Among the first 101 elements in the periodic table, only francium is less stable.

A more numerically stable two-pass algorithm first computes the sample means, and then the covariance:

Even greater accuracy can be achieved by first computing the means, then using the stable one-pass algorithm on the residuals.

After the team had developed a method of purifying penicillin to an effective first stable form in 1940, several clinical trials ensued, and their amazing success inspired the team to develop methods for mass production and mass distribution in 1945.

But the study of these curves was first developed in 1959 by mathematician Paul de Casteljau using de Casteljau's algorithm, a numerically stable method to evaluate Bézier curves.

Of the 118 known elements, only the first 98 are known to occur naturally on Earth ; 80 of them are stable, while the others are radioactive, decaying into lighter elements over various timescales from fractions of a second to billions of years.

The first proposed catalytic cycle for the conversion of hydrogen into helium was at first simply called the carbon – nitrogen cycle ( CN cycle ), also honorarily referred to as the Bethe – Weizsäcker cycle, because it does not involve a stable isotope of oxygen.

The first clinical trial, involving 30 women with breast cancer, combined insulin with low-dose methotrexate ( a common chemotherapy drug ) resulted in greatly increased stable disease, and much reduced progressive disease, compared with insulin or low-dose methotrexate alone.

Even before the Declaration of Boulogne, the language was remarkably stable ; only one set of lexical changes were made in the first year after publication, namely changing " when ", " then ", " never ", " sometimes ", " always " from kian, tian, nenian, ian, ĉian to kiam, tiam, neniam etc., to avoid confusion with the accusative forms of kia " what sort of ", tia " that sort of ", etc.

The first two years of Cerezo's administration were characterized by a stable economy and a marked decrease in political violence.

In 2009, scientists in Japan announced that they had successfully transferred a gene into a primate species ( marmosets ) and produced a stable line of breeding transgenic primates for the first time.

Programming on GnuCash began in 1997, and its first stable release was in 1998.

GDB was first written by Richard Stallman in 1986 as part of his GNU system, after his GNU Emacs was " reasonably stable ".

Many minor problems that existed in the first edition were fixed making it, according to many, the most stable release of the Windows 9x family.

The stable block is a large building built mostly in stone, but with a timber-framed, decoratively panelled first storey designed in an anachronistic, vernacular style.

Major League Baseball returned to the city in 1969 with the Royals, who have proven stable and became the first American League expansion team to reach the playoffs, in 1976, the World Series, in 1980 and to win the World Series, in 1985 against the state-rival St. Louis Cardinals in the " Show-Me Series.

The first three Lagrangian points are technically stable only in the plane perpendicular to the line between the two bodies.

If the spacecraft started to reenter nose first ( another stable reentry attitude for the spacecraft ), airflow over the spoiler would flip the spacecraft around to the proper, heatshield-first reentry attitude, a technique called shuttlecocking.

The first stable compound of argon was reported in 2000 when argon fluorohydride ( HArF ) was formed at a temperature of.

Though not understood at the time by Thomson, this was the first discovery of isotopes of stable atoms.

The first evidence for isotopes of a stable element.

Mieszko I, the first historically recorded ruler of the Polans, and of the early Polish state which they dominated, built one of his main stable headquarters in Poznań.

") He soon became the pastor and overseer of the Brethren meeting, at first over a stable but shortly, under Gosse's preaching and peacemaking, in finer quarters — which he perhaps financed himself.

J. Desaulx suggested in 1877 that the phenomenon was caused by the thermal motion of water molecules, and in 1905 Albert Einstein produced the first mathematical analysis of the motion.

Newton was the first to develop a mathematical model for calculating the speed of sound, but it was not correct until Pierre-Simon Laplace accounted for the molecular behavior of gases and introduced the heat capacity ratio.

The term " Bayesian " refers to the 18th century mathematician and theologian Thomas Bayes, who provided the first mathematical treatment of a non-trivial problem of Bayesian inference.

There are many anecdotes about his precocity while a toddler, and he made his first ground-breaking mathematical discoveries while still a teenager.

The mathematical properties of the catenary curve were first studied by Robert Hooke in the 1670s, and its equation was derived by Leibniz, Huygens and Johann Bernoulli in 1691.

It was first thought to be a tally stick, as it has a series of what has been interpreted as tally marks carved in three columns running the length of the tool, but some scientists have suggested that the groupings of notches indicate a mathematical understanding that goes beyond counting.

Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.

The Clay Mathematics Institute has offered a $ 1 million USD prize for the first correct proof, along with prizes for six other mathematical problems.

In probability theory, the expected value ( or expectation, or mathematical expectation, or mean, or the first moment ) of a random variable is the weighted average of all possible values that this random variable can take on.

Ken Thompson's versions of qed were the first to implement regular expressions, an idea that had previously been formalized in a mathematical paper, which Ken Thompson had read.

The prevailing opinion at the time was that one should first write a program and then provide a mathematical proof of correctness.

A few years later, Peano published his first book dealing with mathematical logic.

In his exposition, he acknowledged the existence of what are now called imaginary numbers, although he did not understand their properties ( described for the first time by his Italian contemporary Rafael Bombelli, although mathematical field theory was developed centuries later ).

In 1905, Henri Poincaré was the first to recognize that the transformation has the properties of a mathematical group,

This philosophy, poorly understood at first, stated that in order for a mathematical statement to be true to a mathematician, that person must be able to intuit the statement, to not only believe its truth but understand the reason for its truth.

The first example of this is a mathematical proof of the confinement mechanisms in EROS, based on a simplified model of the EROS API.

Newton's three laws of motion, along with his law of universal gravitation, explain Kepler's laws of planetary motion, which were the first to accurately provide a mathematical model or understanding orbiting bodies in outer space.

The first complete mathematical formulation of this approach is generally credited to John von Neumann's 1932 book Mathematical Foundations of Quantum Mechanics, although Hermann Weyl had already referred to Hilbert spaces ( which he called unitary spaces ) in his 1927 classic paper and book.

A practical method for investigating neutrino oscillations was first suggested by Bruno Pontecorvo in 1957 using an analogy with kaon oscillations ; over the subsequent 10 years he developed the mathematical formalism and the modern formulation of vacuum oscillations.

By revealing ( in modern terms ) that numbers could be irrational, this discovery seems to have provoked the first foundational crisis in mathematical history ; its proof or its divulgation are sometimes credited to Hippasus, who was expelled or split from the Pythagorean sect.

David Diringer noted that " the first mention of Egyptian documents written on leather goes back to the Fourth Dynasty ( c. 2550-2450 BCE ), but the earliest of such documents extant are: a fragmentary roll of leather of the Sixth Dynasty ( c. twenty-fourth century BCE ), unrolled by Dr. H. Ibscher, and preserved in the Cairo Museum ; a roll of the Twelfth Dynasty ( c. 1990-1777 BCE ) now in Berlin ; the mathematical text now in the British Museum ( MS. 10250 ); and a document of the reign of Ramses II ( early thirtheenth century BCE ).".

The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance.

The first attempt at mathematical rigour in the field of probability, championed by Pierre-Simon Laplace, is now known as the classical definition.

Since the first two were existential axioms, Russell phrased mathematical statements depending on them as conditionals.