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BSD Authentication, otherwise known as BSD Auth, is an authentication framework and software API employed by OpenBSD and accompanying software such as OpenSSH. It originated with BSD/OS, and although the specification and implementation were donated to the FreeBSD project by BSDi, OpenBSD chose to adopt the framework in release 2. 9 | https://huggingface.co/datasets/fmars/wiki_stem |
In computing, busdma, bus_dma and bus_space is a set of application programming interfaces designed to help make device drivers less dependent on platform-specific code, thereby allowing the host operating system to be more easily ported to new computer hardware. This is accomplished by having abstractions for direct memory access (DMA) mapping across popular machine-independent computer buses like PCI, which are used on distinct architectures from IA-32 (NetBSD/i386) to DEC Alpha (NetBSD/alpha). Additionally, some devices may come in multiple flavours supporting more than one bus, e | https://huggingface.co/datasets/fmars/wiki_stem |
CDK is a library written in C that provides a collection of widgets for text user interfaces (TUI) development. The widgets wrap ncurses functionality to make writing full screen curses programs faster. Perl and Python bindings are also available | https://huggingface.co/datasets/fmars/wiki_stem |
CGI. pm is a large and once widely used Perl module for programming Common Gateway Interface (CGI) web applications, providing a consistent API for receiving and processing user input. There are also functions for producing HTML or XHTML output, but these are now unmaintained and are to be avoided | https://huggingface.co/datasets/fmars/wiki_stem |
CheckInstall is a computer program for Unix-like operating systems which eases the installation and uninstallation of software compiled from source by making use of package management systems. After software compilation it can automatically generate a Slackware-, RPM-, or Debian-compatible package that can later be cleanly uninstalled through the appropriate package manager. CheckInstall monitors the installation phase of a normal software build process and notes the files that are added to the system | https://huggingface.co/datasets/fmars/wiki_stem |
clear is a computer operating system command which is used to bring the command line on top of the computer terminal. It is available in various Unix shells on Unix and Unix-like operating systems as well as on other systems such as KolibriOS. Depending on the system, clear uses the terminfo or termcap database, as well as looking into the environment for the terminal type in order to deduce how to clear the screen | https://huggingface.co/datasets/fmars/wiki_stem |
Technical variations of Solaris distributions include support for different hardware devices and systems or software package configurations. Organizational differences may be motivated by historical reasons. Other criteria include security, including how quickly security upgrades are available; ease of package management; and number of packages available | https://huggingface.co/datasets/fmars/wiki_stem |
Conserver is a serial console management system that provides remote access to system consoles and logs to a central (master) host. It supports both local and network serial connections and allows replay of the server console history even if the server is down. Multiple users can connect to a single serial connection, with one having write-access | https://huggingface.co/datasets/fmars/wiki_stem |
Crystal Enterprise is the Business Objects server-based delivery platform for Crystal Reports and Crystal Analysis originally developed by Crystal Decisions.
Crystal Enterprise is what is called a delivery platform in Business Intelligence terms. It provides an infrastructure for data access, which can store report templates | https://huggingface.co/datasets/fmars/wiki_stem |
dbx is a source-level debugger found primarily on Solaris, AIX, IRIX, Tru64 UNIX, Linux and BSD operating systems. It provides symbolic debugging for programs written in C, C++, Fortran, Pascal and Java. Useful features include stepping through programs one source line or machine instruction at a time | https://huggingface.co/datasets/fmars/wiki_stem |
Direct binding is a feature of the linker and dynamic linker on Solaris and OpenSolaris. It provides a method to allow libraries to directly bind symbols to other libraries, rather than weakly bind to them and leave the dynamic linker to figure out which library contains the symbol.
Theory
When linking a shared library or dynamic linked executable, the linker normally populates the symbol table for that library with all required symbols | https://huggingface.co/datasets/fmars/wiki_stem |
Dired (for Directory Editor) is a computer program for editing file system directories. It typically runs inside the Emacs text editor as a specialized mode, though standalone versions have been written. Dired was the first file manager, or visual editor of file system information | https://huggingface.co/datasets/fmars/wiki_stem |
dtlogin is a display manager for the X Window System. It is typically found on Unix and Unix-like computer systems running The Open Group's Common Desktop Environment (CDE) desktop environment. It allows users to log into a local system; it can also handle remote XDMCP requests | https://huggingface.co/datasets/fmars/wiki_stem |
The dump command is a program on Unix and Unix-like operating systems used to back up file systems. It operates on blocks, below filesystem abstractions such as files and directories. Dump can back up a file system to a tape or another disk | https://huggingface.co/datasets/fmars/wiki_stem |
In computing, a dynamic window manager is a tiling window manager where windows are tiled based on preset layouts between which the user can switch. Layouts typically have a main area and a secondary area. The main area usually shows one window, but one can also change the number of windows in this area | https://huggingface.co/datasets/fmars/wiki_stem |
Part of the troff suite of Unix document layout tools, eqn is a preprocessor that formats equations for printing. A similar program, neqn, accepted the same input as eqn, but produced output tuned to look better in nroff. The eqn program was created in 1974 by Brian Kernighan and Lorinda Cherry | https://huggingface.co/datasets/fmars/wiki_stem |
fdm (fetch/filter and deliver mail) is a mail delivery agent and email filtering software for Unix-like operating systems, similar to fetchmail and procmail. It was started in 2006 by Nicholas Marriott who later also started tmux in 2007.
Adoption
fdm is available as a package in many Unix-like operating systems | https://huggingface.co/datasets/fmars/wiki_stem |
fold is a Unix command used for making a file with long lines more readable on a limited width computer terminal by performing a line wrap.
Most Unix terminals have a default screen width of 80, and therefore reading files with long lines could get annoying. The fold command puts a line feed every X characters if it does not reach a new line before that point | https://huggingface.co/datasets/fmars/wiki_stem |
The Unix command fuser is used to show which processes are using a specified computer file, file system, or Unix socket.
Example
For example, to check process IDs and users accessing a USB drive:
The command displays the process identifiers (PIDs) of processes using the specified files or file
systems. In the default display mode, each PID is followed by a
letter denoting the type of access:
c
current directory | https://huggingface.co/datasets/fmars/wiki_stem |
gentoo is a free file manager for Linux and other Unix-like computer systems created by Emil Brink. It is licensed under the GNU General Public License.
gentoo is written in C using the GTK+ toolkit, and the "two-pane" concept | https://huggingface.co/datasets/fmars/wiki_stem |
getty, short for "get tty", is a Unix program running on a host computer that manages physical or virtual terminals (TTYs). When it detects a connection, it prompts for a username and runs the 'login' program to authenticate the user.
Originally, on traditional Unix systems, getty handled connections to serial terminals (often Teletype machines) connected to a host computer | https://huggingface.co/datasets/fmars/wiki_stem |
Dance Dance Revolution Dance Wars, stylized Dance Dance Revolution DANCE WARS and sometimes abbreviated as DDR Dance Wars, is the most recent home release of Dance Dance Revolution, and the third one to be released in iOS. The game stopped functioning at September 1, 2013 due to the team retiring from online.
Gameplay
Dance Dance Revolution Dance Wars retains its core gameplay: matching the hit of arrow according to the song's timing | https://huggingface.co/datasets/fmars/wiki_stem |
Death Come True is a 2020 interactive film adventure game developed by Too Kyo Games and Esquadra and published by IzanagiGames for Android, iOS, macOS, Nintendo Switch, Windows, and PlayStation 4. The game was written and directed by Kazutaka Kodaka, better known as the creator of the Danganronpa series.
Synopsis
Death Come True is an interactive film adventure game in which the player is tasked with finding clues and uncovering the truth of the protagonist's actions | https://huggingface.co/datasets/fmars/wiki_stem |
Decodoku is set of online citizen science games, based on quantum error correction. The project is supported by the NCCR QSIT and the University of Basel, and allows the public to get involved with quantum error correction research. The games present the clues left in a quantum computer when errors occur, and encourage the players to work out how best to correct them | https://huggingface.co/datasets/fmars/wiki_stem |
Defend Your Castle is a series of video games developed by XGen Studios.
The original version of Defend Your Castle is a Macromedia Flash-based browser game. It requires the player to kill all enemy units before they destroy the player's castle | https://huggingface.co/datasets/fmars/wiki_stem |
Detective Grimoire: Secret of the Swamp, also simply called Detective Grimoire, is a murder mystery point-and-click adventure game developed by SFB Games and published by Armor Games, which was released on iOS platforms on January 2, 2014. It was later released on Android, PC, Mac, Linux and Steam by SFB Games.
The game has been well received for its mystery, animation, dialogue and protagonist | https://huggingface.co/datasets/fmars/wiki_stem |
Dice Soccer is an iOS game developed by Singaporean studio LambdaMu Games and released on July 28, 2011.
Critical reception
The game has a Metacritic score of 84% based on 5 critic reviews. Slide To Play wrote "Dice Soccer will have you rolling dice and cheering on cartoons at all hours, but a few glitches and a slow pace hold it back from being great | https://huggingface.co/datasets/fmars/wiki_stem |
The geological history of North America comprises the history of geological occurrences and emergence of life in North America during the interval of time spanning from the formation of the Earth through to the emergence of humanity and the start of prehistory. At the start of the Paleozoic era, what is now "North" America was actually in the southern hemisphere. Marine life flourished in the country's many seas, although terrestrial life had not yet evolved | https://huggingface.co/datasets/fmars/wiki_stem |
Aripo Cave (Aripo Main Cave) is a cave in the Northern Range, in Trinidad and Tobago. This is the longest accessible cave in Trinidad and Tobago, with 862 m length and 160 m depth. It is one of several caves created by recrystallised limestone | https://huggingface.co/datasets/fmars/wiki_stem |
Dunston Cave is an igneous cave on the Northern Range of Trinidad and Tobago. The cave is located on the grounds of the Asa Wright Nature Centre. Originally named Guacharo Cave, it was renamed Dunston Cave in 1972 in honour of engineer John Dunston | https://huggingface.co/datasets/fmars/wiki_stem |
Lopinot Cave is a large cave in the Lopinot Valley in the Northern Range of Trinidad and Tobago. The Caves are home to the Oilbirds. These are the only nocturnal fruit eating birds in the world | https://huggingface.co/datasets/fmars/wiki_stem |
Tamana caves (or Tamana cave) is a cave system located on the northern slope of Mount Tamana in eastern Trinidad. Mount Tamana is a 307-metre flat topped hill of Miocene Guaracara Limestone of the Tamana Formation in the eastern Central Range. Julian Kenny described the main cave as consisting of 18 separate sections | https://huggingface.co/datasets/fmars/wiki_stem |
The Harriman Alaska expedition explored the coast of Alaska for two months from Seattle to Alaska and Siberia and back again in 1899. It was organized by wealthy railroad magnate Edward Harriman. Harriman brought with him an elite community of scientists, artists, photographers, and naturalists to explore and document the Alaskan coast | https://huggingface.co/datasets/fmars/wiki_stem |
The Mace Brown Museum of Natural History is a public natural history museum situated on the campus of The College of Charleston, a public liberal arts college in Charleston, South Carolina. Boasting a collection of over 30,000 vertebrate and invertebrate fossils, the museum focuses on the paleontology of the South Carolina Lowcountry. As an educational and research institution, the museum provides a unique resource for teaching and internationally respected research activities conducted at The College of Charleston | https://huggingface.co/datasets/fmars/wiki_stem |
The International Thylacine Specimen Database (ITSD) is the culmination of a four-year research project to catalogue and digitally photograph all known surviving specimen material of the thylacine (Thylacinus cynocephalus) (or Tasmanian tiger) held within museum, university, and private collections.
Certainly in my experience this is by far the most thorough compilation focused on an extinct or endangered animal ever produced and, as such, bound to be enormously useful to many generations of scientists to come.
The ITSD was first published as an electronic resource on a series of three CD-ROMs in April 2005 | https://huggingface.co/datasets/fmars/wiki_stem |
1987 is the natural number following 1986 and preceding 1988.
In mathematics
1987 is an odd number and the 300th prime number. It is the first number of a sexy prime triplet (1987, 1993, 1999) | https://huggingface.co/datasets/fmars/wiki_stem |
2016 is the natural number following 2015 and preceding 2017.
In mathematics
2016 is a triangular number, being 1 + 2 + 3 + . | https://huggingface.co/datasets/fmars/wiki_stem |
2520 (two thousand five hundred twenty) is the natural number following 2519 and preceding 2521.
In mathematics
2520 is:
the smallest number divisible by all integers from 1 to 10, i. e | https://huggingface.co/datasets/fmars/wiki_stem |
3000 (three thousand) is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English (when "and" is required from 101 forward).
Selected numbers in the range 3001–3999
3001 to 3099
3001 – super-prime; divides the Euclid number 2999# + 1
3003 – triangular number, only number known to appear eight times in Pascal's triangle; no number is known to appear more than eight times other than 1 | https://huggingface.co/datasets/fmars/wiki_stem |
3511 (three thousand, five hundred and eleven) is the natural number following 3510 and preceding 3512.
3511 is a prime number, and is also an emirp: a different prime when its digits are reversed. 3511 is a Wieferich prime, found to be so by N | https://huggingface.co/datasets/fmars/wiki_stem |
6000 (six thousand) is the natural number following 5999 and preceding 6001.
Selected numbers in the range 6001–6999
6001 to 6099
6025 – Rhythm guitarist of the Dead Kennedys from June 1978 to March 1979. Full name is Carlos Cadona | https://huggingface.co/datasets/fmars/wiki_stem |
7825 (seven thousand, eight hundred [and] twenty-five) is the natural number following 7824 and preceding 7826.
In mathematics
7825 is the smallest number n when it is impossible to assign two colors to natural numbers 1 through n such that every Pythagorean triple is multicolored, i. e | https://huggingface.co/datasets/fmars/wiki_stem |
8128 is the integer following 8127 and preceding 8129.
It is most notable for being a perfect number (its divisors 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, and 4064 add up to 8128), and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime 127, 27 – 1, with 26 (27 – 1) yielding 8128 | https://huggingface.co/datasets/fmars/wiki_stem |
8192 is the natural number following 8191 and preceding 8193.
8192 is a power of two:
2
13
{\displaystyle 2^{13}}
(2 to the 13th power).
Because it is two times a sixth power (8192 = 2 × 46), it is also a Bhaskara twin | https://huggingface.co/datasets/fmars/wiki_stem |
60,000 (sixty thousand) is the natural number that comes after 59,999 and before 60,001. It is a round number. It is the value of
φ
{\displaystyle \varphi }
(F25) | https://huggingface.co/datasets/fmars/wiki_stem |
65535 is the integer after 65534 and before 65536.
It is the maximum value of an unsigned 16-bit integer.
In mathematics
65535 is the product of the first four Fermat primes: 65535 = (2 + 1)(4 + 1)(16 + 1)(256 + 1) | https://huggingface.co/datasets/fmars/wiki_stem |
65536 is the natural number following 65535 and preceding 65537.
65536 is a power of two:
2
16
{\displaystyle 2^{16}}
(2 to the 16th power).
65536 is the smallest number with exactly 17 divisors | https://huggingface.co/datasets/fmars/wiki_stem |
65537 is the integer after 65536 and before 65538.
In mathematics
65537 is the largest known prime number of the form
2
2
n
+
1
{\displaystyle 2^{2^{n}}+1}
(
n
=
4
{\displaystyle n=4}
). Therefore, a regular polygon with 65537 sides is constructible with compass and unmarked straightedge | https://huggingface.co/datasets/fmars/wiki_stem |
The number 142,857 is a Kaprekar number. 142857, the six repeating digits of 1/7 (0. 142857), is the best-known cyclic number in base 10 | https://huggingface.co/datasets/fmars/wiki_stem |
144,000 is a natural number. It has significance in various religious movements and ancient prophetic belief systems.
Religion
Christianity
Book of Revelation
The number 144,000 appears three times in the Book of Revelation:
Revelation 7:3–8:saying: "Do not harm the earth or the sea or the trees, until we have sealed the servants of God on their foreheads | https://huggingface.co/datasets/fmars/wiki_stem |
43,112,609 (forty-three million, one hundred twelve thousand, six hundred nine) is the natural number following 43,112,608 and preceding 43,112,610.
In mathematics
43,112,609 is a prime number. Moreover, it is the exponent of the 47th Mersenne prime, equal to M43,112,609 = 243,112,609 − 1, a prime number with 12,978,189 decimal digits | https://huggingface.co/datasets/fmars/wiki_stem |
1,000,000,000 (one billion, short scale; one thousand million or one milliard, one yard, long scale) is the natural number following 999,999,999 and preceding 1,000,000,001. With a number, "billion" can be abbreviated as b, bil or bn. In standard form, it is written as 1 × 109 | https://huggingface.co/datasets/fmars/wiki_stem |
The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes. The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772 | https://huggingface.co/datasets/fmars/wiki_stem |
The number 4,294,967,295 is a whole number equal to 232 − 1. It is a perfect totient number, meaning it is equal to the sum of its iterated totients. It follows 4,294,967,294 and precedes 4,294,967,296 | https://huggingface.co/datasets/fmars/wiki_stem |
In algebraic number theory, an algebraic integer is a complex number which is integral over the integers. That is, an algebraic integer is a complex root of some monic polynomial (a polynomial whose leading coefficient is 1) whose coefficients are integers. The set of all algebraic integers A is closed under addition, subtraction and multiplication and therefore is a commutative subring of the complex numbers | https://huggingface.co/datasets/fmars/wiki_stem |
In recreational mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one. Almost integers are considered interesting when they arise in some context in which they are unexpected.
Almost integers relating to the golden ratio and Fibonacci numbers
Well-known examples of almost integers are high powers of the golden ratio
ϕ
=
1
+
5
2
≈
1 | https://huggingface.co/datasets/fmars/wiki_stem |
There are a number of common mathematical meanings of the term digital sum:
Values
The digit sum - add the digits of the representation of a number in a given base. For example, considering 84001 in base 10 the digit sum would be 8 + 4 + 0 + 0 + 1 = 13.
The digital root - repeatedly apply the digit sum operation to the representation of a number in a given base until the outcome is a single digit | https://huggingface.co/datasets/fmars/wiki_stem |
The digital sum in base b of a set of natural numbers is calculated as follows: express each of the numbers in base b, then take the sum of corresponding digits and discard all carry overs. That is, the digital sum is the same as the normal sum except that no carrying is used.
For example, in decimal (base 10) arithmetic, the digital sum of 123 and 789 is 802:
3 + 9 = 12, discard the 10 leaving 2 | https://huggingface.co/datasets/fmars/wiki_stem |
A dozen (commonly abbreviated doz or dz) is a grouping of twelve.
The dozen may be one of the earliest primitive integer groupings, perhaps because there are approximately a dozen cycles of the Moon, or months, in a cycle of the Sun, or year. Twelve is convenient because it has a maximal number of divisors among the numbers up to its double, a property only true of 1, 2, 6, 12, 60, 360, and 2520 | https://huggingface.co/datasets/fmars/wiki_stem |
In arithmetic and algebra the eighth power of a number n is the result of multiplying eight instances of n together. So:
n8 = n × n × n × n × n × n × n × n. Eighth powers are also formed by multiplying a number by its seventh power, or the fourth power of a number by itself | https://huggingface.co/datasets/fmars/wiki_stem |
A googol is the large number 10100. In decimal notation, it is written as the digit 1 followed by one hundred zeroes: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Its systematic name is 10 duotrigintillion | https://huggingface.co/datasets/fmars/wiki_stem |
A googolplex is the number 10googol, or equivalently, 1010100 or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes; that is, a 1 followed by a googol of zeroes.
History
In 1920, Edward Kasner's nine-year-old nephew, Milton Sirotta, coined the term googol, which is 10100, and then proposed the further term googolplex to be "one, followed by writing zeroes until you get tired" | https://huggingface.co/datasets/fmars/wiki_stem |
The interesting number paradox is a humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting. The "proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a contradiction | https://huggingface.co/datasets/fmars/wiki_stem |
In computer science, an integer literal is a kind of literal for an integer whose value is directly represented in source code. For example, in the assignment statement x = 1, the string 1 is an integer literal indicating the value 1, while in the statement x = 0x10 the string 0x10 is an integer literal indicating the value 16, which is represented by 10 in hexadecimal (indicated by the 0x prefix).
By contrast, in x = cos(0), the expression cos(0) evaluates to 1 (as the cosine of 0), but the value 1 is not literally included in the source code | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a multiple is the product of any quantity and an integer. In other words, for the quantities a and b, it can be said that b is a multiple of a if b = na for some integer n, which is called the multiplier. If a is not zero, this is equivalent to saying that
b
/
a
{\displaystyle b/a}
is an integer | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, the natural numbers are the numbers 1, 2, 3, etc. , possibly including 0 as well. Some definitions, including the standard ISO 80000-2, begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, | https://huggingface.co/datasets/fmars/wiki_stem |
Plato's number is a number enigmatically referred to by Plato in his dialogue the Republic (8. 546b). The text is notoriously difficult to understand and its corresponding translations do not allow an unambiguous interpretation | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a power of three is a number of the form 3n where n is an integer, that is, the result of exponentiation with number three as the base and integer n as the exponent.
In a context where only integers are considered, n is restricted to non-negative values, so there are 1, 3, and 3 multiplied by itself a certain number of times.
The first ten powers of 3 for non-negative values of n are:
1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, | https://huggingface.co/datasets/fmars/wiki_stem |
In number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree two, that is, solutions of equations of the form
x2 + bx + c = 0with b and c (usual) integers. When algebraic integers are considered, the usual integers are often called rational integers | https://huggingface.co/datasets/fmars/wiki_stem |
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for "repeated unit" and was coined in 1966 by Albert H. Beiler in his book Recreations in the Theory of Numbers | https://huggingface.co/datasets/fmars/wiki_stem |
A unit fraction is a positive fraction with one as its numerator, 1/n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number. Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc | https://huggingface.co/datasets/fmars/wiki_stem |
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a divisor of an integer
n
{\displaystyle n}
, also called a factor of
n
{\displaystyle n}
, is an integer
m
{\displaystyle m}
that may be multiplied by some integer to produce
n
{\displaystyle n}
. In this case, one also says that
n
{\displaystyle n}
is a multiple of
m
.
{\displaystyle m | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a half-integer is a number of the form
where
n
{\displaystyle n}
is a whole number. For example,
are all half-integers. The name "half-integer" is perhaps misleading, as the set may be misunderstood to include numbers such as 1 (being half the integer 2) | https://huggingface.co/datasets/fmars/wiki_stem |
The tables contain the prime factorization of the natural numbers from 1 to 1000.
When n is a prime number, the prime factorization is just n itself, written in bold below.
The number 1 is called a unit | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a subset R of the integers is called a reduced residue system modulo n if:
gcd(r, n) = 1 for each r in R,
R contains φ(n) elements,
no two elements of R are congruent modulo n. Here φ denotes Euler's totient function.
A reduced residue system modulo n can be formed from a complete residue system modulo n by removing all integers not relatively prime to n | https://huggingface.co/datasets/fmars/wiki_stem |
The tables below list all of the divisors of the numbers 1 to 1000.
A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21) | https://huggingface.co/datasets/fmars/wiki_stem |
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
History
The term "algebraic combinatorics" was introduced in the late 1970s. Through the early or mid-1990s, typical combinatorial objects of interest in algebraic combinatorics either admitted a lot of symmetries (association schemes, strongly regular graphs, posets with a group action) or possessed a rich algebraic structure, frequently of representation theoretic origin (symmetric functions, Young tableaux) | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included. Antimatroids are commonly axiomatized in two equivalent ways, either as a set system modeling the possible states of such a process, or as a formal language modeling the different sequences in which elements may be included.
Dilworth (1940) was the first to study antimatroids, using yet another axiomatization based on lattice theory, and they have been frequently rediscovered in other contexts | https://huggingface.co/datasets/fmars/wiki_stem |
The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. In algebraic combinatorics, association schemes provide a unified approach to many topics, for example combinatorial designs and the theory of error-correcting codes | https://huggingface.co/datasets/fmars/wiki_stem |
In algebraic combinatorics, a Bender–Knuth involution is an involution on the set of semistandard tableaux, introduced by Bender & Knuth (1972, pp. 46–47) in their study of plane partitions.
Definition
The Bender–Knuth involutions σk are defined for integers k, and act on the set of semistandard skew Young tableaux of some fixed shape μ/ν, where μ and ν are partitions | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a Bose–Mesner algebra is a special set of matrices which arise from a combinatorial structure known as an association scheme, together with the usual set of rules for combining (forming the products of) those matrices, such that they form an associative algebra, or, more precisely, a unitary commutative algebra. Among these rules are:
the result of a product is also within the set of matrices,
there is an identity matrix in the set, and
taking products is commutative. Bose–Mesner algebras have applications in physics to spin models, and in statistics to the design of experiments | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a Buekenhout geometry or diagram geometry is a generalization of projective spaces, Tits buildings, and several other geometric structures, introduced by Buekenhout (1979).
Definition
A Buekenhout geometry consists of a set X whose elements are called "varieties", with a symmetric reflexive relation on X called "incidence", together with a function τ called the "type map" from X to a set Δ whose elements are called "types" and whose size is called the "rank". Two distinct varieties of the same type cannot be incident | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a building (also Tits building, named after Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces. Buildings were initially introduced by Jacques Tits as a means to understand the structure of exceptional groups of Lie type. The more specialized theory of Bruhat–Tits buildings (named also after François Bruhat) plays a role in the study of p-adic Lie groups analogous to that of the theory of symmetric spaces in the theory of Lie groups | https://huggingface.co/datasets/fmars/wiki_stem |
Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of two more established fields, commutative algebra and combinatorics, and frequently uses methods of one to address problems arising in the other. Less obviously, polyhedral geometry plays a significant role | https://huggingface.co/datasets/fmars/wiki_stem |
In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for deriving the generating functions of discrete structures, which allows one to not merely count these structures but give bijective proofs involving them. Examples of combinatorial species are (finite) graphs, permutations, trees, and so on; each of these has an associated generating function which counts how many structures there are of a certain size. One goal of species theory is to be able to analyse complicated structures by describing them in terms of transformations and combinations of simpler structures | https://huggingface.co/datasets/fmars/wiki_stem |
Combinatorics: The Rota Way is a mathematics textbook on algebraic combinatorics, based on the lectures and lecture notes of Gian-Carlo Rota in his courses at the Massachusetts Institute of Technology. It was put into book form by Joseph P. S | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, the Coxeter complex, named after H. S. M | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a differential poset is a partially ordered set (or poset for short) satisfying certain local properties. (The formal definition is given below. ) This family of posets was introduced by Stanley (1988) as a generalization of Young's lattice (the poset of integer partitions ordered by inclusion), many of whose combinatorial properties are shared by all differential posets | https://huggingface.co/datasets/fmars/wiki_stem |
In combinatorial mathematics, an Eulerian poset is a graded poset in which every nontrivial interval has the same number of elements of even rank as of odd rank. An Eulerian poset which is a lattice is an Eulerian lattice. These objects are named after Leonhard Euler | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, the Garnir relations give a way of expressing a basis of the Specht modules Vλ in terms of standard polytabloids.
Specht modules in terms of polytabloids
Given a partition λ of n, one has the Specht module Vλ. In characteristic 0, this is an irreducible representation of the symmetric group Sn | https://huggingface.co/datasets/fmars/wiki_stem |
Error catastrophe refers to the cumulative loss of genetic information in a lineage of organisms due to high mutation rates. The mutation rate above which error catastrophe occurs is called the error threshold. Both terms were coined by Manfred Eigen in his mathematical evolutionary theory of the quasispecies | https://huggingface.co/datasets/fmars/wiki_stem |
In evolutionary biology and population genetics, the error threshold (or critical mutation rate) is a limit on the number of base pairs a self-replicating molecule may have before mutation will destroy the information in subsequent generations of the molecule. The error threshold is crucial to understanding "Eigen's paradox".
The error threshold is a concept in the origins of life (abiogenesis), in particular of very early life, before the advent of DNA | https://huggingface.co/datasets/fmars/wiki_stem |
In genetics, expressivity is the degree to which a phenotype is expressed by individuals having a particular genotype. (Alternately, it may refer to the expression of particular gene by individuals having a certain phenotype. ) Expressivity is related to the intensity of a given phenotype; it differs from penetrance, which refers to the proportion of individuals with a particular genotype that actually express the phenotype | https://huggingface.co/datasets/fmars/wiki_stem |
In population genetics, the four-gamete test is a method for detecting historical recombination events.
Description
Given a set of four or more sampled haploid chromosomes, the four-gamete test (FGT) detects recombination events by locating pairs of segregating sites that cannot have arisen without either recombination or a repeat mutation. Under the infinite-sites assumption (i | https://huggingface.co/datasets/fmars/wiki_stem |
In population genetics, F-statistics (also known as fixation indices) describe the statistically expected level of heterozygosity in a population; more specifically the expected degree of (usually) a reduction in heterozygosity when compared to Hardy–Weinberg expectation.
F-statistics can also be thought of as a measure of the correlation between genes drawn at different levels of a (hierarchically) subdivided population. This correlation is influenced by several evolutionary processes, such as genetic drift, founder effect, bottleneck, genetic hitchhiking, meiotic drive, mutation, gene flow, inbreeding, natural selection, or the Wahlund effect, but it was originally designed to measure the amount of allelic fixation owing to genetic drift | https://huggingface.co/datasets/fmars/wiki_stem |
The Frequency of INherited Disorders database (FINDbase) is a database of frequencies of causative genetic variations worldwide. FINDbase was founded in 2006 to be a relational database for these frequencies of causative genetic variations of inherited genetic disorders, as well as pharmacogenetic markers. Out of all the national/ethnic mutation databases (NEMDBs), FINDbase has the most content and since all the entries are collected from various populations worldwide, it is seen as a great resource for population-specific information | https://huggingface.co/datasets/fmars/wiki_stem |
Fisher's fundamental theorem of natural selection is an idea about genetic variance in population genetics developed by the statistician and evolutionary biologist Ronald Fisher. The proper way of applying the abstract mathematics of the theorem to actual biology has been a matter of some debate.
It states:
"The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time | https://huggingface.co/datasets/fmars/wiki_stem |
Fitness (often denoted
w
{\displaystyle w}
or ω in population genetics models) is the quantitative representation of individual reproductive success. It is also equal to the average contribution to the gene pool of the next generation, made by the same individuals of the specified genotype or phenotype. Fitness can be defined either with respect to a genotype or to a phenotype in a given environment or time | https://huggingface.co/datasets/fmars/wiki_stem |
In evolutionary biology, fitness landscapes or adaptive landscapes (types of evolutionary landscapes) are used to visualize the relationship between genotypes and reproductive success. It is assumed that every genotype has a well-defined replication rate (often referred to as fitness). This fitness is the "height" of the landscape | https://huggingface.co/datasets/fmars/wiki_stem |
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