Sigmoid colon | EPFL Graph Search

The sigmoid colon (or pelvic colon) is the part of the large intestine that is closest to the rectum and anus. It forms a loop that averages about in length. The loop is typically shaped like a Greek letter sigma (ς) or Latin letter S (thus sigma + -oid). This part of the colon normally lies within the pelvis, but due to its freedom of movement it is liable to be displaced into the abdominal cavity. The sigmoid colon begins at the superior aperture of the lesser pelvis, where it is continuous with the iliac colon, and passes transversely across the front of the sacrum to the right side of the pelvis. It then curves on itself and turns toward the left to reach the middle line at the level of the third piece of the sacrum, where it bends downward and ends in the rectum. Its function is to expel solid and gaseous waste from the gastrointestinal tract. The curving path it takes toward the anus allows it to store gas in the superior arched portion, enabling the colon to expel gas without excreting faeces simultaneously. The sigmoid colon is completely surrounded by peritoneum (and thus is not retroperitoneal), which forms a mesentery (sigmoid mesocolon), which diminishes in length from the center toward the ends of the loop, where it disappears, so that the loop is fixed at its junctions with the iliac colon and rectum, but enjoys a considerable range of movement in its central portion. Pelvic splanchnic nerves are the primary source for parasympathetic innervation. Lumbar splanchnic nerves provide sympathetic innervation via the inferior mesenteric ganglion. Behind the sigmoid colon are the external iliac vessels, ovary, obturator nerve, the left Piriformis, and left sacral plexus of nerves. In front, it is separated from the bladder in the male, and the uterus in the female, by some coils of the small intestine. Diverticulosis often occurs in the sigmoid colon in association with increased intraluminal pressure and focal weakness in the colonic wall. It is a common cause of hematochezia.

A new elementary proof of the Prime Number Theorem

Florian Karl Richter

Let

\Omega(n)

denote the number of prime factors of

n

. We show that for any bounded

f\colon\mathbb{N}\to\mathbb{C}

one has [ \frac{1}{N}\sum_{n=1}^N, f(\Omega(n)+1)=\frac{1}{N}\sum_{n=1}^N, f(\Omega(n))+\mathrm{o}_{N\to\infty}(1). ] This yields a ...

2021