• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.741-752
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• 2015

We introduce the warping crossing polynomial of an oriented knot diagram by using the warping degrees of crossing points of the diagram. Given a closed transversely intersected plane curve, we consider oriented knot diagrams obtained from the plane curve as states to take the sum of the warping crossing polynomials for all the states for the plane curve. As an application, we show that every closed transversely intersected plane curve with even crossing points has two independent canonical orientations and every based closed transversely intersected plane curve with odd crossing points has two independent canonical orientations.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.3
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• pp.236-240
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• 2011

The terminal sliding mode control schemes have been studied a lot since they can guarantee that the state error gets to zero in a finite time. However, the conventional terminal sliding surfaces have been designed using power function whose exponent is a rational number between 0 and 1, and whose numerator and denominator should be odd integers. It is clearly restrictive. Thus, in this paper, we propose a novel terminal sliding surface using power function whose exponent can be a real number between 0 and 1.

• Korean Journal of Computational Design and Engineering
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• v.7 no.2
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• pp.75-80
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• 2002

This paper details a robust and efficient algorithm for point classification with respect to a polygon in 2D real number domain. The concept of tolerance makes this algorithm robust and consistent. It enables to define‘on-boundary’ , which can be interpreted as either‘in-’or‘out-’side region, and to manage rounding errors in floating point computation. Also the tolerance is used as a measure of reliability of point classifications. The proposed algorithm is based on a ray-intersection technique known as the most efficient, in which intersections between a ray originating from a given test point and the boundary of a region are counted. An odd number of intersections indicates that the point is inside region. For practical examples the algorithm is most efficient because most edges of the polygon region are processed by simple bit operations.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.321-330
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• 2023

Let G = (V, E) be a graph. Consider the group S₃. Let g : V (G) → S₃ be a function. For each edge xy assign the label 1 if ${\lceil}{\frac{o(g(x))+o(g(y))}{2}}{\rceil}$ is odd or 0 otherwise. g is a group S₃ mean cordial labeling if |v_g(i) - v_g(j)| ≤ 1 and |e_g(0) - e_g(1)| ≤ 1, where vg(i) and e_g(y)denote the number of vertices labeled with an element i and number of edges labeled with y (y = 0, 1). The graph G with group S₃ mean cordial labeling is called group S₃ mean cordial graph. In this paper, we discuss group S3 mean cordial labeling for star related graphs.

• Journal of Power Electronics
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• v.14 no.4
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• pp.671-677
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• 2014

In this paper, a new basic unit is proposed. Then, a cascaded multilevel inverter basded on the series connection of n number of these new basic units is proposed. In order to generate all of the voltage levels (even and odd) at the output, three different algorithms to determine the magnitude of the dc voltage source are proposed. Reductions in the number of power switches, driver circuits and dc voltage sources in addition to increases in the numbr of output voltage levels are some of the advantages of the proposed cascaded multilevel inverter. These results are obtained through a comparison of the proposed inverter and its algorithms with an H-bridge cascaded multilevel inverter from the point of view of the number of power electronic devices. Finally, the capability of the proposed topology with its proposed algorithms in generating all of the voltage levels is verified through experimental results on a laboratorary prototype of a 49-level inverter.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.227-233
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• 1999

Let $k$ be a real abelian field and $k_{\infty}={\bigcup}_{n{\geq}0}k_n$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. For each $n{\geq}0$, we denote the class number of $k_n$ by $h_n$. The following is a well known theorem: Theorem. Suppose $p$ remains inert in $k$ and the prime ideal of $k$ above $p$ totally ramifies in $k_{\infty}$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$ for all $n{\geq}0$. The aim of this paper is to generalize above theorem: Theorem 1. Suppose $H^1(G_n,E_n){\simeq}(\mathbb{Z}/p^n\mathbb{Z})^l$, where $l$ is the number of prime ideals of $k$ above $p$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$. Theorem 2. Let $k$ be a real quadratic field. Suppose that $H^1(G_1,E_1){\simeq}(\mathbb{Z}/p\mathbb{Z})^l$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$ for all $n{\geq}0$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.7
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• pp.2610-2630
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• 2021

The aim of this paper is to propose the alternative algorithm to finish the process in public key cryptography. In general, the proposed method can be selected to finish both of modular exponentiation and point multiplication. Although this method is not the best method in all cases, it may be the most efficient method when the condition responds well to this approach. Assuming that the binary system of the exponent or the multiplier is considered and it is divided into groups, the binary system is in excellent condition when the number of groups is small. Each group is generated from a number of 0 that is adjacent to each other. The main idea behind the proposed method is to convert the exponent or the multiplier as the subtraction between two integers. For these integers, it is impossible that the bit which is equal to 1 will be assigned in the same position. The experiment is split into two sections. The first section is an experiment to examine the modular exponentiation. The results demonstrate that the cost of completing the modular multiplication is decreased if the number of groups is very small. In tables 7 - 9, four modular multiplications are required when there is one group, although number of bits which are equal to 0 in each table is different. The second component is the experiment to examine the point multiplication process in Elliptic Curves Cryptography. The findings demonstrate that if the number of groups is small, the costs to compute point additions are low. In tables 10 - 12, assigning one group is appeared, number of point addition is one when the multiplier of a point is an even number. However, three-point additions are required when the multiplier is an odd number. As a result, the proposed method is an alternative way that should be used when the number of groups is minimal in order to save the costs.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.31 no.2
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• pp.151-157
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• 2013

The law for indicating the address based on the street name has taken effect in 1997. The address based on land-lot number will be changed to the address based on the street name giving odd numbers to the buildings situated on the left side and even numbers to the buildings situated on the right side per street. Searching locations by street name addresses is possible for residential areas, on the other hand, the system of finding locations is insufficient for farmlands, mountains and others, so it is unable to cope with crimes and emergency rescue. In order to make up for the weak points of street name address, the national point number, grid reference system was introduced for finding location of non-residential areas. Therefore, the purpose of this paper is to help the introduction the national point number. In this paper, we proposed a territory-oriented control point and grid range for the national point number. Numbering scheme of grid zone shall be alphanumeric, a two-letter pair Hangul and the grid coordinates in terms of Easting and Northing. We also proposed the notice area for the national point number and location of signs, application about the public and private sector.

• Applied Chemistry for Engineering
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• v.21 no.2
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• pp.230-237
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• 2010

A homologous series of linear liquid crystal dimers, ${\alpha},{\omega}$-bis(4-nitroazobenzene-4'-carbonyloxy)alkanes (NATWESn, n = 2~8, 10, the number of methylene units in the spacer) have been synthesized, and the thermal behavior of the series has been investigated. All the dimers formed enantiotropic nematic phases. The nematic-isotropic transition temperatures of the dimers and their entropy variation at the phase transition showed a large odd-even effect as a function of n. This behavior was rationalized in terms of the change in the average shape of the spacer on varing the parity of the spacer. The thermal stability and degree of order in the nematic phase and the magnitude of the odd-even effect of NATWESn were very similar to those of the corresponding ether compounds, while they were significantly different from those of the monomesogenic compounds, 4-{4'-(nitrophenylazo)phenoxy}alkanoyl chlorides and the side-chain liquid-crystalline polymers, the poly[1-{4-(4'-nitrophenylazo) phenoxycarbonylalkanoyloxy}ethylene]s. The results were discussed in terms of the 'irtual trimer model'by Imrie.

• Applied Chemistry for Engineering
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• v.22 no.4
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• pp.358-366
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• 2011

A homologous series of linear liquid crystal dimers, the ${\alpha},{\omega}$-bis(4-cyano-azobenzene-4'-oxy)alkanes (CATWETn, where n, the number of methylene units in the spacer, is 2~10) were synthesized, and their thermotropic liquid crystalline phase behavior were investigated. The CATWETn with n of 3 and 6 exhibited monotropic nematic phases, whereas other derivatives showed enantiotropic nematic phases. The nematic-isotropic transition temperatures of the dimers and their entropy variation at the phase transition showed a large odd-even effect as a function of n. This phase transition behavior was rationalized in terms of the change in the average shape of the spacer on varying the parity of the spacer. The thermal stability and degree of order in the nematic phase and the magnitude of the odd-even effect of CATWETn were similar to those for the methoxy-, nitro-, and pentyl-substituted dimers, while they were significantly different from those for the monomesogenic compounds, 1-{4-(4'-cyanophenylazo)phenoxy}alkylbromides and the side-chain liquid-crystalline polymers, the poly[1-{4-(4'-cyanophenylazo)phenoxyalkyloxy}ethylene]s. The results were discussed in terms of 'virtual trimer model' by Imrie.