 2, 1)-PATH COLORING OF CERTAIN CLASSES OF GRAPHS

  • DHANYASHREE;K.N. MEERA
    • Journal of applied mathematics & informatics
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    • 제41권3호
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    • pp.511-524
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    • 2023
  • An L(p1, p2, p3, . . . , pm)-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.

전기장에 의한 Bi12SiO20 단결정의 변화된 광행로길이 계산 (Calculation of Changed Optical Path Length of Bi12SiO20Single Crystal by the Electric Field)

  • 이수대
    • 한국전기전자재료학회논문지
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    • 제18권11호
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    • pp.1048-1055
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    • 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.

JORDAN 𝒢n-DERIVATIONS ON PATH ALGEBRAS

  • Adrabi, Abderrahim;Bennis, Driss;Fahid, Brahim
    • 대한수학회논문집
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    • 제37권4호
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    • pp.957-967
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    • 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 𝒢n-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 𝒢n-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.

The development of EASI-based multi-path analysis code for nuclear security system with variability extension

  • Andiwijayakusuma, Dinan;Setiadipura, Topan;Purqon, Acep;Su'ud, Zaki
    • Nuclear Engineering and Technology
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    • 제54권10호
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    • pp.3604-3613
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    • 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 (PI) calculation. EASI uses a single value of the probability of detection (PD) and the probability of alarm communications (PC) 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 PI considers the variability and uncertainty of PD and PC 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 PI 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 PD 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 PD value correctly or set a higher standard for PPS performance that remains reliable.

RIGHT-ANGLED ARTIN GROUPS ON PATH GRAPHS, CYCLE GRAPHS AND COMPLETE BIPARTITE GRAPHS

  • Lee, Eon-Kyung;Lee, Sang-Jin
    • Korean Journal of Mathematics
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    • 제29권3호
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    • pp.577-580
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    • 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 Pk, cycle graphs C and complete bipartite graphs Kn,m, this article characterizes the embeddability of G(Kn,m) in G(Pk) and in G(C).

열원을 이용한 공정에서 지그재그 공구 경로 연결 알고리즘 (Zigzag Tool-Path Linking Algorithm for Shaping Process Using Heat Source)

  • 김효찬;이상호;양동열
    • 한국CDE학회논문집
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    • 제9권4호
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    • pp.286-293
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    • 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.

3D NAND Flash Memory에 Ferroelectric Material을 사용한 Current Path 개선 (Improvement of Current Path by Using Ferroelectric Material in 3D NAND Flash Memory)

  • 이지환;이재우;강명곤
    • 전기전자학회논문지
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    • 제27권4호
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    • pp.399-404
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    • 2023
  • 본 논문에서는 3D NAND Flash memory의 O/N/O(Oxide/Nitride/Oxide) 구조와 blocking oxide를 ferroelectric material로 대체한 O/N/F(Oxide/Nitride/Ferroelectric) 구조의 current path를 분석했다. O/N/O 구조는 Vread가 인가되면 neighboring cell의 E-field로 인해 current path가 channel 후면에 형성된다. 반면 O/N/F 구조는 ferroelectric material의 polarization으로 인해 electron이 channel 전면으로 이동하여 current path가 전면에 형성된다. 또한 channel thickness와 channel length에 따른 소자 특성을 분석했다. 분석 결과 O/N/F 구조의 전면 electron current density 증가는 O/N/O 구조보다 2.8배 더 높았고 O/N/F 구조의 전면 electron current density 비율이 17.7% 높았다. 따라서 O/N/O 구조보다 O/N/F 구조에서 전면 current path가 더 효과적으로 형성된다.

Determination of Strongly Interacting Spin Exchange Path and Spin Lattice Model of (VO)2(H2O){O3P-(CH2)3-PO3}ㆍ2H2O on the Basis of Spin Dimer Analysis

  • Kim, Dae-Hyun;Koo, Hyun-Joo
    • Bulletin of the Korean Chemical Society
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    • 제31권6호
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    • pp.1665-1668
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    • 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.

Interpolation based Single-path Sub-pixel Convolution for Super-Resolution Multi-Scale Networks

  • Alao, Honnang;Kim, Jin-Sung;Kim, Tae Sung;Oh, Juhyen;Lee, Kyujoong
    • Journal of Multimedia Information System
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    • 제8권4호
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    • pp.203-210
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    • 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.

STOCHASTIC MEHLER KERNELS VIA OSCILLATORY PATH INTEGRALS

  • Truman, Aubrey;Zastawniak, Tomasz
    • 대한수학회지
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    • 제38권2호
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    • pp.469-483
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    • 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.

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