• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.229-234
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• 2005

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form $x_{n+l} =\alpha+\frac{x_{n-1}^{p}}{x_{n}^{p}},\;\; n = 0, 1, ...$ is investigated, where all the coefficients are nonnegative real numbers.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.955-961
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• 2009

In this paper, we establish some characterizations which is satisfied by the independence of the upper record values from the Pareto distribution. We prove that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(m)}}$ and $X_{U(m)}$, $1\;{\le}\;m\;<\;n$ are independent. We show that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0 if and only if $\frac{X_{U(n)}+X_{U{(n+1)}}}{X_{U(n)}}$ and $X_{U(n)}$, $n\;{\ge}\;1$ are independent. And we characterize that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(n)}+X_{U{(n+1)}}}$ and $X_{U(n)}$, $n\;{\ge}\;1$ are independent.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.319-326
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• 2020

In this paper, we establish a general solution of the following functional equation $$mf\({\sum\limits_{k=1}^{n}}x_k\)+{\sum\limits_{t=1}^{m}}f\({\sum\limits_{k=1}^{n-i_t}}x_k-{\sum\limits_{k=n-i_t+1}^{n}}x_k\)=2{\sum\limits_{t=1}^{m}}\(f\({\sum\limits_{k=1}^{n-i_t}}x_k\)+f\({\sum\limits_{k=n-i_t+1}^{n}}x_k\)\)$$ where m, n, t, i_t ∈ ℕ such that 1 ≤ t ≤ m < n. Also, we study Hyers-Ulam-Rassias stability for the generalized quadratic functional equation with n-variables and m-combinations form in quasi-𝛽-normed spaces and then we investigate its application.

• Pediatric Infection and Vaccine
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• v.19 no.2
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• pp.61-70
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• 2012

Purpose: This study was performed to compare the clinical characteristics of 2009 pandemic influenza A(H1N1) [A(H1N1) pdm09] and seasonal influenza A infection in the pediatric cancer patients. Methods: A retrospective review was performed in the pediatric cancer patients who had confirmed A(H1N1)pdm09 infection at Samsung Medical Center from August 2009 to February 2010. For the comparison, the medical records of pediatric cancer patients with seasonal influenza A from January 2000 to May 2009 were reviewed retrospectively. Results: Eighty-two A(H1N1)pdm09 infections were confirmed in the pediatric cancer patients. Ten patients (12.2%) developed complicated clinical course by lower respiratory infections or extrapulmonary infections; 4 pneumonia, 1 bronchitis, 1 pericarditis with pneumonia, 1 encephalitis with pneumonia, 2 meningitis and 1 pericarditis. Three patients received mechanical ventilator and ICU care. Three pediatric cancer patients (3.7%) died. The risk factors related to complicated A(H1N1)pdm09 infections were date of infection (44-45th week 2009) and nosocomial infection. When comparing with previous seasonal influenza A infections, more prompt and aggressive antiviral therapy was given in A(H1N1)pdm09 infections. Conclusion: The A(H1N1)pdm09 infections caused a various clinical manifestations including fatal cases in pediatric cancer patient during pandemic season. There was no significant difference in clinical course between influenza A(H1N1)pdm09 and seasonal influenza A infections except the antiviral treatment strategy.

• Journal of Chest Surgery
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• v.29 no.11
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• pp.1248-1256
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• 1996

From June 1987 to December 1994, 372 patients underwent operation for resection of esophageal cancer, and 48 patients with metastasis to distant abdominal lymph nodes were analyzed.. The primary tumors were located predominantly in lower thoracic esophagus(n=29). The location of involved lymph nodes were celiac L/N(n=45), common hepatic L/N(n=4), paraaortic L/N(n=l), and retropancreatic L/N(n=l). Most tumors penetrated the esophageal wall(T3,T4, n=43), metastased to regional L/N(N1, n=41), but a few tumors were limited to the esophageal wall(T1,T2, n=5), metastased to distant abdominal L/N without metastasis to regional L/N(NO, n=7). Resectability rate was 87.5%(42/48), and complete resection was possible in 31 patients(64.6%). The most frequent cause of incomplete resection and unresectability was unresectable T4 lesions(n=8), extranodal invasion(n=7). Overall operative mortality and morbidity was 4.2%, 22.9%, and resection mortality was 4.8%. Adjuvant therapy was given to 27 patients, and postoperative follow-up was possible in all patients(median follow-up, 32 months). The 1 year and 3 year survival for resection group was 54.0%, 18.1%(median, 386 days) including operative deaths. Our results suggest that resection of the esophageal cancer with metastasis to distant abdominal lymph nodes(M1LYN) can be done with acceptable mortality and morbidity, and may playa role in long-term survival in carefully selected patients because prognosis is dismal in unresectable esophageal cancer. We recommend that lymph nodes around celiac axis be dissected thoroughly for exact staging and possible prolongation of survival, and multimodality therapy as necessary because most patients with M1(LYN) esophageal cancer do poorly with only primay surgical treatment.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.3
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• pp.103-109
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• 2013

Miller-Rabin method is the most prevalently used primality test. However, this method mistakenly reports a Carmichael number or semi-prime number as prime (strong lier) although they are composite numbers. To eradicate this problem, it selects k number of m, whose value satisfies the following : m=[2,n-1], (m,n)=1. The Miller-Rabin method determines that a given number is prime, given that after the computation of $n-1=2^sd$, $0{\leq}r{\leq}s-1$, the outcome satisfies $m^d{\equiv}1$(mod n) or $m^{2^rd}{\equiv}-1$(mod n). This paper proposes a step-by-step primality testing algorithm that restricts m=2, hence achieving 98.8% probability. The proposed method, as a first step, rejects composite numbers that do not satisfy the equation, $n=6k{\pm}1$, $n_1{\neq}5$. Next, it determines prime by computing $2^{2^{s-1}d}{\equiv}{\beta}_{s-1}$(mod n) and $2^d{\equiv}{\beta}_0$(mod n). In the third step, it tests ${\beta}_r{\equiv}-1$ in the range of $1{\leq}r{\leq}s-2$ for ${\beta}_0$ > 1. In the case of ${\beta}_0$ = 1, it retests m=3,5,7,11,13,17 sequentially. When applied to n=[101,1000], the proposed algorithm determined 96.55% of prime in the initial stage. The remaining 3% was performed for ${\beta}_0$ >1 and 0.55% for ${\beta}_0$ = 1.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.19-25
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• 2010

$3{\times}3{\times}3$ is the meaningful smallest product of three chains of each size 2n+1 since $1{\times}1{\times}1$ is a 1-element poset. The linear discrepancy of the product of three chains $2n{\times}2n{\times}2n$ is found as $6n^3-2n^2-1$. But the case of the product of three chains $(2n + 1){\times}(2n + 1){\times}(2n + 1)$ is not known yet. In this paper, we determine ld$(3{\times}3{\times}3)$ as a case to determine the linear discrepancy of the product of three chains of each size 2n + 1.

• Asian Journal of Atmospheric Environment
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• v.11 no.3
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• pp.202-216
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• 2017

Nitrogen (N) is an essential macronutrient. Thus, evaluating its flows and stocks in rice paddy ecosystems provides important insights into the sustainability and environmental loads of rice production. Among the N sources of paddy fields, atmospheric deposition and irrigation inputs remain poorly understood. In particular, insufficient information is available for atmosphere-rice paddy exchange of gaseous and particulate reactive N (Nr, all N species other than molecular N) which represents the net input or output through dry deposition and emission. In this study, we assessed the N inputs via atmospheric deposition and irrigation to a Japanese rice paddy area by weekly monitoring for 2 years with special emphasis on gas and particle exchange. The rice paddy during the cropping season acted as a net emitter of ammonia ($NH_3$) to the atmosphere regardless of the N fertilizer applications, which reduced the effects of dry deposition to the N input. Dry N deposition was quantitatively similar to wet N deposition, when subtracting the rice paddy $NH_3$ emissions from N exchange. The annual N inputs to the rice paddy were 3.2 to $3.6\;kg\;N\;ha^{-1}\;yr^{-1}$ for exchange, 8.1 to $9.8\;kg\;N\;ha^{-1}\;yr^{-1}$ for wet deposition, and 11.1 to $14.5\;kg\;N\;ha^{-1}\;yr^{-1}$ for irrigation. The total N input, 22.8 to $27.5\;kg\;N\;ha^{-1}\;yr^{-1}$, corresponded to 38% to 55% of the N fertilizer application rate and 53% to 67% of the brown rice N uptake. Monitoring of atmospheric deposition and irrigation as N sources for rice paddies will therefore be necessary for adequate N management.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.269-282
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• 2005

We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n+1}\;=\;{\alpha}-{\frac{x_{n-1}}{x_{n}},\;n=0,1,\;{\cdots}$$, where ${\alpha}\;\in\; R$ is a real number, and the initial conditions $x_{-1},\;x_0$ are arbitrary real numbers.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.261-271
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• 2007

The symbol C($m_1^{n_1}m_2^{n_2}{\cdots}m_s^{n_s}$) denotes a 2-regular graph consisting of $n_i$ cycles of length $m_i,\;i=1,\;2,\;{\cdots},\;s$. In this paper, we give some construction methods of cyclic($K_v$, G)-designs, and prove that there exists a cyclic($K_v$, G)-design when $G=C((4m_1)^{n_1}(4m_2)^{n_2}{\cdots}(4m_s)^{n_s}\;and\;v{\equiv}1(mod\;2|G|)$.