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Tensors were first conceived by Tullio Levi-Civita and Gregorio Ricci-Curbastro, who continued the earlier work of Bernhard Riemann and Elwin Bruno Christoffel and others, as part of the absolute differential calculus.
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Tensors and were
Tensors were also found to be useful in other fields such as continuum mechanics.
Tensors and by
Tensors are generalized within category theory by means of the concept of monoidal category, from the 1960s.
Tensors and .
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors.
Tensors are used to represent correspondences between sets of geometrical vectors.
Tensors are important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as elasticity, fluid mechanics, and general relativity.
Tensors are another type of quantity that behave in this way ; in fact a vector is a special type of tensor.
Tensors are frequently used in engineering to describe measured quantities.
Ren Li, senior independent study, " Investigating the Ricci and Weyl Curvature Tensors in the Weak Lensing Context.
Tensors are of importance in pure and applied mathematics, physics and engineering.
Some Remarks on the Compressed Matrix Representation of Symmetric Second-Order and Fourth-Order Tensors.
* Léon Brillouin Tensors in Mechanics and Elasticity.
Tensors have a real, physical existence in a material or tissue so that they don't move when the coordinate system used to describe them is rotated.
were and first
At first they were only feathers and dark indistinguishable faces and bodies, hunched over their horses' heads.
Two of the new hands, a Mexican named Jose Amado and a kid known only as Laredo, were picked for the first trick of riding night herd.
After the first two murders, the warning notes were rarely ignored.
Even the knowledge that she was losing another boy, as a mother always does when a marriage is made, did not prevent her from having the first carefree, dreamless sleep that she had known since they dropped down the canyon and into Bear Valley, way, way back there when they were crossing those other mountains.
Out of compulsion to say something cheery, Ben Prime blurted, `` Well, we were lucky to be on soft ground when the first floodheads hit.
His political opponent and lifetime friend, Thomas Jefferson, achieved immortality through his authorship of the Declaration of Independence, but equally notable were the legal and constitutional reforms he instituted in his native Virginia, his role as father of our territorial system, and his acquisition of the Louisiana Territory during his first term as President.
This is the primary function of the imagination operating in the absence of the original experiential stimulus by which the images were first appropriated.
Before being daughter, wife, or mother, before being cultured ( a word now bereft both socially and politically of the sheen you children of frontiersmen bestowed on it ), before being sorry for the poor, progressive about public health, and prettily if somewhat imprecisely humanitarian, indeed first and foremost, you were a lady.
Even the first wave of homesickness had passed, although there were moments when Captain Heard pointed out on his compass the direction of Bradford that she felt a little twinge at her heart.
When they were first written, there was evidently no thought of their being published, and those which refer to the writer's love for Mrs. Meynell particularly have the ring of truth.
The evening of our first day we drove with Christopher and Judy Sakellariadis, who were friends and patients of Norton, to dine at a restaurant on the shores of the Aegean.
So persistent were these attacks that in March of the following year, Woodruff was finally moved to action, and Pike was to learn his first lesson in frontier politics, the subtle art of diversion.
In the next few months of comparative silence, Pike waited patiently until conditions were perfect for a new attack, and then, displaying a remarkable grasp of the subtleties of political infighting, gained from his first bout with Woodruff, he used these changed conditions to excellent advantage.
Although this kind of wholesale objection came at first from some men who were not technically Puritans, still, once the Puritans gained power, they climaxed the affair by passing the infamous ordinance of 1642 which decreed that all `` public stage-plays shall cease and be forborne ''.
Our first impression of the data was that the students were surprisingly orthodox and religiously involved.
But all the reports of this first embassy show that the two Savoyards were the heads of it, for they were the only ones who were empowered to swear for the king that he would abide by the pope's decision and who were allowed to appoint deputies in the event that one was unavoidably absent.
the Low Countries, where the Middle Ages were to last for another two centuries and die out only when Charles the Bold of Burgundy met his first defeat in the fields and forests below the walls of Grandson.
It was the first American war in which the death rate from disease was lower than that from battle, due to the provision of trained medical personnel ( of the 200,000 officers, 42,000 were physicians ), compulsory vaccination, rigorous camp sanitation, and adequate hospital facilities.
There were several men of ninety or more whom I knew first or last, all of whom were still productive and most of whom knew one another as if they had naturally come together at the apex of their lives.
It met a serious rebuff in New Orleans, where the two schools selected for the first moves toward integration were boycotted by white parents.
These microfossils indicate the swamp was `` formed during the Lower Cretaceous period when dinosaurs were at their heyday and when the first flowering plants were just appearing.
were and conceived
Most of these, with horrible exceptions, were conceived as is a ship, not as an attempt to quell the ocean of mankind, nor to deny its force, but as a means to survive and enjoy it.
The early works were conceived for a sophisticated, international audience ; ;
the later works were conceived to affirm a way of life for fellow citizens.
They were works of devotional contemplation in which the musical design corresponded to literary ideas, conceived visually.
Loops and conditional branching were possible, and so the language as conceived would have been Turing-complete as later defined by Alan Turing.
According to Atanasoff's account, several key principles of the Atanasoff – Berry Computer were conceived in a sudden insight after a long nighttime drive during the winter of 1937 – 38.
However, according to Lucius Tarrutius of Firmum, Romulus and Remus were conceived in the womb on the 23rd day of the Egyptian month Choiac, at the time of a total eclipse of the Sun.
As Lovecraft conceived the deities or forces of his mythos, there were, initially, the Elder Gods ... hese Elder Gods were benign deities, representing the forces of good, and existed peacefully ... very rarely stirring forth to intervene in the unceasing struggle between the powers of evil and the races of Earth.
He conceived and developed many of his user interface ideas back in the mid-1960s, long before the personal computer revolution, at a time when most individuals were kept away from computers, and could only use computers through intermediaries ( see batch processing ), and when software tended to be written for vertical applications in proprietary systems.
Although derived from the Latin word feodum or feudum ( fief ), then in use, the term feudalism and the system it describes were not conceived of as a formal political system by the people living in the medieval period.
The idea of feudalism was unknown and the system it describes were not conceived of as a formal political system by the people living in the Medieval Period.
In the late 1930s, the idea of producing a car made entirely in Australia was conceived, but plans were put on hold after the outbreak of World War II.
They played a similar symbolic role in ancient China, where dogs were conceived as representative of the household sphere, and as protective spirits appropriate when transcending geographic and spatial boundaries.
Newcomen apparently conceived the Newcomen steam engine quite independently of Savery, but as the latter had taken out a very wide-ranging patent, Newcomen and his associates were obliged to come to an arrangement with him, marketing the engine until 1733 under a joint patent.
The NASA designs were conceived as replacements for the upper stages of the Saturn V launch vehicle, but the tests revealed reliability problems, mainly caused by the vibration and heating involved in running the engines at such high thrust levels.
Historically, the baby boomers were the largest influx of children conceived after WW2.
The French Benedictine monks of the Keur Moussa Abbey ( Senegal ), who possibly were the first to introduce guitar machine heads instead of leather rings in the late seventies, conceived a method based on scores to teach the instrument.
The stories that constitute the Known Space series were originally conceived as two separate series: the Belter stories, featuring solar-system colonization and slower-than-light travel with fusion-powered and Bussard ramjet ships, and the Neutron Star / Ringworld series of stories, set much further into the future, which feature faster-than-light ships using " hyperdrive ".
The three works were part of what Peake conceived as a lengthy cycle, the completion of which was prevented by his death, and consequently should not be considered a trilogy.
As mentioned above, when MPLS was conceived, label lookup and label switching were faster than a routing table or RIB ( Routing Information Base ) lookup because they could take place directly within the switched fabric and not the CPU.
These goals, conceived in 1980, were to be fulfilled by the end of the decade.
The members of the Camerata considered that the " chorus " parts of Greek dramas were originally sung, and possibly even the entire text of all roles ; opera was thus conceived as a way of " restoring " this situation.
At first, the dictionary was unconnected to Oxford University but was the idea of a small group of intellectuals in London ; it originally was a Philological Society project conceived in London by Richard Chenevix Trench, Herbert Coleridge, and Frederick Furnivall, who were dissatisfied with the current English dictionaries.
Herschel conceived the idea that stars were initially scattered across space, but later became clustered together as star systems because of gravitational attraction.
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