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Topic Review
Biography
Topic Review
Sturm-Liouville Theory
In mathematics and its applications, a classical Sturm–Liouville equation, named after Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882), is a real second-order linear differential equation of the form where y is a function of the free variable x. Here the functions p(x) > 0 has a continuous derivative, q(x), and w(x) > 0 are specified at the outset, and in the simplest of cases are continuous on the finite closed interval [a,b]. In addition, the function y is typically required to satisfy some boundary conditions at a and b. The function w(x), which is sometimes called r(x), is called the "weight" or "density" function. The value of λ is not specified in the equation; finding the values of λ for which there exists a non-trivial solution of (1) satisfying the boundary conditions is part of the problem called the Sturm–Liouville problem (S L). Such values of λ when they exist are called the eigenvalues of the boundary value problem defined by (1) and the prescribed set of boundary conditions. The corresponding solutions (for such a λ) are the eigenfunctions of this problem. Under normal assumptions on the coefficient functions p(x), q(x), and w(x) above, they induce a Hermitian differential operator in some function space defined by boundary conditions. The resulting theory of the existence and asymptotic behavior of the eigenvalues, the corresponding qualitative theory of the eigenfunctions and their completeness in a suitable function space became known as Sturm–Liouville theory. This theory is important in applied mathematics, where S–L problems occur very commonly, particularly when dealing with linear partial differential equations that are separable.
343
01 Dec 2022
Topic Review
Editorialization
Editorialization refers to all operations of organization and structuring of content on the web, and more broadly in the digital environment. Characterized as a continuous process (in time) and open (in space), the concept of editorialization allows to clarify the processes of production, diffusion and validation of knowledge, specific to the digital environment. Editorialization is therefore a key concept in the understanding of digital culture and its epistemological turn.
504
01 Dec 2022
Topic Review
Delay Line Memory
Delay line memory is a form of computer memory, now obsolete, that was used on some of the earliest digital computers. Like many modern forms of electronic computer memory, delay line memory was a refreshable memory, but as opposed to modern random-access memory, delay line memory was sequential-access. Analog delay line technology had been used since the 1920s to delay the propagation of analog signals. When a delay line is used as a memory device, an amplifier and a pulse shaper are connected between the output of the delay line and the input. These devices recirculate the signals from the output back into the input, creating a loop that maintains the signal as long as power is applied. The shaper ensures the pulses remain well-formed, removing any degradation due to losses in the medium. The memory capacity is determined by dividing the time taken to transmit one bit into the time it takes for data to circulate through the delay line. Early delay-line memory systems had capacities of a few thousand bits, with recirculation times measured in microseconds. To read or write a particular bit stored in such a memory, it is necessary to wait for that bit to circulate through the delay line into the electronics. The delay to read or write any particular bit is no longer than the recirculation time. Use of a delay line for a computer memory was invented by J. Presper Eckert in the mid-1940s for use in computers such as the EDVAC and the UNIVAC I. Eckert and John Mauchly applied for a patent for a delay line memory system on October 31, 1947; the patent was issued in 1953. This patent focused on mercury delay lines, but it also discussed delay lines made of strings of inductors and capacitors, magnetostrictive delay lines, and delay lines built using rotating disks to transfer data to a read head at one point on the circumference from a write head elsewhere around the circumference.
902
01 Dec 2022
Topic Review
GIS Live DVD
GIS Live DVD is a type of the thematic Live CD containing GIS/RS applications and related tutorials, and sample data sets. The general sense of a GIS Live DVD is to demonstrate the power of FLOSS GIS and encourage users to start on FLOSS GIS. However, a disc can be used for GIS data processing and training, too. A disc usually includes some selected Linux-based or Wine-enabled Windows applications for GIS and Remote Sensing use. Using this disc the end users can execute GIS functions to get experience in free and open source software solutions or solve some simple business operations. The set-up and the operating behaviour of the applications can also be studied prior to building real FLOSS GIS-based systems. Recently a LiveDVD image is stored and booted from USB (Live USB).
480
01 Dec 2022
Topic Review
Web Television
Web television is original episodic online video content produced for broadcast on the Internet via the World Wide Web. The phrase "web television" is also sometimes used to refer to Internet television in general, which includes Internet-transmission of programs produced for both online and traditional terrestrial, cable, or satellite broadcast. Web television content includes web series such as Carmilla, Husbands, Red vs. Blue, Teenagers, The Lizzie Bennet Diaries, and Video Game High School, among hundreds of others; original miniseries such as Dr. Horrible's Sing-Along Blog; animated shorts such as those of Homestar Runner; and exclusive video content that supplements conventional television broadcasts. The current major distributors of web television are Amazon, Crackle, Hulu, Netflix, Newgrounds, Roku, and YouTube. Examples of web television production companies include: Generate LA-NY, Next New Networks, Revision3, and Vuguru. In 2008, the International Academy of Web Television, headquartered in Los Angeles, formed in order to organize and support web television actors, authors, executives, and producers. The organization also administers the selection of winners for the Streamy Awards. In 2009, the Los Angeles Web Series Festival was founded. Several other festivals and award shows have been dedicated solely to web content, including the Indie Series Awards and the Vancouver Web Series Festival. In 2013, in response to the shifting of the soap opera All My Children from broadcast to web television, a new category for "Fantastic web-only series" in the Daytime Emmy Awards was created. Later that year, Netflix made history by earning the first Primetime Emmy Award nominations for web television series, for Arrested Development, Hemlock Grove, and House of Cards, at the 65th Primetime Emmy Awards. Hulu earned the first Emmy win for Outstanding Drama Series, for The Handmaid's Tale at the 69th Primetime Emmy Awards.
1.8K
01 Dec 2022
Topic Review
Lebesgue Constant (Interpolation)
In mathematics, the Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the interpolant of a function (at the given nodes) is in comparison with the best polynomial approximation of the function (the degree of the polynomials are obviously fixed). The Lebesgue constant for polynomials of degree at most n and for the set of n + 1 nodes T is generally denoted by Λn(T ). These constants are named after Henri Lebesgue.
516
01 Dec 2022
Topic Review
Weierstrass's Elliptic Functions
In mathematics, Weierstrass's elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions are also referred to as p-functions and they are usually denoted by the symbol ℘. They play an important role in theory of elliptic functions. A ℘-function together with its derivative can be used to parameterize elliptic curves and they generate the field of elliptic functions with respect to a given period lattice.
973
01 Dec 2022
Topic Review
The Hussaini Encyclopedia
The Hussaini Encyclopedia (Arabic - دائرة المعارف الحسينية - Dāʾirat al-maʿārif al-Ḥusaynīyah) is a one-of-a-kind encyclopedia in Arabic, completely themed on the third Holy Imam, Husayn ibn Ali, his biography, thought and way of conduct, as well as on the social circle of personalities around him and also of places, chronicles and various other related subjects. This encyclopedia consisted of 700 volumes and well over 95 million words. Sheikh Mohammed Sadiq Al-Karbassi, author of the voluminous Arabic encyclopedia dedicated to Imam al-Hussain started his work by establishing the Hussaini Center for Research in London in 1993. The Hussaini Encyclopedia is a historic study of al-Hussain which provides a heritage owing to its impact on all events, particularly the aftermath of battle of Karbala with its impact being observed in recent times.
673
01 Dec 2022
Topic Review
Applications of VR
Applications of VR (also known as virtual reality) can be found in fields as diverse as entertainment, marketing, education, medicine, and many others. They provide numerous possibilities for users to explore virtual realities for various purposes.
2.4K
01 Dec 2022
Topic Review
BitFAT
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.
394
01 Dec 2022
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