Counterexamples to the uniformity conjecture

AbstractThe Exact Geometric Computing approach requires a zero test for numbers which are built up using standard operations starting with the natural numbers. The uniformity conjecture, part of an attempt to solve this problem, postulates a simple linear relationship between the syntactic length of expressions built up from the natural numbers using field operations, radicals and exponentials and logarithms, and the smallness of non zero complex numbers defined by such expressions. It is shown in this article that this conjecture is incorrect, and a technique is given for generating counterexamples. The technique may be useful to check other conjectured constructive root bounds of this kind. A revised form of the uniformity conjecture is proposed which avoids all the known counterexamples

Placental pouch closure: a novel, safe and effective surgical procedure for conservative management of placenta accreta

Background: Placenta accreta spectrum (PAS) has become a global problem secondary to the high rate of cesarean delivery (CD). The current study presents an effective surgical procedure (placental pouch closure) for uterine preservation in patients with PAS. Methods: We applied this procedure in sixty cases at a tertiary university hospital between September 2017 and January 2019. We included women who were diagnosed as PAS based on preoperative ultrasound and Doppler evaluation, and who had the desire for uterine preservation. Results: The procedure was successful in almost all cases; the uterus was conserved 98.33 % of participants, with no associated severe maternal morbidities or mortality. In all cases, no additional surgical procedures were needed. The mean blood loss was 1263 ml, and the mean number of units of blood required for transfusion was 2.31 units. Conclusion: Identifying and meticulously closing the placental pouch is a novel surgical procedure for conservative management of PAS. In well-selected cases with the availability of facilities and expertise, the technique could have a place as a safe and effective surgical technique in women presenting with placenta accreta who desire uterine preservation. Trial registration number: NCT03241849. Registered on August 8, 201

Edge Even Graceful Labeling of Cylinder Grid Graph

Edge even graceful labeling (e.e.g., l.) of graphs is a modular technique of edge labeling of graphs, introduced in 2017. An e.e.g., l. of simple finite undirected graph G = ( V ( G ) , E ( G ) ) of order P = | ( V ( G ) | and size q = | E ( G ) | is a bijection f : E ( G ) → { 2 , 4 , … , 2 q } , such that when each vertex v ∈ V ( G ) is assigned the modular sum of the labels (images of f ) of the edges incident to v , the resulting vertex labels are distinct mod 2 r , where r = max ( p , q ) . In this work, the family of cylinder grid graphs are studied. Explicit formulas of e.e.g., l. for all of the cases of each member of this family have been proven

Nail ridging in rheumatoid arthritis patients and relation to disease activity: An integrated rheumatology-dermatology multi-centre study

Aim of the work: To evaluate the frequency of nail ridging (NR) in patients with rheumatoid arthritis (RA) and to study its relation to disease activity. Patients and methods: 230 RA patients and 97 matched controls from Helwan, Ain Shams and Mansoura university hospitals were studied. Disease activity score (DAS28) was assessed. NR has been searched for in all patients. The number of affected fingers was recorded. NR was determined by a magnifying lens, seen by naked eye or seen and felt. Dermoscopic photography of the NR using Dermalite DL4 3Gen dermatoscope has been recorded. Results: The median age of patients was 49 years (42–58 years); they were 221 females and 19 males (F:M 11.1:1) with a disease duration 9 years (5–11 years). Their DAS28 was 3.6 (2.9–4.6). NR was significantly increased in RA cases vs. control; 73% vs 20%; p < 0.001. In patients, NR was detected by a magnifying lens in 32.6%, seen in 27% and seen and felt in 13.5%. Joint deformities were significantly higher in those with NR. DAS28 was a significant independent predictor of NR; for every one-point increase in DAS28, there was a 153 times higher odds to exhibit NR at a sensitivity of 93.5%, specificity 80.3% and at a diagnostic accuracy of 90%. Conclusion: NR is a frequent finding in RA. An integrated rheumatological- dermatological clinical evaluation may be helpful and further studies are required to prove the importance of this sign for follow up of RA patients