Partition of an interval

In mathematics, a partition of an interval [a, b] on the real line is a finite sequence x = ( x_i ) of real numbers such that

In other terms, a partition of a compact interval I is a strictly increasing sequence of numbers (belonging to the interval I itself) starting from the initial point of I and arriving at the final point of I.

Every interval of the form [x_i, x_i+1] is referred to as a sub-interval of the partition x.

Refinement of a partition

Another partition of the given interval, Q, is defined as a refinement of the partition, P, when it contains all the points of P and possibly some other points as well; the partition Q is said to be “finer” than P. Given two partitions, P and Q, one can always form their common refinement, denoted P ∨ Q, which consists of all the points of P and Q, re-numbered in order.

Norm of a partition

The norm (or mesh) of the partition

is the length of the longest of these subintervals, that is

Applications

Partitions are used in the theory of the Riemann integral, the Riemann–Stieltjes integral and the regulated integral. Specifically, as finer partitions of a given interval are considered, their mesh approaches zero and the Riemann sum based on a given partition approaches the Riemann integral.

Mesh (disambiguation)

Mesh is a type of material.

Mesh or MESH may also refer to:

In science and mathematics

In computing

In popular culture

In medicine

Meš

The cuneiform MEŠ, or meš is a plural form attached at the end of Mesopotamian cuneiform words as a suffix. As part of a name (PN, personal name, or other), or major class being referenced, in capital letters (a sumerogram form), it is typically separated from other capital letter sumerograms with a period. The name of the group can follow, in lower case letters, for example: (men-massu, Amarna letter EA 365), LÚ.MEŠ–ma-as-sà-meš, (and using a secondary suffix meš, not being typical).

The MEŠ cuneiform is a vertical stroke, followed by three or four angled smaller wedge-strokes. The strokes can also be "not angled", but 45 degree wedges, smaller, or large. For example, Amarna letter EA 161, Aziru to Pharaoh, shows a series of six preparation items listed sequentially. The following wedges (on the meš or sumerogram .MEŠ wedges, are large, and the scribe has a scribing base line, that follows the vertical stroke, a baseline on which the wedges are placed sequentially. EA 161 shows the baseline 'remainder', extending beyond the last 3rd, or 4th wedge.

Day (automobile)

The Day Utility was an automobile manufactured in Detroit, Michigan by the Day Automobile Company from 1911-14. The Day used a four-cylinder, 30 horsepower (22 kW) engine and shaft drive. Removal of the rear seat and doors allowed the car to be converted from a five-seater touring car to a light truck in one minute. As a truck, the Day was able to carry up to 1,000 lb (450 kg) in a 36-inch (910 mm) by 96-inch (2,400 mm) cargo space. The rear seat could be lifted away by triggering two spring locks. The Day had an advertised price of $950US.

References

Day (Michelangelo)

Day is a marble sculpture by Michelangelo, datable to 1526–31. It is a pair with Night on the tomb of Giuliano de' Medici in the Medici Chapel in San Lorenzo in Florence.

External links

Day (surname)

Day is a surname. Notable people with the surname Day include:

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