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In the foundations of mathematics, a covering lemma is used to prove that the non-existence of certain large cardinals leads to the existence of a canonical inner model, called the core model, that is, in a sense, maximal and approximates the structure of the von Neumann universe V. A covering lemma asserts that under some particular anti-large cardinal assumption, the core model exists and is maximal in a sense that depends on the chosen large cardinal. The first such result was proved by Ronald Jensen for the constructible universe assuming 0# does not exist, which is now known as Jensen's covering theorem.
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Wikipedia - Covering lemma - Summary
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In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory. It stands in contrast to other types of mathematics such as constructive mathematics or predicative mathematics. In practice, the most common non-classical systems are used in constructive mathematics.Classical mathematics is sometimes attacked on philosophical grounds, due to constructivist and other objections to the logic, set theory, etc., chosen as its foundations, such as have been expressed by L. E. J. Brouwer. Almost all mathematics, however, is done in the classical tradition, or in ways compatible with it. Defenders of classical mathematics, such as David Hilbert, have argued that it is easier to work in, and is most fruitful; although they acknowledge non-classical mathematics has at times led to fruitful results that classical mathematics could not (or could not so easily) attain, they argue that on the whole, it is the other way round.
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Wikipedia - Classical mathematics - Summary
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In the foundations of mathematics, formalism is associated with a certain rigorous mathematical method: see formal system. In common usage, a formalism means the out-turn of the effort towards formalisation of a given limited area. In other words, matters can be formally discussed once captured in a formal system, or commonly enough within something formalisable with claims to be one. Complete formalisation is in the domain of computer science. Formalism also more precisely refers to a certain school in the philosophy of mathematics, stressing axiomatic proofs through theorems, specifically associated with David Hilbert. In the philosophy of mathematics, therefore, a formalist is a person who belongs to the school of formalism, which is a certain mathematical-philosophical doctrine descending from Hilbert.
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Wikipedia - Formalism (philosophy) - Mathematics
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In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces the notion of class, which is a collection of sets defined by a formula whose quantifiers range only over sets. NBG can define classes that are larger than sets, such as the class of all sets and the class of all ordinals. Morse–Kelley set theory (MK) allows classes to be defined by formulas whose quantifiers range over classes.
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Wikipedia - Von Neumann–Bernays–Gödel set theory - Summary
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NBG is finitely axiomatizable, while ZFC and MK are not. A key theorem of NBG is the class existence theorem, which states that for every formula whose quantifiers range only over sets, there is a class consisting of the sets satisfying the formula. This class is built by mirroring the step-by-step construction of the formula with classes.
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Wikipedia - Von Neumann–Bernays–Gödel set theory - Summary
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Since all set-theoretic formulas are constructed from two kinds of atomic formulas (membership and equality) and finitely many logical symbols, only finitely many axioms are needed to build the classes satisfying them. This is why NBG is finitely axiomatizable. Classes are also used for other constructions, for handling the set-theoretic paradoxes, and for stating the axiom of global choice, which is stronger than ZFC's axiom of choice.
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Wikipedia - Von Neumann–Bernays–Gödel set theory - Summary
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John von Neumann introduced classes into set theory in 1925. The primitive notions of his theory were function and argument. Using these notions, he defined class and set. Paul Bernays reformulated von Neumann's theory by taking class and set as primitive notions. Kurt Gödel simplified Bernays' theory for his relative consistency proof of the axiom of choice and the generalized continuum hypothesis.
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Wikipedia - Von Neumann–Bernays–Gödel set theory - Summary
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In the four color theorem, Kempe was able to prove that all graphs necessarily have a vertex of five or less, or containing a vertex that touches five other vertices, called its neighbors. As such, to prove the four color theorem, it is sufficient to prove that vertices of five or less were all four-colorable. Kempe was able to prove the case of degree four and give a partial proof of degree five using Kempe chains.In this case, Kempe chains are used to prove the idea that no vertex has to be touching four colors different from itself, i.e., having a degree of 4. First, one can create a graph with a vertex v and four vertices as neighbors.
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Wikipedia - Kempe chain - Application to the four colour theorem
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If we remove the vertex v, we can four-color the remaining vertices. We can set the colors as (in clockwise order) red, yellow, blue, and green. In this situation, there can be a Kempe chain joining the red and blue neighbors or a Kempe chain joining the green and yellow neighbors, but not both, since these two paths would necessarily intersect, and the vertex where they intersect cannot be colored.
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Wikipedia - Kempe chain - Application to the four colour theorem
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Supposing that the Kempe chain is connecting the green and yellow neighbors, red and blue must then necessarily not have a Kempe chain between them. So, when placing the original vertex v back into the graph, we can simply reverse the colors of the red vertex and its neighbors (including the red vertex, making it blue) and color vertex v as red. This results in a four-colored graph.
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Wikipedia - Kempe chain - Application to the four colour theorem
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In the four early Bibles moralisées, only one side of each page of parchment was used; this procedure increased the size of the volume as well as made the creation of these bibles very expensive. Unlike the earlier Bibles moralisées, Add. 18719 and other later Bibles moralisées used both sides of the parchment, hence costs as well as size of the manuscript was decreased.
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Wikipedia - Bible moralisée - Technical Analysis
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This change allowed for a more convenient one volume manuscript. Although this change may signal that money was a factor when creating later manuscripts.The text/picture blocks in the Bibles Moralisées are striking for their symmetry. Each of the pages hold 8 medallions with painted gold backgrounds, these 8 medallions are arranged in pairs, so 4 rows of two medallions.
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Wikipedia - Bible moralisée - Technical Analysis
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Where the medallions touch one another a stylized flower joins the two, similar flowers mark where the medallions touch the outer frame and the spaces between the medallions are decorated using squares placed over quatrefoils, in these there are painted angel busts over a gold ground. Each of the paintings within the medallions held figures that were painted on a gold leaf background, and are set on a patterned ground of blue or rose brown.As an example, in BnF MS Français 9561 129 pages are taken up with the Old Testament. Of these the earlier ones are divided horizontally in the centre, and it is the upper part of the page that contains the picture illustrative of some Old Testament event.
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Wikipedia - Bible moralisée - Technical Analysis
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The lower part represents a corresponding scene from the New Testament. further on in the volume, three pictures appear in the upper part of the page, and three below. Seventy-six pages at the end of the volume are devoted to depicting the lives of Jesus Christ and the Blessed Virgin.
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Wikipedia - Bible moralisée - Technical Analysis
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In most of the Bibles moralisées, evidence shows that scribes completed the text after the decorations were completed. The text supplemented the images, being similar to a caption. This can be seen most obviously where the text goes over the gilding or the borders that had been painted for the text to fit in.
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Wikipedia - Bible moralisée - Technical Analysis
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A difference between MS Additional 18719 and the earlier Bibles moralisées is that MS Additional 18719 (and Add.18719) followed the usual procedure for manuscript illumination, where the scribes worked first and then the artists added images.Français 166 copies the layout and text that is used in Français 167. Meanwhile, Vienna 1179 and Toledo are very similar, at times the two be told apart in photographs, since they consist of the same layout. Français 167 is similar to Add. 18719 in that unlike the other Bibles moralisées they both sides of the parchment sheets.
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Wikipedia - Bible moralisée - Technical Analysis
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In the four tables below, the minor branches of decay (with the branching probability of less than 0.0001%) are omitted. The energy release includes the total kinetic energy of all the emitted particles (electrons, alpha particles, gamma quanta, neutrinos, Auger electrons and X-rays) and the recoil nucleus, assuming that the original nucleus was at rest. The letter 'a' represents a year (from the Latin annus).
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Wikipedia - Decay chain - Actinide alpha decay chains
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In the tables below (except neptunium), the historic names of the naturally occurring nuclides are also given. These names were used at the time when the decay chains were first discovered and investigated. From these historical names one can locate the particular chain to which the nuclide belongs, and replace it with its modern name. The three naturally-occurring actinide alpha decay chains given below—thorium, uranium/radium (from U-238), and actinium (from U-235)—each ends with its own specific lead isotope (Pb-208, Pb-206, and Pb-207 respectively). All these isotopes are stable and are also present in nature as primordial nuclides, but their excess amounts in comparison with lead-204 (which has only a primordial origin) can be used in the technique of uranium–lead dating to date rocks.
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Wikipedia - Decay chain - Actinide alpha decay chains
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In the four-dimensional space of quaternions a + b i → + c j → + d k → {\displaystyle a+b{\vec {i}}+c{\vec {j}}+d{\vec {k}}} , the versors u ( θ , r ) = cos θ + r sin θ {\displaystyle u(\theta ,r)=\cos \theta +r\sin \theta } form the unit 3-sphere.Since quaternions are non-commutative, elements of its projective line have homogeneous coordinates written U ( a , b ) {\displaystyle U(a,b)} to indicate that the homogeneous factor multiplies on the left. The quaternion transform is f ( u , q ) = U ( 1 1 − u u ) = U ∼ U . {\displaystyle f(u,q)=U{\begin{pmatrix}1&1\\-u&u\end{pmatrix}}=U\sim U.}
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Wikipedia - Cayley transform - Quaternion homography
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The real and complex homographies described above are instances of the quaternion homography where θ {\displaystyle \theta } is zero or π / 2 {\displaystyle \pi /2} , respectively. Evidently the transform takes u → 0 → − 1 {\displaystyle u\to 0\to -1} and takes − u → ∞ → 1 {\displaystyle -u\to \infty \to 1} . Evaluating this homography at q = 1 {\displaystyle q=1} maps the versor u {\displaystyle u} into its axis: f ( u , 1 ) = ( 1 + u ) − 1 ( 1 − u ) = ( 1 + u ) ∗ ( 1 − u ) / | 1 + u | 2 .
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Wikipedia - Cayley transform - Quaternion homography
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{\displaystyle f(u,1)=(1+u)^{-1}(1-u)=(1+u)^{*}(1-u)/|1+u|^{2}.} But | 1 + u | 2 = ( 1 + u ) ( 1 + u ∗ ) = 2 + 2 cos θ , and ( 1 + u ∗ ) ( 1 − u ) = − 2 r sin θ . {\displaystyle |1+u|^{2}=(1+u)(1+u^{*})=2+2\cos \theta ,\quad {\text{and}}\quad (1+u^{*})(1-u)=-2r\sin \theta .}
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Wikipedia - Cayley transform - Quaternion homography
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Thus f ( u , 1 ) = − r sin θ 1 + cos θ = − r tan θ 2 . {\displaystyle f(u,1)=-r{\frac {\sin \theta }{1+\cos \theta }}=-r\tan {\frac {\theta }{2}}.} In this form the Cayley transform has been described as a rational parametrization of rotation: Let t = tan ϕ / 2 {\displaystyle t=\tan \phi /2} in the complex number identity e − i φ = 1 − t i 1 + t i {\displaystyle e^{-i\varphi }={\frac {1-ti}{1+ti}}} where the right hand side is the transform of t i {\displaystyle ti} and the left hand side represents the rotation of the plane by negative ϕ {\displaystyle \phi } radians.
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Wikipedia - Cayley transform - Quaternion homography
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In the fourteenth century, "the monk Abba Ewostatewos founded a Sabbatarian movement" and fled, with his followers to "isolated parts of northwestern Ethiopia". In the Ethiopian Orthodox Tewahedo Church, "the Sabbatarian controversy divided the kingdom during the fourteenth and fifteenth centuries." Zara Yaqob, the king, eventually "decreed that the Sabbatarian teaching of the northern monks become the position of the church". Later, the 'seventh-day Sabbatarians' (also known as 'Saturday Sabbatarians') sought to re-establish the Mosaic Law itself, along with Pharisaic interpretations and Hebrew Sabbath practices, including observances running from Friday sunset to Saturday sunset. Most identify with the early Jewish Christians, and consider early church condemnations of Judaizing to be the marks of a "Great Apostasy" in early Christianity, which they seek to rectify.
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Wikipedia - Sunday Sabbatarianism - Ethiopian Sabbatarian movement
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In the fourth century AD, the bishop and theologian Augustine of Hippo followed Origen in arguing that the Genesis creation story should be read allegorically. In his book De Genesi ad Litteram (On the Literal Meaning of Genesis) he prefaces saying,In all sacred books, we should consider the eternal truths that are taught, the facts that are narrated, the future events that are predicted, and the precepts or counsels that are given. In the case of a narrative of events, the question arises whether everything must be taken according to the figurative sense only, or whether it must be expounded and defended also as a faithful record of what happened. No Christian would dare say that the narrative must not be taken in a figurative sense.
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Wikipedia - Evolutionary thought - Augustine of Hippo
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For St. Paul says: Now all these things that happened to them were symbolic. And he explains the statement in Genesis, And they shall be two in one flesh, as a great mystery in reference to Christ and to the Church.
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Wikipedia - Evolutionary thought - Augustine of Hippo
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Later he differentiates between the days of the Genesis 1 creation narrative and 24 hour daysBut at least we know are different from the ordinary day of which we are familiarHe also talks about a form of theistic evolutionThe things had potentially created... forth in the course of time on different days according to their different kinds... the rest of the earth filled with its various kinds of creatures, produced their appropriate forms in due time.Which has led Francis Collins of Biologos to believe Augustine espoused a form of theistic evolution.Augustine's idea "that forms of life had been transformed 'slowly over time'" prompted Father Giuseppe Tanzella-Nitti, Professor of Theology at the Pontifical Santa Croce University in Rome, to claim that Augustine had suggested a form of evolution.Henry Fairfield Osborn wrote in From the Greeks to Darwin (1894): If the orthodoxy of Augustine had remained the teaching of the Church, the final establishment of Evolution would have come far earlier than it did, certainly during the eighteenth instead of the nineteenth century, and the bitter controversy over this truth of Nature would never have arisen. ... Plainly as the direct or instantaneous Creation of animals and plants appeared to be taught in Genesis, Augustine read this in the light of primary causation and the gradual development from the imperfect to the perfect of Aristotle. This most influential teacher thus handed down to his followers opinions which closely conform to the progressive views of those theologians of the present day who have accepted the Evolution theory.
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Wikipedia - Evolutionary thought - Augustine of Hippo
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In A History of the Warfare of Science with Theology in Christendom (1896), Andrew Dickson White wrote about Augustine's attempts to preserve the ancient evolutionary approach to the creation as follows: For ages a widely accepted doctrine had been that water, filth, and carrion had received power from the Creator to generate worms, insects, and a multitude of the smaller animals; and this doctrine had been especially welcomed by St. Augustine and many of the fathers, since it relieved the Almighty of making, Adam of naming, and Noah of living in the ark with these innumerable despised species. In Augustine's De Genesi contra Manichæos, on Genesis he says: "To suppose that God formed man from the dust with bodily hands is very childish.
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Wikipedia - Evolutionary thought - Augustine of Hippo
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... God neither formed man with bodily hands nor did he breathe upon him with throat and lips." Augustine suggests in other work his theory of the later development of insects out of carrion, and the adoption of the old emanation or evolution theory, showing that "certain very small animals may not have been created on the fifth and sixth days, but may have originated later from putrefying matter." Concerning Augustine's De Trinitate (On the Trinity), White wrote that Augustine "...develops at length the view that in the creation of living beings there was something like a growth—that God is the ultimate author, but works through secondary causes; and finally argues that certain substances are endowed by God with the power of producing certain classes of plants and animals." Augustine believed, that whatever science shows us the Bible must teach since the Bible is infallible:Usually, even a non-Christian knows something about the earth, the heavens, and the other elements of this world, about the motion and orbit of the stars ... Now, it is a disgraceful and dangerous thing for an infidel to hear a Christian, presumably giving the meaning of Holy Scripture, talking non-sense on these topics; and we should take all means to prevent such an embarrassing situation, in which people show up vast ignorance in a Christian and laugh it to scorn. The shame is not so much that an ignorant individual is derided, but that people outside the household of the faith think our sacred writers held such opinions, and, to the great loss of those for whose salvation we toil, the writers of our Scripture are criticized and rejected as unlearned men.
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Wikipedia - Evolutionary thought - Augustine of Hippo
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In the fourth century BC, Alexander the Great introduced this "Persian nut" (Theophrastus' καρυα ή Περσική) in Macedonian, Ancient Greek ancestral forms with lateral fruiting from Iran and Central Asia. They hybridized with terminal-bearing forms to give lateral-bearing trees with larger fruit. These lateral-bearers were spread in southern Europe and northern Africa by Romans.
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Wikipedia - Persian Walnut - Introduction around the world
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Recent prospections in walnut populations of the Mediterranean Basin allowed to select interesting trees of this type. In the Middle Ages, the lateral-bearing character was introduced again in southern Turkey by merchants travelling along the Silk Road. J. regia germplasm in China is thought to have been introduced from Central Asia about 2,000 years ago, and in some areas has become naturalized.
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Wikipedia - Persian Walnut - Introduction around the world
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Cultivated J. regia was introduced into western and northern Europe very early, in Roman times or earlier, and to the Americas in the 17th century, by English colonists. Important nut-growing regions include California in the United States; France, Serbia, Greece, Bulgaria, Romania and Hungary in Europe; China in Asia; Baja California and Coahuila in Mexico; and Chile in Latin America. Lately, cultivation has spread to other regions, such as New Zealand and the southeast of Australia. It is cultivated extensively from 30° to 50° of latitude in the Northern Hemisphere and from 30° to 40° in the Southern Hemisphere. Its high-quality fruits are eaten both fresh or pressed for their richly flavored oil; numerous cultivars have been selected for larger nuts with thinner shells.
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Wikipedia - Persian Walnut - Introduction around the world
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In the fourth century BC, Theophrastus mentioned komakon, including it with cinnamon and cassia as an ingredient in aromatic confections. Guillaume Budé and Claudius Salmasius have identified komakon with cubeb, probably due to the resemblance which the word bears to the Javanese name of cubeb, kumukus. This is seen as a curious evidence of Greek trade with Java in a time earlier than that of Theophrastus. It is unlikely Greeks acquired them from somewhere else, since Javanese growers protected their monopoly of the trade by sterilizing the berries by scalding, ensuring that the vines were unable to be cultivated elsewhere.In the Tang dynasty, cubeb was brought to China from Srivijaya.
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Wikipedia - Tailed pepper - History
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In India, the spice came to be called kabab chini, that is, "Chinese cubeb", possibly because the Chinese had a hand in its trade, but more likely because it was an important item in the trade with China. In China, this pepper was called both vilenga and viḍaṅga विडङ्ग (the cognate Sanskrit word), which had denoted embelia ribes before being used to denote the Malayan cubeb (simplified Chinese: 荜澄茄; traditional Chinese: 蓽澄茄; pinyin: bì chéng qié). Li Hsun thought it grew on the same tree as black pepper.
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Wikipedia - Tailed pepper - History
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Tang physicians administered it to restore appetite, cure "demon vapors", darken the hair, and perfume the body. However, there is no evidence showing that cubeb was used as a condiment in China.In his 1827 dictionary Nhật dụng thường đàm (日用常談; lit. 'Common Words Used Daily'), Vietnamese scholar-official Phạm Đình Hổ glossed 蓽䔲茄 "cubeb" (Sino-Vietnamese: tất đăng gia) as 乙 ớt, which currently denotes chilli pepper from the Americas.The Book of One Thousand and One Nights, compiled in the 9th century, mentions cubeb as a remedy for infertility, showing it was already used by Arabs for medicinal purposes.
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Wikipedia - Tailed pepper - History
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Cubeb was introduced to Arabic cuisine around the 10th century. The Travels of Marco Polo, written in late 13th century, describes Java as a producer of cubeb, along with other valuable spices.In the 14th century, cubeb was imported into Europe from the Grain Coast, under the name of pepper, by merchants of Rouen and Lippe. Cubeb eventually came to be thought of as repulsive to demons by the people of Europe.
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Wikipedia - Tailed pepper - History
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Ludovico Maria Sinistrari, a Catholic priest who wrote about methods of exorcism in the late 17th century, includes cubeb as an ingredient in an incense to ward off an incubus.After the prohibition of its sale in Portugal in 1640, culinary use of cubeb decreased dramatically in Europe, and only its medicinal application continued to the 19th century. In the early 20th century, cubeb was regularly shipped from Indonesia to Europe and the United States. The trade gradually diminished to an average of 135 t (133 long tons; 149 short tons) annually, and practically ceased after 1940.
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Wikipedia - Tailed pepper - History
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In the fourth century BCE, the two Chinese astronomers responsible for the earliest information going into the star catalogues were Shi Shen and Gan De of the Warring States period. These books appeared to have lasted until the sixth century, but were lost after that. A number of books share similar names, often quoted and named after them.
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Wikipedia - Chinese astronomy - Star catalogues
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These texts should not be confused with the original catalogues written by them. Notable works that helped preserve the contents include: Wu Xian (巫咸) has been one of the astronomers under debate. He is often represented as one of the "Three Schools Astronomical tradition", along with Gan and Shi.
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Wikipedia - Chinese astronomy - Star catalogues
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The Chinese classic text Star Manual of Master Wu Xian (巫咸星經) and its authorship is still in dispute, because it mentioned names of twelve countries that did not exist in the Shang dynasty, the era in which it was supposed to have been written. Moreover, it was customary in the past for the Chinese to forge works of notable scholars, as this could lead to a possible explanation for the inconsistencies found. Wu Xian is generally mentioned as the astronomer who lived many years before Gan and Shi.
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Wikipedia - Chinese astronomy - Star catalogues
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The Han dynasty astronomer and inventor Zhang Heng (78–139 CE) not only catalogued some 2500 different stars, but also recognized more than 100 different constellations. Zhang Heng also published his work Ling Xian, a summary of different astronomical theories in China at the time. In the subsequent period of the Three Kingdoms (220–280 CE), Chen Zhuo (陳卓) combined the work of his predecessors, forming another star catalogue.
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Wikipedia - Chinese astronomy - Star catalogues
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This time, 283 constellations and 1464 stars were listed. The astronomer Guo Shoujin of the Yuan dynasty (1279–1368 CE) created a new catalogue, which was believed to contain thousands of stars. Unfortunately, many of the documents of that period were destroyed, including that of Shoujin. Imperial Astronomical Instruments (儀象考成) was published in 1757 and contains 3083 stars exactly.
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Wikipedia - Chinese astronomy - Star catalogues
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In the fourth century some Jewish Christian groups maintained that Jesus was himself a vegetarian. Epiphanius quotes the Gospel of the Ebionites where Jesus has a confrontation with the high priest. Jesus chastises the leadership saying, "I am come to end the sacrifices and feasts of blood; and if ye cease not offering and eating of flesh and blood, the wrath of God shall not cease from you; even as it came to your fathers in the wilderness, who lusted for flesh, and did sate to their content, and were filled with rottenness, and the plague consumed them. "According to Lightfoot, "the Christianized Essennes condemned the slaughter of victims on grounds very different from those alleged in the Epistle of Hebrews, not because they have been superseded by the Atonement, but because they are in their very nature repulsive to God; not because they have ceased to be right, but because they never were right from the beginning".Other early Christian historical documents observe that many influential Christians during the formative centuries of Christianity were vegetarian, though certainly not all.
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Wikipedia - Christian vegetarianism - Patristic evidence
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The Clementine homilies, a second-century work purportedly based on the teachings of the Apostle Peter, states, "The unnatural eating of flesh meats is as polluting as the heathen worship of devils, with its sacrifices and its impure feasts, through participation in it a man becomes a fellow eater with devils." While the Didascalia does not itself endorse vegetarianism, it records a group of individuals who believe they "should not eat flesh, and said that a man must not eat anything that has a soul in it.
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Wikipedia - Christian vegetarianism - Patristic evidence
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"Although early Christian vegetarianism appears to have been downplayed in favor of more "modern" Christian culture, the practice of vegetarianism appears to have been very widespread in early Christianity, both in the leadership and among the laity. Origen's work Contra Celsum quotes Celsus commenting vegetarian practices among Christians he had contact with. Although not vegetarian himself and vehemently against the idea that Christians must be vegetarians, Augustine nevertheless wrote that those Christians who "abstain both from flesh and from wine" are "without number".
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Wikipedia - Christian vegetarianism - Patristic evidence
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In the fourth century, Arianism, as traditionally understood, taught that the Father existed prior to the Son who was not, by nature, God but rather a changeable creature who was granted the dignity of becoming "Son of God". In 325, the First Council of Nicaea adopted the Nicene Creed which described Christ as "God of God, Light of Light, very God of very God, begotten, not made, being of one substance with the Father", and the "Holy Ghost" as the one by which "was incarnate ... of the Virgin Mary". ("the Word was made flesh and dwelled among us"). About the Father and the Son, the creed used the term homoousios (of one substance) to define the relationship between the Father and the Son.
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Wikipedia - Trinitarian Christianity - First Council of Nicaea (325)
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After more than fifty years of debate, homoousios was recognised as the hallmark of orthodoxy, and was further developed into the formula of "three persons, one being". The Confession of the First Council of Nicaea, the Nicene Creed, said little about the Holy Spirit. At the First Council of Nicea (325) all attention was focused on the relationship between the Father and the Son, without making any similar statement about the Holy Spirit.
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Wikipedia - Trinitarian Christianity - First Council of Nicaea (325)
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In the words of the creed: We believe in one God, the Father Almighty, Maker of all things visible and invisible. And in one Lord Jesus Christ, the Son of God, begotten of the Father Light of Light, very God of very God, begotten, not made, being of one substance with the Father; ... And in the Holy Ghost. ...
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Wikipedia - Trinitarian Christianity - First Council of Nicaea (325)
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In the fourth chapter, Shirky explores how means and motives alone cannot explain new uses for our cognitive surplus, explaining that we take the opportunities made available to us. He argues that we often discover unconventional routes to benefit society. Shirky cites examples such as the elderly adopting the Internet as new means for communication and skateboarders adapting drained swimming pools into skating ramps.
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Wikipedia - Cognitive Surplus - Opportunity
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The narrative about the drought-stricken pools proved an important point: the intended capabilities of something do not necessarily determine its functions. He goes on to discuss the Ultimatum game, in which a proposer and responder are given the task of splitting ten dollars. According to behavioral economics, proposers should always propose a split that heavily favors them and the responder should always accept it, because no matter how small their share is, there is still a gain.
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Wikipedia - Cognitive Surplus - Opportunity
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In practice, however, proposers tend to offer fair deals and responders tend to reject unfair proposals. On some level, we always feel we are in a social situation and will either treat each other fairly or punish those who do not. According to Shirky, this is why what he describes as the Public sector is so popular; it is designed to enrich society without any monetary incentive. In the public sector, digital networks connect people worldwide and give amateurs the opportunity to share their thoughts and work when they normally couldn't. There are no gatekeepers on the Internet; innovation is actively encouraged and younger generations in a changing environment can find their voice there.
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Wikipedia - Cognitive Surplus - Opportunity
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In the fourth era (1974–94), the Britannica introduced its 15th edition, which was reorganized into three parts: the Micropædia, the Macropædia, and the Propædia. Under Mortimer J. Adler (member of the Board of Editors of Encyclopædia Britannica since its inception in 1949, and its chair from 1974; director of editorial planning for the 15th edition of Britannica from 1965), the Britannica sought not only to be a good reference work and educational tool, but to systematize all human knowledge. The absence of a separate index and the grouping of articles into parallel encyclopaedias (the Micro- and Macropædia) provoked a "firestorm of criticism" of the initial 15th edition.
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Wikipedia - Encyclopaedia Britannica - 1974–1994
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In response, the 15th edition was completely reorganized and indexed for a re-release in 1985. This second version of the 15th edition continued to be published and revised until the 2010 print version. The official title of the 15th edition is the New Encyclopædia Britannica, although it has also been promoted as Britannica 3.On 9 March 1976 the US Federal Trade Commission entered an opinion and order enjoining Encyclopædia Britannica, Inc. from using: a) deceptive advertising practices in recruiting sales agents and obtaining sales leads, and b) deceptive sales practices in the door-to-door presentations of its sales agents.
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Wikipedia - Encyclopaedia Britannica - 1974–1994
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In the fourth film The Matrix Resurrections, a new version of Morpheus, originally a program subconsciously created by a suppressed Neo as part of a modal based upon his memories, is released by Bugs from the Matrix. Initially, Morpheus is an amalgamation of Neo's memories of Agent Smith and Morpheus. He retains the same purpose as Smith in The Matrix, serving as the lead Agent in a trio alongside Agents White and Jones. After Bugs infiltrates the modal and frees 'Smith', he assumes the identity of Morpheus and joins Bugs in working to find and free Neo from the Matrix once again.
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Wikipedia - Morpheus (The Matrix) - The Matrix Resurrections
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Morpheus appears before Neo inside Deus Machina during an evacuation due to an impending SWAT assault. He offers Neo the Red Pill, but Neo rejects it and Morpheus is forced to fight against SWAT during his attempt to persuade Neo. After Neo is collected by Bugs, Morpheus decides on using set and setting, with clips from Neo's video game playing in the background to instill a sense of nostalgia, in order to calm Neo.
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Wikipedia - Morpheus (The Matrix) - The Matrix Resurrections
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After Neo accepts the Red Pill, Morpheus fights people on a train through Tokyo under the influence of swarm mode, encouraging Neo to exit the Matrix through a mirror in a bathroom on board. Once Neo and the group reach Io, they visit an elderly Niobe, who is now the leader. She reveals that the new city was built by humans and machines, and that the Oracle warned them about a forthcoming threat before disappearing.
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Wikipedia - Morpheus (The Matrix) - The Matrix Resurrections
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Niobe then leads Neo to Morpheus' statue, telling him that he was elected for the high chair at the council, but ignored the warnings of the new power that was coming, firmly believing what Neo did was right (implying that in the 60 year time period, Zion was destroyed and Morpheus was killed). Morpheus appears aboard the Mnemosyne using a nanobot body, and encourages Neo to escape confinement in Io in order to search the Matrix for Trinity, which the extraction is successful as they manage to rescue her onto the ship. He later aids Bugs in rescuing her crew from the swarm people.
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Wikipedia - Morpheus (The Matrix) - The Matrix Resurrections
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In the fourth film The Matrix Resurrections, during the 60 year time period after Trinity's death in the Machine City, and the subsequent end of the Machine War, her body was recovered by the machines and is revived, only appearing to age twenty years due to the machine's modifications. Trinity was reinserted into the Matrix, where she was given the name "Tiffany" and became a married mother of three. She kept her penchant for motorcycles, working in a motorcycle workshop.
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Wikipedia - Trinity (The Matrix) - The Matrix Resurrections
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She comes into contact with Neo at Simulatte, as his original identity of Thomas Anderson and she begins to feel that something is not right with her life. After Neo is reawakened, he sees Trinity still-plugged-in body in a pod across from him before he is retrieved by machines allied to the humans. Neo enacts a plan to rescue her, but is interrupted by the Analyst; who enters Bullet Time to stop Neo and Trinity from reaching each other.
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Wikipedia - Trinity (The Matrix) - The Matrix Resurrections
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The Analyst reveals that as a machine he had rebuilt Neo and Trinity in the real world by discovering that by keeping Neo and Trinity close but not too close to each other they generated a new form of energy that could give more power to the machines when channeled through the Matrix. Then he built a new matrix with that in mind, posing as its new Architect. In order to keep them subdued, the Analyst suppressed all memories of their life before reinsertion and invented a family for Tiffany in order to dissuade Neo from attempting to form a romantic relationship with her, while himself posing as a therapist for Neo.
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Wikipedia - Trinity (The Matrix) - The Matrix Resurrections
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He also created an illusion that covered their real faces. After Sati contacts Niobe, Neo enacts a new plan to rescue Trinity, agreeing to the Analyst's terms that if Trinity chooses to remain Tiffany, then he will surrender.
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Wikipedia - Trinity (The Matrix) - The Matrix Resurrections
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Tiffany arrives at Simulatte and she appears to reject Neo. However, before her husband can take her from Simulatte, Trinity wakes up and rejects the life created by the Analyst. The Analyst enters Bullet Time again to try and kill Trinity, but is killed by Smith; who can also enter Bullet Time, with a purging gun.
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Wikipedia - Trinity (The Matrix) - The Matrix Resurrections
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Trinity and Neo fight the Analyst's and suites forces and escape into a skyscraper, where they are pursued by helicopters. Neo destroys the helicopters, but they are surrounded by police. Neo and Trinity jump from the building, and Trinity is revealed to have developed the ability to fly on her own and they do not die as she saw in her nightmare.
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Wikipedia - Trinity (The Matrix) - The Matrix Resurrections
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After Trinity is released from the Matrix, she embraces Neo. They re-enter the Matrix to tell the (apparently) alive Analyst that they plan on redesigning the Matrix as they see fit and to warn him to stay out of their way and the Analyst mentions that the leaders of machines, "the suits", did not purge him. The two then fly off together, circling each other while holding hands.
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Wikipedia - Trinity (The Matrix) - The Matrix Resurrections
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In the fourth method the measurer does not interact with the trunk or any internal point of the polygon. The measurer walks the perimeter shooting horizontal distances and azimuth to the next point until the crown's perimeter is circled. This is the simplest and most flexible method of the four. This method can also easily be used to measure the areas of other features encountered, for example, tree groupings or vernal ponds.
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Wikipedia - Tree crown measurement - Azimuth method
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In the fourth phase of prophase I, diplotene (from the Greek for "twofold"), crossing-over is completed. : 99 Homologous chromosomes retain a full set of genetic information; however, the homologous chromosomes are now of mixed maternal and paternal descent. : 99 Visible junctions called chiasmata hold the homologous chromosomes together at locations where recombination occurred as the synaptonemal complex dissolves. : 99 It is at this stage where meiotic arrest occurs in many species. : 99
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Wikipedia - Prophase - Diplotene
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In the fourth quarter of 2001, the company lost $3.4 billion on revenue of $793 million. In January 2002, the company filed bankruptcy. It listed total assets of $22.4 billion and debts of $12.4 billion and was paying annual interest of $600 million. As part of the bankruptcy, Hutchison Whampoa and ST Telemedia agreed to invest $750 million in the company.
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Wikipedia - Global Crossing - Bankruptcy and reemergence
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Hutchinson Whampoa later pulled out of the deal due to regulatory resistance.CIBC realized an estimated gain of $2 billion from its relatively small equity investment in the company, making it one of the most profitable investments by a financial institution in the 1990s. Winnick salvaged $735 million from his $20 million investment, although his interest was worth $6 billion on paper at its peak.In April 2002, Hutchinson Whampoa bought the company's 50% interest in the Hong Kong joint venture for $120 million.In November 2002, Global Crossing's Asian subsidiary, Asia Global Crossing, filed bankruptcy and sold its assets to Asia Netcom, a subsidiary of China Netcom.Between 1998 and 2001, Winnick sold approximately $420 million in company stock and other executives sold an additional $900 million in company stock.On December 9, 2003, the company emerged from bankruptcy and on April 1, 2004, the company once again became a public company.In March 2004, Gary Winnick and other ex-executives settled lawsuits filed by investors and former employees accusing the executives of committing securities fraud by using improper accounting to inflate the company's revenue.In October 2006, the company announced the acquisition of UK-based Fibernet Corp. for £49.8 million.In May 2007, the company acquired Impsat, a leading Argentine telecommunications company. Global Crossing and Impsat have had a commercial relationship since 2000, when Global Crossing selected Impsat as one of its providers of Point of Presence (PoP) facilities for Global Crossing's Latin American network, known as South American Crossing. Impsat has also been a customer of Global Crossing in Latin America since 2000.In October 2011, Level 3 Communications acquired the company for $3 billion, including the assumption of $1.1 billion in debt.
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Wikipedia - Global Crossing - Bankruptcy and reemergence
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In the fourth quarter of 2002 in the United States market, RCA was the biggest selling vendor for MP3 players with a 12.95% market share.As of August 2004 in the United States market, RCA had a 9% share among both flash and hard disk portable media players, ranking it fourth behind Apple, Rio and iRiver.
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Wikipedia - RCA Lyra - Sales and market share
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In the fourth quarter of 2008, two separate branches of Compiz were created: compiz++ and NOMAD; compiz++ was geared toward the separation of compositing and OpenGL layers for the rendering of the window manager without compositing effects, and the port from C to C++ programming language. NOMAD was geared towards the improvement of remote desktop performance for Compiz installations.
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Wikipedia - Compiz Fusion - Further branches
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In the fourth quarter of 2011, the First Quantum Minerals board approved the construction of an ISASMELT-based smelter at Kansanshi in Zambia. The smelter is to process 1.2 million t/y of copper concentrate to produce over 300,000 t/y of copper and 1.1 million t/y of sulfuric acid as a by-product. Construction is expected to be completed by mid-2014, and the capital cost is estimated at US$650 million. The estimated operating cost was given as US$69 per tonne of concentrate.The Kansanshi copper smelter project is estimated to be worth US$340–500 million per year in reduced concentrate freight costs, export duties and sulfuric acid costs.
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Wikipedia - ISASMELT - First Quantum Minerals
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In the fourth quarter of 2014, Dow announced new operating segments in response to its previously announced leadership changes. The company stated it would give further support to its end-market orientation and increase its alignment to Dow's key value chains – ethylene and propylene.
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Wikipedia - Dow Chemical Company - 2014 – New operating segments
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In the fourth reading, remarking that the man had become like God, knowing good and bad, God became concerned that man should also eat from the tree of life and live forever, so God banished him from the garden of Eden, to till the soil. God drove the man out, and stationed cherubim and a fiery ever-turning sword east of the garden to guard the tree of life. A closed portion ends here with the end of chapter 3. In the continuation of the reading in chapter 4, Eve bore Cain and Abel, who became a farmer and a shepherd respectively.
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Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18
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Cain brought God an offering from the fruit of the soil, and Abel brought the choicest of the firstlings of his flock. God paid heed to Abel and his offering, but not to Cain and his, distressing Cain. God asked Cain why he was distressed, because he had free will, and if he acted righteously, he would be happy, but if he did not, sin crouched at the door.
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Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18
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Cain spoke to Abel, and when they were in the field, Cain killed Abel. When God asked Cain where his brother was, Cain replied that he did not know, asking if he was his brother's keeper. God asked Cain what he had done, as his brother's blood cried out to God from the ground.
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Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18
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God cursed Cain to fail at farming and to become a ceaseless wanderer. Cain complained to God that his punishment was too great to bear, as anyone who met him might kill him.
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Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18
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So God put a mark on Cain and promised to take sevenfold vengeance on anyone who would kill him. Cain left God's presence and settled in the land of Nod, east of Eden.
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Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18
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Cain had a son, Enoch, and founded a city, and named it after Enoch. Enoch had a son Irad; and Irad had a son Mehujael; and Mehujael had a son Methushael; and Methushael had a son Lamech. The fourth reading ends here.
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Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18
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In the fourth revision of the DSM (DSM-IV-TR), tic disorders were classified as follows: Transient tic disorder consisted of multiple motor and/or phonic tics with duration of at least 4 weeks, but less than 12 months. Chronic tic disorder was either single or multiple motor or phonic tics, but not both, which were present for more than a year. Tourette syndrome was diagnosed when both motor and phonic tics were present for more than a year. Tic disorder NOS was diagnosed when tics were present, but did not meet the criteria for any specific tic disorder.
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Wikipedia - Tic disorder - DSM-IV-TR
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In the fourth round of China University Subject Rankings by the Ministry of Education released in 2018, ZJU had 31 subjects rated A, the most among Chinese universities, among which 11 subjects were rated A+, the third most after Peking and Tsinghua. Below is the list of A+/A/A- subjects of ZJU.
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Wikipedia - Zhejiang University - China's MOE Evaluation
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In the fourth scene of Richard Wagner’s opera Das Rheingold, the earth Goddess Erda prophesies the impending doom of the Gods. Wagner's orchestration here juxtaposes two significant dramatic leitmotifs, the one ascending to represent Erda and the other, "a descending variant of Erda's motive played over a chord of the Neapolitan sixth" with the intention of conveying their ultimate downfall to ominous and chilling effect. (D in the key of C♯ minor):
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Wikipedia - Neapolitan chord - Romantic period
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In the fourth season (1966–67) Doctor Who story "The Power of the Daleks", second incarnation of the Doctor, played by Patrick Troughton, awakens from his first regeneration and eventually faces one of his old nemeses, the Daleks. Human space colonists examine "dead" Daleks and, upon their re-activation, conjecture as to "what sort of positronic brain must this device possess". However, the Daleks are actually organic life-forms that were encased in robotic shells, and thus do not possess the purported positronic brain and, in any case, do not obey the Three Laws of Robotics.
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Wikipedia - Positronic brain - Doctor Who
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In the seventeenth season (1979–80) story "The Horns of Nimon", the fourth incarnation of the Doctor, played by Tom Baker, recognizes the Labyrinth-like building complex that serves as the lair of the Nimons as resembling both physically and functionally a "giant positronic circuit". When adequately fueled, the circuit was capable of transferring massive amounts of energy over vast distances to generate two black holes as gateways to hyperspace and to sustain a tunnel that served as the motive power between them for the transport of an invading force of Nimons from the dying planet Crinoth to Skonnos. In the fifth series (2010) Doctor Who story "Victory of the Daleks", the Daleks create a human-cyborg scientist "Bracewell", that is implanted in to the British scientific community to develop technology for the war effort. The creation was said to be controlled by a positronic brain.
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Wikipedia - Positronic brain - Doctor Who
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In the fourth section of The Origin of Birds, Heilmann examines the Tetrapteryx hypothesis proposed by William Beebe in 1915. This hypothesis was based on observations of bird embryos and hatchlings, which Beebe found to possess a presumably atavistic fringe of flight feathers on their hindlimbs. His main evidence came from examination of incipient quill feathers on the thigh of a four-day-old white-winged dove. He theorized based on this embryological fringe and the recapitulation theory that birds had once passed through a "Tetrapteryx" stage in their distant evolution, which he represented as a hypothetical four-winged gliding animal.Heilmann, though excited about Beebe's idea, found little evidence for these leg-wings when studying the nestlings in the Zoological Museum collection in Copenhagen.
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Wikipedia - The Origin of Birds - Beebe's leg-wings
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He also examined the nestlings of more basal bird species, such as the ostrich and the emu, searching for a trace of leg-wings there, again without success. Even after studying the nestlings of birds closely related to Beebe's doves, including pigeons, he still found no trace of leg-wings. Instead he found on the nestlings' thighs "a series of permanent feathers, and no atavism.
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Wikipedia - The Origin of Birds - Beebe's leg-wings
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If it were a genuine relic from such a very remote past, it would make its appearance, like a glimpse, in the embryo or squab, quickly to vanish again." Heilmann went on to outline the morphological difficulties involved in such a leg-wing, indicating that it could hinder survival. In effect, Beebe's Tetrapteryx theory was completely disregarded by Heilmann, and this remained the consensus in ornithological literature until much later.
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Wikipedia - The Origin of Birds - Beebe's leg-wings
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Despite this, Heilmann's Proavis illustrations sport a short border of feathers behind the thigh, which some authors have suggested was inspired by Beebe's Tetrapteryx idea. Beebe was relatively undeterred by the scientific community's acceptance of Heilmann's rejection of his theory, as is evidenced by the fact that he was still writing about his Tetrapteryx hypothesis well into the 1940s. His adherence to his theory was well-placed, as in 2003 a revolutionary discovery was made in the early Cretaceous Jiufotang Formation of Liaoning, China: Microraptor gui, the small, four-winged dromaeosaur that had led to renewed credence of the arboreal model for the origin of bird flight.
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Wikipedia - The Origin of Birds - Beebe's leg-wings
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This animal's most remarkable feature was the existence of long, pennaceous feathers on both its arms and legs, forming a set of four aerodynamic wings that its discoverers theorized were used for gliding. This discovery had the immediate effect of resurrecting the idea that leg feathers may have had some bearing on the origin of flight in birds, building on the idea originally proposed by Beebe and rejected by Heilmann.Today, Beebe's 1915 description of his hypothetical four-winged bird ancestor is regarded as prescient, and there is no doubt that Microraptor looks startlingly similar to the almost-century old Tetrapteryx illustrations. After its discovery, Microraptor had the effect of both reinvigorating the arboreal hypothesis as well as finally putting an end to the widespread acceptance of Heilmann's disregard for the Tetrapteryx theory.
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Wikipedia - The Origin of Birds - Beebe's leg-wings
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In the fourth stage, the luminance (Y) and the blue and red chrominance (Cb and Cr) are transformed by 8x8 DCT, so three sets of 64 DCT coefficients are obtained. To calculate the DCT in a 2D array, the formulas below are used. B p q = α p α q ∑ m = 0 M − 1 ∑ n = 0 N − 1 A m n cos π ( 2 m + 1 ) p 2 M cos π ( 2 n + 1 ) q 2 N , 0 ≤ p ≤ M − 1 , 0 ≤ q ≤ N − 1 {\displaystyle B_{pq}=\alpha _{p}\alpha _{q}\sum _{m=0}^{M-1}\sum _{n=0}^{N-1}A_{mn}\cos {\frac {\pi (2m+1)p}{2M}}\cos {\frac {\pi (2n+1)q}{2N}},\qquad 0\leq p\leq M-1,\;0\leq q\leq N-1} α p = { 1 M , p = 0 2 M , 1 ≤ p ≤ M − 1 α q = { 1 N , q = 0 2 N , 1 ≤ q ≤ N − 1 {\displaystyle \alpha _{p}={\begin{cases}{\frac {1}{\sqrt {M}}},&p=0\\{\sqrt {\frac {2}{M}}},&1\leq p\leq M-1\end{cases}}\qquad \alpha _{q}={\begin{cases}{\frac {1}{\sqrt {N}}},&q=0\\{\sqrt {\frac {2}{N}}},&1\leq q\leq N-1\end{cases}}} The inputs and outputs of this stage are summarized in the next table:
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Wikipedia - Color layout descriptor - DCT transformation
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In the fourth standard, "unification criteria for maintaining compatibility with previous standards" (過去の規格との互換性を維持するための包摂規準, kako no kikaku to no gokansei wo iji suru tame no hōsetsu kijun) is defined. Their application is limited to 29 code points whose glyphs vary greatly between the standards JIS C 6226-1983 on and after and JIS C 6226-1978. For those 29 code points, the glyphs from JIS C 6226-1983 on and after are displayed as "A", and the glyphs from JIS C 6226-1978 as "B". On each of them, both "A" and "B" glyphs may be applied. However, in order to claim compatibility with the standard, whether the "A" or "B" form has been used for each code point must be explicitly noted.
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Wikipedia - DEC Kanji - Unification criteria for compatibility
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In the fourth week of development of the human embryo as the respiratory bud grows, the trachea separates from the foregut through the formation of ridges which eventually separate the trachea from the oesophagus, the tracheoesophageal septum. This separates the future trachea from the oesophagus and divides the foregut tube into the laryngotracheal tube. By the start of the fifth week, the left and right main bronchi have begin to form, initially as buds at the terminal end of the trachea.The trachea is no more than 4 mm in diameter during the first year of life, expanding to its adult diameter of approximately 2cm by late childhood. The trachea is more circular and more vertical in children compared to adults, varies more in size, and also varies more in its position in relation to its surrounding structures.
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Wikipedia - Tracheal rings - Development
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In the fourth week of development, the respiratory diverticulum, starts to grow from the ventral (front) side of the foregut into the mesoderm that surrounds it, forming the lung bud. Around the 28th day, during the separation of the lung bud from the foregut it forms the trachea and splits into two bronchial buds, one on each side.
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Wikipedia - Respiratory diverticulum - Early stage
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In the fourth year of his degree course Richard's research project led him to using Oxford's Ferranti Mercury computer to solve integrals. During a fellowship year in France at Centre de Mécanique Ondulatoire Appliquée, he was able to use more powerful computers. Returning to Oxford, he worked on ab initio computations and applied computational techniques to solving quantum mechanical problems in theoretical chemistry, in particular studying spin-orbit coupling. His influential paper Third age of quantum chemistry (1979) marked the development of computational techniques for theoretical analysis whose precision equaled or surpassed experimental results.
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Wikipedia - Graham Richards - Industry involvement
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"The work represents perhaps a near perfect instance of theory being in harmony with experiment, each aspect vital to the other and the combination much more than the sum of the separate parts"– Graham Richards Richards saw the potential to apply computer techniques for examining the structure and properties of compounds in the area of pharmaceutical applications. He became a pioneer in the field of computer-aided molecular design. He was the first to produce coloured images modelling molecular structure graphically, and introduced many of the techniques now widely used in academia and industry.In 1982, Richards became a founding member of the Molecular Graphics Society (now the Molecular Graphics and Modelling Society, MGMS).
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Wikipedia - Graham Richards - Industry involvement
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The society started the Journal of Molecular Graphics in 1983. Richards served as the editor-in-chief of the journal from 1984 to 1996. The journal's name changed to Journal of Molecular Graphics and Modelling in 1997.In 1989 Richards was the scientific co-founder (with Tony Marchington, David Ricketts, James Hiddleston, and Anthony Rees) of Oxford Molecular Limited.
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Wikipedia - Graham Richards - Industry involvement
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The company developed software for modelling of small molecules and proteins, and drug design. The company was possible in part because of economic and legal changes under the government of Margaret Thatcher that enabled British universities to become involved with venture capital and technology transfer. As Oxford Molecular Group, Ltd.
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Wikipedia - Graham Richards - Industry involvement
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(OMG) the company was floated on the London Stock Exchange in 1992, making the university £10 million. The company was worth £450 million at its peak but was eventually sold for £70 million. It was one of several companies that combined to form Accelrys in 2001.Richards was instrumental in raising £64 million to fund a new laboratory for Oxford University through an innovative funding approach.
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Wikipedia - Graham Richards - Industry involvement
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£20 million worth of funding began with an "unusual collaboration" between Graham and David Norwood. Norwood then arranged for Beeson-Gregory to provide £20 million in exchange for half the University's equity share of any spin-out companies emanating from the Chemistry Department for 15 years. In 2003, Beeson-Gregory and Evolution Group merged, later creating a subsidiary, IP2IPO ("Intellectual property to initial public offering".
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Wikipedia - Graham Richards - Industry involvement
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Graham Richards became a non-executive director of IP2IPO in 2001, and non-executive chairman of IP2IPO in 2004.Through this arrangement the Chemistry Department has contributed over £100 million to the University of Oxford. Richards served as a director of ISIS Innovation Ltd., the University of Oxford's technology transfer company. It became Oxford University Innovation as of June 2016.
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Wikipedia - Graham Richards - Industry involvement
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It has brought around 60 spin-out companies into existence. The Financial Times has described the approach as "the way universities should be financed in the future".
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Wikipedia - Graham Richards - Industry involvement
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: 188 Richards also introduced the use of distributed computing in pharmaceutical design. Started in 2000, his Screensaver Lifesaver project exploited idle time on more than 3.5 million personal computers in over 200 countries, whose owners agreed to be involved and downloaded the project's screensaver. Using idle time from these computers, the project's software created a virtual supercomputer that screened billions of compounds against protein targets, searching for possible drug treatments for cancer, anthrax and smallpox.
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Wikipedia - Graham Richards - Industry involvement
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