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The lesser curvature of the stomach forms the upper right or medial border of the stomach. [3] The lesser curvature of the stomach travels between the cardiac and pyloric orifices . It descends as a continuation of the right margin of the esophagus in front of the fibers of the right crus of the diaphragm , and then, turning to the right, it ...
This definition is equivalent to the definition of convex curves from support lines. Every convex curve, defined as a curve with a support line through each point, is a subset of the boundary of its own convex hull. Every connected subset of the boundary of a convex set has a support line through each of its points. [8] [9] [19]
Lordosis is historically defined as an abnormal inward curvature of the lumbar spine. [1] [2] However, the terms lordosis and lordotic are also used to refer to the normal inward curvature of the lumbar and cervical regions of the human spine. [3] [4] Similarly, kyphosis historically refers to abnormal convex curvature of the spine
The abdominal aorta begins at the level of the diaphragm, crossing it via the aortic hiatus, technically behind the diaphragm, at the vertebral level of T12. [1] It travels down the posterior wall of the abdomen, anterior to the vertebral column. It thus follows the curvature of the lumbar vertebrae, that is, convex anteriorly.
The two layers of the greater omentum descend from the greater curvature of the stomach and the beginning of the duodenum. [2] They pass in front of the small intestines, sometimes as low as the pelvis, before turning on themselves, and ascending as far as the transverse colon, where they separate and enclose that part of the intestine. [2]
A function f is concave over a convex set if and only if the function −f is a convex function over the set. The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield.
The term convex is often referred to as convex down or concave upward, and the term concave is often referred as concave down or convex upward. [ 3 ] [ 4 ] [ 5 ] If the term "convex" is used without an "up" or "down" keyword, then it refers strictly to a cup shaped graph ∪ {\displaystyle \cup } .
Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.