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Non-Standard Calculus
In mathematics, non-standard calculus is the modern application of infinitesimals, in the sense of non-standard analysis, to infinitesimal calculus. It provides a rigorous justification that were previously considered merely heuristic. Nonrigourous calculations with infinitesimals were widely used before Karl Weierstrass sought to replace them with the (ε, δ)-definition of limit starting in the 1870s. (See history of calculus.) For almost one hundred years thereafter, mathematicians like Richard Courant viewed infinitesimals as being naive and vague or meaningless. Contrary to such views, Abraham Robinson showed in 1960 that infinitesimals are precise, clear, and meaningful, building upon work by Edwin Hewitt and Jerzy Łoś. According to Howard Keisler, "Robinson solved a three hundred year old problem by giving a precise treatment of infinitesimals. Robinson's achievement will probably rank as one of the major mathematical advances of the twentieth century."
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  • 27 Oct 2022
Topic Review
Law In Modern Society
Law in Modern Society: Toward a Criticism of Social Theory is a 1976 book by philosopher and politician Roberto Mangabeira Unger. In the book, Unger uses the rise and decline of the rule of law as a vehicle to explore certain problems in social theory. According to Unger, problems that were central concerns of classical social theorists like Marx, Durkheim, and Weber—the problems of explanation, order, and modernity—remain unsolved. Unger contends that the failure of classical social theory to solve these dilemmas can be traced to the way in which it asserted its independence from the ancient political philosophers, namely in its denial of a supra-historical human nature and in its insistence upon the contrast of fact and value. Unger argues that a radical reorientation of social theory is needed to solve the problems it faces. "To carry out its own program," Unger writes, social theory must destroy itself." The rise and decline of the rule of law, and the dilemmas of social theory, converge in the need to be able to compare and criticize different forms of society, in order to be able to more effectively submit the organization of society to the human will.
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  • 27 Oct 2022
Topic Review
List of Metric Units
Metric units are units based on the metre, gram or second and decimal (power of ten) multiples or sub-multiples of these. The most widely used examples are the units of the International System of Units (SI). By extension they include units of electromagnetism from the CGS and SI units systems, and other units for which use of SI prefixes has become the norm. Other unit systems using metric units include:
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  • 27 Oct 2022
Topic Review
Autonomous Spaceport Drone Ship
An autonomous spaceport drone ship (ASDS) is an ocean-going vessel derived from a deck barge, outfitted with station-keeping engines and a large landing platform. Construction of such ships was commissioned by aerospace company SpaceX to allow for recovery of rocket first-stages at sea for high-velocity missions which do not carry enough fuel to return to the launch site after lofting spacecraft onto an orbital trajectory. SpaceX has two operational drone ships and has a third under construction as of early 2018. Just Read the Instructions operates in the Pacific for launches from Vandenberg Air Force Base ; Of Course I Still Love You operates in the Atlantic for launches from Cape Canaveral. A Shortfall of Gravitas is under construction. (As of August 2018), 23 Falcon 9 flights have attempted to land on a drone ship, with 17 of them succeeding. The ASDS ships are a key component of the SpaceX reusable launch system development program which aims to significantly lower the price of space launch services through "full and rapid reusability." Any flights going to geostationary orbit or exceeding escape velocity will require landing at sea, encompassing about half of SpaceX missions.
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  • 27 Oct 2022
Topic Review
Maximin Share
Maximin share (MMS) is a criterion of fair item allocation. Given a set of items with different values, the 1-out-of-n maximin-share is the maximum value that can be gained by partitioning the items into n parts and taking the part with the minimum value. An allocation of items among n agents with different valuations is called MMS-fair if each agent gets a bundle that is at least as good as his/her 1-out-of-n maximin-share. MMS fairness was invented by Eric Budish as a relaxation of the criterion of proportionality - each agent gets a bundle that is at least as good as the equal split (1/n of every resource). Proportionality can be guaranteed when the items are divisible, but not when they are indivisible, even if all agents have identical valuations. In contrast, MMS fairness can always be guaranteed to identical agents, so it is a natural alternative to proportionality even when the agents are different.
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  • 31 Oct 2022
Topic Review
Physaliidae
The Portuguese man o' war (Physalia physalis), also known as the man-of-war, bluebottle, blue bottle jellyfish, or floating terror is a marine hydrozoan found in the Atlantic Ocean and the Indian Ocean. It is considered to be the same species as the Pacific man o' war, which is found mainly in the Pacific Ocean. The Portuguese man o' war is the only species in the genus Physalia, which in turn is the only genus in the family Physaliidae. It has numerous venomous microscopic nematocysts which deliver a painful sting powerful enough to kill fish, and has been known to occasionally kill humans. Although it superficially resembles a jellyfish, the Portuguese man o' war is in fact a siphonophore. Like all siphonophores, it is a colonial organism, made up of many smaller units called zooids. All zooids in a colony are genetically identical, but fulfill specialized functions such as feeding and reproduction, and together allow the colony to operate as a single individual.
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  • 27 Oct 2022
Topic Review
Shooting Star (Spacecraft)
The Shooting Star is an expendable American cargo spacecraft (transport vehicle) developed by Sierra Nevada Corporation as part of the Dream Chaser Launch System. It attaches to the back of Dream Chaser® spaceplane serving as a Service Module and holding up to 4,536 kg (10,000 lb) of supplies, cargo and experiments for the International Space Station. It is launched by ULA's Vulcan rocket and is designed to transport supplies to the International Space Station (ISS) and return items to Earth. Shooting Star can support three unpressurized payloads weighing up to 500 kg (1,100 lb) each or one payload weighing as much as 1,500 kg (3,300 lb). Once the module is at the station, the Canadarm2 robotic arm would unload the externally attached payload and install it on the station's exterior. The Shooting Star module is versatile, supplying power and ECLSS for the Dream Chaser system. It can be customized for special mission needs, such as autonomous docking to ISS instead of berthing. Upon re-entry into Earth’s atmosphere, it also performs disposal of cargo from the International Space Station.
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Topic Review
List of Orchidaceae of South Africa
Orchidaceae is a family of flowering plants (anthophytes) in the order Asparagales . 23,420 species of vascular plant have been recorded in South Africa, making it the sixth most species-rich country in the world and the most species-rich country on the African continent. Of these, 153 species are considered to be threatened. Nine biomes have been described in South Africa: Fynbos, Succulent Karoo, desert, Nama Karoo, grassland, savanna, Albany thickets, the Indian Ocean coastal belt, and forests. The 2018 South African National Biodiversity Institute's National Biodiversity Assessment plant checklist lists 35,130 taxa in the phyla Anthocerotophyta (hornworts (6)), Anthophyta (flowering plants (33534)), Bryophyta (mosses (685)), Cycadophyta (cycads (42)), Lycopodiophyta (Lycophytes(45)), Marchantiophyta (liverworts (376)), Pinophyta (conifers (33)), and Pteridophyta (cryptogams (408)). 67 genera are represented in the literature. Listed taxa include species, subspecies, varieties, and forms as recorded, some of which have subsequently been allocated to other taxa as synonyms, in which cases the accepted taxon is appended to the listing. Multiple entries under alternative names reflect taxonomic revision over time.
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Topic Review
Substantive Due Process
Substantive due process, in United States constitutional law, is a principle allowing courts to protect certain fundamental rights from government interference, even if procedural protections are present or the rights are not specifically mentioned elsewhere in the US Constitution. Courts have identified the basis for such protection from the due process clauses of the Fifth and Fourteenth Amendments to the Constitution, which prohibit the federal and state governments, respectively, from depriving any person of "life, liberty, or property, without due process of law." Substantive due process demarcates the line between the acts that courts hold that are subject to government regulation or legislation and the acts that courts place beyond the reach of governmental interference. Whether the Fifth or Fourteenth Amendments were intended to serve that function continues to be a matter of scholarly as well as judicial discussion and dissent. Substantive due process is to be distinguished from procedural due process. The distinction arises from the words "of law" in the phrase "due process of law." Procedural due process protects individuals from the coercive power of government by ensuring that adjudication processes, under valid laws, are fair and impartial. Such protections, for example, include sufficient and timely notice on why a party is required to appear before a court or other administrative body, the right to an impartial trier of fact and trier of law, and the right to give testimony and present relevant evidence at hearings. In contrast, substantive due process protects individuals against majoritarian policy enactments that exceed the limits of governmental authority: courts may find that a majority's enactment is not law and cannot be enforced as such, regardless of whether the processes of enactment and enforcement were actually fair. The term was first used explicitly in 1930s legal casebooks as a categorical distinction of selected due process cases, and by 1952, it had been mentioned twice in Supreme Court opinions. The term "substantive due process" itself is commonly used in two ways: to identify a particular line of case law and to signify a particular political attitude toward judicial review under the two due process clauses. Much substantive due process litigation involves legal challenges about unenumerated rights that seek particular outcomes instead of merely contesting procedures and their effects. In successful cases, the Supreme Court recognizes a constitutionally based liberty that considers laws that seek to limit that liberty to be unenforceable or limited in scope. Critics of substantive due process decisions usually assert that there is no textual basis in the Constitution for such protection and that such liberties should be left under the purview of the more politically accountable branches of government.
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  • 27 Oct 2022
Topic Review
Nanotechnology in Cosmetics
Nanomaterials are materials with a size ranging from 1 to 100 nm in at least one dimension. At the nanoscale, material properties become different. These unique properties can be exploited for a variety of applications, including the use of nanoparticles in skincare and cosmetics products. Cosmeceuticals is one of the fastest growing industries in terms of personal care, accompanied by an increase in nanocosmeceuticals research and applications.
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