Most quantitative calculations in modern quantum chemistry use either valence bond or molecular orbital theory as a starting point, although a third approach, Density Functional Theory, has become increasingly popular in recent years.

Omar Khayyám ( 1048 – 1131 ), a Persian scientist, calculated the length of a solar year to 10 decimal places and was only out by a fraction of a second when compared to our modern day calculations.

Katsufumi Sato, a Japanese scientist, did calculations using modern birds and decided that it is impossible for a pterosaur to stay aloft.

Furthermore, most of the calculations performed in modern computational chemistry rely on quantum mechanics.

Despite this, most modern scholars do not consider Dionysius ' calculations authoritative, placing the event several years earlier ( see Chronology of Jesus ).

Some systems ( particularly older, microcode-based architectures ) can also perform various transcendental functions such as exponential or trigonometric calculations, though in most modern processors these are done with software library routines.

Although Newton's theory has been superseded, most modern non-relativistic gravitational calculations are still made using Newton's theory because it is a much simpler theory to work with than general relativity, and gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies.

In particular, many Monte Carlo calculations carried out on modern massively parallel supercomputers are embarrassingly parallel applications, whose results can be very accurate.

In modern process diode leakage is very small compared to sub threshold and tunnelling currents, so these may be neglected during power calculations.

Most modern scholars do not consider Dionysius ' calculations authoritative, placing the event several years earlier ( see Chronology of Jesus ).

The modern Iranian calendar is based on his calculations.

Since the first work by Wigner and Huntington, the more modern theoretical calculations were pointing toward higher but nonetheless potentially accessible metallization pressures.

Gauquelin's work was not limited to the Mars effect: his calculations led him first to reject most of the conventions of natal astrology as it is practised in the modern west but he singled out " highly significant statistical correlations between planetary positions and the birth times of eminently successful people.

Working in collaboration with Sir Ernest Rutherford, he used radioactive decay in minerals to estimate, in 1913, that the beginning of the Devonian period could not be less than 400 million years ago, an estimate which is in line with modern calculations.

While far-field simplifications are very useful in engineering calculations, this does not mean the near-field functions cannot be calculated, especially using modern computer techniques.

According to modern calculations, eight capstans were needed to hoist the 55 t base block, while the length of rope required for the highest drums measured some 210 m assuming two-block pulleys.

Explicit calculations for particular purposes have been known in modern times ( for example Shioda, with the binary octavics ).

Typically, in modern Hartree – Fock calculations, the one-electron wave functions are approximated by a linear combination of atomic orbitals.

However, in most modern computer programs for molecular Hartree – Fock calculations this procedure is not followed due to the high numerical cost of orthogonalization and the advent of more efficient, often sparse, algorithms for solving the generalized eigenvalue problem, of which the Roothaan – Hall equations are an example.

The modern hydraulic engineer uses the same kinds of computer-aided design ( CAD ) tools as many of the other engineering disciplines while also making use of technologies like computational fluid dynamics to perform the calculations to accurately predict flow characteristics, GPS mapping to assist in locating the best paths for installing a system and laser-based surveying tools to aid in the actual construction of a system.

The author claims that results show excellent agreement with six degree of freedom numerical calculations for modern tank ammunition and available published firing tables for center-fired rifle ammunition having a wide variety of shapes and sizes.

Abraham Sperling, director of New York City's Aptitude Testing Institute, allegedly said after Sidis ' death that according to his calculations, Sidis " easily had an IQ between 250 and 300 ", meaning that at some time his intellectual age was 2. 5 to 3 times his actual age ( not the same scale as modern deviation IQ ).

Such calculations are possible on modern computers, but the sheer magnitude of such numbers causes the speed of calculations to slow considerably.

This is certainly an irrational dogmatism, in which the modern mind attempts to understand the spirit of the sixteenth century on twentieth-century terms.

Medieval scholars may be considered forerunners of modern anthropology as well, insofar as they conducted or wrote detailed studies of the customs of peoples considered " different " from themselves in terms of geography.

When making use of modern cultural divisions in the American Southwest, it is important to comprehend that current terms and conventions have significant limitations:

The Analytical Engine incorporated an arithmetic logic unit, control flow in the form of conditional branching and loops, and integrated memory, making it the first design for a general-purpose computer that could be described in modern terms as Turing-complete.

The modern terms " electricity " and " electron " derive from the Greek word for amber, and come from William Gilbert's research showing that amber could attract other substances.

Since the 1970s, self-help books, psychology, and some modern expressions of Christianity have viewed this disparity in terms of grace being an innate quality within all people who must be inspired or strong enough to find it: something to achieve.

He was on uneasy terms with the Catholic bishops of Arelate ( modern Arles ) as epitomized in the career of the Frankish Caesarius, bishop of Arles, who was appointed bishop in 503.

Most modern English grammarians no longer use the Latin accusative / dative model, though they tend to use the terms objective for oblique, subjective for nominative, and possessive for genitive ( see Declension in English ).

One of these was the property, an essential universal true of the species, but not in the definition ( in modern terms, some examples would be grammatical language, a property of man, or a spectral pattern characteristic of an element, both of which are defined in other ways ).

The invention of the bicycle has had an enormous effect on society, both in terms of culture and of advancing modern industrial methods.

The political terms of " modern ", " progressive " or " new " Liberalism began to appear in the mid to late 1880s and became increasingly common to denote the tendency in the Liberal Party to favour an increased role for the state as more important than the classical liberal stress on self-help and freedom of choice.

Hindu religious texts contain account of saints and hermits practicing what would be called inedia, breatharianism or Sustenance through Light in modern terms.

) In reliance on this assumption, modern statutes often leave a number of terms and fine distinctions unstated — for example, a statute might be very brief, leaving the precise definition of terms unstated, under the assumption that these fine distinctions will be inherited from pre-existing common law.

In reality, the terms ' Scots / Scottish ' and ' Irish ' are purely modern geographical references to a people who share a common Celtic ancestry and consequently, a common musical heritage.

His forecast of the form of government suitable to the modern world may be seen as prophetic: the largely ceremonial offices of president in some modern parliamentary democracies in Europe and e. g. Israel can be perceived as elected or appointed versions of Hegel's constitutional monarch ; the Russian and French presidents, with their stronger powers, may also be regarded in Hegelian terms as wielding powers suitable to the embodiment of the national will.

As a result of this loaning, Chinese, Korean, Japanese, and Vietnamese share a corpus of linguistic terms describing modern terminology, paralleling the similar corpus of terms built from Greco-Latin and shared among European languages.

" Several different terms are used in different situations, several of which are of modern origin:

Carl Philipp Gottfried von Clausewitz (; July 1, 1780 – November 16, 1831 ) was a Prussian soldier and military theorist who stressed the moral ( in modern terms, " psychological ") and political aspects of war.

The modern usage of terms for mail armour is highly contested in popular and, to a lesser degree, academic culture.

In computability theory, the Church – Turing thesis ( also known as the Turing-Church thesis, the Church – Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis ) is a combined hypothesis (" thesis ") about the nature of functions whose values are effectively calculable ; or, in more modern terms, functions whose values are algorithmically computable.

In modern terms the impost ( or pier ) is the topmost member of a column.

The modern sense of the term first appears sometime around the 12th century ; its popularity spread in the medieval period along with the terms isle, ylle, inis, eilean, oileán There is some confusion on what the term crannog originally referred to, the structure atop the island or the island itself The additional meanings of crannog can be variously related as " structure / piece of wood ; wooden pin ; crow's nest ; pulpit ; driver's box on a coach and vessel / box / chest " for crannóg.