• Title/Summary/Keyword: common proximity point

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SOME RESULTS ON COMMON BEST PROXIMITY POINT AND COMMON FIXED POINT THEOREM IN PROBABILISTIC MENGER SPACE

  • Shayanpour, Hamid
    • Journal of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1037-1056
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    • 2016
  • In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized ${\varphi}$-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized ${\varphi}$-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.

SOME RESULTS ON BEST PROXIMITY POINT FOR CYCLIC B-CONTRACTION AND S-WEAKLY CYCLIC B-CONTRACTION MAPPINGS

  • V. Anbukkarasi ;R. Theivaraman;M. Marudai ;P. S. Srinivasan
    • The Pure and Applied Mathematics
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    • v.30 no.4
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    • pp.417-427
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    • 2023
  • The purpose of this paper is establish the existence of proximity point for the cyclic B-contraction mapping on metric spaces and uniformly convex Banach spaces. Also, we prove the common proximity point for the S-weakly cyclic B-contraction mapping. In addition, a few examples are provided to demonstrate our findings.

A Motion Correspondence Algorithm based on Point Series Similarity (점 계열 유사도에 기반한 모션 대응 알고리즘)

  • Eom, Ki-Yeol;Jung, Jae-Young;Kim, Moon-Hyun
    • Journal of KIISE:Software and Applications
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    • v.37 no.4
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    • pp.305-310
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    • 2010
  • In this paper, we propose a heuristic algorithm for motion correspondence based on a point series similarity. A point series is a sequence of points which are sorted in the ascending order of their x-coordinate values. The proposed algorithm clusters the points of a previous frame based on their local adjacency. For each group, we construct several potential point series by permuting the points in it, each of which is compared to the point series of the following frame in order to match the set of points through their similarity based on a proximity constraint. The longest common subsequence between two point series is used as global information to resolve the local ambiguity. Experimental results show an accuracy of more than 90% on two image sequences from the PETS 2009 and the CAVIAR data sets.

Trends of the Precedent Case concerning Hospitalized Acquired Infection (병원감염에 관한 판례의 동향)

  • Lee, Dong-Pil
    • The Korean Society of Law and Medicine
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    • v.8 no.1
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    • pp.61-105
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    • 2007
  • The Hospitalized Acquired Infection is defined as the case where the hidden infection or not found at the time of hospitalization occurs during the hospitalized period or, within 30 days to those who performed the surgery operation and then left the hospital. About 2/3 of the Hospitalized Acquired Infection are found as having the internal infection cases that are occurred by the patients' own virus due to the lowered immune system, while about 1/3 are found as having the external infection. The latter 1/3 of the external infection cases can be prevented through the infection management. And in case the new Hospitalized Acquired Infection case occur to the patient who was treated in the hospital, its responsibility issue will matter. As well in the disputes over the Hospitalized Acquired Infection cases, the cause-result relation between the damages and the medical staff's fault and as to whether there is failure of the medical staff or not. personnel should be proved in the medical-malpractice cases. In addition, the difficulties in proving such as expertise, secrecy propensity, discrete propensity and incompleteness will be considered to ease the burden of patient side's proving. Probability theory, Fact based assumption theory, Most adequate plaintiff preassumption or Expressed evidence theories are being discussed as the theories of eased burden of proof. In the result of gathering and reviewing Korea's precedent cases concerning the Hospitalized Acquired Infection, there are only a few accumulated prece dent cases and the attitude of the court also are also not consistent. Therefore, there are the precedents where the cause-result relation and the failure are immediately assumed when (1) timely proximity between the medical behavior and malpractice results, (2) proximity between the medical behavior-applied parts and the malpractice results-found parts, and (3) lack of other causes are separately evidenced; while the are the precedents only when 'the existence of the medical faults based on the common sense' is separately evidenced. It was found that the former and latter cases coexisted. The former is considered as based on the theory that separates the fault and cause-result relation not to consider them together, or regarded as based on the doubts that assumes the medical staff's neglect even though the Hospitalized Acquired Infection might be completely prevented by their efforts. However, the modern medical technology has the limitation as far as the prevention of the Hospitalized Acquired Infection. In conclusion, the assumption of the cause-result relation and that of the fault should be separately reviewed. Therefore, the latter precedents are considered as more reasonable, in the point the faulty behavior may be proved based on the common sense.

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Effects of Low Level Laser Therapy on Oral Mucositis Caused by Anticancer Chemotherapy in Pediatric Patients (소아 암 환자에서 항암제 치료 후 발생한 구내염에 대한 저출력 레이저의 효과)

  • Kim, Hae-Ja;Rho, Shi-Youn;Shin, Yong-Sup
    • The Korean Journal of Pain
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    • v.14 no.1
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    • pp.51-55
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    • 2001
  • Background: Oral mucositis is a common complication of anticancer chemotherapy. The sequelae of this consist of an increased risk of infection, moderate to severe pain, compromised oral function, and bleeding. This study was performed to evaluated the effects of the He-Ne laser and the Ga-Al-As laser on oral mucositis caused by anticancer chemotherapy in pediatric patients. Methods: There were 3 cases of osteosarcoma and 6 cases of leukemia. All patients received He-Ne laser (632.8 nm wavelength, power 60 mW) application on 400-600 Hz scanning for 5-20 minutes and Ga-Al-As laser (904 nm wavelength, power 40 mW) application by fiberoptic hand piece placed in immediate proximity to the tissue without direct contact with it for 30 seconds per point for 5 days per week. During the application patients wore wavelength-specific dark glasses and were instructed to keep their eyes closed. Results: The mean number of treatments with oral intake was $4.89{\pm}0.64$. The mean number of total treatments was $9.44{\pm}2.59$. There were no significant side effects during and after the laser treatments. Conclusions: He-Ne laser and Ga-Al-As (IR) laser treatment were well tolerated and reduced the severity and duration of chemotherapy-induced oral mucositis in pediatric oncologic patients.

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