According to his lemma, a group of four manuscripts including Codex Monacensis 1086 are copies directly from the original.

According to Schur's lemma, a non-zero morphism between two irreducible complex representations is invertible, and moreover, is given in matrix form as a scalar multiple of the identity matrix.

According to this doctrine, the universe was ruled by Heaven, T'ien -- as a natural force, or in the personification of a Supreme Sky-god -- governing all things by means of a process called the Tao, which can be roughly interpreted as `` the Order of the Universe '' or `` the Universal Way ''.

According to Plutarch's natural order of attribution of the vowels to the planets, alpha was connected with the Moon.

According to Tylor, animism often includes " an idea of pervading life and will in nature "; i. e., a belief that natural objects other than humans have souls.

According to some interpretations, the concept of ahimsa as expounded in the scriptures and law books is not meant to imply pacifism ; war is seen as a normal part of life and the natural duty of the warriors.

According to one historical account, aboriginal tribes of Australia were " most certainly cannibals ", and would willingly eat anyone who was killed in a fight ; they would also eat men famed for their fighting ability who had died natural deaths "... out of pity and consideration for the body ".

According to Aristotle, the four elements rise or fall toward their natural place in concentric layers surrounding the center of the earth and form the terrestrial or sublunary spheres.

According to Charles Darwin's theory of natural selection, characteristics such as camouflage that help an animal to survive will tend to evolve in any population.

According to Charles Darwin's 1859 theory of natural selection, features such as camouflage evolved by providing individual animals with a reproductive advantage, enabling them to leave more offspring, on average, than other members of the same species.

According to historians, Caligula was an excellent natural actor and, recognizing danger, hid all his resentment towards Tiberius.

It is an “ instrument of wholesale destruction, dependency and systematic exploitation producing distorted economies, socio-psychological disorientation, massive poverty and neocolonial dependency .” According to some Marxist historians, in all of the colonial countries ruled by Western European countries “ the natives were robbed of more than half their natural span of life by undernourishment ”.

According to Rewald, Pissarro had taken on an attitude more simple and natural than the other artists.

According to the U. S. Department of Commerce, opportunities exist for both on-and offshore oil and natural gas exploration ; however, these prospects have yet to come to fruition.

According to his letters, he was associated with the Venetian natural philosopher, Giulio Camillo, but, apart from this, he had a less active association with Italian scholars than might have been expected.

According to Aristotle, these four terrestrial elements are capable of inter-transformation and move toward their natural place, so a stone falls downward toward the center of the cosmos, but flames rise upward toward the circumference.

According to Swinford, this change can be attributed in part to the fact that " science and technical culture have changed perceptions of the natural world, have significantly changed the natural world itself, thereby altering the vocabulary of symbols applicable to epistemological and allegorical attempts to understand it.

According to Rousseau, by joining together into civil society through the social contract and abandoning their claims of natural right, individuals can both preserve themselves and remain free.

According to Kerry Gaynor, one of her former research assistants, " many felt Kirlian photography ’ s effects were just a natural occurrence.

According to one theory, myths began as allegories for natural phenomena: Apollo represents the sun, Poseidon represents water, and so on.

According to these thinkers, the ancients worshipped natural phenomena such as fire and air, gradually coming to describe them as gods.

According to Chee Soo in The Tao of Long Life, natural dietary therapy, or ch ' ang ming, has been developed in China since prehistoric times, along with a range of health arts that have become what we now know as traditional Chinese medicine, or TCM.

According to Dan Gill, geological investigations in the early 1990s confirmed earlier observations that the high assault ramp consisted mostly of a natural spur of bedrock that required a ramp only high built atop it in order to reach the Masada defenses.

According to natural law theory, which holds that morality is a function of human nature and reason can discover valid moral principles by looking at the nature of humanity in society, the content of positive law cannot be known without some reference to natural law ( or something like it ).

According to some, Aquinas conflates the natural law and natural right, the latter of which Aristotle posits in Book V of the Nicomachean Ethics ( Book IV of the Eudemian Ethics ).

According to this definition, supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the Poincaré group of symmetry transformations, of which the Lorentz transformations are a subgroup.

According to the principle of relativity, there is no privileged frame of reference, so the inverse transformations frame F ′ to frame F must be given by simply negating v.

According to the Roman poet Ovid, who wrote about transformations in his Metamorphoses, Iphis ( or Iphys ) was the daughter of Telethusa and Ligdus in Crete.

According to Kalupahana, instead of positing additional consciousnesses, the Triṃśikaikā-kārikā describes the transformations of this consciousness:

According to Kalupahana, instead of positing additional consciousnesses, the Triṃśikaikā-kārikā describes the transformations of this consciousness:

According to Liouville's theorem a Möbius transformation can be expressed as a composition of translations, similarities, orthogonal transformations and inversions.

According to this school, drawing its basic premise from the Pirenne thesis, the Roman world underwent a gradual ( though often violent ) series of transformations, morphing into the medieval world.

According to Daniel Chandler, the commutation test may involve any of four basic transformations which, to a greater or lesser extent, involve modification of the syntagm:

" According to scholar Wiliam Waldron, " Indian Buddhists see the ' evolution ' of mind i terms of the continuity of individual mind-streams from one lifetime to the next, with karma as the basic causal mechanism whereby transformations are transmitted from one life to the next.

`` According to Rose, he arrived here a couple minutes before nine and spotted Thor in the water, got a hooked pole from the pool-equipment locker and started hauling him out.

According to the official interpretation of the Charter, a member cannot be penalized by not having the right to vote in the General Assembly for nonpayment of financial obligations to the `` special '' United Nations' budgets, and of course cannot be expelled from the Organization ( which you suggested in your editorial ), due to the fact that there is no provision in the Charter for expulsion.

According to the new theories, the nineteenth century corporate sovereign was `` sovereign '' in a quite new and different sense from his historical predecessors.

According to the researchers, the results suggest that altruistic behavior may originate from how people view the world rather than how they act in it.

According to the Greek tradition the Dipylon master was named Daedalus, and in his statues the limbs were freed from the body, giving the impression that the statues could move.

According to the fossil record, Lissamphibia, which includes all modern amphibians and is the only surviving lineage, may have branched off from the extinct groups Temnospondyli and Lepospondyli at some period between the Late Carboniferous and the Early Triassic.

According to the Catholic Encyclopedia, an Allocution is a solemn form of address or speech from the throne employed by the Pope on certain occasions.

According to the poet Saadi Shirazi: Arslan possessed a fort, which raised at the height of Alwand, from all were those within its walls, for its roads were a labyrinth, like the curls of a bride.

According to the formulations of Daniels, abjads differ from alphabets in that only consonants, not vowels, are represented among the basic graphemes.

According to the studies of James Curran, the system of shared values among editors in Britain has generated a pressure among authors to write to fit the editors ' expectations, removing the focus from the reader-audience and putting a strain on the relationship between authors and editors and on writing as a social act.

According to a research report by the Centers for Disease Control and Prevention, Oran was decimated by the plague in 1556 and 1678, but outbreaks after European colonization, in 1921 ( 185 cases ), 1931 ( 76 cases ), and 1944 ( 95 cases ), were very far from the scale of the epidemic described in the novel.

( Despite common belief, he did not take a day from February ; see the debunked theory on month lengths ) According to a Senatus consultum quoted by Macrobius, he chose this month because it was the time of several of his great triumphs, including the conquest of Egypt.

According to research funded by the USAID CAPS project, Armenia's exceptionally high rate of economic growth during the last decade has been largely dependent on external factors ( e. g., remittances, assistance from international financial and donor organization ).

According to the Central Bank of Armenia, in 2005, cash remittances from Armenians working abroad reached a record-high level of $ 1 billion, which is worth more than one fifth of the country ’ s 2005 Gross Domestic Product.

According to a World Bank official, 30 percent of Armenia's economy in 2009 came from the construction sector.

According to official data, in 2007, a record-high 500, 000 tourists visited Armenia — most of them ethnic Armenians from Europe, Russia and the United States.

According to economist Eduard Aghajanov, Armenia could have repaid them with low-interest loans from other, presumably Western sources, or with some of its hard currency reserves which then totaled about $ 450 million.

According to Scott Simpson, the Gona Project's physical anthropologist, the fossil evidence from the Middle Awash indicates that both A. kadabba and A. ramidus lived in " a mosaic of woodland and grasslands with lakes, swamps and springs nearby ," but further research is needed to determine which habitat Ardipithecus at Gona preferred.

According to Hesiod's Theogony, she was born when Cronus cut off Uranus ' genitals and threw them into the sea, and from the sea foam ( aphros ) arose Aphrodite.

According to this interpretation, the name is from aphrós " foam " and déatai " seems " or " shines " ( infinitive form * déasthai ), meaning " she who shines from the foam ", a byname of the dawn goddess ( Eos ).

According to Maimonides, an afterlife continues for the soul of every human being, a soul now separated from the body in which it was " housed " during its earthly existence.

According to the Gospel of Matthew, at the death of Jesus tombs were opened, and at his resurrection many saints who had died emerged from their tombs and went into " the holy city ", presumably New Jerusalem.

According to Price after death the self will find itself in a dream world of memories and mental images from their life.

According to Steven H Silver, alternate history requires three things: 1 ) the story must have a point of divergence from the history of our world prior to the time at which the author is writing, 2 ) a change that would alter history as it is known, and 3 ) an examination of the ramifications of that change.