A greatest element of a partially ordered subset must not be confused with maximal elements of the set, which are elements that are not smaller than any other elements.A set can have several maximal elements without having a greatest element.However, if it has a greatest element, it can't have any other maximal element.…

A being's excellence in a particular world depends only on its properties in that world; a being's greatness depends on its properties in all worlds.Therefore, the greatest possible being must have maximal excellence in every possible world.Plantinga then restated Malcolm's argument, using the concept of "maximal greatness".…

The maximal order question can be examined at a local field level.This technique is applied in algebraic number theory and modular representation theory.…

The corner strength is defined as the smallest SSD between the patch and its neighbors (horizontal, vertical and on the two diagonals).If this number is locally maximal, then a feature of interest is present.As pointed out by Moravec, one of the main problems with this operator is that it is not isotropic: if an edge is present that is not in the direction of the neighbours, then the smallest SSD will be large and the edge will be incorrectly chosen as an interest point.…

Congenital hemangioma can be distinguished from infantile hemangioma because it is fully developed at birth.It forms during prenatal life and has reached its maximal size at birth.Congenital hemangioma can even be diagnosed in utero by prenatal ultrasound.…

We will now assign to each remaining edge e a word in F n in the following way.Consider the closed path starting with e and then going back to the origin of e in the maximal tree.Composing this path with f we get a closed path in a bouquet of n circles and hence an element in its fundamental group F n, This element is not well defined; if we change f by a free homotopy we obtain another element.…

Service life is a unique commitment made by the item's manufacturer and is usually specified as a median.Actual service life is the maximal recorded life of a product.…

Chief series can be thought of as breaking the group down into simple pieces which may be used to characterize various qualities of the group.A chief series is a maximal normal series for a group.Equivalently, a chief series is a composition series of the group G under the action of inner automorphisms.…

If R is a commutative ring and m is a maximal ideal, then the residue field is the quotient ring k = R/m, which is a field.Frequently, R is a local ring and m is then its unique maximal ideal.…

The maximal ice age on the current shelf dates from only two hundred years ago.The speed of Crane Glacier increased threefold after the collapse of the Larsen B and this is likely to be due to the removal of a buttressing effect of the ice shelf.…

A set can have several maximal elements without having a greatest element.However, if it has a greatest element, it can't have any other maximal element.In a totally ordered set both terms coincide; it is also called maximum; in the case of function values it is also called the absolute maximum, to avoid confusion with a local maximum.…

One of the most common is in the proof that the axiom of choice implies Zorn's lemma.We first prove it for the case where X is chain complete and has no maximal element.…

Now consider the set S of all sets that contain at most ten natural numbers.The set S has many maximal elements, i.e. elements for which there is no greater element.In fact, all sets with ten elements are maximal.…

Maxima and minima can also be defined for sets.In general, if an ordered set S has a greatest element m, m is a maximal element.Furthermore, if S is a subset of an ordered set T and m is the greatest element of S with respect to order induced by T, m is a least upper bound of S in T. The similar result holds for least element, minimal element and greatest lower bound.…

A force line represents graphically the internal force acting within a body across imaginary internal surfaces.The force lines show the maximal internal forces and their directions.…

In cryptography he is known for his contributions showing that any one-way function can be used as the basis for private cryptography, and for his analysis, in collaboration with Charles Rackoff, of the Feistel cipher construction.His distributed algorithm to find a maximal independent set in a computer network has also been very influential.He has also contributed to average-case complexity.…

In the dark it will be the same at first, but will approach the maximum distance for a wide pupil 3 to 8 mm.In any human age group there is however considerable variation in maximal pupil size.For example, at the peak age of 15, the dark-adapted pupil can vary from 4 mm to 9 mm with different individuals.…

Functions should be divided into atomic units to allow for maximal re-composition freedom.A fundamental concept of Control theory, the closed control loop, is among the fundamental principles of autonomic networking.…

Since miglitol works by preventing digestion of carbohydrates, it lowers the degree of postprandial hyperglycemia.It must be taken at the start of main meals to have maximal effect.Its effect will depend on the amount of non-monosaccharide carbohydrates in a person's diet.…

An independent set that is not the subset of another independent set is called maximal.