• East Asian mathematical journal
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• v.28 no.4
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• pp.419-433
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• 2012

In this paper, by using the inductive method, recurrence relation, the unit circle, circle to inscribe a right-angled triangle, formula of multiple angles, solution of quadratic equation and Fibonacci numbers, we study various problem solving methods to find pythagorean triple.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1497-1510
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• 2019

In this paper we compute the stopping times in the game Rock-Paper-Scissors. By exploiting the recurrence relation we compute the mean values of stopping times. On the other hand, by constructing a transition matrix for a Markov chain associated with the game, we get also the distribution of the stopping times and thereby we compute the mean stopping times again. Then we show that the mean stopping times increase exponentially fast as the number of the participants increases.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1269-1277
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• 2022

In this paper we consider a sequence of polynomials defined by some recurrence relation. They include, for instance, Poupard polynomials and Kreweras polynomials whose coefficients have some combinatorial interpretation and have been investigated before. Extending a recent result of Chapoton and Han we show that each polynomial of this sequence is a self-reciprocal polynomial with positive coefficients whose all roots are unimodular. Moreover, we prove that their arguments are uniformly distributed in the interval [0, 2𝜋).

• The Transactions of the Korea Information Processing Society
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• v.6 no.1
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• pp.75-83
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• 1999

recently, a new hypercube-like interconnection network, the Z-cube, was proposed. The Z-cube retains most good topological properties, however, its node degree is 3/4 of hypercube's one. Considering hardware implementations, the Z-cube is a good alternative to the hypercube. In this paper, we obtained the diameter, fault diameter and the average distance between two nodes to evaluate the communication performance of the Z-cube. The recursive structure, the shortest path between two nodes I Z-cube and recurrence relation on the average distance were deduced, and node disjoint path was introduced. Although it is generally expected that the communication performance in an interconnection network with reduced node degree falls as much as that, this paper shows that the Z-cube's diameter is the same as the hypercube's one and the average distance between two nodes in Z-cube is about 1.125 times the average distance between two nodes in the hypercube and the fault diameter of Z-cube ranges approximately from 1.4times to 1.7times the fault diameter of the hypercube.

• Radiation Oncology Journal
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• v.21 no.2
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• pp.143-148
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• 2003

Purpose: The purpose of this study was to evaluate treatment results in terms of the survival and failure patterns subsequent to radiation therapy in recurrent cervical cancer, fellowing primary surgery. Material and Methods: Between January 1990 and December 1999, 27 patients, with recurrent cervical cancer following primary surgery, were subsequently treated with radiation in the Department of Radiation Oncology, at the Keimyung University Dongsan Medical Center. Their median age was 48, ranging from 31 to 70 years old. With regard to the Initial FIGO stage on presentation, 20 and 7 patients were stages I and II, respectively. Twenty three patients had squamous cell carcinomas and 4 had adenocarcinomas. The time interval from the primary surgery to the recurrence ranged from 2 to 90 months with a median of 29 months. The recurrent sites were the vaginal cuff alone, the pelvic cavity and combined recurrence in 14, 9 and 4 patients, respectively. Radiation was peformed, with external and vaginal intracavitary radiation in 13 patients, external radiation alone in 13 and vaginal intracavitary radiation alone in another one. The median follow-up period was 55 months, ranging from 6 to 128 months. Results: The five year disease free survival (5y DFS) and five year overall survival (5y OS) rates were 68.2 and 71.9$\%$, respectively. There was a marginal statistically significant difference in the 5y DFS in relation to the recurrent site (5y DFS, 85.7$\%$ in vaginal cuff recurrence alone, 53.3$\%$ in pelvic cavity recurrence, p=0.09). There was no difference in the survival according to the time interval between the primary surgery and a recurrence. There was only a 7$\%$ local failure rate in the patients with a vaginal cuff recurrence. The major failure patterns were local failure in the patients with pelvic cavity recurrence, and distant failure in the patients with a combined recurrence. There were no complications above grade 3 after the radiation therapy. Conclusion: Radiation therapy was safe and effective treatment for a recurrent carcinoma of the uterine cervix following primary surgery, especially the external beam radiation and vaginal intracavitary irradiation achieved the best results in the patients with a vaginal cuff recurrence following primary surgery.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.211-222
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• 2017

In this paper, we consider three inverse eigenvalue problems for a special type of acyclic matrices. The acyclic matrices considered in this paper are described by a graph called a broom on n + m vertices, which is obtained by joining m pendant edges to one of the terminal vertices of a path on n vertices. The problems require the reconstruction of such a matrix from given partial eigen data. The eigen data for the first problem consists of the largest eigenvalue of each of the leading principal submatrices of the required matrix, while for the second problem it consists of an eigenvalue of each of its trailing principal submatrices. The third problem has an eigenvalue and a corresponding eigenvector of the required matrix as the eigen data. The method of solution involves the use of recurrence relations among the leading/trailing principal minors of ${\lambda}I-A$, where A is the required matrix. We derive the necessary and sufficient conditions for the solutions of these problems. The constructive nature of the proofs also provides the algorithms for computing the required entries of the matrix. We also provide some numerical examples to show the applicability of our results.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.97-102
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the Pareto distribution. Let ｛$X_n,n\qeq1$｝be a sequence of independent and identically distributed random variables with a common continuous distribution function(cdf) F($chi$) and probability density function(pdf) f($chi$). Let $Y_n\;=\;mas{X_1,X_2,...,X_n}$ for $ngeq1$. We say $X_{j}$ is an upper record value of {$X_{n},n\geq1$}, if $Y_{j}$＞$Y_{j-1}$,j＞1. The indices at which the upper record values occur are given by the record times ${u( n)}n,\geq1$, where u(n) = min{j｜j ＞u(n-l), $X_{j}$＞$X_{u(n-1)}$,n\qeq2$ and u(l) = 1. Suppose $X{\epsilon}PAR(\frac{1}{\beta},\frac{1}{\beta}$ then E$(\frac{{X^\tau}}_{u(m)}}{{X^{s+1}}_{u(n)})\;=\;\frac{1}{s}E$ E$(\frac{{X^\tau}}_{u(m)}{{X^s}_{u(n-1)}})$ - $\frac{(1+\betas)}{s}E(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}}$ and E$(\frac{{X^{\tau+1}}_{u(m)}}{{X^s}_{u(n)}})$ = $\frac{1}{(r+1)\beta}$ [E$(\frac{{X^{\tau+1}}}_u(m)}{{X^s}_{u(n-1)}})$ - E$(\frac{{X^{\tau+1}}_u(m)}}{{X^s}_{u(n-1)}})$ - (r+1)E$(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}})$]

• Journal of Korean Medical Ki-Gong Academy
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• v.13 no.1
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• pp.105-144
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• 2013

This study intended to provide fundamental data to take countermeasures against recurrent stress by analyzing the health-related quality of life and factors for recurrent stress of alcohol dependents. Structured questionnaire was prepared for patients who quitted drinking after they had been hospitalized for alcohol dependence to take medical treatment but suffered recurrence, and analysis on health-related quality of life and environmental factors with drinking risk was conducted. The quality of life was at a relatively satisfactory level, where pain was found at the highest level and general health condition was found at the lowest level. Environmental factors with drinking risk were found to be a moderate level, drinking for the reason of family and friends in terms of complications with other persons was found to be highest, and then job, self control, bad emotions, and social pressure on drinking were found in order. For health-related quality of life, the quality of life was found to be high in case of the only son, professional job, well-educated persons, and no history of hospitalization. Regarding factors for recurrent stress, stress was found to be high in case of the eldest son and being without religion, and the lower was the quality of life, the higher were recurrent stress and environmental factors with drinking risk. It was found that demographic factors including age, marriage, and job influenced the recurrence of alcohol dependence, and factors for recurrent stress, etc. also influenced recurrent alcohol dependence with drinking risks. Specially, the lower was the quality of life, the higher were factors for recurrent stress, and drinking risks, therefore measures to improve the quality of life are required to be taken to prevent alcohol dependence from recurrence.

• Maxillofacial Plastic and Reconstructive Surgery
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• v.29 no.1
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• pp.24-32
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• 2007

The odontogenic keratocyst(OKC) is a common developmental odontogenic cyst and represents approximately 11% of odontogenic cysts. It is decided by microscopic and histopathologic determinant rather than by clinical appearance. In this study, expression of RANKL and OPG in OKC in relation to age and gender of patient and recurrence, location of lesion were examined through immuno- histochemical study. The RANKL and OPG antibody staining were used. The obtained result were as follow. 1. Positive immunoreactivity to RANKL/OPG in all specimens was found. 2. There was no significant difference in immunohistochemical expression of RANKL relating to recurrence, location of OKCs and age, gender of patients. 3. There was no significant difference in immunohistochemical expression of OPG relating to recurrence, location of OKCs and age, gender of patients. From above results, it is suggested that activation of osteoclasts by RANKL is an important mechanism by which OKCs cause bone destruction.

• Annals of Hepato-Biliary-Pancreatic Surgery
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• v.26 no.1
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• pp.40-46
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• 2022

Backgrounds/Aims: The role of inflammation in malignant cell proliferation has been well described. High values of platelet-to-lymphocyte ratio (PLR) and neutrophil-to-lymphocyte ratio (NLR) as markers of systemic inflammation have shown associations with unfavorable long-term outcomes. The purpose of this study was to determine values of NLR and PLR evaluated prior to and after surgery and their associations with mortality and recurrence rates of liver transplant patients with hepatocellular carcinoma (HCC). Methods: A total of 105 patients with HCC who underwent orthotopic liver transplantation (OLT) were retrospectively reviewed. NLR and PLR values were obtained from complete blood counts prior to and after surgery. Overall survival (OS) and recurrence-free survival (RFS) in relation with delta NLR and PLR were estimated. Results: Serum alpha-fetoprotein levels > 100 ng/mL (p = 0.014) and lymphovascular emboli in the specimen (p = 0.048) were identified to be significant predictors of RFS. Child-Pugh score (p = 0.016) was found to be an independent factor associated with poorer OS. An increasing delta PLR was associated with worse RFS, although it showed no significant association with OS. Conclusions: The analysis of PLR as a continuous variable may predict recurrence outcomes in patients undergoing OLT for HCC. It is more representative than isolated values.