ARC (file format)

ARC is a lossless data compression and archival format by System Enhancement Associates (SEA). It was very popular during the early days of networked dial-up BBS. The file format and the program were both called ARC. The ARC program made obsolete the previous use of a combination of the SQ program to compress files and the LU program to create .LBR archives, by combining both compression and archiving functions into a single program. Unlike ZIP, ARC is incapable of compressing entire directory trees. The format was subject to controversy in the 1980s—an important event in debates over what would later be known as open formats.

The .arc file extension is often used for several file archive-like file types. For example, the Internet Archive uses its own ARC format to store multiple web resources into a single file. The FreeArc archiver also uses .arc extension, but uses a completely different file format.

Nintendo uses an unrelated 'ARC' format for resources, such as MIDI, voice samples, or text, in GameCube and Wii games. Several unofficial extractors exist for this type of ARC file.

Arc (projective geometry)

A (simple) arc in finite projective geometry is a set of points which satisfies, in an intuitive way, a feature of curved figures in continuous geometries. Loosely speaking, they are sets of points that are far from "line-like" in a plane or far from "plane-like" in a three-dimensional space. In this finite setting it is typical to include the number of points in the set in the name, so these simple arcs are called k-arcs. An important generalization of the k-arc concept, also referred to as arcs in the literature, are the (k, d)-arcs.

k-arcs in a projective plane

In a finite projective plane π (not necessarily Desarguesian) a set A of k (k ≥ 3) points such that no three points of A are collinear (on a line) is called a k - arc. If the plane π has order q then k ≤ q + 2, however the maximum value of k can only be achieved if q is even. In a plane of order q, a (q + 1)-arc is called an oval and, if q is even, a (q + 2)-arc is called a hyperoval.

Every conic in the Desarguesian projective plane PG(2,q), i.e., the set of zeros of an irreducible homogeneous quadratic equation, is an oval. A celebrated result of Beniamino Segre states that when q is odd, every (q + 1)-arc in PG(2,q) is a conic. This is one of the pioneering results in finite geometry.

Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph, or set of vertices connected by edges, where the edges have a direction associated with them. In formal terms, a directed graph is an ordered pair G = (V, A) (sometimes G = (V, E)) where

It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called edges, arcs, or lines.

A directed graph is called a simple digraph if it has no multiple arrows (two or more edges that connect the same two vertices in the same direction) and no loops (edges that connect vertices to themselves). A directed graph is called a directed multigraph or multidigraph if it may have multiple arrows (and sometimes loops). In the latter case the arrow set forms a multiset, rather than a set, of ordered pairs of vertices.

Sim (Korean surname)

Sim or Shim is a Korean surname. There are six Shim clans in Korea based in the regions ofCheongsong, Pungsan, Samcheok, Buyu, Uiryeong, and Jeonju. The biggest Sim clan is Cheongsong; they comprise about 85% of the all those with the surname Shim. Fourteen percent of all Korean Shims are members of the Pungsan and Samcheok clans. As of 2000, there were 252,255 people with this surname in South Korea, less than 1% of the population.

List of famous people

Sim (album)

Sim is the third album by Brazilian singer-songwriter Vanessa da Mata, released on May 28, 2007 by Sony BMG. It was partially recorded at Kingston, Jamaica with musicians Sly & Robbie. It spawned the hit single "Boa Sorte/Good Luck", a duet with Ben Harper, which peaked at number one in both Brazil and Portugal, and was the most played song in Brazilian radio stations in the year of 2008. The second single, "Amado", also became a number-one hit in Brazil and the 15th most played song in the same year.

Track listing

Sim (pencil game)

The game of Sim is played by two players on a board consisting of six dots ('vertices'). Each dot is connected to every other dot by a line ('edge').

Two players take turns coloring any uncolored lines. One player colors in one color, and the other colors in another color, with each player trying to avoid the creation of a triangle made solely of their color (only triangles with the dots as corners count; intersections of lines are not relevant); the player who completes such a triangle loses immediately.

Ramsey theory can also be used to show that no game of Sim can end in a tie. Specifically, since the Ramsey number R(3,3)=6, any two-coloring of the complete graph on 6 vertices (K₆) must contain a monochromatic triangle, and therefore is not a tied position. This will also apply to any super-graph of K₆. For another proof that there must eventually be a triangle of either color, see the Theorem on friends and strangers.

Computer search has verified that the second player can win Sim with perfect play, but finding a perfect strategy that humans can easily memorize is an open problem.