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=== War with the Omahas ===
== 1806: Melgares and Pike ==
=== Pike at the village ===
Pike refused to be intimidated. He told the chief
There is no firm documentary evidence of occupation of the Webster County village after 1809. However, analysis of pottery and glass beads suggests that the site was re-occupied during the second decade of the 19th century; and three letters from 1823 and 1825 suggest that the Kitkehahki were living on the Republican. By 1833, however, the village had been abandoned and the band was living on the Loup River. In that year, the four Pawnee bands, treated as a single tribe by the U.S. government, signed a treaty in which they gave up their lands south of the Platte.
=== A. T. Hill ===
=== Nebraska versus Kansas ===
Although Elizabeth Johnson was mistaken about the Pike village site, her mistake is held to be a fortunate one. The Webster County site had been subjected to decades of cultivation and relic hunting. The Republic County site was not entirely pristine, due to surface collecting and possibly to amateur excavation; but it was far better preserved. Today, the Kansas Historical Society operates a museum on the site, built in 1967 over one of the excavated earth lodges.
== Preservation ==
The Australian national baseball team represents Australia in international baseball tournaments and competitions. They are ranked as the top team in Oceania, and are the Oceanian Champions, having been awarded the title in 2007 when New Zealand withdrew from the Oceania Baseball Championship. After achieving a last (16th) place in the 2013 World Baseball Classic, their ranked dropped to 13, which is the lowest rank Australia ever got. The highest rank they have achieved was 9th.
* – Player has not played for Australia in international competition prior to 2013 WBC
* * – Multiple tournaments were held since the previous release of the rankings.
===== United States, 2006 =====
Australia was based in Peoria, Arizona — the site of the Seattle Mariners spring training camp — for their preparation for the formal start of their 2009 campaign. Unlike 2006, in which they had one exhibition game, they competed against three different Major League clubs: the Seattle Mariners, the Milwaukee Brewers and the Chicago White Sox. Their game against Seattle was Ken Griffey, Jr. ' s first game playing for the Mariners since October 1999, and was also their first victory as part of a World Baseball Classic tour.
Australia has participated in ten of the IBAF World Cup tournaments. To date its best result has been 5th, which Australia has achieved twice in both of the most recent tournaments held — 2009 and 2011. At the 2007 tournament, Trent Oeltjen became the first Australian player to be named in a World Cup All Star team, in recognition of his tournament-leading hitting and base-running statistics. Australia is currently participating in the 2011 tournament in Panama.
==== Intercontinental Cup ====
It was only the third time Cuba had been beaten in the gold medal match in the tournament's history, having reached the tournament decider every time they have participated. Australia also shares another honour with Cuba: of the nine nations to have hosted the tournament, only Australia and Cuba have won as hosts, combining for five tournament wins from five times hosted. (Cuba in 1979, 1987, 1995 and 2002, Australia in 1999.)
==== Asian Baseball Championship ====
=== Characters ===
Once the Kongs collect all DK coins, they give the coins to Funky, who in exchange gives them a gyrocopter. The duo then finds an enigmatic creature called the Banana Bird Queen, who is bound to a barrier cast by K. Roolenstein. She tells the Kongs that she can only be freed if her separated children are returned to her, and that she will rid the land of K. Rool if she is freed. The Kongs find each of her children in a cave, where one of the birds is trapped in an egg which hatches when the Kongs complete a Simon-like memory game. After rescuing them and completing a large trade sequence between the Brothers Bear, the Kongs return the children to the Queen. The Queen and her children all sing, annihilating the barrier. The Queen proceeds to chase K. Rool, who is fleeing in a hovercraft. When she catches up to him, she drops a giant eggshell on top of him, which Dixie and Kiddy land on. The Kongs repeatedly knock on the shell, annoying K. Rool.
Herbert Jefferis Pennock (February 10, 1894 – January 30, 1948) was an American professional baseball pitcher. He played in Major League Baseball from 1912 through 1933. He is best known for his time spent with the star-studded New York Yankee teams of the mid to late 1920s and early 1930s.
Pennock missed most of the 1913 season with an illness. In the 1914 season, Pennock posted an 11 – 4 win – loss record with a 2.79 earned run average (ERA) in 151 2 ⁄ 3 innings pitched for the Athletics, and pitched three scoreless innings in the 1914 World Series, which the Athletics lost to the Boston Braves. Mack let Bender go after the season, naming Pennock his Opening Day starting pitcher in 1915. On Opening Day, Pennock threw a one-hit complete game shutout against the Boston Red Sox. However, as the Athletics struggled, Pennock's nonchalant playing style drew Mack's ire. Concluding that Pennock "lacked ambition", Mack sold Pennock to the Red Sox for the waiver price of $ 2,500 ($ 58,479 in current dollar terms). Mack later regarded this sale as his greatest mistake.
=== New York Yankees ===
=== Return to Boston ===
In December 1943, R. R. M. Carpenter, Jr., the new owner of the Philadelphia Phillies, hired Pennock as his general manager, after receiving a recommendation from Mack. Carpenter gave Pennock a lifetime contract. Pennock filled Carpenter's duties when the team's owner was drafted into service during World War II in 1944. As general manager, Pennock changed the team's name to the "Blue Jays", and invested $ 1 million ($ 13,442,344 in current dollar terms) into players who would become known as the "Whiz Kids", who won the National League pennant in 1950, including Curt Simmons and Willie Jones. He also created a "Grandstand Managers Club", the first in baseball history, allowing fans to give feedback to the team, and advocated for the repeal of the Bonus Rule.
By mid-1944 the 4th Armoured Brigade was located in Southport, Queensland. As of 1 June, the brigade had a strength of 4,719 men and was scheduled to be ready for offensive operations by October that year. During June it also established a training area at Nerang in Queensland, where armoured units could practice operating in tropical conditions. In September 1944 the brigade gained the 2 / 1st Armoured Brigade Reconnaissance Squadron when the 1st Armoured Brigade Group was disbanded; this unit was reorganised to become the Armoured Squadron (Special Equipment) in January 1945. The 2 / 6th Armoured Regiment was also re-assigned to the 4th Armoured Brigade, but was stationed in the Sydney area. Following the disbandment of the 1st Armoured Brigade Group the 4th Armoured Brigade was the last remaining armoured brigade in the Australian Army.
During 1944 the 4th Armoured Brigade provided crews for comparative trials of the American M4 Sherman and British Churchill tank in New Guinea conditions that were conducted by the Australian Army in response to a request from the British War Office. Before the tanks were sent to New Guinea, the 4th Armoured Brigade trialled two Sherman tanks alongside Grants and Matilda IIs in Queensland during mid-1944. The Churchills and Shermans were subsequently trialled in the Madang region of New Guinea; the Churchill proved better suited to jungle conditions. The Australian Army later ordered 510 Churchills, but none were delivered before the end of the war.
The song was leaked to internet on October 21, 2009, one day after ex-girlfriend Rihanna's ballad "Russian Roulette" was also leaked. The song, which has been described as "melancholy", sees Brown singing about a relationship that has slipped out of his hands with its chorus calling for an "incremental reconciliation" of the unspecified relationship. Jayson Rodriguez of MTV News noted that both "Crawl" and Rihanna's "Russian Roulette" would inevitably be interpreted as being about Brown and Rihanna's relationship.
On November 2, 2009, several stills from the video were released onto the internet. The photos focused on two sets of the video, a desert location, and a snow and puddle-spotted alleyway. In both settings, Brown wears the same thick black glasses, brown leather trench coat, white t-shirt, and fingerless gloves, among other attire. Cassie appears in a photo from the alleyway scenes, as the desert scenes show Brown in "deep contemplation". The video first aired on The Wendy Williams Show on Friday, November 13, 2009, when Brown was a guest on the show. The video opens with Brown sitting on an edge of a bed wearing a plain white t-shirt. As the music begins and he starts singing, his heart is shown lit up red and beating in his chest. The singer then walks into an alleyway on a winter's night, revealed in the air as he breathes. Brown walks past several storefronts, seeing images of Cassie broadcast on television. He then sees paparazzi taking photos of her, but she does not notice him. Brown is shown in a desert scene, and then returns to the winter night scene as Cassie sees him and they walk towards each other meeting face-to-face. They gather close, but Brown does not reel her in as the video ends. The music video ranked at forty-eight on the BET: Notarized Top 100 Videos of 2009 countdown.
Digital download
Songwriting - Chris Brown, Nasri Atweh, Adam Messinger, Luke Boyd
In 1924, Bonner Park was created out of John L. Bonner's estate near the university. The park today has multiple athletic fields and courts in addition a band shell used by the Missoula City band through the summer. The Kiwanis club set up a park downtown in 1934, making Kiwanis Park the first of a string of parks which line both sides of the Clark Fork River. One of those parks on the southern bank of the river is McCormick Park, which was created with WPA funds out of surplus highway land, a parcel from the American Hide and Fur Company, and land donated from the Kate McCormick estate. The 26-acre (11 ha) park, named for Washington J. McCormick and his wife is home to a skate park, aquatics center, a free bike check-out and a children's fishing pond. Other popular parks include the Jacobs Island Bark Park, a designated area for dogs to play off-leash; the Montana State veterans' memorial rose garden; Waterwise Garden, a "living laboratory" garden utilizing water conservation techniques; and Splash Montana Waterpark at Playfair Park.
Missoula's system of government has changed four times since 1883 when an aldermanic form of government was approved with the town charter. The city adopted a commission-council form of government in 1911 with the opening of new City Hall and a council – manager government in 1954 before returning to an aldermanic form of government in 1959. Since January 1, 1997, Missoula has been governed in accordance with the Missoula City Charter, which calls for a mayor-council system of government.
Missoula's public schools are part of the Missoula County Public School districts 1, 4, 20, and 23. In Missoula, there are nine public elementary schools (kindergarten to 5th grade), three public middle schools (6th to 8th grades), four public high schools (9th to 12th grades), and three public schools serving kindergarten to 8th grade. Missoula also has several private schools including an international school, religious-affiliated schools, as well as Next Step Prep, a theater academy high school operated by the Missoula Children's Theatre.
Missoula's single – broadcast over – air television media market is the largest in Montana and ranked 165 nationally in as of 2015. Though Missoula itself is second in population to Billings, Montana, Missoula's single-broadcast over-air television media market includes all of Missoula, Ravalli, Granite, Mineral, Lake, Flathead, and Sanders Counties in the more densely populated western region of Montana and serves over 112,600 television homes as of 2015. Missoula is home to three local affiliate channels: KPAX-TV (CBS / MTN, The CW; founded 1970; channel 8), KECI-TV (NBC; founded 1954 as KGVO-TV; channel 13, and KTMF-TV ( ABC, FOX; founded 1991; channel 23). Also based in Missoula at the University of Montana is Montana PBS (founded 1984; channel 11). There are seventeen FM radio stations and four AM radio stations licensed in the city.
Following the deregulation of Montana's electricity market in 1997, Montana Power Company began to divest its energy business. MPC sold substantially all its electrical generating assets to the PPL Corporation in December 1997 and its energy transmission and distribution business to NorthWestern Corporation in February 2002. Despite filing for bankruptcy in 2002, NorthWestern Corporation's subsidiary NorthWestern Energy is the primary provider of electric and natural gas service to Missoula in addition to the Rural Utilities Service's Missoula Electric Cooperative.
==== Trail system ====
Direct intercity ground travel needs are provided by bus carriers Greyhound Lines and Rimrock Trailways. Intercity rail travel was available from 1883, when the Northern Pacific Railway began service through Missoula, until 1979 when Amtrak discontinued its North Coast Hiawatha route across southern Montana. In 1901, Northern Pacific built their station at the terminus of Higgins Avenue; since 1985, it has been on the National Register of Historic Places. A feasibility study was commissioned by Congress in 2008 to examine the merits of reopening the North Coast Hiawatha, but as of 2008, the nearest rail station to Missoula is the Whitefish station of Amtrak's Empire Builder, 136 miles (219 km) to the north.
Missoula has produced and been home to a number of notable individuals in varying fields. Its natives and residents are referred to as "Missoulians". In politics, Jeannette Rankin, the first woman in congress, was born and raised in Missoula while Senators Mike Mansfield, the U.S.'s longest serving Senate Majority Leader, and Max Baucus, Montana's longest serving U.S. Senator both established careers and joined politics while living in the city. Noted athletes who were born or resided in Missoula include five Olympic medalists, Pro Football Hall of Fame Quarterback John Elway, and former Milwaukee Bucks coach Larry Krystowiak. Actor Dana Carvey, filmmaker David Lynch, and award ‑ winning biologist Leroy Hood were born in Missoula while Carroll O 'Connor and J. K. Simmons both attended the University of Montana. Composer David Maslanka, musician Jeff Ament, and musician and vlogger Hank Green reside in Missoula. Academically, Missoula has been home to Nobel Prize winners Harold C. Urey and Steve Running as well as 20th century Montana historian K. Ross Toole Noted names in literature include Native-American poet James Welch, crime novelist James Crumley, former head of the University of Montana's Creative Writing Program Richard Hugo, and Norman Maclean, whose A River Runs Through It chronicles his life in early 20th-century Missoula.
== History ==
Sixteen years later, in 1905, the word genetics was first used by William Bateson, while Eduard Strasburger, amongst others, still used the term pangene for the fundamental physical and functional unit of heredity. In 1909 the Danish botanist Wilhelm Johannsen shortened the name to "gene".
The vast majority of living organisms encode their genes in long strands of DNA (deoxyribonucleic acid). DNA consists of a chain made from four types of nucleotide subunits, each composed of: a five-carbon sugar (2 ' -deoxyribose), a phosphate group, and one of the four bases adenine, cytosine, guanine, and thymine.
The majority of eukaryotic genes are stored on a set of large, linear chromosomes. The chromosomes are packed within the nucleus in complex with storage proteins called histones to form a unit called a nucleosome. DNA packaged and condensed in this way is called chromatin. The manner in which DNA is stored on the histones, as well as chemical modifications of the histone itself, regulate whether a particular region of DNA is accessible for gene expression. In addition to genes, eukaryotic chromosomes contain sequences involved in ensuring that the DNA is copied without degradation of end regions and sorted into daughter cells during cell division: replication origins, telomeres and the centromere. Replication origins are the sequence regions where DNA replication is initiated to make two copies of the chromosome. Telomeres are long stretches of repetitive sequence that cap the ends of the linear chromosomes and prevent degradation of coding and regulatory regions during DNA replication. The length of the telomeres decreases each time the genome is replicated and has been implicated in the aging process. The centromere is required for binding spindle fibres to separate sister chromatids into daughter cells during cell division.
Additionally, genes can have regulatory regions many kilobases upstream or downstream of the open reading frame. These act by binding to transcription factors which then cause the DNA to loop so that the regulatory sequence (and bound transcription factor) become close to the RNA polymerase binding site. For example, enhancers increase transcription by binding an activator protein which then helps to recruit the RNA polymerase to the promoter; conversely silencers bind repressor proteins and make the DNA less available for RNA polymerase.
A broad operational definition is sometimes used to encompass the complexity of these diverse phenomena, where a gene is defined as a union of genomic sequences encoding a coherent set of potentially overlapping functional products. This definition categorizes genes by their functional products (proteins or RNA) rather than their specific DNA loci, with regulatory elements classified as gene-associated regions.
The nucleotide sequence of a gene's DNA specifies the amino acid sequence of a protein through the genetic code. Sets of three nucleotides, known as codons, each correspond to a specific amino acid. Additionally, a "start codon", and three "stop codons" indicate the beginning and end of the protein coding region. There are 64 possible codons (four possible nucleotides at each of three positions, hence 43 possible codons) and only 20 standard amino acids; hence the code is redundant and multiple codons can specify the same amino acid. The correspondence between codons and amino acids is nearly universal among all known living organisms.
=== Mendelian inheritance ===
After DNA replication is complete, the cell must physically separate the two copies of the genome and divide into two distinct membrane-bound cells. In prokaryotes (bacteria and archaea) this usually occurs via a relatively simple process called binary fission, in which each circular genome attaches to the cell membrane and is separated into the daughter cells as the membrane invaginates to split the cytoplasm into two membrane-bound portions. Binary fission is extremely fast compared to the rates of cell division in eukaryotes. Eukaryotic cell division is a more complex process known as the cell cycle; DNA replication occurs during a phase of this cycle known as S phase, whereas the process of segregating chromosomes and splitting the cytoplasm occurs during M phase.
=== Sequence homology ===
De novo or "orphan" genes, whose sequence shows no similarity to existing genes, are extremely rare. Estimates of the number of de novo genes in the human genome range from 18 to 60. Such genes are typically shorter and simpler in structure than most eukaryotic genes, with few if any introns. Two primary sources of orphan protein-coding genes are gene duplication followed by extremely rapid sequence change, such that the original relationship is undetectable by sequence comparisons, and formation through mutation of "cryptic" transcription start sites that introduce a new open reading frame in a region of the genome that did not previously code for a protein.
Genetic engineering is now a routine research tool with model organisms. For example, genes are easily added to bacteria and lineages of knockout mice with a specific gene's function disrupted are used to investigate that gene's function. Many organisms have been genetically modified for applications in agriculture, industrial biotechnology, and medicine.
== The celestial material and its natural motions ==
=== Later Greek interpreters ===
An interpreter of Aristotle from Muslim Spain, al-Bitruji (d. c.1024), proposed a radical transformation of astronomy that did away with epicycles and eccentrics, in which the celestial spheres were driven by a single unmoved mover at the periphery of the universe. The spheres thus moved with a "natural nonviolent motion". The mover's power diminished with increasing distance from the periphery so that the lower spheres lagged behind in their daily motion around the Earth; this power reached even as far as the sphere of water, producing the tides.
Thomas Aquinas (c.1225 – 1274), following Avicenna, interpreted Aristotle to mean that there were two immaterial substances responsible for the motion of each celestial sphere, a soul that was an integral part of its sphere, and an intelligence that was separate from its sphere. The soul shares the motion of its sphere and causes the sphere to move through its love and desire for the unmoved separate intelligence. Avicenna, al-Ghazali, Moses Maimonides, and most Christian scholastic philosophers identified Aristotle's intelligences with the angels of revelation, thereby associating an angel with each of the spheres. Moreover, Aquinas rejected the idea that celestial bodies are moved by an internal nature, similar to the heaviness and lightness that moves terrestrial bodies. Attributing souls to the spheres was theologically controversial, as that could make them animals. After the Condemnations of 1277, most philosophers came to reject the idea that the celestial spheres had souls.
Although Nicolaus Copernicus (1473 – 1543) transformed Ptolemaic astronomy and Aristotelian cosmology by moving the Earth from the center of the universe, he retained both the traditional model of the celestial spheres and the medieval Aristotelian views of the causes of its motion. Copernicus follows Aristotle to maintain that circular motion is natural to the form of a sphere. However, he also appears to have accepted the traditional philosophical belief that the spheres are moved by an external mover.
In their development process, Boxleiter and Wohlwend both proposed and worked on each other's ideas, and would drop the ideas they found unexciting. Wohlwend said they often argued over aspects of their games, which he found normal and natural. Their labor as a team was divided in that Wohlwend always did the art and Boxleiter the programming, as reflective of their skills at the time. The pair agreed to an assessment of their partnership as "left-brain right-brain", and saw the majority of their joint work as "editing". Aside from the business aspects, they were grateful to have the "creative freedom" to do their own work. Wohlwend appreciated the benefits of not doing contract work, but struggled with the relative "isolation" of having few colleagues, a low salary, and job instability. He disagreed with the "cinematic action games" he saw to be popular at the time and hoped to contribute more compelling ideas to the young industry. They thought of themselves as artists and of their work as experimental. Boxleiter and Wohlwend worked long hours when making the Flash games, which they found exciting and unsustainable. At Intuition, they worked on games such as Dinowaurs, Gray, Fig. 8, and Lifecraft and participated in at least six game jams. As of April 2010, they had created 10 games together.
Their first game as Mikengreg was the sport-inspired Solipskier, where the player's finger draws the ground for the on-screen skier to pass through a level filled with gates, tunnels, and walls. It was designed as a Flash game, which set the limitations for its mechanics. The game concept came from a brainstorming session about parallax scrolling, and was revised in fits of creativity. They paired the parallax scrolling with speed and began to prototype. Wohlwend saved the skier's character design for last since he felt it was his weakest area. Mikengreg then decided to develop for iOS in addition to Flash, and to release both versions simultaneously. It was released simultaneously for Kongregate (Flash) and iOS on August 29, 2010. Solipskier became their first game to receive public appreciation. The iOS version made around $ 70,000 in its first two months (as compared to $ 15,000 from the Flash release), which gave them enough stability to branch out into non-Flash platforms.
Wohlwend, Vollmer, and Hinson of Puzzlejuice collaborated again on Threes!, a game where the player slides numbered tiles on a four-by-four grid to combine addends and multiples of three. Its development began before Ridiculous Fishing's March 2013 release. Vollmer presented an idea similar to the final product in its simplicity: pair tiles as multiples of three. The first prototype was written in a single night. Vollmer and Wohlwend spent at least half a year of the game's 14-month development iterating on this main idea. Early Threes designs had no inclination towards minimalism: the pair felt that the game needed to appear more complex so as to interest players. Wohlwend sent Vollmer designs with themes such as sushi, chess, broccoli and cheese soup, and hydrogen atoms, which confused their test audiences. They received a "wake-up call" from fellow game designer Zach Gage, who encouraged them to return from their foray into complexity. The final game returned to its original theme of numbers. Speaking in retrospect, Wohlwend said the game "always wanted to be simple". He noted that players "think math" upon seeing the game's numbers, though the game is more about "spatial relationships" and just happens to have a "number theme".
=== TumbleSeed ===
Intrigued by an ominous figure in one of Vincent van Gogh's paintings, alien time traveller the Doctor (Matt Smith) and his companion Amy Pond (Karen Gillan) go back in time to meet Van Gogh (Tony Curran) and discover that Provence has been plagued by an invisible monster, known as the Krafayis, which only Van Gogh can see. The Doctor and Amy work with Van Gogh to defeat the Krafayis, but in their attempt to have Van Gogh realise his legacy through bringing him to the future they ultimately realise that not all of time can be rewritten and there are some evils which are out of the Doctor's reach.
The Doctor has taken Amy to the Musée d 'Orsay in Paris, where they admire the work of the post-impressionist painter Vincent van Gogh. The Doctor discovers a seemingly alien figure in a window of the painting The Church at Auvers, and decides they must travel back in time to speak to Vincent around when he painted the painting. In 1890, they find Vincent at a cafe in Arles, a lonely man with a bad reputation. Vincent opens up when he notices Amy, sensing a loss she herself is not aware of. Outside the cafe a young girl is murdered, when the trio go out to see what happened they are stoned by locals who blame Vincent's insanity for the killing. The Doctor and Amy talk Vincent into letting them stay the night and they return to his home.
Curtis wanted to write for Doctor Who because he thought it would be "something my kids would like." When writing "Vincent and the Doctor", Curtis put up prints of Van Gogh paintings around the house as well as a board with index cards outlining the plot. His children helped him come up with some ideas. Gillan commented that the story had a different style and approach and was more character-driven. Though it was a subject he knew "quite a lot" about, he still read a 200-page biography of Van Gogh, which was more research than he normally would have done if working on other projects; he took Van Gogh very seriously. As such, he wanted to be "truthful rather than cruel" and refused to write any jokes about Van Gogh's ears after he famously cut one of them off. However, he did incorporate other humour as he naturally wanted to "try to make things funny".
On The Guardian film blog, Peter Bradshaw considered "Vincent and the Doctor" to be a "terrifically clever, funny, likeable wildly surreal episode". He praised the "unmistakeably [sic] Curtis dialogue" and the "uproariously emotional ending of the sort only Richard Curtis could get away with". Dan Martin on the same paper's regular Doctor Who blog was more critical, writing that its "main problem [was] that it doesn't feel much like a Doctor Who story" and would have worked better if "the middle section with the monster had been stripped out". He also criticised the script for its "lashings of weapons-grade sentimentality" and for "throwing up possibilities that weren 't followed up" and the monster as an "afterthought [posing] ... no tangible threat". However, he did praise Curran's "great performance" along with the episode's treatment of depression, concluding like Wollaston that he enjoyed the episode despite his misgivings.
== History ==
A photon goes from one place and time to another place and time.
=== Probability amplitudes ===
Addition and multiplication are familiar operations in the theory of complex numbers and are given in the figures. The sum is found as follows. Let the start of the second arrow be at the end of the first. The sum is then a third arrow that goes directly from the start of the first to the end of the second. The product of two arrows is an arrow whose length is the product of the two lengths. The direction of the product is found by adding the angles that each of the two have been turned through relative to a reference direction: that gives the angle that the product is turned relative to the reference direction.
where a shorthand symbol such as <formula> stands for the four real numbers which give the time and position in three dimensions of the point labeled A.
Within the above framework physicists were then able to calculate to a high degree of accuracy some of the properties of electrons, such as the anomalous magnetic dipole moment. However, as Feynman points out, it fails totally to explain why particles such as the electron have the masses they do. "There is no theory that adequately explains these numbers. We use the numbers in all our theories, but we don 't understand them – what they are, or where they come from. I believe that from a fundamental point of view, this is a very interesting and serious problem."
<formula>, called "psi-bar", is sometimes referred to as the Dirac adjoint;
=== Equations of motion ===
<formula>
The two terms this time are
which is a wave equation for the four potential, the QED version of the classical Maxwell equations in the Lorenz gauge. (In the above equation, the square represents the D 'Alembert operator.)
and so, one has
To these rules we must add a further one for closed loops that implies an integration on momenta <formula>, since these internal ("virtual") particles are not constrained to any specific energy – momentum – even that usually required by special relativity (see this article for details). From them, computations of probability amplitudes are straightforwardly given. An example is Compton scattering, with an electron and a photon undergoing elastic scattering. Feynman diagrams are in this case
that, being closed loops, imply the presence of diverging integrals having no mathematical meaning. To overcome this difficulty, a technique called renormalization has been devised, producing finite results in very close agreement with experiments. It is important to note that a criterion for theory being meaningful after renormalization is that the number of diverging diagrams is finite. In this case the theory is said to be renormalizable. The reason for this is that to get observables renormalized one needs a finite number of constants to maintain the predictive value of the theory untouched. This is exactly the case of quantum electrodynamics displaying just three diverging diagrams. This procedure gives observables in very close agreement with experiment as seen e.g. for electron gyromagnetic ratio.
=== Books ===
Milonni, Peter W., (1994) The quantum vacuum - an introduction to quantum electrodynamics. Academic Press. ISBN 0-12-498080-5
== Background ==
Construction of the section between Asker and Sandvika started in 2001, and was completed in 2005. It was officially opened by Torild Skogsholm, Minister of Transport from the Liberal Party, on 27 August. This section is dominated by the 3,590-metre (2.23 mi) Tanum Tunnel and the 3,790-metre (2.35 mi) Skaugum Tunnel, and cost NOK 3.7 billion. For the last 1.5 kilometres (0.93 mi) of track west of Sandvika, the Asker and Drammen Line have been built along the same, new, right-of-way. The Drammen Line, leaves Slependen Station, and joins the Asker Line just after the latter leaves the Tanum Tunnel.
Construction of the second section started in 2007 and was completed in 2011. The section between Sandvika and Lysaker is 6.7 kilometres (4.2 mi), most of which runs through the 5.5-kilometre (3.4 mi) Bærum Tunnel. There was local debate whether the tunnel should be built using a tunnel boring machine or by drilling and blasting. The latter was preferred by the Rail Administration, since it allowed a shorter construction time, and a NOK 700 million saving. Total budget is NOK 2,787 million.
== 1986 – 1996: Startup and initial expansion ==
In April 2004, DM & E was awarded the power of eminent domain in South Dakota by the United States Court of Appeals for the Eighth Circuit in Pierre, South Dakota. The ruling overturned part of South Dakota legislation passed in 1999 (two years after the railroad first announced its intentions to expand) that would have impaired railroad operations and construction in the state. This decision restores the legal process by which the railroad can effectively force landowners along the proposed new route to sell their land to the railroad.
DM & E hauled nearly 60,000 carloads of various freight shipments in fiscal year 2002, serving approximately 130 customers along the railroad's mainline. Of these shipments, 53 % were grains or grain products, 24 % were bentonite and kaolin clay, 7 % were cement, and 5 % were wood and lumber products; the remaining 11 % were split among all other types of freight.
The acquisition will give CP access to shipments of agricultural products and ethanol in addition to coal from the Wyoming coal fields. CP has stated its intention to use this purchase to gain access to the Powder River and ship coal to midwestern and eastern utilities. The transaction is subject to approval of the Surface Transportation Board, which is expected to take a year. Securities analysts have stated that competing railroads for Powder River coal, the Union Pacific and BNSF, could challenge the acquisition and delay STB approval, but are unlikely to prevent it. At least until approval is received, the DM & E will continue to operate as a separate entity.
Mansfield Subdivision — Redfield to Mansfield, South Dakota
J. C. (Pete) McIntyre (1986 – 1996) began his railroad career in 1953, eventually working for Chicago and North Western in the early 1980s. When DM & E was formed in 1986, McIntyre became the new railroad's first president.
López attended the University of Virginia, earning a degree in psychology despite leaving early to begin his baseball career. He was selected by the Arizona Diamondbacks in the fourth round of the 1998 Major League Baseball (MLB) Draft. He began his career as a starting pitcher but struggled and converted into a sidearm (or submarine) reliever while still in the Diamondbacks'organization. Before the 2003 season, he was selected by the Boston Red Sox in the Rule 5 draft, but he was traded to the Colorado Rockies during spring training. He spent all of 2003 on Colorado's roster, nearly tying the franchise record for most consecutive batters retired and finishing third among major league rookies in games pitched. He struggled the next two seasons, getting claimed off waivers and later sent to the minors by Arizona in 2005. In 2006, he signed with the Chicago White Sox but failed to make the team and spent the first part of the season in the minors before getting traded to Boston during the year.
== Professional career ==
=== Colorado Rockies (2003 – 2005) ===
López made the Red Sox 'Opening Day roster in 2007, but after four scoreless outings he was optioned to Pawtucket on April 9 to make room for Mike Timlin, who had started the season on the disabled list. He was recalled on May 11 when Devern Hansack was sent down. On this stint, he posted a 3.18 ERA in 40 appearances before getting sent down on August 5 to make room for Curt Schilling, who was returning from the disabled list. With the Red Sox about to face several tough left-handed hitters in late August, Jon Lester was sent down on August 23 to make room for López on the roster. In 2007, López made 61 appearances, posting a 2 – 1 record with a 3.10 ERA in 40 2 ⁄ 3 innings. Despite his three stints in the minors, his 61 appearances ranked second on the club to Hideki Okajima's 66. He made 17 appearances for Pawtucket, going 2 – 1 with a 3.78 ERA. López was a member of the playoff roster for the Red Sox, posting a 15.43 ERA but winning his first World Series as the Red Sox swept the Rockies in four games.
== Personal life ==
Domitian's youth and early career were largely spent in the shadow of his brother Titus, who gained military renown during the First Jewish – Roman War. This situation continued under the rule of his father Vespasian, who became emperor in 69 following the civil war known as the Year of the Four Emperors. While Titus held a great many offices under the rule of his father, Domitian was left with honours but no responsibilities. Vespasian died in 79 and was succeeded by Titus, whose own reign came to an unexpected end when he was struck by a fatal illness in 81. The following day Domitian was declared Emperor by the Praetorian Guard, commencing a reign that lasted fifteen years – longer than any man who had ruled since Tiberius.
=== Youth and character ===
Historian Brian Jones concludes in The Emperor Domitian that assessing the true nature of Domitian's personality is inherently complicated by the bias of the surviving sources. Common threads nonetheless emerge from the available evidence. He appears to have lacked the natural charisma of his brother and father. He was prone to suspicion, displayed an odd, sometimes self-deprecating sense of humour, and often communicated in cryptic ways.
On 9 June 68, amid growing opposition of the Senate and the army, Nero committed suicide and with him the Julio-Claudian dynasty came to an end. Chaos ensued, leading to a year of brutal civil war known as the Year of the Four Emperors, during which the four most influential generals in the Roman Empire — Galba, Otho, Vitellius and Vespasian — successively vied for imperial power.
By the afternoon of 20 December, Vitellius was dead, his armies having been defeated by the Flavian legions. With nothing more to be feared, Domitian came forward to meet the invading forces; he was universally saluted by the title of Caesar and the mass of troops conducted him to his father's house. The following day, 21 December, the Senate proclaimed Vespasian emperor of the Roman Empire.
When news arrived of Cerialis' victory over Civilis, Mucianus tactfully dissuaded Domitian from pursuing further military endeavours. Domitian then wrote to Cerialis personally, suggesting he hand over command of his army but, once again, he was snubbed. With the return of Vespasian in late September, his political role was rendered all but obsolete and Domitian withdrew from government devoting his time to arts and literature.