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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 ... | Wikipedia - Covering lemma - Summary |
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-cla... | Wikipedia - Classical mathematics - Summary |
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 c... | Wikipedia - Formalism (philosophy) - Mathematics |
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 de... | Wikipedia - Von Neumann–Bernays–Gödel set theory - Summary |
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 ... | Wikipedia - Von Neumann–Bernays–Gödel set theory - Summary |
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 handlin... | Wikipedia - Von Neumann–Bernays–Gödel set theory - Summary |
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 ... | Wikipedia - Von Neumann–Bernays–Gödel set theory - Summary |
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 wa... | Wikipedia - Kempe chain - Application to the four colour theorem |
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 w... | Wikipedia - Kempe chain - Application to the four colour theorem |
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)... | Wikipedia - Kempe chain - Application to the four colour theorem |
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 c... | Wikipedia - Bible moralisée - Technical Analysis |
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... | Wikipedia - Bible moralisée - Technical Analysis |
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 m... | Wikipedia - Bible moralisée - Technical Analysis |
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. | Wikipedia - Bible moralisée - Technical Analysis |
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. | Wikipedia - Bible moralisée - Technical Analysis |
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. Meanwhil... | Wikipedia - Bible moralisée - Technical Analysis |
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 th... | Wikipedia - Decay chain - Actinide alpha decay chains |
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... | Wikipedia - Decay chain - Actinide alpha decay chains |
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 li... | Wikipedia - Cayley transform - Quaternion homography |
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} . Evaluatin... | Wikipedia - Cayley transform - Quaternion homography |
{\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 .} | Wikipedia - Cayley transform - Quaternion homography |
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 numb... | Wikipedia - Cayley transform - Quaternion homography |
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 kin... | Wikipedia - Sunday Sabbatarianism - Ethiopian Sabbatarian movement |
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 tau... | Wikipedia - Evolutionary thought - Augustine of Hippo |
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. | Wikipedia - Evolutionary thought - Augustine of Hippo |
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 t... | Wikipedia - Evolutionary thought - Augustine of Hippo |
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 g... | Wikipedia - Evolutionary thought - Augustine of Hippo |
... 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... | Wikipedia - Evolutionary thought - Augustine of Hippo |
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 we... | Wikipedia - Persian Walnut - Introduction around the world |
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 fro... | Wikipedia - Persian Walnut - Introduction around the world |
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;... | Wikipedia - Persian Walnut - Introduction around the world |
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... | Wikipedia - Tailed pepper - History |
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 emb... | Wikipedia - Tailed pepper - History |
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 ... | Wikipedia - Tailed pepper - History |
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 L... | Wikipedia - Tailed pepper - History |
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 applicatio... | Wikipedia - Tailed pepper - History |
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... | Wikipedia - Chinese astronomy - Star catalogues |
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. | Wikipedia - Chinese astronomy - Star catalogues |
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 no... | Wikipedia - Chinese astronomy - Star catalogues |
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... | Wikipedia - Chinese astronomy - Star catalogues |
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 Instrume... | Wikipedia - Chinese astronomy - Star catalogues |
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... | Wikipedia - Christian vegetarianism - Patristic evidence |
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 t... | Wikipedia - Christian vegetarianism - Patristic evidence |
"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 pract... | Wikipedia - Christian vegetarianism - Patristic evidence |
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 ... | Wikipedia - Trinitarian Christianity - First Council of Nicaea (325) |
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 w... | Wikipedia - Trinitarian Christianity - First Council of Nicaea (325) |
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. ... | Wikipedia - Trinitarian Christianity - First Council of Nicaea (325) |
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... | Wikipedia - Cognitive Surplus - Opportunity |
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, propose... | Wikipedia - Cognitive Surplus - Opportunity |
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; i... | Wikipedia - Cognitive Surplus - Opportunity |
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 editoria... | Wikipedia - Encyclopaedia Britannica - 1974–1994 |
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 Brit... | Wikipedia - Encyclopaedia Britannica - 1974–1994 |
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 sa... | Wikipedia - Morpheus (The Matrix) - The Matrix Resurrections |
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 fro... | Wikipedia - Morpheus (The Matrix) - The Matrix Resurrections |
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 h... | Wikipedia - Morpheus (The Matrix) - The Matrix Resurrections |
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 ... | Wikipedia - Morpheus (The Matrix) - The Matrix Resurrections |
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 ... | Wikipedia - Trinity (The Matrix) - The Matrix Resurrections |
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 t... | Wikipedia - Trinity (The Matrix) - The Matrix Resurrections |
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 th... | Wikipedia - Trinity (The Matrix) - The Matrix Resurrections |
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. | Wikipedia - Trinity (The Matrix) - The Matrix Resurrections |
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. | Wikipedia - Trinity (The Matrix) - The Matrix Resurrections |
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 ... | Wikipedia - Trinity (The Matrix) - The Matrix Resurrections |
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 th... | Wikipedia - Trinity (The Matrix) - The Matrix Resurrections |
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 ea... | Wikipedia - Tree crown measurement - Azimuth method |
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 c... | Wikipedia - Prophase - Diplotene |
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 ... | Wikipedia - Global Crossing - Bankruptcy and reemergence |
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 mill... | Wikipedia - Global Crossing - Bankruptcy and reemergence |
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. | Wikipedia - RCA Lyra - Sales and market share |
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 i... | Wikipedia - Compiz Fusion - Further branches |
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 expec... | Wikipedia - ISASMELT - First Quantum Minerals |
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. | Wikipedia - Dow Chemical Company - 2014 – New operating segments |
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 ... | Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18 |
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... | Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18 |
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. | Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18 |
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. | Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18 |
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. | Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18 |
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. | Wikipedia - Bereshit (parashah) - Fourth reading—Genesis 3:22–4:18 |
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 pre... | Wikipedia - Tic disorder - DSM-IV-TR |
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. | Wikipedia - Zhejiang University - China's MOE Evaluation |
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 ... | Wikipedia - Neapolitan chord - Romantic period |
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 ... | Wikipedia - Positronic brain - Doctor Who |
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... | Wikipedia - Positronic brain - Doctor Who |
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... | Wikipedia - The Origin of Birds - Beebe's leg-wings |
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 nestl... | Wikipedia - The Origin of Birds - Beebe's leg-wings |
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... | Wikipedia - The Origin of Birds - Beebe's leg-wings |
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 h... | Wikipedia - The Origin of Birds - Beebe's leg-wings |
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 th... | Wikipedia - The Origin of Birds - Beebe's leg-wings |
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 + ... | Wikipedia - Color layout descriptor - DCT transformation |
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... | Wikipedia - DEC Kanji - Unification criteria for compatibility |
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 foregu... | Wikipedia - Tracheal rings - Development |
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... | Wikipedia - Respiratory diverticulum - Early stage |
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... | Wikipedia - Graham Richards - Industry involvement |
"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 compoun... | Wikipedia - Graham Richards - Industry involvement |
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 Hiddlesto... | Wikipedia - Graham Richards - Industry involvement |
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 Mol... | Wikipedia - Graham Richards - Industry involvement |
(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... | Wikipedia - Graham Richards - Industry involvement |
£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 ... | Wikipedia - Graham Richards - Industry involvement |
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 tr... | Wikipedia - Graham Richards - Industry involvement |
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". | Wikipedia - Graham Richards - Industry involvement |
: 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... | Wikipedia - Graham Richards - Industry involvement |
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