The number of triangles is more when they have no common vertex

Polygons Whose Vertex Triangles Have Equal Area

When do Three Longest Paths have a Common Vertex?

It is well known that any two longest paths in a connected graph share a vertex. It is also known that there are connected graphs where 7 longest paths do not share a common vertex. It was conjectured that any three longest paths in a connected graph have a vertex in common. In this note we prove the conjecture for outerplanar graphs and give sufficient conditions for the conjecture to hold in ...

Many Empty Triangles have a Common Edge

Given a finite point set X in the plane, the degree of a pair {x, y} ⊂ X is the number of empty triangles t = conv{x, y, z}, where empty means t∩X = {x, y, z}. Define degX as the maximal degree of a pair in X. Our main result is that if X is a random sample of n independent and uniform points from a fixed convex body, then degX ≥ cn/ lnn in expectation.

Is Aflatoxin More in the Milk of Lactating Mothers Who Have Previously Had COVID-19?

Background: Breast milk provides the ideal nutrition for infants. It has a nearly perfect mix of vitamins, protein, and fat. Breastfeeding has many health benefits for both the mother and infant. Breast milk contains all the nutrients an infant needs in the first six months of life. The present study aimed to measure aflatoxin M1 (AFM1) levels in breast milk and identify nutritional and socio-d...

Are Those with Darker Personality Traits more Willing to Corrupt When They Feel Anxious?

This unprecedented research endeavors to investigate the relationship between dark personality traits (i.e., narcissism, Machiavellianism, and psychopathy) and corruption intention through the mediation of anxiety.  Based on the resource conservation theory, it is hypothesized that those higher in dark personality traits are more inclined to corrupt when they feel anxious. Having collected data...