17 citations · 64 across the 29 of their papers we have counts for
6 papers · 1 filter
An order-refined and generalized version of the Erdos-Szekeres theorem on convex polygons
Iosif Pinelis
The Erdos-Szekeres theorem states that for any natural k there is a natural number g(k) such that any set of at least g(k) points on a plane in general position contains a set of k…
L'Hospital-type rules for monotonicity and limits: Discrete case
Iosif Pinelis
Assuming that a "derivative" ratio rho:=f'/g' of the ratio r:=f/g of differentiable functions f and g is monotonic (that is, rho is increasing or decreasing), it was shown in previ…
"Non-strict" l'Hospital-Type Rules for Monotonicity: Intervals of Constancy
Iosif Pinelis
Assuming that a "derivative" ratio rho:=f'/g' of the ratio r:=f/g of differentiable functions f and g is strictly monotonic (that is, rho is increasing or decreasing), it was shown…
Convexity of Sub-polygons of Convex Polygons
Iosif Pinelis
A convex polygon is defined as a sequence (V_0,...,V_{n-1}) of points on a plane such that the union of the edges [V_0,V_1],..., [V_{n-2},V_{n-1}], [V_{n-1},V_0] coincides with the…
Polygon Convexity: A Minimal O(n) Test
Iosif Pinelis
An O(n) test for polygon convexity is stated and proved. It is also proved that the test is minimal in a certain exact sense.
Student's t-test without symmetry conditions
Iosif Pinelis
An explicit representation of an arbitrary zero-mean distribution as the mixture of (at-most-)two-point zero-mean distributions is given. Based in this representation, tests for (i…