On the bridge number of knot diagrams with minimal crossings

Given a diagram $D$ of a knot $K$, we consider the number $c(D)$ of crossings and the number $b(D)$ of overpasses of $D$. We show that, if $D$ is a diagram of a nontrivial knot $K$ whose number $c(D)$ of crossings is minimal, then $1+\sqrt{1+c(D)} \leq b(D)\leq c(D)$. These inequalities are shape in the sense that the upper bound of $b(D)$ is achieved by alternating knots and the lower bound of $b(D)$ is achieved by torus knots. The second inequality becomes an equality only when the knot is an alternating knot. We prove that the first inequality becomes an equality only when the knot is a torus knot.Comment: 18 pages, 7 figure

Silicon nanowire devices

Transport measurements were carried out on 15–35 nm diameter silicon nanowires grown using SiH4 chemical vapor deposition via Au or Zn particle-nucleated vapor-liquid-solid growth at 440°C. Both Al and Ti/Au contacts to the wires were investigated. The wires, as produced, were essentially intrinsic, although Au nucleated wires exhibited a slightly higher conductance. Thermal treatment of the fabricated devices resulted in better electrical contacts, as well as diffusion of dopant atoms into the nanowires, and increased the nanowire conductance by as much as 10^4. Three terminal devices indicate that the doping of the wires is p type

Survival and reproductive outcome of childbearing age ovarian cancer patients taking fertility-sparing surgery

Background: Surgical management of ovarian cancer includes total hysterectomy and bilateral salpingo-oophorectomy which results in the loss of fertility. Fertility-sparing surgery in the reproductive aged women with early-stage ovarian cancer with favourable histology has been proposed by American College of Obstetrics and Gynecology and European Society for Medical Oncology. We sought to access the survival and fertility outcome of Korean women in their reproductive age who undertook fertility-sparing surgery.Methods: Based on the Korean National Insurance Claims Data and the National Health Information Database, 328 women with newly developed ovarian cancer in 2010 were followed up for the survival and pregnancy outcome until 2020. Patients who were diagnosed with cancer or underwent hysterectomy before 2010 were excluded. The control group consisted of 552 women matched by age, economic status and place of living.Results: Out of 120, 10 deaths occurred in the fertility-sparing surgery group showing a survival rate of 91.7%. Women undertaking fertility-sparing surgery had a lower chance of delivering a new-born compared to the control group (OR 0.46; 95% CI 0.26-0.81). Diagnosis of infertility, ectopic pregnancy, and abortion appeared higher in the fertility-sparing surgery group, but it did not reach a statistical significance.Conclusions: The pregnancy rate of the ovarian cancer patients with fertility-sparing surgery was lower than that of women without ovarian cancer. Undergoing fertility-sparing surgery per se should not deter women of trying to get pregnant as the pregnancy outcome indicators do not show statistically significant differences compared to the control group

Clinical characteristics and treatment modalities of vulvovaginal atrophy in genitourinary syndrome of menopause

Background: Genitourinary syndrome of menopause (GSM) causes symptoms such as vaginal dryness, dysuria, repetitive urinary tract infection and urinary urgency may affect daily activities, sexual relationships, and overall quality of life. The aim of the study was to provide the clinical characteristics of VVA patients in South Korea and the effectiveness as well as complications of the currently used low dose estrogen vaginal suppository.Methods: 52 women who has visited the outpatient gynecology clinic of the National Health Insurance Service Ilsan Hospital from January 2018 to December 2019 were recruited as study subjects. For the analysis of the clinical characteristics, subjective symptoms described by the patient’s own words such as vaginal dryness, pain, dysuria, dyspareunia, or no symptoms at all were included. Objective signs such as thinning of vaginal rugae, mucosal dryness, and mucosal fragility and the presence of petechiae were recorded.Results: Vaginal dryness was the most common complaint (92.3%). Thinning of the vaginal rugae was the most commonly noted objective sign (73.1%). Of the 52 subjects, 31 (59.6%) refrained from using the low dose estrogen vaginal suppository. The most common reason for not being able to use the suppository was the inability to insert the suppository (32.3%).Conclusions: Although patient-reported symptoms and clinical objectivity through physical examination are two components in diagnosing VVA, further study is warranted for a more objective and discriminatory diagnosis criteria for VVA. As the only available treatment modality was low dose vaginal estrogen suppository, comparison with other treatment modalities were not available