Periodic sequence

In mathematics, a periodic sequence (sometimes called a cycle) is a sequence for which the same terms are repeated over and over:

The number p of repeated terms is called the period (period).

Definition

A periodic sequence is a sequence a₁, a₂, a₃, ... satisfying

for all values of n. If we regard a sequence as a function whose domain is the set of natural numbers, then a periodic sequence is simply a special type of periodic function.

Examples

The sequence of digits in the decimal expansion of 1/7 is periodic with period six:

More generally, the sequence of digits in the decimal expansion of any rational number is eventually periodic (see below).

The sequence of powers of −1 is periodic with period two:

More generally, the sequence of powers of any root of unity is periodic. The same holds true for the powers of any element of finite order in a group.

A periodic point for a function ƒ: X → X is a point p whose orbit

is a periodic sequence. Periodic points are important in the theory of dynamical systems. Every function from a finite set to itself has a periodic point; cycle detection is the algorithmic problem of finding such a point.

Sequence (game)

Sequence, a board-and-card game, was invented by Douglas Reuter in Minneapolis, Minnesota, over a two-year period in the 1970s. Mr. Reuter originally called the game, "Sequence Five". Reuter spent years developing the concept, and, in June 1981, granted Jax Ltd. an exclusive license to manufacture, distribute and sell the board game, Sequence, and its subsequent variations. The game was first sold in a retail store in 1982.

Gameplay

Objective

The object of the game is to form rows of five poker chips on the board by placing the chips on the board spaces corresponding to cards played from your hand.

Equipment

Playing Board (19-3/4” x 15-1/4”); Instructions; 135 poker chips (50 blue, 50 green, 35 red); two full standard card decks (52 cards each, 104 cards total, no Jokers)

Directions

Sequence can be played with two to 12 players, so long as the number of players is divisible by two or three (i.e., not 5, 7 or 11). If there are more than three individual players, they should divide evenly into two or three teams (up to three teams of four players). With two teams, players alternate their physical positions with opponents around the playing surface. With three teams, players of a team must be positioned at every third player around the playing surface.

The Sequence

The Sequence was a female old school hip hop trio signed to the Sugar Hill label in the late-1970s and early-1980s. The group consisted of Cheryl Cook (Cheryl The Pearl), Gwendolyn Chisolm (Blondie), and lead singer/rapper Angie Brown Stone (Angie B.). The group originated from Columbia, South Carolina as a group of high school cheerleaders.

Their most notable single was "Funk You Up" (1979), which was the first rap record released by a female group and the second single released by Sugar Hill Records. Elements of "Funk You Up" were later used by Dr. Dre for his 1995 single "Keep Their Heads Ringin'".

The group backed Spoonie Gee on the single "Monster Jam" (1980). Their single "Funky Sound (Tear the Roof Off)" (1981) was a remake of the single "Give Up the Funk (Tear the Roof off the Sucker)" (1976) by Parliament. The groups other charting single was "I Don't Need Your Love (Part One)" (1982). Angie Stone subsequently became a member of Vertical Hold and later a solo artist. In September 2011, without Angie Stone, Cheryl Cook and Gwendolyn Chisolm released a single entitled "On Our Way to the Movies". "On Our Way to the Movies" contains a sample of The Staple Singers' song "Let's Do It Again"

Sequence (2013 film)

Sequence is a 2013 short fantasy horror film written and directed by Carles Torrens, and starring Joe Hursley, Emma Fitzpatrick, and Ronnie Gene Blevins. The film premiered September 6, 2013, at the Los Angeles International Short Film Festival.

Plot

Billy (Joe Hursley) wakes up one morning only to discover that everyone else in the world had a disturbing nightmare about him the night before. He finds a suspicions note on his car simply saying "You're it" and each person he meets has fearful, strange, or hostile reactions to seeing him in person after their dreams. Billy is unable to find anyone willing tell him the contents of their dream. After a bitter attack by another, Billy wakes with a start in his own bed and realizes that the days events were themselves a nightmare of his own, itself shared by everyone else in the world. But the sequence continues.

Main cast

Cycle (film)

Cycle is a 2008 Indian Malayalam film directed by Johny Antony and written by James Albert, starring Vineeth Sreenivasan, Vinu Mohan, Sandhya, Bhama, and Jagathy Sreekumar. The tale is about two friends, Roy (Vineeth Sreenivasan) and Sanju (Vinu Mohan), struggling to make both ends meet with their low salaries, working respectively as a cashier in a private finance company and as a salesman in an electronics goods shop. It was a box office success.

Synopsis

The film, set at City Centre, a shopping mall in Kochi as backdrop, is all about a few youngsters, Roy and Sanju and their love interests, Annie and Meenakshy. Long-ignored and mistreated by society for reasons none of theirs, they decide to take matters into their own hands. Roy (Vineeth Sreenivasan) is an accountant in a private financing company of Kaustubhan, (deftly played with ease and characteristic gags by Jagathy) who pays his staff, the modest of all salaries. Sanju (Vinu Mohan) is a desperate cricketer, left out of Ranji team, who is working in the same commercial mall in an electronics shop. Roy has a soft corner for Annie (Bhama) who works as a receptionist in a travel agency in the same complex. And Meenakshy (Sandhya), the daughter of Kaushtubhan, is madly in love, always chasing Sanju.

Cycle (graph theory)

In graph theory, there are several different types of object called cycles, principally a closed walk and a simple cycle; also, e.g., an element of the cycle space of the graph.

A closed walk consists of a sequence of vertices starting and ending at the same vertex, with each two consecutive vertices in the sequence adjacent to each other in the graph. In a directed graph, each edge must be traversed by the walk consistently with its direction: the edge must be oriented from the earlier of two consecutive vertices to the later of the two vertices in the sequence. The choice of starting vertex is not important: traversing the same cyclic sequence of edges from different starting vertices produces the same closed walk.

A simple cycle may be defined either as a closed walk with no repetitions of vertices and edges allowed, other than the repetition of the starting and ending vertex, or as the set of edges in such a walk. The two definitions are equivalent in directed graphs, where simple cycles are also called directed cycles: the cyclic sequence of vertices and edges in a walk is completely determined by the set of edges that it uses. In undirected graphs the set of edges of a cycle can be traversed by a walk in either of two directions, giving two possible directed cycles for every undirected cycle. (For closed walks more generally, in directed or undirected graphs, the multiset of edges does not unambiguously determine the vertex ordering.) A circuit can be a closed walk allowing repetitions of vertices but not edges; however, it can also be a simple cycle, so explicit definition is recommended when it is used.

Cycle (album)

Cycle is an album by the Japanese noise musician Merzbow. It features recordings of Masami Akita's pet chickens. Material from this album was performed live at Radio Nova in Oslo, which was released as Mini Cycle / Yoshino Tamago / Yonos Bigfoot.

Track listing

All music composed by Masami Akita.

Personnel

References