• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.259-267
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• 2005

In 2000 a general conjecture was proposed: a special polygon cannot be cut into an odd number of triangles of equal areas. It has been proved that the conjecture holds for polygons with at most six sides. In this paper we prove the existence of special n-polygon for any integer n > 6 and discuss the conjecture for special polygons with seven sides.

• 대한수학회논문집
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• 제20권3호
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• pp.467-485
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• 2005

Let p and q be odd primes with p=2q+1. We study the number of solutions of congruence equations $ax^i\;+\;by^j\;{\equiv}\;c$ (mod p) and a$ax^i\;+\;by^j\;+\;dz^t\;{\equiv}\;c(modp)$

• East Asian mathematical journal
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• 제30권3호
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• pp.321-326
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• 2014

In this paper, we present a simple proof of Corollary 3.3 in [5] using the fact that for a K3 surface of finite height over a field of odd characteristic, the height is a multiple of the non-symplectic order. Also we prove for a non-symplectic CM K3 surface defined over a number field the Frobenius invariant of the reduction over a finite field is determined by the congruence class of residue characteristic modulo the non-symplectic order of the K3 surface.

• Journal of Applied and Pure Mathematics
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• 제4권3_4호
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• pp.85-97
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• 2022

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}\;=\;\{\array{{\frac{p}{2}}&p\text{ is even}\\{\frac{p-1}{2}}\;&p\text{ is odd,}}$$ and M = {±1, ±2, ⋯ ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{S}}_{{\lambda}_1}-\bar{\mathbb{S}}_{{\lambda}^c_1}{\mid}{\leq}1$ where $\bar{\mathbb{S}}_{{\lambda}_1}$ and $\bar{\mathbb{S}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling of graphs which are obtained from path and cycle.

• Journal of Applied and Pure Mathematics
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• 제5권3_4호
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• pp.237-253
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• 2023

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} & \;\;p\text{ is even} \\ {\frac{p-1}{2}} & \;\;p\text{ is odd,}$$ and M = {±1, ±2, … ± ρ} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling ${\frac{{\lambda}(u)+{\lambda}(v)}{2}}$ if λ(u) + λ(v) is even and ${\frac{{\lambda}(u)+{\lambda}(v)+1}{2}}$ if λ(u) + λ(v) is odd such that ${\mid}{\bar{{\mathbb{S}}}}_{\lambda}{_1}-{\bar{{\mathbb{S}}}}_{{\lambda}^c_1}{\mid}{\leq}1$ where ${\bar{{\mathbb{S}}}}_{\lambda}{_1}$ and ${\bar{{\mathbb{S}}}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of few graphs including the closed helm graph, web graph, jewel graph, sunflower graph, flower graph, tadpole graph, dumbbell graph, umbrella graph, butterfly graph, jelly fish, triangular book graph, quadrilateral book graph.

• Journal of Applied and Pure Mathematics
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• 제6권1_2호
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• pp.55-69
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• 2024

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} && p\;\text{is even} \\ {\frac{p-1}{2}} && p\;\text{is odd,}}$$ and M = {±1, ±2, … ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{s}}_{{\lambda}_1}-\bar{\mathbb{s}}_{{\lambda}^c_1}{\mid}\,{\leq}\,1$ where $\bar{\mathbb{s}}_{{\lambda}_1}$ and $\bar{\mathbb{s}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G with a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of some union of graphs.

• 대한임베디드공학회논문지
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• 제19권2호
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• pp.115-121
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• 2024

Each ADS must have a validation and evaluation scenario for ODD. This requires a large number of scenarios, so a scenario library must be developed. In order to effectively utilize the scenario library, a system that supports testing in the ODD of the user's choice is required. In other words, in order to develop a scenario library, it is necessary to build a database on actual driving road conditions (geometry, etc.). Accordingly, in this study, we establish a domestic driving environment database based on HD-Map for driving safety testing, design a system that can search test target sections in connection with the ODD of the scenario, and present the implementation results. In the future, it is expected that the domestic driving environment database will be able to create scenarios through linking with the scenario library and directly utilize them for scenario-based evaluation of various demand sources.

• Journal of Astronomy and Space Sciences
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• 제38권1호
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• pp.23-29
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• 2021

Utilizing a new version of the sunspot number and group sunspot number dataset available since 2015, we have statistically studied the relationship between solar activity parameters describing solar cycles and the slope of the linear relationship between the monthly sunspot numbers and the monthly number of active days in percentage (AD). As an effort of evaluating possibilities in use of the number of active days to predict solar activity, it is worthwhile to revisit and extend the analysis performed earlier. In calculating the Pearson's linear correlation coefficient r, the Spearman's rank-order correlation coefficient rs, and the Kendall's τ coefficient with the rejection probability, we have calculated the slope for a given solar cycle in three different ways, namely, by counting the spotless day that occurred during the ascending phase and the descending phase of the solar cycle separately, and during the period corresponding to solar minimum ± 2 years as well. We have found that the maximum solar sunspot number of a given solar cycle and the duration of the ascending phase are hardly correlated with the slope of a linear function of the monthly sunspot numbers and AD. On the other hand, the duration of a solar cycle is found to be marginally correlated with the slope with the rejection probabilities less than a couple of percent. We have also attempted to compare the relation of the monthly sunspot numbers with AD for the even and odd solar cycles. It is inconclusive, however, that the slopes of the linear relationship between the monthly group numbers and AD are subject to the even and odd solar cycles.

• 전기의세계
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• 제24권6호
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• pp.92-96
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• 1975

A generalized theroretical method is developed to eliminate a given number of harmonics in AC chopper output waves. The results show that halfwave symmetric and sinusoidal symmetric chopping are required to eliminate all even numbers of harmonics and , at least, M+1 times per half cycle chopping is required to eliminate any M odd number of harmonics in the given effective value of the output wave.

• 한국인쇄학회지
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• 제13권1호
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• pp.1-12
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• 1995

Polymeric mesogens having a regularly alternating rigid-flexible repeating structure in the main-chain polymer exhibit distinct even-odd oscillation in their thermodynamic quantities with respect to the number of methylene units in the spacer. The even-odd oscillation depends on the number of methylene groups in the spacer the entropy change at the NI(nematic-isotropic) phase transition becomes less distinct when the linking group is replaced by the carbonate. In our previous work, we have suggested that the characteristics arise from the geometrical arrangement of the linkage. In this work, we have prepared a series of carbonate-type monomer and dimer liquid crystals. The thermodynamic behaviors at the NI phase transition have been compared with those previous reported for the ether- or ester-type liquid crystals. For the dimer series, the orientational order parameter of the mesogenic core was determined by using H-NMR technique. The origin of the difference observed among linking groups was found to the geometrical characteristics of chemical structure.