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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.
  • 1.1K
  • 01 Dec 2022
Topic Review
Cumulus
Cumulus is a digital asset management software designed for client/server system which is developed by Canto Software. The product line includes editions targeted to smaller organizations and larger enterprises. The product makes use of metadata for indexing, organizing, and searching.
  • 1.4K
  • 06 Dec 2022
Topic Review
Biorhythm
A biorhythm (from Greek βίος – bios, "life" and ῥυθμός – rhuthmos, "any regular recurring motion, rhythm") is an attempt to predict various aspects of a person's life through simple mathematical cycles. The theory was developed by Wilhelm Fliess in the late 19th century, and was popularized in the United States in late 1970s. Scientific analysis shows that biorhythms have no more predictive power than chance, providing no evidence for their existence. "The theory of biorhythms is a theory that claims our daily lives are significantly affected by rhythmic cycles."
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  • 01 Dec 2022
Topic Review
List of Kakapo
There are fewer than 250 living individuals of the critically endangered kakapo, a large, flightless parrot native to New Zealand. Every known living kakapo, except some young chicks, has been given a name by officials of the Kakapo Recovery Programme. Many of the older birds were given English-language names, but more recent chicks have been given Māori names. Some kakapo, such as Richard Henry and Moorhouse, are named after people who have provided assistance to the preservation efforts. A kakapo interactive family tree is available.
  • 7.9K
  • 17 Sep 2024
Topic Review
Seismometer
A seismometer is an instrument that responds to ground motions, such as caused by earthquakes, volcanic eruptions, and explosions. Seismometers are usually combined with a timing device and a recording device to form a seismograph. The output of such a device—formerly recorded on paper (see picture) or film, now recorded and processed digitally—is a seismogram. Such data is used to locate and characterize earthquakes, and to study the Earth's internal structure.
  • 7.1K
  • 01 Dec 2022
Topic Review
Christian Psychology
Christian psychology is a merger of theology and psychology. It is an aspect of psychology adhering to the religion of Christianity and its teachings of Jesus Christ to explain the human mind and behavior. Christian psychology is a term typically used in reference to Protestant Christian psychotherapists who strive to fully embrace both their religious beliefs and their psychological training in their professional practice. However, a practitioner in Christian psychology would not accept all psychological ideas, especially those that contradicted or defied the existence of God and the scriptures of the Bible. In the United States, American Psychological Association approved courses in Christian psychology are available at undergraduate and graduate levels based on applied science, Christian philosophy and a Christian understanding of psychology. In modern psychological practices, Christianity is incorporated through various therapies. The main choice of practice is Christian counseling. It allows aspects of psychology, such as emotion, to be partially explained by Christian beliefs. The understanding of the human mind is thought of as both psychological and spiritual. G. C. Dilsaver is considered "the father of Christian psychology" according to the Catholic University of America, but the authors of Psychology and the Church: Critical Questions/Crucial Answers suggest that Norman Vincent Peale pioneered the merger of the two fields. Clyde M. Narramore had a major impact on the field of Christian psychology. He was the founding president of the Rosemead School of Psychology, now affiliated with Biola University., and which has published the Journal of Psychology & Theology since 1973. The Russian Journal Konsultativnaya Psikhologiya i Psikhoterapiya publishes a special issue on Christian Psychology every year.
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  • 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.
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  • 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.
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  • 01 Dec 2022
Topic Review
Fatawa 'Alamgiri
Fatawa 'Alamgiri, also known as Al-Fatawa al-'Alamgiriyya (Arabic: الفتاوى العالمگيرية) or Al-Fatawa al-Hindiyya (Arabic: الفتاوى الهندية), is a 17th-century sharia based compilation on statecraft, general ethics, military strategy, economic policy, justice and punishment, that served as the law and principal regulating body of the Mughal Empire, during the reign of the Mughal emperor Muhammad Muhiuddin Aurangzeb Alamgir. It subsequently went on to become the reference legal text to enforce Sharia in colonial south Asia in the 18th century through early 20th century, and has been heralded as "the greatest digest of Muslim law made in India ".
  • 39.8K
  • 01 Dec 2022
Topic Review
Drain Fly
Drain flies, sink flies, filter flies, or sewer gnats (Psychodidae) are small true flies (Diptera) with short, hairy bodies and wings giving them a "furry" moth-like appearance, hence one of their common names, moth flies. There are more than 2,600 described species worldwide, most of them native to the humid tropics. This makes them one of the most diverse families of their order. Drain flies sometimes inhabit plumbing drains and sewage systems, where they are harmless, but cause persistent annoyance.
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  • 01 Dec 2022
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