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In the first era, reconstruction Klans did not burn crosses. The belief that reconstruction Klans burned crosses was introduced by Thomas Dixon Jr., in his novel The Clansman: A Historical Romance of the Ku Klux Klan (1905). A cross burning is first described in Book IV Chapter 2 "The Fiery Cross" on pages 324–326 of t... | Wikipedia - Cross lighting - Symbol of the Ku Klux Klan |
It will send a thrill of inspiration to every clansmen in the hills." It is further elaborated that In olden times when the Chieftain of our people summoned the clan on an errand of life and death, the Fiery Cross, extinguished in sacrificial blood, was sent by swift courier from village to village. This call was never... | Wikipedia - Cross lighting - Symbol of the Ku Klux Klan |
Here, on this spot made holy ground by the blood of those we hold dearer than life, I raise the ancient symbol of an unconquered race of men— This scene is accompanied by an unnumbered plate illustration by Arthur I. Keller, captioned "'The fiery cross of old Scotland's hills'", showing two robed, unmasked Klansmen, on... | Wikipedia - Cross lighting - Symbol of the Ku Klux Klan |
In the first era, the Sun ignited, heating the surrounding molecular cloud. 60 new minerals were produced and were preserved as inclusions in chondrites. The accretion of dust into asteroids and planets, bombardments, heating and reactions with water raised the number to 250. | Wikipedia - Mineral evolution - Planetary accretion |
In the first example, Rodolfo's first aria in La Sonnambula (1831), the portamento is indicated by the slur between the third and fourth notes. The second example, Judit's first line in Duke Bluebeard's Castle (1912) by Hungarian composer Béla Bartók, employs an inclining, wavy line between the fourth and fifth notes t... | Wikipedia - Pitch bending - Vocal portamento |
In the first example, a researcher attempts to determine if a drug has an effect on a particular disease. There are 314 patients, and they are diagnosed (disease: present or absent) before and after using the drug, which means that each sample can be described using 1 out of 4 combinations. Counts of individuals are gi... | Wikipedia - McNemar's test - Examples |
In this example, the null hypothesis of "marginal homogeneity" would mean there was no effect of the treatment. From the above data, the McNemar test statistic: χ 2 = ( 121 − 59 ) 2 121 + 59 {\displaystyle \chi ^{2}={(121-59)^{2} \over {121+59}}} has the value 21.35, which is extremely unlikely to form the distribution... | Wikipedia - McNemar's test - Examples |
A second example illustrates differences between the asymptotic McNemar test and alternatives. The data table is formatted as before, with different numbers in the cells: With these data, the sample size (161 patients) is not small, however results from the McNemar test and other versions are different. The exact binom... | Wikipedia - McNemar's test - Examples |
In the first example, we will show how to use a mass balance to derive a relationship between the percent excess air for the combustion of a hydrocarbon-base fuel oil and the percent oxygen in the combustion product gas. First, normal dry air contains 0.2095 mol of oxygen per mole of air, so there is one mole of O2 in ... | Wikipedia - Material balance - Reactive example |
For 1 kg of fuel oil containing 86.1% C, 13.6% H, 0.2% O, and 0.1% S the stoichiometric mass of air is 14.56 kg, so AFR = 14.56. The combustion product mass is then 15.56 kg. At exact stoichiometry, O2 should be absent. | Wikipedia - Material balance - Reactive example |
At 15 percent excess air, the AFR = 16.75, and the mass of the combustion product gas is 17.75 kg, which contains 0.505 kg of excess oxygen. The combustion gas thus contains 2.84 percent O2 by mass. The relationships between percent excess air and %O2 in the combustion gas are accurately expressed by quadratic equation... | Wikipedia - Material balance - Reactive example |
Assume we have a closed reactor in which the following liquid phase reversible reaction occurs: The mass balance for substance A becomes As we have a liquid phase reaction we can (usually) assume a constant volume and since n A = V ∗ C A {\displaystyle n_{\rm {A}}=V*C_{\rm {A}}} we get or In many textbooks this is give... | Wikipedia - Material balance - Reactive example |
In the first experiment, participants evaluated a poem with respect to how much they enjoyed it, the overall quality of the poem, and the amount of money a poetry magazine would pay for the poem. They were told that the experiment concerned the way in which people evaluate poetry. The subjects were randomly assigned to... | Wikipedia - Effort heuristic - Experiment 1 |
Participants in the low effort condition were told that the writer spent 4 hours on the poem while participants in the high effort condition were told the poet spent 18 hours on the piece. The researchers combined the liking and quality measures into one composite result and found participants provided more favorable e... | Wikipedia - Effort heuristic - Experiment 1 |
In the first experiments with laser heating, temperature came from a calibration of laser power made with known melting points of various materials. When using the pulsed ruby laser this was unreliable due to the short pulse. YAG lasers quickly become the standard, heating for relatively long duration, and allowing obs... | Wikipedia - Diamond anvil - Temperature measurement |
The first temperature measurements had a standard deviation of 30 °C from the brightness temperature, but due to the small sample size was estimated to be 50 °C with the possibility that the true temperature of the sample being was 200 °C higher than that of the brightness measurement. Spectrometry of the incandescent ... | Wikipedia - Diamond anvil - Temperature measurement |
In the first feature film, The Matrix, Morpheus successfully finds and monitors a man named Thomas A. Anderson, a hacker who calls himself Neo. Despite a close call with Agents that capture, interrogate, and place a surveillance device on Neo, Morpheus and his crew locate him. Morpheus offers Neo a choice of ingesting ... | Wikipedia - Morpheus (The Matrix) - The Matrix |
The Nebuchadnezzar crew is then able to eject Neo's body from the Matrix power plant and retrieve him from the cold sewers beneath the Earth's surface. Morpheus takes a risk in helping Neo escape the Matrix, as human minds that live too long in the Matrix may have trouble in comprehending the reality. Initially, Neo do... | Wikipedia - Morpheus (The Matrix) - The Matrix |
Shortly after Neo visits the Oracle, Morpheus is captured by agents who plan to hack into his mind. Because Morpheus, as a hovercraft captain, possesses access codes to the Zion mainframe computer, the surviving members of the ship's crew are about to unplug Morpheus from the Matrix, without reconnecting his mind and b... | Wikipedia - Morpheus (The Matrix) - The Matrix |
In the first feature-length Superman film in 1978, a vastly less idyllic image of Krypton was presented. Whereas in the comics Krypton was colorful and bright, the film depicted the planet with stark bluish-white terrain of jagged frozen plateaus under heavy, dark skies. The planet was threatened by their sun turning i... | Wikipedia - Krypton glossary - Superman |
Kryptonians themselves were portrayed as coolly cerebral and morally enlightened, clad in stark white bodysuits emblazoned with each family's house symbol. The architecture featured halls of white crystal under crystalline arches. The crystalline motif was employed not only in the architecture, but in the landscape and... | Wikipedia - Krypton glossary - Superman |
In 1948, Krypton was ultimately destroyed when its red sun began to collapse; the planet was pulled into the sun and steadily crushed, then exploded in the ensuing supernova. When Krypton was destroyed, fragments from the planet were launched into space, resulting in the creation of a harmful radioactive substance know... | Wikipedia - Krypton glossary - Superman |
On Clark Kent's eighteenth birthday, a glowing crystal revealed itself in the ship and compelled Clark to take it north. He eventually reached the Arctic, where the crystal constructed the massive crystalline Fortress of Solitude. | Wikipedia - Krypton glossary - Superman |
Inside, an artificially intelligent hologram of Jor-El appeared to him and initiated twelve years of Kryptonian education. These virtual versions of Jor-El and Lara remained as constructs within the Fortress throughout the series. Superman's symbol was given a Kryptonian origin in the film. Male Kryptonians were shown ... | Wikipedia - Krypton glossary - Superman |
In the first few centimeters of travel down the bore, the bullet reaches a significant percentage of its final velocity, even for high-capacity rifles, with slow burning powder. The acceleration is on the order of tens of thousands of gravities, so even a projectile as light as 40 grains (2.6 g) can provide over 1,000 ... | Wikipedia - Interior ballistics - The role of inertia |
In the first few days after giving birth the levels of cortisol are high which correlates with maternal approach behavior and positive maternal attitudes. Mothers with high levels of cortisol were also found to be more vocal towards their children. Mothers who experienced adversity in their own childhood, had higher da... | Wikipedia - Parental brain - Cortisol |
In the first few days following childbirth, the risk of a deep vein thrombosis (DVT) is relatively high as hypercoagulability increases during pregnancy and is maximal in the postpartum period, particularly for women with C-section with reduced mobility. Anti-coagulants or physical methods such as compression may be us... | Wikipedia - Postnatal care - Physical recovery in the subacute postpartum period |
The cervix gradually narrows and lengths over a few weeks. Postpartum infections can lead to sepsis and if untreated, death. Postpartum urinary incontinence is experienced by about 33% of all women; women who deliver vaginally are about twice as likely to have urinary incontinence as women who give birth via a cesarean... | Wikipedia - Postnatal care - Physical recovery in the subacute postpartum period |
Urinary incontinence in this period increases the risk of long term incontinence. In the subacute postpartum period, 87% to 94% of women report at least one health problem.Kegel exercises are recommended to strengthen the pelvic floor muscles and control urinary incontinence. Discharge from the uterus, called lochia, w... | Wikipedia - Postnatal care - Physical recovery in the subacute postpartum period |
Women are advised in this period to wear adult diapers or nappies, disposable maternity briefs, maternity pads or towels, or sanitary napkins. The use of tampons or menstrual cups are contraindicated as they may introduce bacteria and increase the risk of infection. An increase in lochia between 7–14 days postpartum ma... | Wikipedia - Postnatal care - Physical recovery in the subacute postpartum period |
If an episiotomy or perineal tear had to be sutured, the use of a donut pillow allows the woman to sit pain-free or at least with reduced pain. Some women feel uterine contractions, called afterpains, during the first few days after delivery. They have been described as similar to menstrual cramps and are more common d... | Wikipedia - Postnatal care - Physical recovery in the subacute postpartum period |
In the first few decades of nuclear magnetic resonance, spectrometers used a technique known as continuous-wave (CW) spectroscopy, where the transverse spin magnetization generated by a weak oscillating magnetic field is recorded as a function of the oscillation frequency or static field strength B0. When the oscillati... | Wikipedia - Nuclear Magnetic Resonance - Continuous-wave (CW) spectroscopy |
As of 1996, CW instruments were still used for routine work because the older instruments were cheaper to maintain and operate, often operating at 60 MHz with correspondingly weaker (non-superconducting) electromagnets cooled with water rather than liquid helium. One radio coil operated continuously, sweeping through a... | Wikipedia - Nuclear Magnetic Resonance - Continuous-wave (CW) spectroscopy |
As of 2014, low-end refurbished 60 MHz and 90 MHz systems were sold as FT-NMR instruments, and in 2010 the "average workhorse" NMR instrument was configured for 300 MHz.CW spectroscopy is inefficient in comparison with Fourier analysis techniques (see below) since it probes the NMR response at individual frequencies or... | Wikipedia - Nuclear Magnetic Resonance - Continuous-wave (CW) spectroscopy |
In the first few decades of the 1900s, especially in-between World War I and II, the keeping and breeding of the budgerigar had become very popular all around the world. Consequently, various mutations occurred and were soon established during this period. | Wikipedia - Budgerigar colour genetics - History |
In the first few decades of the 20th century, most field naturalists continued to believe that alternative mechanisms of evolution such as Lamarckism and orthogenesis provided the best explanation for the complexity they observed in the living world. But as the field of genetics continued to develop, those views became... | Wikipedia - Mutationism-biometrics debate - Modern synthesis |
Dobzhansky examined the genetic diversity of wild populations and showed that, contrary to the assumptions of the population geneticists, these populations had large amounts of genetic diversity, with marked differences between sub-populations. The book also took the highly mathematical work of the population geneticis... | Wikipedia - Mutationism-biometrics debate - Modern synthesis |
Ford's work would contribute to a shift in emphasis during the course of the modern synthesis towards natural selection over genetic drift.The evolutionary biologist Ernst Mayr was influenced by the work of the German biologist Bernhard Rensch showing the influence of local environmental factors on the geographic distr... | Wikipedia - Mutationism-biometrics debate - Modern synthesis |
Mayr also formulated the biological species concept that defined a species as a group of interbreeding or potentially interbreeding populations that were reproductively isolated from all other populations.In the 1944 book Tempo and Mode in Evolution, George Gaylord Simpson showed that the fossil record was consistent w... | Wikipedia - Mutationism-biometrics debate - Modern synthesis |
It received its name from the 1942 book Evolution: The Modern Synthesis by Julian Huxley.The modern synthesis provided a conceptual core—in particular, natural selection and Mendelian population genetics—that tied together many, but not all, biological disciplines: developmental biology was one of the omissions. It hel... | Wikipedia - Mutationism-biometrics debate - Modern synthesis |
In the first few decades of the 20th century, several men's sides were formed, and in 1934 the Morris Ring was founded by six revival sides: Cambridge Morris Men Letchworth Morris Thaxted Morris Men East Surrey Morris Men Greensleeves Morris Men (based in Wimbledon) Oxford Morris (which was not at the initial ring meet... | Wikipedia - Morris dance - Organisations |
Partly because women's and mixed sides were not eligible for full membership of the Morris Ring (this has now changed), two other national (and international) bodies were formed, the Morris Federation and Open Morris. All three bodies provide communication, advice, insurance, instructionals (teaching sessions) and soci... | Wikipedia - Morris dance - Organisations |
In the first few issues of the Belt Pulley magazine, Kurt Aumann wrote nearly all the articles contained in each issue. If any inclination toward any one brand of tractor or any one antique farm collectors organization could be perceived in the new publication, it would be an inclination toward the products of the Oliv... | Wikipedia - Belt Pulley - Belt Pulley reporters, contributors, and correspondents |
Toward this end, the magazine announced its intention of establishing a network of the reporters from around the nation to contribute articles. Originally, the writers or contributors to Belt Pulley magazine were called "Reporters." An early list of Reporters for the Belt Pulley magazine included Ed Westen of Kewaunee,... | Wikipedia - Belt Pulley - Belt Pulley reporters, contributors, and correspondents |
In 1989, Kevin Talley of Vermillion, South Dakota and Sam Meeker of North Henderson, Illinois were added as reporters. The reporters attended antique tractor shows across the nation and submitted "show reports" to the magazine on the shows they had attended. Humorous reminiscences from Walter M. Buescher, a retired All... | Wikipedia - Belt Pulley - Belt Pulley reporters, contributors, and correspondents |
In the first few months after arriving at Bletchley Park in September 1939, Alan Turing correctly deduced that the message-settings of Kriegsmarine Enigma signals were enciphered on a common Grundstellung (starting position of the rotors), and were then super-enciphered with a bigram and a trigram lookup table. These t... | Wikipedia - Banburismus - History |
The Germans did not have time to destroy all their cryptographic documents, and the captured material revealed the precise form of the indicating system, supplied the plugboard connections and Grundstellung for 23 and 24 April and the operators' log, which gave a long stretch of paired plaintext and enciphered message ... | Wikipedia - Banburismus - History |
The first day to be broken was 8 May 1940, thereafter celebrated as "Foss's Day" in honour of Hugh Foss, the cryptanalyst who achieved the feat. This task took until November that year, by which time the intelligence was very out of date, but it did show that Banburismus could work. It also allowed much more of the big... | Wikipedia - Banburismus - History |
However, the Kriegsmarine had changed the bigram tables on 1 July. By the end of 1940, much of the theory of the Banburismus scoring system had been worked out. The First Lofoten pinch from the trawler Krebs on 3 March 1941 provided the complete keys for February – but no bigram tables or K book. The consequent decrypt... | Wikipedia - Banburismus - History |
In the first few weeks of April, the two groups CORE and NAACP combined forces to make a change in racial equality. Both groups of protesters constructed a plan to shut down construction of the city's Municipal Services Building, by marching in front of Mayor James Tate's North Philadelphia row house. Furthermore, many... | Wikipedia - Racial equality - Accomplishments of CORE and NAACP |
In the first few weeks of the American military occupation of Japan, rape and other violent crime was widespread in naval ports like Yokohama and Yokosuka but declined shortly afterward. There were 1,336 reported rapes during the first 10 days of the occupation of Kanagawa prefecture. Historian Toshiyuki Tanaka relates... | Wikipedia - Aftermath of World War II - In Japan |
Eighth Army, recorded that in the one instance when the Japanese formed a self-help vigilante guard to protect women from off-duty GIs, the Eighth Army ordered armoured vehicles in battle array into the streets and arrested the leaders, and the leaders received long prison terms.According to Takemae and Ricketts, membe... | Wikipedia - Aftermath of World War II - In Japan |
Such behavior was commonplace, but news of criminal activity by Occupation forces was quickly suppressed. Rape committed by U.S. soldiers occupying Okinawa was also a notable phenomenon. | Wikipedia - Aftermath of World War II - In Japan |
Okinawan historian Oshiro Masayasu (former director of the Okinawa Prefectural Historical Archives) writes: Soon after the U.S. marines landed, all the women of a village on Motobu Peninsula fell into the hands of American soldiers. At the time, there were only women, children and old people in the village, as all the ... | Wikipedia - Aftermath of World War II - In Japan |
Soon after landing, the marines "mopped up" the entire village, but found no signs of Japanese forces. Taking advantage of the situation, they started "hunting for women" in broad daylight and those who were hiding in the village or nearby air raid shelters were dragged out one after another. According to Toshiyuki Tan... | Wikipedia - Aftermath of World War II - In Japan |
In the first few years after the 'Science Wars' edition of Social Text, the seriousness and volume of discussion increased significantly, much of it focused on reconciling the 'warring' camps of postmodernists and scientists. One significant event was the 'Science and Its Critics' conference in early 1997; it brought t... | Wikipedia - Science wars - Continued conflict |
In the same year, Collins organized the Southampton Peace Workshop, which again brought together a broad range of scientists and sociologists. The Peace Workshop gave rise to the idea of a book that intended to map out some of the arguments between the disputing parties. The One Culture? | Wikipedia - Science wars - Continued conflict |
: A Conversation about Science, edited by chemist Jay A. Labinger and sociologist Harry Collins, was eventually published in 2001. The book, the title of which is a reference to C.P. Snow's The Two Cultures, contains contributions from authors such as Alan Sokal, Jean Bricmont, Steven Weinberg and Steven Shapin.Other i... | Wikipedia - Science wars - Continued conflict |
by Ian Hacking (1999) and Who Rules in Science by James Robert Brown. To John C. Baez, the Bogdanov Affair in 2002 served as the bookend to the Sokal controversy: the review, acceptance, and publication of papers, later alleged to be nonsense, in peer-reviewed physics journals. Cornell physics professor Paul Ginsparg, ... | Wikipedia - Science wars - Continued conflict |
The new editor in chief of the journal Annals of Physics, who was appointed after the controversy along with a new editorial staff, had said that the standards of the journal had been poor leading up to the publication since the previous editor had become sick and died.Interest in the science wars has waned considerabl... | Wikipedia - Science wars - Continued conflict |
In 1999 Bruno Latour said "Scientists always stomp around meetings talking about 'bridging the two-culture gap', but when scores of people from outside the sciences begin to build just that bridge, they recoil in horror and want to impose the strangest of all gags on free speech since Socrates: only scientists should s... | Wikipedia - Science wars - Continued conflict |
In the first few years of its existence, training on education and the internet were a regular part of the development of E@I, aiding it in finding many new members. For its first few years, E@I was a scholarly branch of TEJO. As a result, E@I's first few seminars were a collaboration with TEJO. E@I-2000 – Esperanto@In... | Wikipedia - E@I - Seminars |
In the first few years of production, the Trident 2 was popular with a large number sold to large bus operators such as Stagecoach, FirstGroup, Travel West Midlands and Lothian Buses. A total of 2,255 Dennis Tridents would be built for London bus operators, 998 of these built for Stagecoach London with Alexander ALX400... | Wikipedia - Dennis Trident 2 - Orders |
In the first field season during the summer of 2001, six separate crews of five to seven people occupied the station and began work. From 2002 to 2013, seven crews occupied the remote outpost. | Wikipedia - Flashline Mars Arctic Research Station - Timeline of operations |
In the first fifth of the 21st Century, Fender turned to digital technology to expand its lineup of amplifiers. The first of these, the Cyber Twin and Cyber Deluxe, used circuits within the computer chips to replicate famous amps and effects. The preamp is tube-driven, and the power amp is solid state.Next came the G-D... | Wikipedia - Fender amplifier - The 21st Century: reissues and modeling |
It was released in 2007 along with a PC software package to allow it to emulate a wide array of pedals, stompboxes, and amplifiers. The G-Dec won high praise at the time but its effects, based on three-decade-old MIDI technology, were rapidly outdated. An updated G-DEC 3 was released in 2010, followed by the Mustang in... | Wikipedia - Fender amplifier - The 21st Century: reissues and modeling |
2014 saw the traditionally-styled Champion amplifier (not to be confused with the classic and reissue Champion/Champ tube amplifiers) released. This amp eschewed the Fuse software in favor of an on-board system, selected by knobs. 2015 saw the release of the Mustang v.2 amplifiers, along with a refresh of the Fuse PC a... | Wikipedia - Fender amplifier - The 21st Century: reissues and modeling |
In 2017, the Mustang GT series was launched, with Bluetooth capability and wi-fi for over-the-air software updates, with a modernized look and smartphone-enabled functionality through the new Fender Tone app. At the same time, Fender re-released a number of classic amplifiers such as the Bassman and Bandmaster, to high... | Wikipedia - Fender amplifier - The 21st Century: reissues and modeling |
In the first film, Smith is one of the three Agents sent to deal with Morpheus. After Neo is successfully removed from the Matrix, Smith arranges Morpheus' capture by bribing Cypher, a disillusioned member of Morpheus' crew, with reintegration into The Matrix. Upon his capture of Morpheus, he then attempts, to no avail... | Wikipedia - Agent Smith - The Matrix |
When Neo manages to free Morpheus, Smith, after ordering the dispatch of Sentinels to the Nebuchadezzer, then interferes with Neo's escape, with Neo managing to put up a fight against Smith while the latter dominated the fight overall, and narrowly win by breaking free of Smith when the latter tried to force him to be ... | Wikipedia - Agent Smith - The Matrix |
In the first film, the Oracle is depicted as a cheerful old lady who smokes cigarettes and bakes cookies. She possesses the power of foresight, which she uses to advise and guide the humans attempting to fight the Matrix. Later, she is revealed to be a sapient program who is integral to the very nature of the Matrix it... | Wikipedia - The Oracle (The Matrix) - Character history |
In reality, Mary Alice played the Oracle because Gloria Foster died of complications from diabetes before her role in Matrix Revolutions was shot. In The Matrix Revolutions and Enter the Matrix, it is explained that Kamala and Rama Kandra, the parents of Sati, traded with the Merovingian, giving the Oracle's terminatio... | Wikipedia - The Oracle (The Matrix) - Character history |
Neo meets the Oracle in two different locations over the course of the film series. In The Matrix, he finds her in an apartment filled with various "potentials"—children whose ability to control their surroundings suggests that they may be The One. During Reloaded, he returns to the apartment only to find it empty, the... | Wikipedia - The Oracle (The Matrix) - Character history |
She has with her a purse filled with candies that resemble the red pill Neo took to free himself from the Matrix. In Revolutions, the two meet in the kitchen of the apartment, sometime after Morpheus and Trinity seek her advice in the living room. In the first film, Agent Smith revealed that the first Matrix was a fail... | Wikipedia - The Oracle (The Matrix) - Character history |
This has been revealed in The Matrix Online continuity as the Paradise version of the Matrix. The Architect confirms this (and his own responsibility for its creation) in the second film, adding that he also created a second failed Matrix based on human history and nature (as he perceived it without the Oracle), which ... | Wikipedia - The Oracle (The Matrix) - Character history |
In The Matrix Reloaded and The Matrix Revolutions, the Oracle succeeds in unbalancing the Matrix (seeing the simultaneous rise of both Neo and Smith) to the extent that it is almost destroyed. In doing so, she manages to bring about a resolution in which the machines and the humans can coexist in peace. The Architect t... | Wikipedia - The Oracle (The Matrix) - Character history |
The Architect also promises to the Oracle that the humans desiring to be free from the Matrix will gain their freedom as part of the peacemaking between the humans and the machines. When asked whether Neo will return, she says she suspects that they will see him again, indicating that he may still be alive, that he may... | Wikipedia - The Oracle (The Matrix) - Character history |
In the first form given above, the Wirtinger inequality can be used to prove the isoperimetric inequality for curves in the plane, as found by Adolf Hurwitz in 1901. Let (x, y) be a differentiable embedding of the circle in the plane. Parametrizing the circle by so that (x, y) has constant speed, the length L of the c... | Wikipedia - Wirtinger's inequality for functions - Application to the isoperimetric inequality |
Since the integrand of the integral defining L is assumed constant, there is L 2 2 π − 2 A = ∫ 0 2 π ( x ′ ( t ) 2 + y ′ ( t ) 2 + 2 y ( t ) x ′ ( t ) ) d t {\displaystyle {\frac {L^{2}}{2\pi }}-2A=\int _{0}^{2\pi }{\big (}x'(t)^{2}+y'(t)^{2}+2y(t)x'(t){\big )}\,\mathrm {d} t} which can be rewritten as ∫ 0 2 π ( x ′ ( ... | Wikipedia - Wirtinger's inequality for functions - Application to the isoperimetric inequality |
Without changing the area or length of the curve, (x, y) can be replaced by (x, y + z) for some number z, so as to make y have average value zero. Then the Wirtinger inequality can be applied to see that the second integral is also nonnegative, and therefore L 2 4 π ≥ A , {\displaystyle {\frac {L^{2}}{4\pi }}\geq A,} w... | Wikipedia - Wirtinger's inequality for functions - Application to the isoperimetric inequality |
In the first generation of chain boats the chain ran over chain drums at the side of the boat. In fast-flowing currents or when there were problems lifting the chain due to silting or obstacles on the riverbed such as large rocks, the boat could swing off-course markedly and list to one side. As a result, on later chai... | Wikipedia - Chain boat - Chain driver |
In the first group of examples u is an unknown function of x, and c and ω are constants that are supposed to be known. Two broad classifications of both ordinary and partial differential equations consist of distinguishing between linear and nonlinear differential equations, and between homogeneous differential equatio... | Wikipedia - Order of differential equation - Examples |
Homogeneous second-order linear ordinary differential equation: d 2 u d x 2 − x d u d x + u = 0. {\displaystyle {\frac {d^{2}u}{dx^{2}}}-x{\frac {du}{dx}}+u=0.} Homogeneous second-order linear constant coefficient ordinary differential equation describing the harmonic oscillator: d 2 u d x 2 + ω 2 u = 0. | Wikipedia - Order of differential equation - Examples |
{\displaystyle {\frac {d^{2}u}{dx^{2}}}+\omega ^{2}u=0.} Heterogeneous first-order nonlinear ordinary differential equation: d u d x = u 2 + 4. {\displaystyle {\frac {du}{dx}}=u^{2}+4.} | Wikipedia - Order of differential equation - Examples |
Second-order nonlinear (due to sine function) ordinary differential equation describing the motion of a pendulum of length L: L d 2 u d x 2 + g sin u = 0. {\displaystyle L{\frac {d^{2}u}{dx^{2}}}+g\sin u=0.} In the next group of examples, the unknown function u depends on two variables x and t or x and y. Homogeneous... | Wikipedia - Order of differential equation - Examples |
{\displaystyle {\frac {\partial u}{\partial t}}+t{\frac {\partial u}{\partial x}}=0.} Homogeneous second-order linear constant coefficient partial differential equation of elliptic type, the Laplace equation: ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 = 0. {\displaystyle {\frac {\partial ^{2}u}{\partial x^{2}}}+{\frac {\partial ^{2}u}{... | Wikipedia - Order of differential equation - Examples |
In the first group of examples, let the ring R of coefficients be Z {\displaystyle \mathbb {Z} } . A free group has cohomological dimension one. As shown by John Stallings (for finitely generated group) and Richard Swan (in full generality), this property characterizes free groups. This result is known as the Stallings... | Wikipedia - Cohomological dimension - Examples |
The Stallings-Swan theorem for a group G says that G is free if and only if every extension by G with abelian kernel is split. The fundamental group of a compact, connected, orientable Riemann surface other than the sphere has cohomological dimension two. More generally, the fundamental group of a closed, connected, or... | Wikipedia - Cohomological dimension - Examples |
In the first group, the pessimists, is framed the same Olduvai theory of Duncan and other works such as the die-off or catastrophic collapse proposed by David Price, Reg Morrison and Jay Hanson. They usually invoke a number of determinisms such as strong, genetic, and energetic determinism (Leslie A. White's Basic Law ... | Wikipedia - Olduvai Theory - Catastrophic collapse or die-off |
In the first half of 1871, 1,527 brumbies were reported shot on the east side of the Bogan River, with similar numbers expected as the hunt moved to the west side. Alexander Ryrie, owner of Micelago Run in Monaro, killed about 1,400 brumbies in two-and-a-half years. Under contract to the Australian Agricultural Company... | Wikipedia - Brumby shooting - Notable hunts and shooters |
Many thousands a year were killed on a run of the Dawson River. Over 8,000 were trapped and shot in a summer season at Eurombah in the 1890s. Ben Supple was a well-known hunter credited for exterminating the extensive number of brumbies at Walra station on the Macleay River. | Wikipedia - Brumby shooting - Notable hunts and shooters |
In the mid-1890s, J. Nixon led a party that shot nearly 3,500 brumbies over eighteen months at Rawbelle station and Culcralgie station. The Brisbane Courier reported on 15 May 1924 that brumbies had become a severe pest in the Cape York Peninsula, and that Mr. Massey and his son had killed 964 brumbies. Massey stated t... | Wikipedia - Brumby shooting - Notable hunts and shooters |
In 1927, the Western Star And Roma Advertiser reported that a shooter on Alexander Downs had killed 2,000 brumbies in a season at one shilling each. In 1930, a "brumby menace" was reported by the Queensland Times. Some of the brumbies were reported to be the offspring of animals set free when the Beerburrum Soldier Set... | Wikipedia - Brumby shooting - Notable hunts and shooters |
Proclamations named the Bowen, Maryborough and Townsville, Roma, Toowoomba and Rockhampton stock districts, and newspapers reported "open season" on brumbies. Additional hunts were authorized through the mid-1930s. | Wikipedia - Brumby shooting - Notable hunts and shooters |
By the mid-1940s, brumbies were again considered a serious problem threatening big stock rearing. At Clifton Hill Station, 4,000–5,000 brumbies had been shot without diminishing their impact. In 18 months, 8,000 brumbies had been shot along the Cooper River. In 1949, the eastern suburbs of Sydney were invaded by brumbi... | Wikipedia - Brumby shooting - Notable hunts and shooters |
In the first half of 1926, building on de Broglie's hypothesis, Erwin Schrödinger developed the equation that describes the behavior of a quantum-mechanical wave. The mathematical model, called the Schrödinger equation after its creator, is central to quantum mechanics, defines the permitted stationary states of a quan... | Wikipedia - History of quantum mechanics - Wave mechanics |
This calculation accurately reproduced the energy levels of the Bohr model. In May 1926, Schrödinger proved that Heisenberg's matrix mechanics and his own wave mechanics made the same predictions about the properties and behavior of the electron; mathematically, the two theories had an underlying common form. | Wikipedia - History of quantum mechanics - Wave mechanics |
Yet the two men disagreed on the interpretation of their mutual theory. For instance, Heisenberg accepted the theoretical prediction of jumps of electrons between orbitals in an atom, but Schrödinger hoped that a theory based on continuous wave-like properties could avoid what he called (as paraphrased by Wilhelm Wien)... | Wikipedia - History of quantum mechanics - Wave mechanics |
In the first half of 2007, David Nicholson announced the "National Programme, Local Ownership programme" (known as "NLOP") which dissolved the 5 clusters and devolved responsibility for the delivery of the programme to the ten English strategic health authorities (SHAs). Connecting for Health retains responsibility for... | Wikipedia - NHS Connecting for Health - Local ownership |
In the first half of 2008, a small area of the Sea World Ski Lake north of the bridge was filled with sand to aid in the construction of a new roller coaster. The Sea World Train was closed to give vehicles access to the construction site and remains closed to this day. By July, some of the footings of the roller coast... | Wikipedia - Jet Rescue - History |
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