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Topic Review
False Position Method
In mathematics, the false position method or regula falsi is a very old method for solving an equation in one unknown, that, in modified form, is still in use. In simple terms, the method is the trial and error technique of using test ("false") values for the variable and then adjusting the test value according to the outcome. This is sometimes also referred to as "guess and check". Versions of the method predate the advent of algebra and the use of equations. As an example, consider problem 26 in the Rhind papyrus, which asks for a solution of (written in modern notation) the equation x + x/4 = 15. This is solved by false position, using a technique that predates formally written equations. First, guess that x = 4 to obtain, on the left, 4 + 4/4 = 5. This guess is a good choice since it produces an integer value. However, 4 is not the solution of the original equation, as it gives a value which is three times too small. To compensate, multiply x (currently set to 4) by 3 and substitute again to get 12 + 12/4 = 15, verifying that the solution is x = 12. Modern versions of the technique employ systematic ways of choosing new test values and are concerned with the questions of whether or not an approximation to a solution can be obtained, and if it can, how fast can the approximation be found.
  • 3.8K
  • 15 Nov 2022
Topic Review
Infinite–dimensional Vector Function
An infinite–dimensional vector function is a function whose values lie in an infinite-dimensional topological vector space, such as a Hilbert space or a Banach space. Such functions are applied in most sciences including physics.
  • 290
  • 15 Nov 2022
Topic Review
MRCI (Interface)
DriveSpace (initially known as DoubleSpace) is a disk compression utility supplied with MS-DOS starting from version 6.0 in 1993 and ending in 2000 with the release of Windows Me. The purpose of DriveSpace is to increase the amount of data the user could store on disks by transparently compressing and decompressing data on-the-fly. It is primarily intended for use with hard drives, but use for floppy disks is also supported. This feature was removed in Windows XP and later.
  • 232
  • 15 Nov 2022
Topic Review
Acronis True Image
Acronis True Image is a software product produced by Acronis that provides data protection for personal users including, backup, archive, access and recovery for Windows, macOS, iOS, and Android operating systems. As disk imaging software, True Image can restore the previously captured image to another disk, replicating the structure and contents to the new disk, also allowing disk cloning and partition resizing, even if the new disk is of a different capacity. The backups are in a proprietary format which saves using a .tib filename format. Acronis was launched in 2003 and in December 2014 claimed to have over 5 million consumer and 500,000 businesses users.
  • 2.6K
  • 15 Nov 2022
Topic Review
Machine Learning Methods
Machine learning (ML) has a well-established reputation for successfully enabling automation through its scalable predictive power.
  • 570
  • 15 Nov 2022
Topic Review
Pandora Radio
Pandora Media Inc. (also known as Pandora Internet Radio or simply Pandora) is a music streaming and automated music recommendation internet radio service powered by the Music Genome Project. As of August 1, 2017, the service, operated by Pandora Media, Inc., is available only in the United States. The service plays songs that have similar musical traits. The user then provides positive or negative feedback (as thumbs up or thumbs down) for songs chosen by the service, and the feedback is taken into account in the subsequent selection of other songs to play. The service can be accessed either through a web browser or with its mobile app. Pandora is a freemium service; basic features are free with advertisements or limitations, while additional features, such as improved streaming quality, music downloads and offline channels are offered via paid subscriptions. On September 24, 2018, Sirius XM Holdings announced its intent to acquire Pandora for $3.5 billion.
  • 2.6K
  • 15 Nov 2022
Topic Review
Zermelo's Theorem (Game Theory)
In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which chance does not affect the decision making process. It says that if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. can force a win). An alternate statement is that for a game meeting all of these conditions except the condition that a draw is now possible, then either the first-player can force a win, or the second-player can force a win, or both players can force a draw. The theorem is named after Ernst Zermelo, a German mathematician and logician, who proved the theorem for the example game of chess in 1913.
  • 734
  • 15 Nov 2022
Topic Review
Circumscribed Circle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic. A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm. Even if a polygon has a circumscribed circle, it may be different from its minimum bounding circle. For example, for an obtuse triangle, the minimum bounding circle has the longest side as diameter and does not pass through the opposite vertex.
  • 4.6K
  • 15 Nov 2022
Topic Review
MIDI 1.0
The Musical Instrument Digital Interface (MIDI) specification version 1.0 describes the communications protocol and the message format, as well electrical connector. MIDI 1.0 is a one-way connection from the MIDI Out connector of the sending device to the MIDI In connector of the receiving device, transmitted serially at a rate of 31.25 kbit/s.
  • 460
  • 15 Nov 2022
Topic Review
Features New to Windows 7
Some of the new features included in Windows 7 are advancements in touch, speech and handwriting recognition, support for virtual hard disks, support for additional file formats, improved performance on multi-core processors, improved boot performance, and kernel improvements. Some of the features which are present in versions up to and including Windows Vista were removed or changed.
  • 4.7K
  • 15 Nov 2022
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