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Descartes' Rule of Signs
In mathematics, Descartes' rule of signs, first described by René Descartes in his work La Géométrie, is a technique for getting information on the number of positive real roots of a polynomial. It asserts that the number of positive roots is at most the number of sign changes in the sequence of polynomial's coefficients (omitting the zero coefficients), and that the difference between these two numbers is always even. This implies, in particular, that if the number of sign changes is zero or one, then there are exactly zero or one positive roots, respectively. By a homographic transformation of the variable, one may use Descartes' rule of signs for getting a similar information on the number of roots in any interval. This is the basic idea of Budan's theorem and Budan–Fourier theorem. By repeating the division of an interval into two intervals, one gets eventually a list of disjoints intervals containing together all real roots of the polynomial, and containing each exactly one real root. Descartes rule of signs and homographic transformations of the variable are, nowadays, the basis of the fastest algorithms for computer computation of real roots of polynomials (see Real-root isolation). Descartes himself used the transformation x → –x for using his rule for getting information of the number of negative roots.
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  • 03 Nov 2022
Topic Review
Tropical Monsoon Climate
An area of tropical monsoon climate (occasionally known as a tropical wet climate or a tropical monsoon and trade-wind littoral climate) is a type of climate that corresponds to the Köppen climate classification category "Am". Tropical monsoon climates have monthly mean temperatures above 18 °C (64 °F) in every month of the year and a dry season. :200–1 Tropical monsoon climates is the intermediate climate between the wet Af (or tropical rainforest climate) and the drier Aw (or tropical savanna climate). A tropical monsoon climate, however, has its driest month seeing on average less than 60 mm, but more than [math]\displaystyle{ 100-\left ( \frac{Total\ Annual\ Precipitation\ (mm)}{25} \right ) }[/math]. This latter fact is in direct contrast to a tropical savanna climate, whose driest month sees less than 60 mm of precipitation and also less than [math]\displaystyle{ 100-\left ( \frac{Total\ Annual\ Precipitation\ (mm)}{25} \right ) }[/math] of average monthly precipitation. In essence, a tropical monsoon climate tends to either see more rainfall than a tropical savanna climate or have less pronounced dry seasons. Additionally, a tropical monsoon climate tends to see less variance in temperatures during the course of the year than a tropical savanna climate. This climate has a driest month which nearly always occurs at or soon after the "winter" solstice for that side of the equator.
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  • 03 Nov 2022
Topic Review
Leaving a Doll's House: A Memoir
Leaving a Doll's House: A Memoir is an autobiography written by British actress Claire Bloom and published in 1996. Bloom writes about her life, career and relationships, including her first marriage to Rod Steiger. The main focus is on her troubled relationship with writer Philip Roth.
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  • 03 Nov 2022
Topic Review
Combo Washer Dryer
A combo washer dryer (also known more simply as a washer-dryer in the United Kingdom ) is a combination in a single cabinet of a washing machine and a clothes dryer. It should not be confused with a "stackable" combination of a separate washing machine and a separate clothes dryer.
  • 2.7K
  • 08 Nov 2022
Topic Review
White Flag
Flag White flags have had different meanings throughout history and depending on the locale.
  • 21.4K
  • 02 Nov 2022
Topic Review
Cretaceous–Paleogene Extinction Event
The Cretaceous–Paleogene (K–Pg) extinction event, also known as the Cretaceous–Tertiary (K–T) extinction,[lower-alpha 2] was a sudden mass extinction of three-quarters of the plant and animal species on Earth, approximately 66 million years ago. With the exception of some ectothermic species such as the sea turtles and crocodilians, no tetrapods weighing more than 25 kilograms (55 pounds) survived. It marked the end of the Cretaceous period, and with it the end of the entire Mesozoic Era, opening the Cenozoic Era that continues today. In the geologic record, the K–Pg event is marked by a thin layer of sediment called the K–Pg boundary, which can be found throughout the world in marine and terrestrial rocks. The boundary clay shows high levels of the metal iridium, which is rare in the Earth's crust, but abundant in asteroids. As originally proposed in 1980 by a team of scientists led by Luis Alvarez and his son Walter, it is now generally thought that the K–Pg extinction was caused by the impact of a massive comet or asteroid 10 to 15 km (6 to 9 mi) wide, 66 million years ago, which devastated the global environment, mainly through a lingering impact winter which halted photosynthesis in plants and plankton. The impact hypothesis, also known as the Alvarez hypothesis, was bolstered by the discovery of the 180 km (112 mi) Chicxulub crater in the Gulf of Mexico's Yucatán Peninsula in the early 1990s, which provided conclusive evidence that the K–Pg boundary clay represented debris from an asteroid impact. The fact that the extinctions occurred simultaneously provides strong evidence that they were caused by the asteroid. A 2016 drilling project into the Chicxulub peak ring confirmed that the peak ring comprised granite ejected within minutes from deep in the earth, but contained hardly any gypsum, the usual sulfate-containing sea floor rock in the region: The gypsum would have vaporized and dispersed as an aerosol into the atmosphere, causing longer-term effects on the climate and food chain. In October 2019, researchers reported that the event rapidly acidified the oceans producing ecological collapse and, in this way as well, produced long-lasting effects on the climate, and accordingly was a key reason for the end-Cretaceous mass extinction. In January 2020, scientists reported new evidence that the extinction event was mostly a result of the meteorite impact and not volcanism. Other causal or contributing factors to the extinction may have been the Deccan Traps and other volcanic eruptions, climate change, and sea level change. A wide range of species perished in the K–Pg extinction, the best-known being the non-avian dinosaurs. It also destroyed a myriad of other terrestrial organisms, including some mammals, pterosaurs, birds, lizards, insects, and plants. In the oceans, the K–Pg extinction killed off plesiosaurs and mosasaurs and devastated teleost fish, sharks, mollusks (especially ammonites, which became extinct), and many species of plankton. It is estimated that 75% or more of all species on Earth vanished. Yet the extinction also provided evolutionary opportunities: In its wake, many groups underwent remarkable adaptive radiation — sudden and prolific divergence into new forms and species within the disrupted and emptied ecological niches. Mammals in particular diversified in the Paleogene, evolving new forms such as horses, whales, bats, and primates. The surviving group of dinosaurs were avians, ground and water fowl who radiated into all modern species of bird. Teleost fish, and perhaps lizards also radiated.
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  • 03 Nov 2022
Topic Review
Georg Cantor's First Set Theory Article
Georg Cantor published his first set theory article in 1874, and it contains the first theorems of transfinite set theory, which studies infinite sets and their properties. One of these theorems is "Cantor's revolutionary discovery" that the set of all real numbers is uncountably, rather than countably, infinite. This theorem is proved using Cantor's first uncountability proof, which differs from the more familiar proof using his diagonal argument. The title of the article, "On a Property of the Collection of All Real Algebraic Numbers" ("Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen"), refers to its first theorem: the set of real algebraic numbers is countable. Cantor's article also contains a proof of the existence of transcendental numbers. As early as 1930, mathematicians have disagreed on whether this proof is constructive or non-constructive. Books as recent as 2014 and 2015 indicate that this disagreement has not been resolved. Since Cantor's proof either constructs transcendental numbers or does not, an analysis of his article can determine whether his proof is constructive or non-constructive. Cantor's correspondence with Richard Dedekind shows the development of his ideas and reveals that he had a choice between two proofs, one that uses the uncountability of the real numbers and one that does not. Historians of mathematics have examined Cantor's article and the circumstances in which it was written. For example, they have discovered that Cantor was advised to leave out his uncountability theorem in the article he submitted; he added it during proofreading. They have traced this and other facts about the article to the influence of Karl Weierstrass and Leopold Kronecker. Historians have also studied Dedekind's contributions to the article, including his contributions to the theorem on the countability of the real algebraic numbers. In addition, they have looked at the article's legacy, which includes the impact that the uncountability theorem and the concept of countability have had on mathematics.
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  • 02 Nov 2022
Topic Review
List of Women Warriors in Folklore
This is a list of women who engaged in war, found throughout mythology and folklore, studied in fields such as literature, sociology, psychology, anthropology, film studies, cultural studies, and women's studies. A mythological figure does not always mean a fictional one, but rather, someone of whom stories have been told that have entered the cultural heritage of a people. Some women warriors are documented in the written record and as such form part of history (e.g. the Ancient Briton queen Boudica, who led the Iceni into battle against the Romans). However, to be considered a warrior, the woman in question must have belonged to some sort of military, be it recognized, like an organized army, or unrecognized, like revolutionaries.
  • 30.7K
  • 02 Nov 2022
Topic Review
Cyber Mimic Defense
From the inspiration of defensive guise behaviors based on mimic phenomenon in biology, Cyber Mimic Defense (CMD) introduces the mechanism of dynamic multi-dimensional reconfiguration into a dissimilar redundancy structure (DRS) which is widely used in the field of reliability. It addresses certain or uncertain threats in cyberspace by the principle of uncertain defense, and provides the strategic varieties and transformations of DRS elements inside objects in quantity or type, time or space dimension under the condition of unchanged visual functions. It provides a generally innovative defense theory and method to deal with the “known unknown risk” and “unknown unknown risk” which exist in related application levels of different areas of cyberspace and are based on unknown vulnerabilities, backdoors, viruses, Trojans, etc. This method can provide not only endogenous security gains which are independent of traditional security means and achieved via integrated structural technologies for critical infrastructures or key information equipment, but also resilient or restorable service ability with intensive attributes inherited from the architecture. Further it acquires super nonlinear effects combining mature defense technologies. It's aimed at creating a non-closed, self-controlled and sustainable-developed ecological environment which adapts to globalization technologies and industrial development models and integrates with win-win cooperation and open sources.
  • 2.1K
  • 02 Nov 2022
Topic Review
ThinkCentre M Series
The M-series of desktops are part of Lenovo's ThinkCentre product line. Formerly an IBM brand, Lenovo acquired the ThinkCentre desktop brand following its purchase of IBM's Personal Computing Division (PCD) in 2005. Following its acquisition of IBM's PCD, Lenovo has released M-series desktops in multiple form factors, ranging from traditional tower, to small form factor, and all-in-ones (AIOs).
  • 9.8K
  • 02 Nov 2022
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