Non-commutative hypergroup of order five

We prove that all hypergroups of order four are commutative and that there exists a non-comutative hypergroup of order five. These facts imply that the minimum order of non-commutative hypergroups is five even though the minimum order of non-commutative groups is six

Non-commutative hypergroup of order five

We prove that all hypergroups of order four are commutative and that there exists a non-comutative hypergroup of order five. These facts imply that the minimum order of non-commutative hypergroups is five, even though the minimum order of non-commutative groups is six.ArticleJournal of Algebra and Its Applications.16(7):1750127(2016)journal articl

The prognostic effect of tumor volume, reduction ratio, and cumulative doses on external beam radiotherapy with central-shielding method and image-guided adaptive brachytherapy for cervical cancer

ObjectiveTo evaluate the prognostic effect of tumor volume at diagnosis, tumor reduction ratio during external beam radiotherapy (EBRT) with central-shielding method, and cumulative minimal dose to 90% of the high-risk clinical target volume (CTVHR D90) on combined EBRT and image-guided adaptive brachytherapy (IGABT) for cervical cancer.MethodsConsecutive patients who underwent definitive radiotherapy or concurrent chemoradiotherapy for cervical cancer at Gunma University Hospital between January 2010 and December 2019 were retrospectively reviewed. Tumor volume at diagnosis and reduction ratio were calculated using magnetic resonance imaging at diagnosis and before the first IGABT session. The cumulative dose of EBRT and IGABT was calculated as an equivalent dose in 2 Gy fractions (EQD2). Optimal cutoff values were determined according to a receiver operating characteristic curve. Treatment outcomes were evaluated using the Kaplan–Meier method and compared using the log-rank test and Cox proportional hazards regression.ResultsA total of 254 patients were included in the analysis. The median follow-up for all patients was 57 (2–134) months. The 5-year overall survival (OS) was 81.9%, progression-free survival (PFS) was 71.3%, and local control (LC) was 94.5%. The patients were divided into four groups according to tumor volume at diagnosis and reduction ratio. The group with tumor volume at diagnosis ≥ 34.1 cm3 and reduction ratio < 68.8% showed significantly worse OS, PFS, and LC than the other three groups (All p < 0.05). In this group, the patients with a cumulative CTVHR D90 < 69.6 GyEQD2 showed significantly worse PFS and LC (p = 0.042 and p = 0.027, respectively). In the multivariate analysis of OS, adenocarcinoma/adenosquamous carcinoma, International Federation of Gynecology and Obstetrics 2009 stage III/IV, and a reduction ratio of < 68.8% were independent significant poor prognostic factors (p = 0.045, p = 0.009 and p = 0.001, respectively). In the univariate analysis of LC, a reduction ratio of < 68.8% was the only poor prognostic factor (p = 0.041).ConclusionThe patients with large and poorly responding tumors had significantly worse prognoses in terms of OS, PFS, and LC, suggesting that dose escalation should be considered for such tumors

Video-Assisted Thoracoscopic Surgery Using Extracorporeal Membrane Oxygenation for Intractable Pneumothorax

Intractable pneumothorax with poor lung function that has received multiple conservative treatments may occur. Case 1 was a 70-year-old woman with aspergilloma who was admitted for pneumothorax. Case 2 was a 68-year-old man with acute exacerbation of interstitial pneumonia who developed pneumothorax. In both cases, multiple conservative therapies were administered, but the leak continued; thus, operations using veno-venous extracorporeal membrane oxygenation (ECMO) were planned. By video-assisted thoracoscopic surgery (VATS), we obtained the optimal surgical field by lung collapse. We removed many blood clots that were used for pleurodesis, ligated the bulla in case 1, and covered the leak point with strengthening agents in case 2. For cases of intractable pneumothorax, lung collapse by ECMO is advantageous because we can check details and leak points even in blood clots or in poor condition of the lung, and we can maneuver the lung in poor condition with a clear surgical field

Use of FDG-PET in Radiation Treatment Planning for Thoracic Cancers

Radiotherapy plays an important role in the treatment for thoracic cancers. Accurate diagnosis is essential to correctly perform curative radiotherapy. Tumor delineation is also important to prevent geographic misses in radiotherapy planning. Currently, planning is based on computed tomography (CT) imaging when radiation oncologists manually contour the tumor, and this practice often induces interobserver variability. F-18 fluorodeoxyglucose positron emission tomography (FDG-PET) has been reported to enable accurate staging and detect tumor extension in several thoracic cancers, such as lung cancer and esophageal cancer. FDG-PET imaging has many potential advantages in radiotherapy planning for these cancers, because it can add biological information to conventional anatomical images and decrease the inter-observer variability. FDG-PET improves radiotherapy volume and enables dose escalation without causing severe side effects, especially in lung cancer patients. The main advantage of FDG-PET for esophageal cancer patients is the detection of unrecognized lymph node or distal metastases. However, automatic delineation by FDG-PET is still controversial in these tumors, despite the initial expectations. We will review the role of FDG-PET in radiotherapy for thoracic cancers, including lung cancer and esophageal cancer