• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.1065-1081
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• 2011

For any field F, a polynomial f $\in$ F[$x_1,x_2,{\ldots},x_k$] can be associated with a polytope, called its Newton polytope. If the polynomial f has integrally indecomposable Newton polytope, in the sense of Minkowski sum, then it is absolutely irreducible over F, i.e., irreducible over every algebraic extension of F. We present some results giving new integrally indecomposable classes of polygons. Consequently, we have some criteria giving many types of absolutely irreducible bivariate polynomials over arbitrary fields.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.7 no.3
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• pp.137-141
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• 2014

RFID system is applied to various industry such as process control, distribution management, access control, environment sensing, entity identification, etc. Since RFID system uses wireless communication, it has more weak points for security. In this paper, an authentication protocol is suggested between tags and a reader, which is basic property for security. A suggested protocol use a bivariate polynomial over a finite field and is secure against snooping, replay attack, position tracking and traffic analysis.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.133-159
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• 2024

In a previous work we studied generalized Stirling numbers of the second kind S^{(a₂,b₂,p₂)}_a1,b1 (p₁, k), where a₁, a₂, b₁, b₂ are given complex numbers, a₁, a₂ ≠ 0, and p₁, p₂ are non-negative integers given. In this work we use these generalized Stirling numbers to define Bernoulli polynomials in two variables B_p1,p2 (x₁, x₂), and Euler polynomials in two variables E_p1p2 (x₁, x₂). By using results for S^{(1,x₂,p₂)}_1,x1 (p₁, k), we obtain generalizations, to the bivariate case, of some well-known properties from the standard case, as addition formulas, difference equations and sums of powers. We obtain some identities for bivariate Bernoulli and Euler polynomials, and some generalizations, to the bivariate case, of several known identities for Bernoulli and Euler numbers and polynomials of the standard case.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.2
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• pp.58-65
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• 2021

Meta-heuristic algorithms have been developed to efficiently solve difficult problems and obtain a global optimal solution. A common feature mimics phenomenon occurring in nature and reliably improves the solution through repetition. And at the same time, the probability is used to deviate from the regional optimal solution and approach the global optimal solution. This study compares the algorithm created based on the above common points with existed SA and HS to show advantages in time and accuracy of results. Existing algorithms have problems of low accuracy, high memory, long runtime, and ignorance. In a two-variable polynomial, the existing algorithms show that the memory increases and the accuracy decrease. In order to improve the accuracy, the new algorithm increases the number of initial inputs and increases the efficiency of the search by introducing a direction using vectors. And, in order to solve the optimization problem, the results of the last experiment were learned to show the learning effect in the next experiment. The new algorithm found a solution in a short time under the experimental conditions of long iteration counts using a two-variable polynomial and showed high accuracy. And, it shows that the learning effect is effective in repeated experiments.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.491-497
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• 2015

In this paper, we have suggested an extended double Newton's method with sixth-order convergence by considering a control parameter ${\gamma}$ and a weight function H(s, u). We have determined forms of ${\gamma}$ and H(s, u) in order to induce the greatest order of convergence and established the main theorem utilizing related properties. The developed theory is ensured by numerical experiments with high-precision computation for a number of test functions.

• The KIPS Transactions:PartC
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• v.12C no.4 s.100
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• pp.473-480
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• 2005

We can obtain useful information by deploying large scale sensor networks in various situations. Security is also a major concern in sensor networks, and we need to establish pairwise keys between sensor nodes for secure communication. In this paper, we propose new pairwise key establishment mechanism based on clustering and polynomial sharing. In the mechanism, we divide the network field into clusters, and based on the polynomial-based key distribution mechanism we create bivariate Polynomials and assign unique polynomial to each cluster. Each pair of sensor nodes located in the same cluster can compute their own pairwise keys through assigned polynomial shares from the same polynomial. Also, in our proposed scheme, sensors, which are in each other's transmission range and located in different clusters, can establish path key through their clusterheads. However, path key establishment can increase the network overhead. The number of the path keys and tine for path key establishment of our scheme depend on the number of sensors, cluster size, sensor density and sensor transmission range. The simulation result indicates that these schemes can achieve better performance if suitable conditions are met.

• Health Policy and Management
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• v.29 no.4
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• pp.412-421
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• 2019

Background: The purpose of this study was to identify the status of Successful Aging among the elderly aged 65 and over in rural areas and to compare factors related with Successful Aging between "kyung-ro-dang" users and non-users. Methods: A total of 181 elderly aged 65 or older were selected from four districts (Heung-upri, Mejiri, Sajerri, and Daeanri) of Wonju city. A survey method using face to face interviews was applied to collect information. Successful aging was measured on a 5-point Likert-type scale using the successful aging scale developed for the Korean elderly, which indicates the higher the score, the higher the level of successful aging. Descriptive statistics, bivariate, and multivariate analyses were computed; the level of significance was set at 5%. Hierarchical polynomial regression was applied to find out the factors associated with successful aging. Results: Of the total, 112 elders used kyung-ro-dang and 69 elders who did not use kyung-ro-dang. The level of successful aging of the elderly was higher among kyung-ro-dang users than non-users. The factors related to successful aging among kyung-ro-dang users were walking and social participation. Users who walk more than 4 times per week and social participation activities have a higher level of satisfaction. In the case of non-users, a higher level of monthly income, having a spouse, social support, and social participation associated with a higher level of successful aging. Conclusion: Monthly income, social participation, and social factors were found to be related to successful aging along with physical and mental health conditions among the elderly in rural areas. Therefore, it can be concluded that income, social as well as mental and physical factors, are more critical for successful aging in the rural community care in Korea.