At the same time, but independently, Dirac formulated quantum mechanics in a way that is close to an axiomatic system, as did Hermann Weyl with the assistance of Erwin Schrödinger.

Since the 1960s, following the work of Arthur Wightman and Rudolf Haag, also modern quantum field theory can be considered close to an axiomatic description.

This push to confine the study of mass behaviour to the measurements of parameters involved in differential equations has led sociology perilously close to the reduction of the word `` mass '' to mean a small group in which certain relations between all pairs of individuals in such a group can be studied.

A major problem confronting the study of the early history of gunpowder is ready access to sources close to the events described.

Anatoli's example of broad-minded study of Christian literature and intercourse with Christian scholars found many followers, as, for example, Moses ben Solomon of Salerno ; and his work was an important factor in bringing the Jews of Italy into close contact with their Christian fellow students.

The Kaddish d ' Rabbanan is used after any part of the service that includes extracts from the Mishnah or the Talmud, as its original purpose was to close a study session.

In his study of French and Burgundian courtly culture, Johan Huizinga noted that " at the close of the Middle Ages, a sombre melancholy weighs on people's souls.

* Yale Papyrus Collection — numbers over six thousand inventoried items and is cataloged, digitally scanned, and accessible online for close study.

The study also notes that it is the more secular, pro-evolution societies that come close to " cultures of life " ( although these countries are far from perfect, they have low rates of lethal crime, for example ).

According to a study by Menna Jones, " gene flow appears extensive up to ", meaning a high assignment rate to source or close neighbour populations " in agreement with movement data.

" After long study and experience, I have come to the conclusion that all religions are true ; all religions have some error in them ; all religions are almost as dear to me as my own Hinduism, in as much as all human beings should be as dear to one as one's own close relatives.

Julius Caesar mentions in his Gallic Wars that those Celts who wanted to make a close study of druidism went to Britain to do so.

The Near Earth Asteroid Rendezvous-Shoemaker ( NEAR Shoemaker ), renamed after its 1996 launch in honor of planetary scientist Eugene M. Shoemaker, was a robotic space probe designed by the Johns Hopkins University Applied Physics Laboratory for NASA to study the near-Earth asteroid Eros from close orbit over a period of a year.

The mission's goals were to study the surface and atmosphere of Mars during close flybys, in order to establish the basis for future investigations, particularly those relevant to the search for extraterrestrial life, and to demonstrate and develop technologies required for future Mars missions.

One old study from 1997 found that it did not matter how close you were to a power line or a sub-station, there was no increased risk of cancer or illness.

In 2010, a detailed field study was conducted in the Garonne River ( France ) in the Arcins channel between Arcins Island and the right bank close to Lastrene township.

The development of space travel gave scientists the opportunity to study the comet at close quarters, and several probes were launched to do so.

Oscar Levant wrote that Newman initially was hesitant to leave New York for Hollywood: " Too close to the cake ," he reported him saying, " Also, no place to study.

In the ringing studies birds ringed as chicks are recapatured close to their original nests, a tendency which can be extreme at times ; in Laysan Albatross the average distance between hatching site and the site where a bird established its own territory was, and a study of Cory's Shearwaters nesting near Corsica found that of nine out of 61 male chicks that returned to breed at their natal colony actually bred in the burrow they were raised in.

Bolívar was especially close to Fernando and in 1822 sent him to study in the United States, where he attended the University of Virginia.

The study very clearly showed that intensive management ( i. e., close control ) of insulin-dependent diabetes prevents or slows the development of the long-term complications of diabetes ( eye, kidney, and nerve damage caused by diabetes ), essentially to the ' normal ' level.

Early in his career, he wanted to be a history painter, a calling for which he was well prepared by his rigorous academic training and close study of classic art.

Nanking is the capital of China and the capture thereof is an international affair ; therefore, careful study should be made so as to exhibit the honor and glory of Japan and augment the trust of the Chinese people, and that the battle in the vicinity of Shanghai is aimed at the subjugation of the Chinese Army, therefore protect and patronize Chinese officials and people, as afar as possible ; the Army should always bear in mind not to involve foreign residents and armies in trouble and maintain close liaison with foreign authorities in order to avoid misunderstandings.

Curtius wrote as follows in the opening pages of European Literature and the Latin Middle Ages ( 1953 English translation ), following close on Toynbee, as he sets the stage for his vast study of medieval Latin literature.

According to an INSEE 2006 study, " The natural increase is close to 300, 000 persons, a level that has not been reached in more than thirty years.

Their study focuses on the normative period of sonata practice, notable ones being the works of Haydn, Mozart, Beethoven, Schubert, and their close contemporaries, projecting this practice forward to development of the sonata-allegro form into the 19th and 20th centuries.

This has occurred despite the study of semiconductors, early in the 20th century, being regarded as the ' physics of dirt ' and not deserving of close attention.

Āryabhaṭa ( 476 – 550 CE ) showed that pairs of simultaneous congruences, could be solved by a method he called kuṭṭaka, or pulveriser ; this is a procedure close to ( a generalisation of ) the Euclidean algorithm, which was probably discovered independently in India.

On the average, space is observed to be very nearly flat ( close to zero curvature ), meaning that Euclidean geometry is experimentally true with high accuracy throughout most of the Universe.

Mathematical applications required geometry of four or more dimensions ; the close scrutiny of the foundations of the traditional Euclidean geometry had revealed the independence of the parallel postulate from the others, and non-Euclidean geometry had been born.

relates how John Leech about 1964 investigated close packings of spheres in Euclidean spaces of large dimension.

In the Euclidean field theory, these boosts analytically continue to rotations, and the rotations close after.

In that setting one can use birational geometry, techniques from number theory, Galois theory and commutative algebra, and close analogues of the methods of algebraic topology, all in an integrated way.

However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori.

The eleventh century Persian mathematician Omar Khayyám saw a strong relationship between geometry and algebra, and was moving in the right direction when he helped to close the gap between numerical and geometric algebra with his geometric solution of the general cubic equations, but the decisive step came later with Descartes.

The Sun synchronous orbit is in general sufficiently close to polar to get the desired global coverage while the relatively constant geometry to the Sun mostly is an advantage for the instruments.

Ancient Greek mathematics contributed many important developments to the field of mathematics, including the basic rules of geometry, the idea of formal mathematical proof, and discoveries in number theory, mathematical analysis, applied mathematics, and approached close to establishing integral calculus.

To obtain a specific geometry, the EDM tool is guided along the desired path very close to the work ; ideally it should not touch the workpiece, although in reality this may happen due to the performance of the specific motion control in use.

There exists a close analogy of differential geometry with the mathematical structure of defects in regular crystals.

However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori.

In conjunction with computational geometry, a computational synthetic geometry has been founded, having close connection, for example, with matroid theory.

The term Cartesian planning given to the planning of cities using a grid plan, shows the close association between architecture and geometry.

Only very recently has it been possible to do the comparison the other way round, by bringing a well-prepared probe so close to a well-prepared surface that approximate parallel-plate geometry can be assumed and the conversion factor can be taken as 1 / W, where W is the measured probe-to emitter separation.

While it is impossible to construct a perfect regular 56-sided polygon using simple ' square and circle ' geometry, a close approximation has recently been discovered which it is claimed might have been used at Stonehenge.

The symmetry of the model space is then built in to the Cartan geometry or pseudogroup structure by positing that the model spaces of nearby points are related by a transformation in G. The fundamental difference between a Cartan geometry and pseudogroup geometry is that the symmetry for a Cartan geometry relates infinitesimally close points by an infinitesimal transformation in G ( i. e., an element of the Lie algebra of G ) and the analogous notion of symmetry for a pseudogroup structure applies for points that are physically separated within the manifold.

As described below, a similar formula can be written using cosines ( sometimes called the spherical law of cosines, not to be confused with the law of cosines for plane geometry ) instead of haversines, but if the two points are close together ( e. g. a kilometer apart, on the Earth ) you might end up with cos ( d / R ) = 0. 99999999, leading to an inaccurate answer.

He found that the ring was slightly egg-shaped with a complex geometry of circles and ellipses which could be set out around a central triangle, using sizes which are close to whole multiples of what he called the Megalithic yard.

In Riemannian geometry, a Jacobi field is a vector field along a geodesic in a Riemannian manifold describing the difference between the geodesic and an " infinitesimally close " geodesic.