Sea snakeSea snakes, or coral reef snakes, are elapid snakes that inhabit marine environments for most or all of their lives. They belong to two subfamilies, Hydrophiinae and Laticaudinae. Hydrophiinae also includes Australasian terrestrial snakes, whereas Laticaudinae only includes the sea kraits (Laticauda), of which three species are found exclusively in freshwater. If these three freshwater species are excluded, there are 69 species of sea snakes divided between seven genera.
Stirling numbers of the first kindIn mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations. In particular, the Stirling numbers of the first kind count permutations according to their number of cycles (counting fixed points as cycles of length one). The Stirling numbers of the first and second kind can be understood as inverses of one another when viewed as triangular matrices. This article is devoted to specifics of Stirling numbers of the first kind.
Dirichlet's approximation theoremIn number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real numbers and , with , there exist integers and such that and Here represents the integer part of . This is a fundamental result in Diophantine approximation, showing that any real number has a sequence of good rational approximations: in fact an immediate consequence is that for a given irrational α, the inequality is satisfied by infinitely many integers p and q.
Stirling's approximationIn mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. One way of stating the approximation involves the logarithm of the factorial: where the big O notation means that, for all sufficiently large values of , the difference between and will be at most proportional to the logarithm.
Stirling numbers of the second kindIn mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by or . Stirling numbers of the second kind occur in the field of mathematics called combinatorics and the study of partitions. They are named after James Stirling. The Stirling numbers of the first and second kind can be understood as inverses of one another when viewed as triangular matrices.
Real numberIn mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives.
Snake venomSnake venom is a highly toxic saliva containing zootoxins that facilitates in the immobilization and digestion of prey. This also provides defense against threats. Snake venom is injected by unique fangs during a bite, whereas some species are also able to spit venom. The glands that secrete zootoxins are a modification of the parotid salivary glands found in other vertebrates and are usually located on each side of the head, below and behind the eye, and enclosed in a muscular sheath.
Snake charmingSnake charming is the practice of appearing to hypnotize a snake (often a cobra) by playing and waving around an instrument called a pungi. A typical performance may also include handling the snakes or performing other seemingly dangerous acts, as well as other street performance staples, like juggling and sleight of hand. The practice was historically the profession of some tribesmen in India well into the 20th century but snake charming declined rapidly after the government banned the practice in 1972.
Basis (linear algebra)In mathematics, a set B of vectors in a vector space V is called a basis (: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called . Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.
