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.

Destroyer

In naval terminology, a destroyer is a fast maneuverable long-endurance warship intended to escort larger vessels in a fleet, convoy or battle group and defend them against smaller powerful short-range attackers. They were originally developed in the late 19th century as a defence against torpedo boats, and by the time of the Russo-Japanese War in 1904, these "torpedo boat destroyers" (TBD) were "large, swift, and powerfully armed torpedo boats designed to destroy other torpedo boats." Although the term "destroyer" had been used interchangeably with "TBD" and "torpedo boat destroyer" by navies since 1892, the term "torpedo boat destroyer" had been generally shortened to simply "destroyer" by nearly all navies by the First World War.

Before World War II, destroyers were light vessels with little endurance for unattended ocean operations; typically a number of destroyers and a single destroyer tender operated together. After the war, the advent of the guided missile allowed destroyers to take on the surface combatant roles previously filled by battleships and cruisers. This resulted in larger and more powerful guided missile destroyers more capable of independent operation.

Destroyer (Thor)

The Destroyer is a fictional object appearing in American comic books published by Marvel Comics. The Destroyer is usually depicted as an opponent to Thor. It is a suit of Asgardian armor, animated by magic, which first appears in Journey into Mystery #118 (Jul. 1965) and was created by Stan Lee and Jack Kirby.

Debuting in the Silver Age of Comic Books, the Destroyer is featured in over four decades of Marvel continuity and other Marvel-endorsed products such as animated television series, live-action films, video games, and merchandise such as action figures and trading cards. Due to trademark issues, at least one toy version of this character is marketed as Marvel's Destroyer.

Fictional history

Destroyer (Kiss album)

Destroyer is the fourth studio album by American rock band Kiss, released on March 15, 1976 in the US. It was the third successive Kiss album to reach the top 40 in the US, as well as the first to chart in Germany and New Zealand. The album was certified gold by the RIAA on April 22, 1976, and platinum on November 11 of the same year, the first Kiss album to achieve platinum. The album marked a departure from the raw sound of the band's first three albums.

Album information

After attaining modest commercial success with their first three studio albums, Kiss achieved a commercial breakthrough with the 1975 concert album Alive!. It was the first album by the band to be certified gold, and eventually went multi-platinum. The success of Alive!, which spent 110 weeks on the charts, benefited not only the struggling band but their cash-strapped label Casablanca Records. Kiss signed a new contract with Casablanca in late 1975, partly because the label had been very supportive from the start of the band's career. The contract was for two albums, an indication that Casablanca was unsure if the group could duplicate the accomplishments of Alive!.