Recursion occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic; the most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this defines an infinite number of instances, it is done in such a way that no infinite loop or infinite chain of references can occur. In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties: A simple base case — a terminating scenario that does not use recursion to produce an answer A recursive step — a set of rules that reduces all other cases toward the base caseFor example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent's ancestor; the Fibonacci sequence is another classic example of recursion: Fib = 0 as base case 1, Fib = 1 as base case 2, For all integers n > 1, Fib:= Fib + Fib.
Many mathematical axioms are based upon recursive rules. For example, the formal definition of the natural numbers by the Peano axioms can be described as: "Zero is a natural number, each natural number has a successor, a natural number." By this base case and recursive rule, one can generate the set of all natural numbers. Other recursively defined mathematical objects include factorials, functions and fractals. There are various more tongue-in-cheek definitions of recursion. Recursion is the process a procedure goes through when one of the steps of the procedure involves invoking the procedure itself. A procedure that goes through recursion is said to be'recursive'. To understand recursion, one must recognize the distinction between a procedure and the running of a procedure. A procedure is a set of steps based on a set of rules, while the running of a procedure involves following the rules and performing the steps. Recursion is related to, but not the same as, a reference within the specification of a procedure to the execution of some other procedure.
When a procedure is defined as such, this creates the possibility of an endless loop. But if it is properly defined, a recursive procedure is not easy for humans to perform, as it requires distinguishing the new from the old executed invocation of the procedure. For this reason, recursive definitions are rare in everyday situations. Linguist Noam Chomsky, among many others, has argued that the lack of an upper bound on the number of grammatical sentences in a language, the lack of an upper bound on grammatical sentence length, can be explained as the consequence of recursion in natural language; this can be understood in terms of a recursive definition of a syntactic category, such as a sentence. A sentence can have a structure in which what follows the verb is another sentence: Dorothy thinks witches are dangerous, in which the sentence witches are dangerous occurs in the larger one. So a sentence can be defined recursively as something with a structure that includes a noun phrase, a verb, optionally another sentence.
This is just a special case of the mathematical definition of recursion. This provides a way of understanding the creativity of language—the unbounded number of grammatical sentences—because it predicts that sentences can be of arbitrary length: Dorothy thinks that Toto suspects that Tin Man said that.... There are many structures apart from sentences that can be defined recursively, therefore many ways in which a sentence can embed instances of one category inside another. Over the years, languages in general have proved amenable to this kind of analysis. However, the accepted idea that recursion is an essential property of human language has been challenged by Daniel Everett on the basis of his claims about the Pirahã language. Andrew Nevins, David Pesetsky and Cilene Rodrigues are among many. Literary self-reference can in any case be argued to be different in kind from mathematical or logical recursion. Recursion plays a crucial role not only in syntax, but in natural language semantics; the word and, for example, can be construed as a function that can apply to sentence meanings to create new sentences, for noun phrase meanings, verb phrase meanings, others.
It can apply to intransitive verbs, transitive verbs, or ditransitive verbs. In order to provide a single denotation for it, suitably flexible, is defined so that it can take any of these different types of meanings as arguments; this can be done by defining it for a simple case in which it combines sentences, defining the other cases
Lithophaga lithophaga known as date shell or date mussel, is a species of Bivalvia belonging to the family Mytilidae. Fossils of Lithophaga lithophaga are found in marine strata from the Miocene until the Quaternary; this species can be found in the Mediterranean Sea and the Red Sea. They are found on the Adriatic coast of Montenegro under the name prstaci; these bivalves live in the area battered by the waves, but they can reach depths of 125 to 200 m. They bore into marine rocks, their growth is slow, to reach the 5 cm length, they require 15 to 35 years. They feed on plankton and debris by filtering them from the water, they reach the sexual maturity after about two years. The number of eggs that are released in a season reach about 120,000 to about 4.5 million. The fertilization takes place in the open water. Shells of Lithophaga lithophaga can reach a length of about 8.5 centimetres. They are yellowish or brownish cylindrical, rounded at both ends; the interior is whitish iridescent purple with a pink tinge.
These shells are thin. The surface is nearly smooth, covered with growth lines; the Lithophaga lithophaga's name is derived from the Greek word lithos: meaning rock/stone and the Greek word phaga/phago: meaning to eating or devouring. These shells are considered a delicacy and served in a broth of white wine and parsley; the extraction of the shells require dismantling of the rocks where they live and can lead to desertification of the coast. Several governments have restricted the collection of these shells or made it wholly illegal, in order to protect the rocks on which they are found; these countries include Croatia, Slovenia, Greece and others, including participants in the Convention on the Conservation of European Wildlife and Natural Habitats and the Convention on International Trade in Endangered Species of Wild Fauna and Flora. As of 2004, its population distributed over the Turkish coastline is not considered to be under threat
Viper was a roller coaster located at Six Flags Great Adventure in Jackson Township, New Jersey. Manufactured by TOGO, the ride opened to the public in June 1995; the roller coaster closed at the end of the 2004 season and was demolished the following year for various reasons. It was replaced with El Toro. Viper reached a top speed of 48 mph, it had two inversions. The ride ran three trains with four cars per train. Riders were seated two across and each train seated a total of 16 passengers; the trains were colored light green and orange. In 1990, Six Flags Great Adventure had 5 roller coasters, but due to ride rotation programs and the purchase of Batman the Ride, the park was down to only three by the end of 1992. Batman's opening brought the park back up to four coasters in 1993. At that point a decision was made to buy a new coaster for the park; because Ultra Twister, the ride that occupied the site chosen for Viper, was gaining in popularity at its new home park, Six Flags Astroworld, TOGO was hired to design and build a similar coaster to occupy the site that Ultra Twister once stood on.
In September 1994 construction of Viper began. Construction ended in April 1995. In May 1995, Viper shortly closed due to technical difficulties, it ran by June. In 1996, due to its uncomfortable restraints, Viper's popularity began to fade and as a result, the lines shortened. In 1997, the ride did not operate for a majority of the season due to Six Flags having difficulty procuring replacement parts as TOGO experienced financial issues due to problems with Windjammer Surf Racers; the ride was scheduled to reopen on Labor Day of 1998. In 2001, Viper stood shut down throughout the season, being considered "Standing but not operating". Following the closure, Viper was withdrawn from the official website, the park guides, map. Six Flags planned to remove Viper that year, but it was canceled because Six Flags had failed to find a replacement attraction to fit the land occupied by Viper. In 2002, after some modifications on the restraints and track, Viper reopened; the ride continued to be rough and the coaster experienced mechanical issues.
In 2004, Viper operated with one train during normal operations. On Labor Day, Six Flags experienced failed attempts of fixing to ride due to the issues, they decided to permanently shut down the ride. In 2005, demolition for Viper began in May. Multiple issues were found including frequent performance issues with the ride, mechanical issues, big amounts of down time. Nearby rides including Rodeo Stampede and Taz Twister were removed as well to make way for El Toro. In 2006, Six Flags utilized Viper's station for El Toro being the only part of Viper still in use