• 한국인터넷방송통신학회논문지
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• 제17권3호
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• pp.159-166
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• 2017

본 논문은 홀수, 이중 짝수와 단일 짝수 마방진 알고리즘을 제안하였다. 홀수 마방진은 de la $Loub{\grave{e}}re$가 제안한 방법으로 $O(n^2)$회를 수행하는 단점이 있다. 이중 짝수 마방진은 2가지의 교차 알고리즘이 제안되었다. 단일 짝수 마방진은 ${\frac{n}{2}}{\times}{\frac{n}{2}}$의 홀수 마방진에 기반하여 여러 가지 방법이 제안되었지만 Strachey 알고리즘이 적용이 가장 쉽다. 본 논문에서는 홀수 마방진에 대해 3회 수행, 이중 짝수 마방진에 대해서는 4회 수행으로 마방진을 얻는 방법을 제안하였다. 또한, 단일 짝수 마방진에 대해서는 홀수 마방진에 기반을 두지 않고 직접 구하는 알고리즘을 제안하였다.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 하계학술대회 논문집 C
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• pp.1453-1455
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• 1996

The odd-even effect of the alkyl chain length of rubbed polyimide Langmuir-Blodgett (LB) surfaces on the extrapolation length of 5CB has been successfully evaluated for the first time by measuring polar anchoring strength. The extrapolation length of 5CB for rubbed PI-LB surfaces with even-numbers is small compared with odd-numbers for alkyl chain lengths of greater than 7 carbons. The extrapolation length of 5CB on rubbed PI-LB surfaces with odd-numbers increases gradually as the temperature increases but tends to diverge near the clearing temperature (Tc=$35.3^{\circ}C$). The extrapolation length diverges because of rapidly decreasing surface order near $T_c$. We suggest that the polar anchoring strength on rubbed PI-LB surfaces with even-number is strong because of relatively high surface ordering caused by more crystalline surfaces. Finally, we conclude that the odd-even effects of the polar anchoring strength in NLCs are strongly related to the character of the polymer and observed clearly for long alkyl chain lengths.

• Structural Engineering and Mechanics
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• 제45권5호
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• pp.595-611
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• 2013

This paper aims to compare three collocation point methods associated with the odd order stochastic response surface method (SRSM) in a systematical and quantitative way. The SRSM with the Hermite polynomial chaos is briefly introduced first. Then, three collocation point methods, namely the point method, the root method and the without origin method underlying the odd order SRSMs are highlighted. Three examples are presented to demonstrate the accuracy and efficiency of the three methods. The results indicate that the condition that the Hermite polynomial information matrix evaluated at the collocation points has a full rank should be satisfied to yield reliability results with a sufficient accuracy. The point method and the without origin method are much more efficient than the root method, especially for the reliability problems involving a large number of random variables or requiring complex finite element analysis. The without origin method can also produce sufficiently accurate reliability results in comparison with the point and root methods. Therefore, the origin often used as a collocation point is not absolutely necessary. The odd order SRSMs with the point method and the without origin method are recommended for the reliability analysis due to their computational accuracy and efficiency. The order of SRSM has a significant influence on the results associated with the three collocation point methods. For normal random variables, the SRSM with an order equaling or exceeding the order of a performance function can produce reliability results with a sufficient accuracy. The order of SRSM should significantly exceed the order of the performance function involving strongly non-normal random variables.

• 충청수학회지
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• 제37권1호
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• pp.27-40
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• 2024

In this paper, we consider the higher-order HartreeFock equations. The higher-order linear Schrödinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudorelativistic linear Schrödinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L² space but also proved that the solutions stay bounded uniformly in c. We address the remaining question on the convergence of higherorder Hartree-Fock equations when the Taylor expansion order is even. The distinguished feature from the odd case is that the group velocity of phase function would be vanishing when the size of frequency is comparable to c. Owing to this property, the kinetic energy of solutions is not coercive and only weaker Strichartz estimates compared to the odd case were obtained in [13]. Thus, we only manage to establish the existence of local solutions in H^s space for s > $\frac{1}{3}$ on a finite time interval [-T, T], however, the time interval does not depend on c and the solutions are bounded uniformly in c. In addition, we provide the convergence result of higher-order Hartree-Fock equations to the pseudo-relativistic equation with the same convergence rate as the odd case, which holds on [-T, T].

• Kyungpook Mathematical Journal
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• 제60권2호
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• pp.297-305
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• 2020

We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.653-659
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• 2009

It is proved that if $M\;=\;B_p(3)$ or $C_p(3)$, p is an odd prime, G is a finite group and has the same order components of M, then $G\;{\cong}\;Bp(3)$ or $C_p(3)$.

• 한국ITS학회 논문지
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• 제21권5호
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• pp.197-217
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• 2022

자율주행자동차(Automated vehicle, AV) 교통사고가 지속적으로 발생하면서 자율주행시스템(automated driving system, ADS)의 안전성 및 신뢰성을 확보하기 위한 안전성 검증의 중요성이 강조되고 있다. 안전성 및 신뢰성을 확보하기 위해서는 ADS의 운행가능영역(operational design domain, ODD)을 정의하고 ODD를 벗어나는 상황에서의 대응 능력을 평가하면서 ADS의 안전성을 검증해야 할 필요가 있다. 이를 위해 SAE, BSI, NHTSA, ISO 등의 국제 기구에서는 ODD 분류 기준 및 표준을 규정하고 있으나 국내의 경우 ODD 기준이 부재하여 AV의 ODD 표현 방법 및 안전성 검증 및 평가가 적절히 이루어지지 않고 있다. 이에 본 연구에서는 해외 ODD 분류 기준을 분석하고 안전성 검증 및 평가에 적합한 분류 기준을 선정하였다. 선정된 ODD를 기반으로 ADS 안전성 검증 및 평가에 필요한 평가요소를 제시하였다. 특히, ADS 기술 개발을 지원하는 자율주행 실험도시(K-City)의 평가환경을 분석하여 평가요소를 제시하였다.

• 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.

• 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.