• Title/Summary/Keyword: Two Point Recurrence

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A FIFTH ORDER NUMERICAL METHOD FOR SINGULAR PERTURBATION PROBLEMS

  • Chakravarthy, P. Pramod;Phaneendra, K.;Reddy, Y.N.
    • Journal of applied mathematics & informatics
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    • v.26 no.3_4
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    • pp.689-706
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    • 2008
  • In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

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A Study on Behaviors for Preventing Recurrence and Quality of Life in Breast Cancer Survivors (유방암 생존자의 재발방지 행위와 삶의 질)

  • Min, Hyo-Suk;Park, Sun-Young;Lim, Joung-Sun;Park, Mi-Ok;Won, Hyo-Jin;Kim, Jong-Im
    • Journal of Korean Academy of Nursing
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    • v.38 no.2
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    • pp.187-194
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    • 2008
  • Purpose: This study was to identify behaviors preventing the recurrence of breast cancer and the level of quality of life. Methods: This descriptive study was conducted using a structured questionnaire from November 1, 2006 to December 25, 2006. One hundred and twenty two women breast cancer survivors were recruited by convenience sampling. Results: The most frequent behavior for preventing recurrence of the breast cancer was dietary treatment (90.9%) and exercise (86.8%) was the second behavior. In addition, most of them perceived these behaviors as 'very effective' (82.8%). The degree of the quality of life of a breast cancer survivor was 5.34 point indicating a 'medium level'. Conclusion: Breast cancer survivors pursued various behaviors for preventing recurrence of breast cancer. Therefore, the nursing interventions should be focused on a systematic educational approach considering healthy behaviors to prevent breast cancer recurrence for breast cancer survivors.

NUMERICAL METHOD FOR SINGULAR PERTURBATION PROBLEMS ARISING IN CHEMICAL REACTOR THEORY

  • Andargie, Awoke
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.411-423
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    • 2010
  • In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

NUMERICAL INTEGRATION METHOD FOR SINGULAR PERTURBATION PROBLEMS WITH MIXED BOUNDARY CONDITIONS

  • Andargie, Awoke;Reddy, Y.N.
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.1273-1287
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    • 2008
  • In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

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Long-Term Survival Following Port-Site Metastasectomy in a Patient with Laparoscopic Gastrectomy for Gastric Cancer: A Case Report

  • Kim, Sang Hyun;Kim, Dong Jin;Kim, Wook
    • Journal of Gastric Cancer
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    • v.15 no.3
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    • pp.209-213
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    • 2015
  • A 78-year-old man underwent laparoscopy-assisted total gastrectomy for gastric cancer (pT3N0M0). Multiple port sites were used, including a 10 mm port for a videoscope at the umbilical point and three other working ports. During the six-month follow-up evaluation, a 2 cm enhancing mass confined to the muscle layer was found 12 mm from the right lower quadrant port site, suggesting a metastatic or desmoid tumor. Follow-up computed tomography imaging two months later showed that the mass had increased in size to 3.5 cm. We confirmed that there was no intra-abdominal metastasis by diagnostic laparoscopy and then performed a wide resection of the recurrent mass. The histologic findings revealed poorly differentiated adenocarcinoma, suggesting a metastatic mass from the stomach cancer. The postoperative course was uneventful, and the patient completed adjuvant chemotherapy with TS-1 (tegafur, gimeracil, and oteracil potassium). There was no evidence of tumor recurrence during the 50-month follow-up period.

Pathologic Lead Points in Childhood Intussusception (소아 장중첩증의 병리적 유발병변)

  • Jang, Seon-Mo;Kang, Su-Hwan;Lee, Jung-Hoon;Huh, Young-Soo
    • Advances in pediatric surgery
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    • v.6 no.1
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    • pp.50-55
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    • 2000
  • Pathologic lead points are found in a few intussusception patients. To evaluate the pathologic lead points in childhood intussusception, a retrospective review of 227 operated cases of intussusception treated at the Yeungnam University Hospital from January 1986 to April 1999. The patients were divided into 2 groups; idiopathic group 209 cases, (92.1 % and lead points group 18 cases, 7.9 %). Intussusception developed between age two months and six months in both groups. Enteroenteric type of intussusception was relatively more frequent in the lead point group than in idiopathic group. The lead points were veil (10 cases, 52.6 %), Meckel's diverticulum(3 cases, 15.8 %), lymphoma(3 cases, 15.8 %), ectopic pancreas(2 cases, 10.5 %), Henoch-Sch$\ddot{o}$nlein purpura(1 cases, 5.3 %). The bowel resection rate was 44.4 % in the lead point group and 8.6% in idiopathic group. The recurrence rate was 5.56 % in lead points group and 1.44 % in idiopathic group.

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A Brachial Artery Pseudoaneurysm Treated with a Bifurcated Y-Shaped Artificial Vessel Graft

  • Joon seok Oh;Seokchan Eun
    • Archives of Plastic Surgery
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    • v.49 no.6
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    • pp.755-759
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    • 2022
  • Brachial artery aneurysms are rare diseases that may be caused by infection or trauma. We report a case of a 71-year-old man who presented with a mass in his right antecubital fossa that increased in size slowly over time. Three years ago, the patient underwent ascending and total-arch replacement with artificial vessel graft to treat aortic root and ascending aorta aneurysm. Preoperative physical examination of right upper extremity showed a nonpulsatile mass with normal pulse of axillary, brachial, and radial arteries. The mass was removed and brachial artery reconstruction was done initially using saphenous vein graft. Two months later, the patient revisited with recurrent pseudoaneurysm, involving the bifurcation point of brachial artery. Aneurysm was totally resected and the brachial artery was reconstructed by interposition graft using a bifurcated GORE-TEX artificial vessel graft. The patient healed without complication and no recurrence was observed. Artificial vessel graft is an available option for reconstruction, and revascularization of vessel defect after excision of brachial artery aneurysm may involve bifurcation point.

Blood Blister-Like Aneurysm with Rupture Point Close to Origin of Anterior Choroidal Artery

  • Park, Jaechan
    • Journal of Korean Neurosurgical Society
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    • v.56 no.6
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    • pp.500-503
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    • 2014
  • If a ruptured blood blister-like aneurysm (BBA) arises from the lateral or superolateral wall of the internal carotid artery (ICA) at the level of the anterior choroidal artery (AChA), its proximity to the origin of the AChA presents a serious surgical challenge to preserve the patency of the AChA. Two such rare cases are presented, along with successful surgical techniques, including the application of a C-shaped aneurysm clip parallel to the ICA and a microsuture technique to repair the arterial defect. The patency of the AChA and ICA was successfully preserved without recurrence or rebleeding of the BBA during a 1-year follow-up after the operation.

A Study on the Recurrence for the Transition Functions of Finite Cellular Automata (유한 셀룰러 오토마타 천이함수의 재귀식에 대한 연구)

  • Lee, Hyen-Yeal;Lee, Geon-Seon
    • The KIPS Transactions:PartA
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    • v.14A no.4
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    • pp.245-248
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    • 2007
  • This paper provides some simple recursive formulas generation transition functions of finite cellular automata with triplet local transition functions under two states (0 and 1) and four different boundary conditions (0-0,0-1,1-0,1-1), and classify transition functions into several classes.

Ovarian Transposition for Stage Ib Squamous Cell Cervical Cancer - Lack of Effects on Survival Rates?

  • Turan, A. Taner;Keskin, H. Levent;Dundar, Betul;Gundogdu, Burcu;Ozgul, Nejat;Boran, Nurettin;Tulunay, Gokhan;Kose, M. Faruk
    • Asian Pacific Journal of Cancer Prevention
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    • v.14 no.1
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    • pp.133-137
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    • 2013
  • Background: To investigate the impact of ovarian transposition (OT) on survival rates of the patients with stage Ib squamous cell cervical cancer. Materials and Methods: Ninety-two subjects who underwent a radical hysterectomy including oophorectomy were evaluated. For nineteen (20.7%), OT was performed. Patients were divided into two groups, OT versus oophorectomy alone. The primary end-point of this study was to investigate the impact of OT on tumor recurrence rate and time, 5-year disease-free survival (DFS) and overall survival (OS). These comparisons were performed for subgroups including patients who received radiotherapy versus who did not. Statistical analyses were conducted using the Chi-square test, T-test and Mann-Whitney test. OS was examined using the Kaplan-Meier method. $P{\leq}0.05$ was considered to be statistically significant. Results: The median follow-up period was 89 months for OT and 81 months for the oophorectomy group (p>0.05). Both groups experienced similar recurrence rates (31.6% vs. 26.4%, p=0.181). The median duration from surgery to recurrence, and surgery to death were also similar between the groups (p>0.05). The 5-year DFS and OS rates were both 68.4% for the OT group, and 73.6% and 77.8% for the oophorectomy group (p=0.457 and p=0.307, respectively). While the 5-year DFS rate was not statistically significant between the OT and oophorectomy groups who did not receive radiotherapy (p=0.148), the 5-year OS rate was significantly higher in the oophorectomy group (95.4% vs 66.7%, respectively) without radiotherapy (p=0.05). The 5-year DFS and OS rates were statistically similar between the groups who received adjuvant radiotherapy (p>0.05). Conclusions: Ovarian transposition has not significantly negative effect on the survival rates when adjuvant radiotherapy will be applied, while 5-year OS may be less in OT group if radiotherapy is not mandatory.