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Leonidas Alaoglu
Leonidas (''Leon'') Alaoglu ( el, Λεωνίδας Αλάογλου; March 19, 1914 – August 1981) was a mathematician, known for his result, called Alaoglu's theorem on the weak-star compactness of the closed unit ball in the dual of a normed space, also known as the Banach–Alaoglu theorem. Life and work Alaoglu was born in Red Deer, Alberta to Greek parents. He received his BS in 1936, Master's in 1937, and PhD in 1938 (at the age of 24), all from the University of Chicago. His thesis, written under the direction of Lawrence M. Graves was entitled ''Weak topologies of normed linear spaces''. His doctoral thesis is the source of Alaoglu's theorem. The Bourbaki–Alaoglu theorem is a generalization of this result by Bourbaki to dual topologies. After some years teaching at Pennsylvania State College, Harvard University and Purdue University, in 1944 he became an operations analyst for the United States Air Force. In his last position, from 1953 to 1981 he wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Red Deer, Alberta
Red Deer is a city in Alberta, Canada, located midway on the Calgary–Edmonton Corridor. Red Deer serves central Alberta, and key industries include health care, retail trade, construction, oil and gas, hospitality, manufacturing and education. It is surrounded by Red Deer County and borders on Lacombe County. The city is located in aspen parkland, a region of rolling hills, alongside the Red Deer River. History The area was inhabited by First Nations including the Blackfoot, Plains Cree and Stoney before the arrival of European fur traders in the late eighteenth century. A First Nations trail ran from the Montana Territory across the Bow River near present-day Calgary and on to Fort Edmonton, later known as the Calgary and Edmonton Trail. The trail crossed the Red Deer River at a wide, stony shallows. The "Old Red Deer Crossing" is upstream from the present-day city. Cree people called the river , which means "Elk River." European arrivals sometimes called North America ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Sphere
In mathematics, a unit sphere is simply a sphere of radius one around a given center. More generally, it is the set of points of distance 1 from a fixed central point, where different norms can be used as general notions of "distance". A unit ball is the closed set of points of distance less than or equal to 1 from a fixed central point. Usually the center is at the origin of the space, so one speaks of "the unit ball" or "the unit sphere". Special cases are the unit circle and the unit disk. The importance of the unit sphere is that any sphere can be transformed to a unit sphere by a combination of translation and scaling. In this way the properties of spheres in general can be reduced to the study of the unit sphere. Unit spheres and balls in Euclidean space In Euclidean space of ''n'' dimensions, the -dimensional unit sphere is the set of all points (x_1, \ldots, x_n) which satisfy the equation : x_1^2 + x_2^2 + \cdots + x_n ^2 = 1. The ''n''-dimensional open unit ball ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Caltech
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasionally referred to as "CIT", most notably in its alma mater, but this is uncommon. is a private university, private research university in Pasadena, California. Caltech is ranked among the best and most selective academic institutions in the world, and with an enrollment of approximately 2400 students (acceptance rate of only 5.7%), it is one of the world's most selective universities. The university is known for its strength in science and engineering, and is among a small group of Institute of Technology (United States), institutes of technology in the United States which is primarily devoted to the instruction of pure and applied sciences. The institution was founded as a preparatory and vocational school by Amos G. Throop in 1891 and began ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seminar
A seminar is a form of academic instruction, either at an academic institution or offered by a commercial or professional organization. It has the function of bringing together small groups for recurring meetings, focusing each time on some particular subject, in which everyone present is requested to participate. This is often accomplished through an ongoing Socratic dialogue with a seminar leader or instructor, or through a more formal presentation of research. It is essentially a place where assigned readings are discussed, questions can be raised and debates can be conducted. Etymology The word ''seminar'' was borrowed from German (always capitalized, as a common noun, as ''Seminar''), and is ultimately derived from the Latin word ''seminarium'', meaning "seed plot" (an old-fashioned term for “seedbed”). Its root word is ''semen'' (Latin for "seed"). Overview The term ''seminar'' is also used to describe a research talk, often given by a visiting researcher and primaril ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classified Information
Classified information is material that a government body deems to be sensitive information that must be protected. Access is restricted by law or regulation to particular groups of people with the necessary security clearance and need to know, and mishandling of the material can incur criminal penalties. A formal security clearance is required to view or handle classified material. The clearance process requires a satisfactory background investigation. Documents and other information must be properly marked "by the author" with one of several (hierarchical) levels of sensitivity—e.g. restricted, confidential, secret, and top secret. The choice of level is based on an impact assessment; governments have their own criteria, including how to determine the classification of an information asset and rules on how to protect information classified at each level. This process often includes security clearances for personnel handling the information. Some corporations and non-governm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burbank, California
Burbank is a city in the southeastern end of the San Fernando Valley in Los Angeles County, California, United States. Located northwest of downtown Los Angeles, Burbank has a population of 107,337. The city was named after David Burbank, who established a sheep ranch there in 1867. Billed as the "Media Capital of the World" and only a few miles northeast of Hollywood, numerous media and entertainment companies are headquartered or have significant production facilities in Burbank, including Warner Bros. Entertainment, The Walt Disney Company, Nickelodeon Animation Studio, The Burbank Studios, Cartoon Network Studios with the West Coast branch of Cartoon Network, and Insomniac Games. The broadcast network The CW is also headquartered in Burbank. The Hollywood Burbank Airport was the location of Lockheed's Skunk Works, which produced some of the most secret and technologically advanced airplanes, including the U-2 spy planes that uncovered Soviet Union missile components ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lockheed Corporation
The Lockheed Corporation was an American aerospace manufacturer. Lockheed was founded in 1926 and later merged with Martin Marietta to form Lockheed Martin in 1995. Its founder, Allan Lockheed, had earlier founded the similarly named but otherwise-unrelated Loughead Aircraft Manufacturing Company, which was operational from 1912 to 1920. History Origins Allan Loughead and his brother Malcolm Loughead had operated an earlier aircraft company, Loughead Aircraft Manufacturing Company, which was operational from 1912 to 1920. The company built and operated aircraft for paying passengers on sightseeing tours in California and had developed a prototype for the civil market, but folded in 1920 due to the flood of surplus aircraft deflating the market after World War I. Allan went into the real estate market while Malcolm had meanwhile formed a successful company marketing brake systems for automobiles. On December 13, 1926, Allan Lockheed, Jack Northrop, John Northrop, Kenneth K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operations Research
Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making. It is considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym. Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlap with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Topology
In functional analysis and related areas of mathematics a dual topology is a locally convex topology on a vector space that is induced by the continuous dual of the vector space, by means of the bilinear form (also called ''pairing'') associated with the dual pair. The different dual topologies for a given dual pair are characterized by the Mackey–Arens theorem. All locally convex topologies with their continuous dual are trivially a dual pair and the locally convex topology is a dual topology. Several topological properties depend only on the dual pair and not on the chosen dual topology and thus it is often possible to substitute a complicated dual topology by a simpler one. Definition Given a dual pair (X, Y, \langle , \rangle), a dual topology on X is a locally convex topology \tau so that :(X, \tau)' \simeq Y. Here (X, \tau)' denotes the continuous dual of (X,\tau) and (X, \tau)' \simeq Y means that there is a linear isomorphism :\Psi : Y \to (X, \tau)',\quad y \mapsto (x \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bachelor Of Science
A Bachelor of Science (BS, BSc, SB, or ScB; from the Latin ') is a bachelor's degree awarded for programs that generally last three to five years. The first university to admit a student to the degree of Bachelor of Science was the University of London in 1860. In the United States, the Lawrence Scientific School first conferred the degree in 1851, followed by the University of Michigan in 1855. Nathaniel Southgate Shaler, who was Harvard's Dean of Sciences, wrote in a private letter that "the degree of Bachelor of Science came to be introduced into our system through the influence of Louis Agassiz, who had much to do in shaping the plans of this School." Whether Bachelor of Science or Bachelor of Arts degrees are awarded in particular subjects varies between universities. For example, an economics student may graduate as a Bachelor of Arts in one university but as a Bachelor of Science in another, and occasionally, both options are offered. Some universities follow the Oxford a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greeks
The Greeks or Hellenes (; el, Έλληνες, ''Éllines'' ) are an ethnic group and nation indigenous to the Eastern Mediterranean and the Black Sea regions, namely Greece, Cyprus, Albania, Italy, Turkey, Egypt, and, to a lesser extent, other countries surrounding the Mediterranean Sea. They also form a significant diaspora (), with Greek communities established around the world.. Greek colonies and communities have been historically established on the shores of the Mediterranean Sea and Black Sea, but the Greek people themselves have always been centered on the Aegean and Ionian seas, where the Greek language has been spoken since the Bronze Age.. Until the early 20th century, Greeks were distributed between the Greek peninsula, the western coast of Asia Minor, the Black Sea coast, Cappadocia in central Anatolia, Egypt, the Balkans, Cyprus, and Constantinople. Many of these regions coincided to a large extent with the borders of the Byzantine Empire of the late 11th cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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