The imaginary unit or unit imaginary number is a solution to the quadratic equation x2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is 2 + 3i. Imaginary numbers are an important mathematical concept, which extend the real number system ℝ to the complex number system ℂ, which in turn provides at least one root for every nonconstant polynomial P; the term "imaginary" is used. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root. In contexts where i is ambiguous or problematic, j or the Greek ι is sometimes used. In the disciplines of electrical engineering and control systems engineering, the imaginary unit is denoted by j instead of i, because i is used to denote electric current. For the history of the imaginary unit, see Complex number § History.
The imaginary number i is defined by the property that its square is −1: i 2 = − 1. With i defined this way, it follows directly from algebra that i and −i are both square roots of −1. Although the construction is called "imaginary", although the concept of an imaginary number may be intuitively more difficult to grasp than that of a real number, the construction is valid from a mathematical standpoint. Real number operations can be extended to imaginary and complex numbers by treating i as an unknown quantity while manipulating an expression, using the definition to replace any occurrence of i2 with −1. Higher integral powers of i can be replaced with −i, 1, i, or −1: i 3 = i 2 i = i = − i i 4 = i 3 i = i = − = − = 1 i 5 = i 4 i = i = i Similarly, as with any non-zero real number: i 0 = i 1 − 1 = i 1 i − 1 = i 1 1 i = i 1 i = i i = 1 As a complex number, i is represented in rectangular form as 0 + 1⋅i, with a zero real component and a unit imaginary component. In polar form, i is represented as 1⋅eiπ/2, with an absolute value of 1 and an argument of π/2.
In the complex plane, a special interpretation of a Cartesian plane, i is the point located one unit from the origin along the imaginary axis. Being a quadratic polynomial with no multiple root, the defining equation x2 = −1 has two distinct solutions, which are valid and which happen to be additive and multiplicative inverses of each other. More once a solution i of the equation has been fixed, the value −i, distinct from i, is a solution. Since the equation is the only definition of i, it appears. However, no ambiguity results as long as one or other of the solutions is chosen and labelled as "i", with the other one being labelled as −i; this is because, although −i and i are not quantitatively equivalent, there is no algebraic difference between i and −i. Both imaginary numbers have equal claim to being the number whose square is −1. If all mathematical textbooks and published literature referring to imaginary or complex numbers were rewritten with −i replacing every occurrence of +i, all facts and theorems would continue to be equivalently valid.
The distinction between the two roots x of x2 + 1 = 0 with one of them labelled with a minus sign is purely a notational relic. The issue can be a subtle one; the most precise explanation is to say that although the complex field, defined as ℝ/, is unique up to isomorphism, it is not unique up to a unique isomorphism — there are two field automorphisms of ℝ/ which keep each real number fixed: the identity and the automorphism sending x to −x. See Complex conjugate and Galois group. A similar issue arises if the complex numbers are interpreted as 2 × 2 real matrices, because both X = and X = ( 0 1 −
Moreland is a now-defunct association football team that competed in various leagues in Victoria, Australia between 1934 and 1985. The team was known as Moreland Victoria and as Moreland Thistle between 1965 and 1970. After the 1985 season, Moreland merged with Park Rangers to form Moreland Park Rangers. In 1990 Moreland Park Rangers merged with Coburg to form the team now known as Moreland City; the team played its home matches at Coburg. In a history spanning 50 years, Moreland won the Victorian Division 1 title the top tier of soccer in the state, three times. In 1934 Moreland Soccer Club was formed by a breakaway from what was known as the Brunswick Soccer Club and trophy success came to Moreland early in its history; the team won the Victorian Division Three title in its first season and Division Two in 1935. Despite losing just one game in 1935 it was Moreland's superior goal difference that handed them the title ahead of Navy, who finished with the same points; the following season, 1936, Moreland won the first of its Victorian Division 1 championship titles.
Moreland topped the eight-team league finishing the season on 20 points, one ahead of Royal Caledonians. Royal Caledonians had finished on 21 points but were penalised 2 points and were, denied the title. In 1937, Moreland won its third consecutive title and second top-tier trophy in a row finishing with 21 points, one ahead of Prahran in second; the club won the Dockerty Cup on four occasions, three times as Moreland and once, in 1945, as Moreland Hakoah. The club's first Dockety Cup victory came in 1941, a 1–0 win over Prahran at Olympic Park, Melbourne. In the first round of that year's tournament, Moreland beat Heidelberg 10–2; the second Dockerty Cup final victory came against Box Hill in October 1945 and was followed the next season with a third Division One championship. As with its previous two championships, Moreland topped the table by just one point; the Dockerty Cup victory of 1945 came under the name of Moreland Hakoah. During World War II, there was a temporary merger between Moreland and Hakoah, a club who had a predominantly Jewish supporter base.
Some clubs had difficulty fielding teams during the war years while others were forced to close down because many players had left and enlisted for the armed services. By 1946, the merger between Moreland and Hakoah came to an end with clubs again participating as separate teams. In 1950, Moreland finished in last place and were relegated to Division 2, they did, record their third Dockerty Cup triumph, beating Box Hill 2–0 in the final. 1952 brought a first division two title, the team winning 17 of its 18 games and scoring 110 league goals. They hit double figures in four games, defeated George Cross 12–0 and 10–0. Back in the top flight, the team consolidated its position finishing fourth in 1953, sixth in 1954, seventh in 1955 and eighth in 1956. Two Moreland players, midfielder Frank Loughran and forward Ted Smith were included in Australia's 20-man soccer squad for the 1956 Summer Olympics in Melbourne, it was the first Olympic football tournament for Australia. Before the opening games with Japan, the squad trained at Moreland's ground.
Australia played Great Britain and Yugoslavia in a warm-up matches at Moreland, losing 3–1 and 5–1. In their first Olympic soccer match, a 2–0 win over Japan, Loughran scored the second goal; this game was refereed by Mervin Rogers from Brisbane, the youngest international soccer referee at the age of 19. During the 1950s and 1960s, the face of Victorian soccer started to change with the ethnic clubs becoming stronger on and off the pitch, they were able to offer players, for a wage. Presidents of the powerful ethnic clubs travelled around Melbourne buying up the best players. Moreland was numerous players left to play with the cashed up clubs. Despite the decimation of the team, Moreland did win the 1957 Dockerty Cup, for the fourth and last time. In 1962 Moreland had a written guarantee that the great Stanley Matthews would play eight games with the club. However, this deal fell through because of a FIFA ban on foreign players coming to Australia. Eric Heath said his team had correspondence with Mathews and he "really wanted to come".
"He remembered Frank Loughran, his old sparring partner, from the Blackpool tour in 1958. You see Tommy Trinder and Harry Hopman were both patrons of the Moreland Soccer club," said Heath. Moreland finished in second place in the league in 1957 winning promotion to the new Victorian State League for the 1958 season. At the end of the 1962 season, the team's fifth in the State League, Moreland finished bottom, winning just one game and losing 21. In 1968 – now known as Moreland Thistle – they were relegated from Metropolitan League Division One, they remained in Victorian Metropolitan League Division Two – now the 3rd tier in the state – until 1978 when they finished 2nd winning promotion. Moreland were not relegated, they were relegated in 1985, the final year of their existence. When they returned in 1986 in Division Two, they had merged with Park Rangers to become Moreland Park Rangers. Victorian Division 1Winners: 1936, 1937, 1946, Runners-up: 1957Victorian Division 2Winners: 1935, 1952Victorian Metropolitan League Division 2Runners-up: 1978 Dockerty CupWinners: 1941, 1945, 1950, 1957 Runners-up: 1942, 1943, 1946 Otto Pecnick, the man who timed John Landy's attempts upon the mile record at Olympic Park was a treasurer of the club.
The Sasanian army was the primary military body of the Sasanian armed forces, serving alongside the Sasanian navy. The birth of the army dates back to the rise of Ardashir I, the founder of the Sasanian Empire, to the throne. Ardashir aimed at the revival of the Persian Empire, to further this aim, he reformed the military by forming a standing army, under his personal command and whose officers were separate from satraps, local princes and nobility, he restored the Achaemenid military organizations, retained the Parthian cavalry model, employed new types of armour and siege warfare techniques. This was the beginning for a military system which served him and his successors for over 400 years, during which the Sasanian Empire was, along with the Roman Empire and the East Roman Empire, one of the two superpowers of Late Antiquity in Western Eurasia; the Sasanian army protected Eranshahr from the East against the incursions of central Asiatic nomads like the Hephthalites and Turks, while in the west it was engaged in a recurrent struggle against the Roman Empire.
In the character of their warfare, the Persians of the Sasanian period differed from their forebears under the Achaemenid kings. The principal changes which time had brought about were an entire disuse of the war chariot, the advance of the elephant corps into a prominent and important position, the increased use and pre-eminence of cavalry on the Parthian model, including both heavy cataphracts and horse-archers. Four main arms of the service were recognized, each standing on a different level: the elephants, the horse, the archers, the ordinary footmen; the number of the field armies could reach 45,000-50,000 up to 100,000-130,000, according to recent archaeological evidence on campaign bases near the Great Wall of Gorgan. In Pahlavi language, smaller divisions of the spāh were referred to as vasht and larger divisions were designated as gond; the Arabic word jund, meaning "army", is derived from the latter. Head of the military was the Shahanshah; the empire's military command was split into four.
The offices of the Great King of Armenia, King of Meshan, King of Gilan, King of Sakastan fulfilled these roles. After the reforms of Khosrow I, there were each for a cardinal direction. Other attested military ranks throughout the Sasanian period are as follows: Wuzurg-framadar, who could become the commander-in-chief and was entrusted to engage in diplomatic negotiations. Ērān-spāhbed, spāhbedān-spāhbed, artēštārān-sālār: the regular commander-in-chief chosen from the House of Suren. Spāhbed: Field general. Aswārān-sardār, aswārān-sālār: "Commander of the Cavalry", but its duties are unknown. Aspbed means "Commander of the Cavalry" Andarzbad-i Aspwaragan, chief instructor of the cavalry Paygān-sālār: Commander of the Infantry Kanārang, commander in the Abarshahr. Marzbān: Commander of the border guards. Pushtigbān-sālār: Head of the royal guard. Pāygōsbān or pādhūspān: military commander of a district or province. Shahrab, commander of a rural district. Erān anbāraghbad: Senior rank responsible for army supplies.
Stor Bezashk: Senior vet who looked after the cavalry elite's mounts. Argbed, commander of a citadel or fort. Gund-sālār: Commander of a gond division. Hazāruft or hazārbed: Commander of a Thousand the commander of the Royal Bodygaurd Sarhang Framadar or Framandar, battlefield commanderThe military appointments were dominated by the noble houses of Suren and Spandiyadh; the backbone of the Spâh in the Sasanian era was its heavy armoured cavalry, known since Classical antiquity in the west as Cataphracts. This was made up of noblemen who underwent extensive exercises in warfare and military manoeuvres through military training, gaining discipline and becoming true soldiers. Within the Sasanian military, the cavalry was the most influential element, Sasanian cavalry tactics were adopted by the Romans and Turks, their weaponry, battle tactics, medallions, court customs, costumes influenced their Romano-Byzantine neighbours. The Romans had long contended against opponents who fielded heavy cavalry, notably the Sarmatians and the Parthians, the recurrent wars with the Sasanian were an important factor in the Roman turn to new military organizations and battlefield tactics that centered around the use of heavy cavalry in the 3rd and 4th centuries.
The Romans called these newly formed units clibanarii. Another, more direct and quoted, etymology is the Greek word ho klibanos, which refers to a covered pot in which bread was baked or a small oven; the Roman term appears for the first time in the vita Alexandri Severi in the Historia Augusta, a work from the end of the 4th century AD. Shapur II further reformed the army by adopting more effective cavalry; these mounted. This made them look much like moving iron statues; some mace. Depictions of aforementioned cavalry still survive, with one of the best preserved ones being a rock relief at Taq-e Bostan where Khosrau II is seen riding his favourite horse, Shabdiz; the fighting equipment of the armed Sasanian horsemen were: Clibanarii/Cataphract cavalry: helmet, breas
Yu Hong is a Chinese contemporary artist. Her works characteristically portray the female perspectives in all stages of life and the relationship between the individual and the rapid social changes taking place in China, she works in oil paint but in pastels, fabric dye on canvas and resin. Yu Hong is "routinely named amongst China’s leading female artists", her work is celebrated for its intimacy and tactility. Yu Hong was born in Xi'an, Shaanxi Province in 1966 and received her first degree from the Oil Painting Department of the Central Academy of Fine Arts in 1988 in Beijing. There she received a thorough training in the techniques of figural realism. Early in her career, her paintings combined realistic portraits with surreal environments and colors. However, as she progressed, her focus on surrealism dissipated. Instead, she focused more on her skills of observation and became sensitive to facial expressions and body posture, she married fellow Chinese contemporary artist Liu Xiaodong in the summer of 1993 and became a mother not long after.
In 1995, Hong received an MFA in Oil Painting from the Central Arts Institute of Beijing. In addition, she and a small group of colleagues became known as the “New Generation” artists, known for their personal figurative works. Hong now holds tenure as a professor of Oil painting at the Central Academy of Fine Arts in Beijing. Hong’s subjects are predominately women. In the history of Chinese art, women were depicted engaged in everyday activities created by men who overlaid that subject with symbolic ramifications – the female point of view was not a viable mode of creation. Hong’s work is different because she honors the female in all phases of life, from childhood to maturity, she does not swathe her images with extreme sentimentality. Her subjects consist of herself, her friends and her daughter, Liu Wa, her method of painting is immensely personal and has been criticized as mundane, but she highlights the beauty in the intricacies of daily life, friendship and the impact of the environment on people.
In 2000, Hong began to work on ‘Witness to Growth’. Each painting is a one-meter square canvas with an image of herself based on the photograph taken at the time, she does not pay special attention to keeping a similar image. Hong uses compositions and colors to capture important ideas or experiences/moods to commemorate that time. For her 29th year/painting, she painted two portraits. From there, Hong began to paint her young daughter in attempts to chronicle her life as well. Upon exhibiting ‘Witness to Growth’ for the first time, Hong placed a newspaper or magazine article to complement each image. ‘Witness to Growth’ is a ubiquitous series of works because it is a self-examination of the artist and her surroundings. By linking herself to events that happened around her or around the world, Hong puts herself and her life on critical display; the juxtaposition of social and political events against personal moments creates a tension and highlights the disparity between inner and outer events.
“I show that my life and China changes: from a cultural revolution to right now.”. In 2003, Hong embarked on a new visual journey with her series ‘She’. According to Hong, she “knew all these women so went to their place – where they live, where they work and I painted what I saw in their life.”The paintings included: “She: Beautiful Writer Zhao Bo”, “She: Art School Student” and “She: Tibetan Woman Zhou Ma” among others. These paintings make clear the possibilities to be mined within the subject and highlight the role of the contemporary woman in Chinese society. In particular, “She: Beautiful Writer Zhao Bo” captured the attitude and lifestyle of successful young women in the new China; the splashes of bold color exhibit signature painterly manner. Hong and her husband Liu Xiaodong are compared as having similar approaches to their work and as Liu’s work has grown more famous, Hong’s work took a slight backseat to his. However, in recent years she has begun to explore different approaches to her work, distinguishing herself from the work of her husband without abandoning her usual subject matter.
‘Golden Horizon’ displayed works created before 2011 that displayed the application of gold foil, connected to ancient traditional Chinese painting and religious painting. ‘Golden Sky’, 2009, features four works exhibited on the ceiling of the gallery so one must look up as if in a cathedral or a palace. This was done to maintain a certain distance from the audience to the paintings; this method was chosen to reproduce the atmosphere around traditional religious paintings as the piece works in tandem with the environment to create an overall feeling in those who view it. Each work is a spin on a preexisting and famous work of art. Others are inspired by Buddhist cave frescoes. Hong places contemporary renderings of people against golden backdrops with the intention of making the viewer look more at those around them. “The gold series is about the relationship ancient and modern relationships in Western and in China." Placing them on the ceiling monumentalizes them and forces the viewer to contemplate the meaning of the piece.
“I think gold leaf is special powerful. It suits
Extra calvinisticum is a theological terminus technicus given by Lutheran scholastic theologians around 1620 to the teaching that Christ's divine nature cannot be enclosed or imprisoned within a human nature, but remains infinite despite being in union with a finite body. The doctrine is named for and associated with John Calvin, but is found in the church fathers and is prominent in Augustine's Christology; this theological distinction is in contrast to scholastic Lutheran Christology. In the theology of Martin Luther Jesus Christ is omnipresent, not only his divine nature but his human nature, this is because the two natures cannot be separated from one another, but are shared by the same individual; the Reformed, on the other hand, argued that "the Word is united to but never contained within the human nature and, therefore in the incarnation is to be conceived of as beyond or outside of the human nature."For this reason, the Reformed argue that Christ cannot be present corporeally in the Lord's supper, because he reigns bodily from heaven.
Chalcedonian Christianity Hypostatic union
Metro Zócalo is a station on Line 2 of the Mexico City Metro system. It is located in the Colonia Centro district of the Cuauhtémoc borough on the heart of Mexico City; the station serves the main central square, known as the Zócalo, but formally called the "Plaza de la Constitución". The station logo shows the Mexican Coat of Arms, the Presidential Seal. Artwork on the walls of the station reflects the evolution of the central square over time. Three large display cases contain miniature models showing the site during three periods in history starting from the Aztec pyramids until the present day. Buildings surrounding the square include the Metropolitan Cathedral, Palacio Nacional, where the President's office is located, the Mexico City Town Hall; the station opened on 14 September 1970. Zócalo station has a cultural display, it connects with the Metro Pino Suárez station at the south side through a long underground passage, called Pasaje Zócalo–Pino Suárez. This corridor is filled with bookstores, has a free mini-cinema.
The two underground entrances leading to the station are not signposted as is the case with other stations in the network. Zócalo, Mexico City's main square. Metropolitan Cathedral National Palace, seat of the federal executive in Mexico. Templo Mayor, archeological site and museum. Nacional Monte de Piedad, not-for-profit institution and pawnshop. Supreme Court of Justice of the Nation, supreme court of Mexico. Museo de la Secretaría de Hacienda y Crédito Público, art museum. Academy of San Carlos, building of the Faculty of Arts and Design of the UNAM. Museo Nacional de las Culturas, museum dedicated to education about the world's cultures. Sociedad Mexicana de Geografía y Estadística, building of the Mexican Society for Geography and Statistics. Museum of Light, museum dedicated to the phenomena of light. Librería Porrúa, bookseller and publishing company. Secretariat of Public Education List of Mexico City metro stations