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Linear equation

In mathematics, a linear equation is an equation that may be put in the form a 1 x 1 + ⋯ + a n x n + b = 0, where x 1, …, x n are the variables, b, a 1, …, a n are the coefficients, which are real numbers. The coefficients may be considered as parameters of the equation, may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients a 1, …, a n are required to not all be zero. Alternatively a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken; the solutions of such an equation are the values that, when substituted for the unknowns, make the equality true. In the case of just one variable, there is one solution; the term linear equation refers implicitly to this particular case, in which the variable is sensibly called the unknown. In the case of two variables, each solution may be interpreted as the Cartesian coordinates of a point of the Euclidean plane.

The solutions of a linear equation form a line in the Euclidean plane, conversely, every line can be viewed as the set of all solutions of a linear equation in two variables. This is the origin of the term linear for describing this type of equations. More the solutions of a linear equation in n variables form a hyperplane in the Euclidean space of dimension n. Linear equations occur in all mathematics and their applications in physics and engineering because non-linear systems are well approximated by linear equations; this article considers the case of a single equation with coefficients from the field of real numbers, for which one studies the real solutions. All of its content applies to complex solutions and, more for linear equations with coefficients and solutions in any field. For the case of several simultaneous linear equations, see system of linear equations; the term linear equation refers implicitly to the case of just one variable. In this case, the equation can be put in the form a x + b = 0, it has a unique solution x = − b a in the general case where a ≠ 0.

In this case, the name unknown is sensibly given to the variable x. If a = 0, there are two cases. Either b equals 0, every number is a solution. Otherwise b ≠ 0, there is no solution. In this latter case, the equation is said to be inconsistent. In the case of two variables, any linear equation can be put in the form a x + b y + c = 0, where the variables are x and y, the coefficients are a, b and c. An equivalent equation is A x + B y = C, with A = a, B = b, C = –c These equivalent variants are sometimes given generic names, such as general form or standard form. There are other forms for a linear equation, which can all be transformed in the standard form with simple algebraic manipulations, such as adding the same quantity to both members of the equation, or multiplying both members by the same nonzero constant. If b ≠ 0, the equation a x + b y + c = 0 is a linear equation in the single variable y for every value of x, it has therefore a unique solution for y, given by y = − a b x − c b. This defines a function.

The graph of this function is a line with slope − a b and y-intercept − c b. The functions whose graph is a line are called linear functions in the context of calculus. However, in linear algebra, a linear function is a function that maps a sum to the sum of the images of the summands. So, for this definition, the above function is linear only when c = 0, when the line passes through the origin. For avoiding confusion, the functions whose graph is an arbitrary line are called affine functions; each solution of a linear equation a x + b y + c = 0 may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all solutions of a linear equation; the phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of

Shah Bhopal Chand Lodha

Shah Bhopalchandji Lodha was Public Works Secretary of the former Jodhpur State. A commerce graduate from Sydenham College, Bombay he went on to become the Public Works Secretary of the former Jodhpur State; as Secretary PWD he was instrumental in the overall development of Jodhpur. The Water Canal, he was honoured with the title of Rai Sahib for his extraordinary services to the state. His greatest quality was his enduring belief that nothing is impossible for which the late Maharaja Hanwant Singhji of Jodhpur named him Alladin ka Chirag, he was the 20th century titan of Marwar and remembered as the architect and builder of Modern Jodhpur. In 1940, he was presented a stick of honour on behalf of His Majesty by the Viceroy of India, Lord Linlithgow for his contributions to the development of Jodhpur

Sekolah Seri Puteri

Sekolah Seri Puteri is a premier all-girls boarding school located in Cyberjaya, Malaysia. In 2010, Sekolah Seri Puteri was awarded the prestigious Sekolah Berprestasi Tinggi or High Performance School title; the school specialises in wind basketball as well as their debate team. In the Sijil Pelajaran Malaysia 2013, the national examination taken by all fifth-year secondary school students in Malaysia, SSP obtained a grade value average of 1.26. Sekolah Seri Puteri was founded on 6 May 1968, the original name was Sekolah Menengah Kebangsaan Perempuan Jalan Kolam Ayer, Kuala Lumpur, it was established to provide secondary education for students from across Malaysia. Built on a 19-acre site at Jalan Kolam Ayer owned by a technical school, the school opened with 144 Form 4 students, 10 teachers, three non-academics who assisted Puan Khalidah Adibah Amin, the first principal. In 1969, the school started contracting teachers from Bangladesh to fill vacancies in the science and mathematics departments.

The first group of 102 Form 6 students was admitted in May 1971. Form 1 students were first admitted in 1975. In 1975, pre-university matriculation courses from Universiti Kebangsaan Malaysia were first attended by 88 students. In 1976, the wind orchestra, Seri Puteri Winds, was formed by the third principal Puan Hajah Badiah Bt Hj, Abdul Manan, the vice-principal Wilma Lesurf; the school celebrated its tenth anniversary on 16 September 1978. At this event, the fourth school principal, Puan Zainab Bt Haji Mohd Yusop named the school as Sekolah Seri Puteri, signifying "beauty and leadership"; the school emblem was introduced in the same year. On 1 May 2003, Sekolah Seri Puteri moved from Jalan Kolam Ayer to its current location in Cyberjaya; the grand opening of the new facility was held on 10 April 2007. Sultanah Nur Zahirah, the thirteenth Raja Permaisuri Agong of Malaysia, officiated at the opening. Sekolah Seri Puteri occupies a 20-acre site in the Cyberjaya Flagship Zone on high ground overlooking an artificial lake, Putrajaya Lake.

Development of Sekolah Seri Puteri began on 5 April 2001, with a total construction cost of RM 56 Million. Construction ended on 26 January 2003; the school can support staff. The main building contains a large hall and sports facilities, classrooms and workshops blocks; the site includes a student residence, a teachers residence, a dining hall. A great hall holds 1,200 people, a lecture hall seats 255 people. In 2013, the school hosted the Fully Residential School International Symposium with the theme "Go Green, Initiatives for the Future"; the keynote speaker was the prime minister of Dato' Najib Razak. In 2011, the school's wind orchestra, Seri Puteri Winds, was featured in the flashmob-style reality programme Refleksi Orkestra in conjunction with Radio Televisyen Malaysia's golden jubilee concert, Orkestra RTM 50. In 2013, SP Winds won the gold medal at the 24th Australian International Music Festival in Sydney; this accomplishment earned the school three entries in the Malaysian Book of Records: "first Malaysian government residential school to qualify for the Australian International Music Festival" "first Malaysian government residential school to play at the Sydney Opera House, Australia" "first Malaysian government residential school to win a gold medal in AIMF" The alumni association of SSP is known as Persatuan Alumni Sekolah Seri Puteri.

Harlina Halizah Siraj – Head, Department of Medical Education, Universiti Kebangsaan Malaysia Medical Centre Mastura Ma'sudLawyer Azlina Jamaluddin - Lawyer Sawiah Jusoh – Chief Executive Officer Success Precession Wellbeing Ltd, United Kingdom. Safiah Atan – Senior Biotechnology Researcher, Malaysian Rubber Board Jamia Azdina Jamal-Dean, Faculty of Pharmacy, National University Malaysia Azlina Mehtab-Lawyer Sharifah Fauziyah Syed Mohtar-Director, Pharmaniaga Bhd Shafida Abd Hamid-Dean, Kuliyyah of Science, IIUM. Vivy Yusof-Fashion Icon,Entrepreneur List of schools in Selangor Blown away by wind orchestra Official website


Autokratōr is a Greek epithet applied to an individual who exercises absolute power, unrestrained by superiors. In a historical context, it has been applied to military commanders-in-chief, to Roman and Byzantine emperors as the translation of the Latin title imperator, its connection with Byzantine-style absolutism gave rise to the modern terms autocracy. In modern Greek, it means "emperor", the female form of the title is autokrateira; the title appeared in Classical Greece in the late 5th century BC, was used for generals given independent authority, i.e. a supreme commander. In Classical Athens, stratēgoi autokratores were generals endowed with autonomous power of command, i.e. they were able to make certain military and diplomatic decisions without prior consultation with the Athenian assembly. This was enacted when the general was expected to operate far from Athens, for instance during the Sicilian Expedition; the generals remained accountable to the assembly for their conduct upon their return.

Similar practices were followed by other Greek states, such as Syracuse, where the post served as a power base for several of the city's tyrants. Stratēgoi autokratores were appointed by various leagues of city-states to head their combined armies, thus Philip II of Macedon was declared as hēgemōn and stratēgos autokratōr of the southern Greek states by the League of Corinth, a position given to his son Alexander the Great as well. The term was employed for envoys entrusted with plenipotentiary powers. In the Iranian languages, the term * hwatā́wā ` sovereign. In times, with the rise of the Roman Republic, autokratōr was used by Greek historians to translate different Roman terms: Polybius uses the term to translate the title dictator, while Plutarch uses it in its sense as a translation of the victory title imperator. Autokratōr became entrenched as the official translation of the latter during the Roman Empire, where imperator was part of the titelature of the Roman emperors; as such it continued to be used in Greek translations from Latin until the adoption of the Greek title basileus by Emperor Heraclius in 629.

It was retained in archaic forms of address during ceremonies in the East Roman Empire, was revived in the form of basileus autokratōr, which designated the senior of several ruling co-emperors, who held the actual power. In the Palaiologan period, this use was extended to include the designated heir; the title is evidenced in coins from 912, in imperial chrysobulls from the 11th century, in numerous illuminated manuscripts. The term stratēgos autokratōr continued to be used in the Byzantine period as well; the title is prevalent in the 6th century, re-appears in the 10th-11th centuries for senior military commanders. Thus, for instance, Basil II installed David Arianites as stratēgos autokratōr of Bulgaria, implying powers of command over the other regional stratēgoi in the northern Balkans; the Byzantine imperial formula was imitated among the Byzantine influenced nations such as Georgia and Balkan states, most notably, the emerging Tsardom of Russia. One of the titles of Georgian kings of Bagrationi dynasty was "Autocrat of all the east and the west", title introduced during David IV and lasted until dissolution of the unified Georgian monarchy during the reign of George VIII, dissolution confirmed at 1490.

The rulers of the Second Bulgarian Empire used the title "Emperor of the Bulgarians", in the early reigns with the addition of "and the Vlachs", but Ivan Asen II, who after the Battle of Klokotnitsa in 1230 expanded his control over most of the Byzantine Empire's former European possessions adopted the title of "Tsar and autokrator of all the Bulgarians and the Greeks", a title which had first been claimed by Prince Simeon I. When the Serbian king Stefan Dušan claimed the imperial title in 1345/46, he used the title "basileus and autokratōr of Serbia and of Romania" in Greek, "Tsar of the Serbs and Greeks" in Serbian; the use of "Romania" and not the usual Byzantine formula "of the Romans" signified that although he claimed the direct succession to all Byzantine emperors from the time of Constantine the Great, he lacked possession of Constantinople and of the Ecumenical Patriarchate, which alone conferred full legitimacy. Deriving from this usage, the Russian tsars, from the establishment of the Russian Empire up to the fall of the Russian monarchy in 1917, used the formula "Emperor and Autocrat of All the Russias".

In the Slavic languages, the title was used in a translated form. Bury, J. B.. The Constitution of the Later Roman Empire. Cambridge University Press. Pp. 18–24. ISBN 978-1-107-68053-1. Ferjančić, Božidar. "Samodržac". LSSV: 642–643. Kršljanin, Nina. "The Title of Samoderzhets in Serbia and Russia: Two Ways of Byzantine Heritage Development". Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 4, Istoriya. Regionovedenie. Mezhdunarodnye otnosheniya [Sc

Who Are You? (2008 TV series)

Who Are You? is a 2008 South Korean television series starring Yoon Kye-sang, Go Ara and Kang Nam-gil. It aired on MBC from March 3 to May 2008 on Wednesdays and Thursdays at 21:55 for 17 episodes. Son Il-gun is a middle-aged devoted father to his daughter, Young-in. Young-in just graduated from high school and is an aspiring cartoonist, but she is working part-time instead of going to college due to financial difficulties, which the quick-tempered young woman blames on her "loser" father, she has no idea that Il-gun was once a struggling artist in his youth, but now that one of his paintings was sold for an exorbitant amount to a collector in New York, a local gallery offers Il-gun a solo exhibition. But before he can make a decision, Il-gun dies in a traffic accident. According to Buddhism, the soul of a dead person is allowed to wander for 49 days in order to let go of all earthly attachments before going to the afterlife, but Il-gun loves his daughter so much that he takes it one step further, possesses a stranger's body to care for Young-in and make it up to her.

Cha Seung-hyo was abandoned as a child adopted and raised in the United States. He is now a perfectionist corporate raider without any meaningful relationships. However, after a traffic accident, he begins to lose time and wake up in strange situations, he learns that Il-gun is spiritually possessing him for three hours a day. Not only does Young-in find it suspicious that this stranger is concerned about her well-being, buying her expensive clothes and food, but Seung-hyo's subordinates find it weird that he periodically acts out of character like a manically cheerful, old-fashioned man. Against his will, Seung-hyo gets drawn into Young-in's life, discovers that Shin Jae-ha, owner of Nuri Art Gallery, is ingratiating himself with her, hoping to find more of the late Il-gun's paintings and buy them off her for less than they're worth. Young-in dislikes and mistrusts Seung-hyo, but the more she gets to know him, she glimpses his loneliness and falls for him, which leads to awkwardness and hijinks.

Yoon Kye-sang as Cha Seung-hyo Go Ara as Son Young-in Kang Nam-gil as Son Il-gun, Young-in's father Jin Yi-han as Shin Jae-ha, owner of Nuri Art Gallery Park Ji-young as Kim Young-ae, Il-gun's girlfriend Kim Sung-eun as Yoon Ha-young, gallery curator Lee Eon as Kwon Yong-deok, Young-in's friend Lee Min-jung as Yang Ji-sook, Young-in's friend Jung Ho-bin as Yoon Hoo-jin, Seung-hyo's lawyer Ahn Sun-young as Yeo Ji-won, Seung-hyo's secretary Jo Deok-hyun as Driver Pi, Seung-hyo's chauffeur Gi Ju-bong as Cha Chul-soo, Seung-hyo's father Kim Mi-kyung as Oh Young-hee, Seung-hyo's mother Kim Hyung-jong as Loan shark 1 Jung Hwan-gyu as Loan shark 2 Yoon Joo-sang as Sa Shin Sunwoo Yong-nyeo as Geum Nan-hee, Jae-ha's mother Baek Jung-min as Jang Dong-gun Kim Sung-kyum as President Kim Kwon Hae-hyo as Funeral service counselor Min Ah-ryung Park Kwang-jung Who Are You? official MBC website Who Are You? at MBC Global Media Who Are You? at HanCinema Who Are You? on IMDb

William B. Bader

William Banks Bader was United States Assistant Secretary of State for Educational and Cultural Affairs from 1999 to 2001. Bader's paternal grandfather was Edward Lawrence Bader, mayor of Atlantic City, New Jersey, he was educated at Pomona College, receiving a BA in 1953. He studied as a Fulbright scholar at Ludwig Maximilian University of Munich and the University of Vienna. During his time in Munich, Bader married his Pomona college classmate, sculptor Gretta Lange, he served in the United States Navy from 1955 to 1958 on active duty and transferred to the Reserves before retiring with the rank of captain. He studied German history at Princeton University under Gordon A. Craig, earning an MA in 1960 and a PhD in 1964. Bader joined the United States Foreign Service in 1965, was posted to the Office of Regional Political-Military Affairs in Washington, D. C. In 1966, Sen. J. William Fulbright invited Bader to join the staff of the United States Senate Committee on Foreign Relations where he was a senior staff member overseeing international security and arms control from 1966 to 1969.

During this time, he worked for the United States Senate Foreign Relations Subcommittee on Near Eastern and South and Central Asian Affairs, chaired by Sen. Stuart Symington. In the early 1970s, Bader worked for the Ford Foundation in Paris, he became a fellow of the Woodrow Wilson International Center for Scholars in 1974. Bader returned to government in 1976 when he was appointed Deputy Under Secretary of Defense for Policy, he returned to the staff of the United States Senate Committee on Foreign Relations in 1978 as Staff Director at a time when the committee was considering the Camp David Accords, the Taiwan Relations Act, SALT II. In 1981, Bader became Vice President and Senior Officer of the Washington, D. C. office of SRI International. He moved to California in 1988 to become Vice President of SRI International's policy division, he became president of the Eurasia Foundation in 1992. He spent 1996–97 as a visiting fellow at the World Bank Group. In 1999, President of the United States Bill Clinton nominated Bader to be Assistant Secretary of State for Educational and Cultural Affairs and, after Senate confirmation, Bader held this office from November 18, 1999 until January 20, 2001.

Bader and his wife had four children, including actor Diedrich Bader. "Oesterreich in Potsdam" in Oesterreichische Zeitschrift für Aussenpolitik, Vol. II, No. 4, June 1962 "The United States and the'German Problem'" in Foreign Affairs, 1965 Austria Between East and West: 1945–1955, Stanford University Press, 1966 The United States and the Spread of Nuclear Weapons, Pegasus, 1968 "The Congress and National Security" in Naval War College Review, 1970 "The Proliferation of Conventional Weapons" in The Future of the International Legal Order, Vol. III, ed. C. E. Black and Richard Falk, 1971 "Congress and the Making of the U. S. Security Policies," Adelphi Paper No. 173, IISS, England, 1982 "Austria, The United States, the Path to Neutrality" in The Austrian Solution, ed. Robert A. Bauer, 1982 "Western Europe" in TRANSACTION/SOCIETY, Vol. 22, No. 4, May/June 1985 "Western Europe: From Roosevelt to Reagan" in The President, the Congress and Foreign Policy: A Joint Policy Project of the Association of Former Members of Congress and the Atlantic Council of the United States, New York.

Bader "The 60th Anniversary of the Fulbright Program in Austria: 1950 – 2010: Seeing the World as Others See It", Bridges: The OST's Publication on S&T Policy, vol. 26, July 2010