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Topic Review
μ-Recursive Function
In mathematical logic and computer science, the general recursive functions (often shortened to recursive functions) or μ-recursive functions are a class of partial functions from natural numbers to natural numbers that are "computable" in an intuitive sense. In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines(this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions. However, not every μ-recursive function is a primitive recursive function—the most famous example is the Ackermann function. Other equivalent classes of functions are the λ-recursive functions and the functions that can be computed by Markov algorithms. The subset of all total recursive functions with values in {0,1} is known in computational complexity theory as the complexity class R.
  • 2.2K
  • 01 Dec 2022
Topic Review
Euler–Mascheroni Constant
The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma (γ). It is defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by [math]\displaystyle{ \log: }[/math] Here, [math]\displaystyle{ \lfloor x\rfloor }[/math] represents the floor function. The numerical value of the Euler–Mascheroni constant, to 50 decimal places, is: 0.57721566490153286060651209008240243104215933593992... 
  • 2.1K
  • 02 Dec 2022
Topic Review
Energy Condition
In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically-phrased mathematical formulation. There are multiple possible alternative ways to express such a condition such that can be applied to the matter content of the theory. The hope is then that any reasonable matter theory will satisfy this condition or at least will preserve the condition if it is satisfied by the starting conditions. Energy conditions are not physical constraints per se, but are rather mathematically imposed boundary conditions that attempt to capture a belief that "energy should be positive". Many energy conditions are known to not correspond to physical reality—for example, the observable effects of dark energy are well-known to violate the strong energy condition. In general relativity, energy conditions are often used (and required) in proofs of various important theorems about black holes, such as the no hair theorem or the laws of black hole thermodynamics.
  • 2.1K
  • 07 Nov 2022
Topic Review
Machine Learning and Student Performance Prediction
Improving the quality, developing and implementing systems that can provide advantages to students, and predicting students’ success during the term, at the end of the term, or in the future are some of the primary aims of education. Due to its unique ability to create relationships and obtain accurate results, artificial intelligence and machine learning are tools used in this field to achieve the expected goals.
  • 2.1K
  • 08 Dec 2021
Topic Review
Well-Known Text
Well-known text (WKT) is a text markup language for representing vector geometry objects on a map, spatial reference systems of spatial objects and transformations between spatial reference systems. A binary equivalent, known as well-known binary (WKB), is used to transfer and store the same information on databases. The formats were originally defined by the Open Geospatial Consortium (OGC) and described in their Simple Feature Access and Coordinate Transformation Service specifications. The current standard definition is in the ISO/IEC 13249-3:2016 standard, "Information technology – Database languages – SQL multimedia and application packages – Part 3: Spatial" (SQL/MM) and ISO 19162:2015, "Geographic information – Well-known text representation of coordinate reference systems".
  • 2.1K
  • 27 Oct 2022
Topic Review
Insect Euthanasia
Insect euthanasia is the process of killing insects "in a way that minimizes or eliminates pain and distress.":6 It may apply to animals in the laboratory, schools, as pets, as food, or otherwise. Euthanasia of insects and other invertebrates has historically received limited attention.:75 While vertebrate animal experimentation typically requires approval by an Institutional Animal Care and Use Committee in the United States, use of invertebrate animals has few guidelines, and many research papers make no mention of how their invertebrate subjects were killed. Many of the euthanasia methods developed for vertebrates do not transfer well to invertebrates. While a number of euthanasia methods have been proposed for various invertebrate taxa, many have not been adequately vetted, and more research is needed.
  • 2.1K
  • 17 Nov 2022
Topic Review
Core (Game Theory)
In cooperative game theory, the core is the set of feasible allocations that cannot be improved upon by a subset (a coalition) of the economy's agents. A coalition is said to improve upon or block a feasible allocation if the members of that coalition are better off under another feasible allocation that is identical to the first except that every member of the coalition has a different consumption bundle that is part of an aggregate consumption bundle that can be constructed from publicly available technology and the initial endowments of each consumer in the coalition. An allocation is said to have the core property if there is no coalition that can improve upon it. The core is the set of all feasible allocations with the core property.
  • 2.1K
  • 08 Oct 2022
Topic Review
List of ISBN Identifier Groups
This is a list of ISBN identifier groups, the second element in 13-digit ISBNs (the first element in 10-digit ISBNs). The identifier is assigned to mark either a publisher's place of business or the language of the books it publishes. The "original" set of identifiers, assigned prior to the introduction of 13-digit ISBNs and, as such, prior to 978-prefix books, ranged from one to five numerical digits, according to the following structure: They are assigned in approximate descending order of publishing volume. Because the smaller identifiers have room for fewer publishers and ISBNs, several countries have had more than one identifier assigned to them. On the other hand, several countries (Australia, Canada, France, Austria, Switzerland...) have no identifier because they fall in the "language groups". The structure for the identifiers of the 979- prefix and whether it will have language-specific identifiers is not well known, but four identifiers have been assigned (979-10, to France, 979-11, to the Republic of Korea, 979-12, to Italy, and 979-8, to the United States of America). Also, 979-0 has been reserved for the use of International Standard Music Number for sheet music. A 977- prefix indicates International Standard Serial Numbers.
  • 2.1K
  • 28 Oct 2022
Topic Review
WordNet
WordNet is a lexical database of semantic relations between words in more than 200 languages. WordNet links words into semantic relations including synonyms, hyponyms, and meronyms. The synonyms are grouped into synsets with short definitions and usage examples. WordNet can thus be seen as a combination and extension of a dictionary and thesaurus. While it is accessible to human users via a web browser, its primary use is in automatic text analysis and artificial intelligence applications. WordNet was first created in the English language and the English WordNet database and software tools have been released under a BSD style license and are freely available for download from that WordNet website.
  • 2.1K
  • 11 Nov 2022
Topic Review
Italian Fiscal Code Card
The Italian fiscal code card, officially known as Italy's Codice fiscale, is the tax code card in Italy, similar to a Social Security Number (SSN) card in the United States or the National Insurance Number issued in the United Kingdom. The tax code in Italy is an alphanumeric code of 16 characters. The card serves to identify unambiguously individuals residing in Italy irrespective of residency status. Designed by and for the Italian tax office, it is now used for several other purposes, e.g. uniquely identifying individuals in the health system, or natural persons who act as parties in private contracts. The number is issued by the Italian tax office. Each person in the past was handed a plastic card with a magnetic strip, bearing the tax code as well as the surname, given name(s), sex, place and province of birth (or country of birth if foreign), date of birth and date of issue. Today, the tax or fiscal code card has been replaced by a combined Italian health insurance card for qualifying residents which shows an expiration date.
  • 2.1K
  • 03 Nov 2022
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