source stringlengths 31 203 | text stringlengths 28 2k |
|---|---|
https://en.wikipedia.org/wiki/Periodogram | In signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898. Today, the periodogram is a component of more sophisticated methods (see spectral estimation). It is the most common tool for examining the amplitude vs frequency characteristics of FIR filters and window functions. FFT spectrum analyzers are also implemented as a time-sequence of periodograms.
Definition
There are at least two different definitions in use today. One of them involves time-averaging, and one does not. Time-averaging is also the purview of other articles (Bartlett's method and Welch's method). This article is not about time-averaging. The definition of interest here is that the power spectral density of a continuous function, is the Fourier transform of its auto-correlation function (see Cross-correlation theorem, Spectral density#Power spectral density, and Wiener–Khinchin theorem):
Computation
For sufficiently small values of parameter an arbitrarily-accurate approximation for can be observed in the region of the function:
which is precisely determined by the samples that span the non-zero duration of (see Discrete-time Fourier transform).
And for sufficiently large values of parameter , can be evaluated at an arbitrarily close frequency by a summation of the form:
where is an integer. The periodicity of allows this to be written very simply in terms of a Discrete Fourier transform:
where is a periodic summation:
When evaluated for all integers, , between 0 and -1, the array:
is a periodogram.
Applications
When a periodogram is used to examine the detailed characteristics of an FIR filter or window function, the parameter is chosen to be several multiples of the non-zero duration of the sequence, which is called zero-padding (see ). When it is used to implement a filter bank, is several sub-multiples of the non-zero duration of the sequence (see ).
One of the periodogram's |
https://en.wikipedia.org/wiki/H%C3%A9non%20map | In mathematics, the Hénon map, sometimes called Hénon–Pomeau attractor/map, is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior. The Hénon map takes a point in the plane and maps it to a new point
The map depends on two parameters, and , which for the classical Hénon map have values of and . For the classical values the Hénon map is chaotic. For other values of and the map may be chaotic, intermittent, or converge to a periodic orbit. An overview of the type of behavior of the map at different parameter values may be obtained from its orbit diagram.
The map was introduced by Michel Hénon as a simplified model of the Poincaré section of the Lorenz model. For the classical map, an initial point of the plane will either approach a set of points known as the Hénon strange attractor, or diverge to infinity. The Hénon attractor is a fractal, smooth in one direction and a Cantor set in another. Numerical estimates yield a correlation dimension of 1.21 ± 0.01 or 1.25 ± 0.02 (depending on the dimension of the embedding space) and a Box Counting dimension of 1.261 ± 0.003 for the attractor of the classical map.
Attractor
The Hénon map maps two points into themselves: these are the invariant points. For the classical values of a and b of the Hénon map, one of these points is on the attractor:
This point is unstable. Points close to this fixed point and along the slope 1.924 will approach the fixed point and points along the slope -0.156 will move away from the fixed point. These slopes arise from the linearizations of the stable manifold and unstable manifold of the fixed point. The unstable manifold of the fixed point in the attractor is contained in the strange attractor of the Hénon map.
The Hénon map does not have a strange attractor for all values of the parameters a and b. For example, by keeping b fixed at 0.3 the bifurcation diagram shows that for a = 1.25 the Hénon map |
https://en.wikipedia.org/wiki/Primitive%20ideal | In mathematics, specifically ring theory, a left primitive ideal is the annihilator of a (nonzero) simple left module. A right primitive ideal is defined similarly. Left and right primitive ideals are always two-sided ideals.
Primitive ideals are prime. The quotient of a ring by a left primitive ideal is a left primitive ring. For commutative rings the primitive ideals are maximal, and so commutative primitive rings are all fields.
Primitive spectrum
The primitive spectrum of a ring is a non-commutative analog of the prime spectrum of a commutative ring.
Let A be a ring and the set of all primitive ideals of A. Then there is a topology on , called the Jacobson topology, defined so that the closure of a subset T is the set of primitive ideals of A containing the intersection of elements of T.
Now, suppose A is an associative algebra over a field. Then, by definition, a primitive ideal is the kernel of an irreducible representation of A and thus there is a surjection
Example: the spectrum of a unital C*-algebra.
See also
Dixmier mapping
Notes
References
External links
Ideals (ring theory)
Module theory |
https://en.wikipedia.org/wiki/Semiprimitive%20ring | In algebra, a semiprimitive ring or Jacobson semisimple ring or J-semisimple ring is a ring whose Jacobson radical is zero. This is a type of ring more general than a semisimple ring, but where simple modules still provide enough information about the ring. Rings such as the ring of integers are semiprimitive, and an artinian semiprimitive ring is just a semisimple ring. Semiprimitive rings can be understood as subdirect products of primitive rings, which are described by the Jacobson density theorem.
Definition
A ring is called semiprimitive or Jacobson semisimple if its Jacobson radical is the zero ideal.
A ring is semiprimitive if and only if it has a faithful semisimple left module. The semiprimitive property is left-right symmetric, and so a ring is semiprimitive if and only if it has a faithful semisimple right module.
A ring is semiprimitive if and only if it is a subdirect product of left primitive rings.
A commutative ring is semiprimitive if and only if it is a subdirect product of fields, .
A left artinian ring is semiprimitive if and only if it is semisimple, . Such rings are sometimes called semisimple Artinian, .
Examples
The ring of integers is semiprimitive, but not semisimple.
Every primitive ring is semiprimitive.
The product of two fields is semiprimitive but not primitive.
Every von Neumann regular ring is semiprimitive.
Jacobson himself has defined a ring to be "semisimple" if and only if it is a subdirect product of simple rings, . However, this is a stricter notion, since the endomorphism ring of a countably infinite dimensional vector space is semiprimitive, but not a subdirect product of simple rings, .
References
Algebraic structures
Ring theory |
https://en.wikipedia.org/wiki/Primitive%20ring | In the branch of abstract algebra known as ring theory, a left primitive ring is a ring which has a faithful simple left module. Well known examples include endomorphism rings of vector spaces and Weyl algebras over fields of characteristic zero.
Definition
A ring R is said to be a left primitive ring if it has a faithful simple left R-module. A right primitive ring is defined similarly with right R-modules. There are rings which are primitive on one side but not on the other. The first example was constructed by George M. Bergman in . Another example found by Jategaonkar showing the distinction can be found in .
An internal characterization of left primitive rings is as follows: a ring is left primitive if and only if there is a maximal left ideal containing no nonzero two-sided ideals. The analogous definition for right primitive rings is also valid.
The structure of left primitive rings is completely determined by the Jacobson density theorem: A ring is left primitive if and only if it is isomorphic to a dense subring of the ring of endomorphisms of a left vector space over a division ring.
Another equivalent definition states that a ring is left primitive if and only if it is a prime ring with a faithful left module of finite length (, Ex. 11.19, p. 191).
Properties
One-sided primitive rings are both semiprimitive rings and prime rings. Since the product ring of two or more nonzero rings is not prime, it is clear that the product of primitive rings is never primitive.
For a left Artinian ring, it is known that the conditions "left primitive", "right primitive", "prime", and "simple" are all equivalent, and in this case it is a semisimple ring isomorphic to a square matrix ring over a division ring. More generally, in any ring with a minimal one sided ideal, "left primitive" = "right primitive" = "prime".
A commutative ring is left primitive if and only if it is a field.
Being left primitive is a Morita invariant property.
Examples
Every simple r |
https://en.wikipedia.org/wiki/142%20%28number%29 | 142 (one hundred [and] forty-two) is the natural number following 141 and preceding 143.
In mathematics
There are 142 connected functional graphs on four labeled vertices, 142 planar graphs with 6 unlabeled vertices, and 142 partial involutions on five elements.
See also
The year AD 142 or 142 BC
List of highways numbered 142
References
Integers |
https://en.wikipedia.org/wiki/Grammy%20Award%20for%20Best%20Engineered%20Album%2C%20Classical | The Grammy Award for Best Engineered Recording, Classical has been awarded since 1959. The award had several minor name changes:
In 1959 the award was known as Best Engineered Record (Classical)
From 1960 to 1962 it was awarded as Best Engineering Contribution - Classical Recording
From 1963 to 1964 it was awarded as Best Engineered Recording - Classical
In 1965 it was awarded as Best Engineered Recording
From 1966 to 1994 it returned to the title Best Engineered Recording, Classical
From 1966 to 1994 it was awarded as Best Classical Engineered Recording
Since 1992 it has been awarded as Best Engineered Album, Classical
This award is presented alongside the Grammy Award for Best Engineered Album, Non-Classical. From 1960 to 1965 a further award was presented for Best Engineered Recording - Special or Novel Effects.
Years reflect the year in which the Grammy Awards were presented, for works released in the previous year.
The award is presented to engineers (and, if applicable, mastering engineers), not to artists, orchestras, conductors or other performers on the winning works, except if the engineer is also a performer.
Winners and nominees
Notes
References
Engineered Album Classical
Audio engineering
Album awards |
https://en.wikipedia.org/wiki/Boulder%20Dash%20%28video%20game%29 | Boulder Dash is a 2D maze-puzzle video game released in 1984 by First Star Software for Atari 8-bit computers. It was created by Canadian developers Peter Liepa and Chris Gray. The player controls Rockford, who collects treasures while evading hazards.
Boulder Dash was ported to many 8-bit and 16-bit systems and turned into a coin-operated arcade game. It was followed by multiple sequels and re-releases and influenced games such as Repton and direct clones such as Emerald Mine.
As of January 2018, BBG Entertainment GmbH owns the intellectual property rights to Boulder Dash.
Gameplay
Boulder Dash takes place in a series of caves, each of which is laid out as rectangular grid of blocks. The player guides the player character, Rockford, with a joystick or cursor keys. In each cave, Rockford has to collect as many diamonds as are needed and avoid dangers, such as falling rocks. When enough diamonds have been collected, the exit door opens, and going through this exit door completes the cave.
Development
As an aspiring game developer, Peter Liepa reached out to a local publisher called Inhome Software. They put him in touch with a young man—Chris Gray—who had submitted a game programmed in BASIC that was not commercial quality, but had potential. The project began with the intention of converting this game to machine language and releasing it through Inhome, but according to Liepa, the game was very primitive. He decided to expand the concept and add more interesting dynamics, and he wrote the new version in Forth in about six months. When it became clear that the game was worth releasing, Liepa rewrote Boulder Dash in 6502 assembly language.
Dissatisfied with the lack of a contact from Inhome Software, Liepa searched for a new publisher He settled on First Star Software, which, according to him, was very happy to publish the game.
Ports
The game was licensed by Exidy for use with their Max-A-Flex arcade cabinet. Released in 1984, it allows buying 30 seconds of ga |
https://en.wikipedia.org/wiki/Aliquot%20sequence | In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.
Definition and overview
The aliquot sequence starting with a positive integer can be defined formally in terms of the sum-of-divisors function or the aliquot sum function in the following way:
If the condition is added, then the terms after 0 are all 0, and all aliquot sequences would be infinite, and we can conjecture that all aliquot sequences are convergent, the limit of these sequences are usually 0 or 6.
For example, the aliquot sequence of 10 is because:
Many aliquot sequences terminate at zero; all such sequences necessarily end with a prime number followed by 1 (since the only proper divisor of a prime is 1), followed by 0 (since 1 has no proper divisors). See for a list of such numbers up to 75. There are a variety of ways in which an aliquot sequence might not terminate:
A perfect number has a repeating aliquot sequence of period 1. The aliquot sequence of 6, for example, is
An amicable number has a repeating aliquot sequence of period 2. For instance, the aliquot sequence of 220 is
A sociable number has a repeating aliquot sequence of period 3 or greater. (Sometimes the term sociable number is used to encompass amicable numbers as well.) For instance, the aliquot sequence of 1264460 is
Some numbers have an aliquot sequence which is eventually periodic, but the number itself is not perfect, amicable, or sociable. For instance, the aliquot sequence of 95 is Numbers like 95 that are not perfect, but have an eventually repeating aliquot sequence of period 1 are called aspiring numbers.
The lengths of the aliquot sequences that start at are
1, 2, 2, 3, 2, 1, 2, 3, 4, 4, 2, 7, 2, 5, 5, 6, 2, 4, 2, 7, 3, 6, 2, 5, 1, 7, 3, 1, 2, 15, 2, 3, 6, 8, 3, 4, 2, 7, 3, 4, 2, 14, 2, 5, 7, 8, 2, 6, 4, 3, ...
The fina |
https://en.wikipedia.org/wiki/Grammy%20Award%20for%20Best%20Engineered%20Album%2C%20Non-Classical | The Grammy Award for Best Engineered Album, Non-Classical has been awarded since 1959. The award had several minor name changes:
In 1959, the award was known as Best Engineered Record – Non-Classical
In 1960, it was awarded as Best Engineering Contribution – Other Than Classical or Novelty
From 1961 to 1962, it was awarded as Best Engineering Contribution – Popular Recording
In 1963, it was awarded as Best Engineering Contribution – Other Than Novelty and Other Than Classical
In 1964, it was awarded as Best Engineered Recording – Other Than Classical
From 1965 to 1991, it returned to the title Best Engineered Recording – Non-Classical
Since 1992, it has been awarded as Best Engineered Album, Non-Classical
This award is presented alongside the Grammy Award for Best Engineered Album, Classical. From 1960 to 1965 a further award was presented for Best Engineered Recording – Special or Novel Effects.
Years reflect the year in which the Grammy Awards were presented, for works released in the previous year. The award is presented to the audio engineer(s) (and, since 2012, also to the mastering engineer[s]) on the winning work, not to the artist or performer, except if the artist is also a credited engineer.
Winners and nominees
1950s
1960s
1970s
1980s
1990s
2000s
2010s
2020s
Summary
References
Engineered Album Non-Classical
Audio engineering
Album awards |
https://en.wikipedia.org/wiki/Processor%20register | A processor register is a quickly accessible location available to a computer's processor. Registers usually consist of a small amount of fast storage, although some registers have specific hardware functions, and may be read-only or write-only. In computer architecture, registers are typically addressed by mechanisms other than main memory, but may in some cases be assigned a memory address e.g. DEC PDP-10, ICT 1900.
Almost all computers, whether load/store architecture or not, load items of data from a larger memory into registers where they are used for arithmetic operations, bitwise operations, and other operations, and are manipulated or tested by machine instructions. Manipulated items are then often stored back to main memory, either by the same instruction or by a subsequent one. Modern processors use either static or dynamic RAM as main memory, with the latter usually accessed via one or more cache levels.
Processor registers are normally at the top of the memory hierarchy, and provide the fastest way to access data. The term normally refers only to the group of registers that are directly encoded as part of an instruction, as defined by the instruction set. However, modern high-performance CPUs often have duplicates of these "architectural registers" in order to improve performance via register renaming, allowing parallel and speculative execution. Modern x86 design acquired these techniques around 1995 with the releases of Pentium Pro, Cyrix 6x86, Nx586, and AMD K5.
When a computer program accesses the same data repeatedly, this is called locality of reference. Holding frequently used values in registers can be critical to a program's performance. Register allocation is performed either by a compiler in the code generation phase, or manually by an assembly language programmer.
Size
Registers are normally measured by the number of bits they can hold, for example, an "8-bit register", "32-bit register", "64-bit register", or even more. In some instruc |
https://en.wikipedia.org/wiki/Non-access%20stratum | Non-access stratum (NAS) is a functional layer in the NR, LTE, UMTS and GSM wireless telecom protocol stacks between the core network and user equipment.
This layer is used to manage the establishment of communication sessions and for maintaining continuous communications with the user equipment as it moves. The NAS is defined in contrast to the Access Stratum which is responsible for carrying information over the wireless portion of the network.
A further description of NAS is that it is a protocol for messages passed between the User Equipment, also known as mobiles, and Core Nodes (e.g. Mobile Switching Center, Serving GPRS Support Node, or Mobility Management Entity) that is passed transparently through the radio network. Examples of NAS messages include Update or Attach messages, Authentication Messages, Service Requests and so forth. Once the User Equipment (UE) establishes a radio connection, the UE uses the radio connection to communicate with the core nodes to coordinate service. The distinction is that the Access Stratum is for dialogue explicitly between the mobile equipment and the radio network and the NAS is for dialogue between the mobile equipment and core network nodes.
For LTE, the Technical Specification for NAS is 3GPP TS 24.301. For NR, the Technical Specification for NAS is TS 24.501.
+- – - – - -+ +- – - – - – -+
| HTTP | | Application |
+- – - – - -+ +- – - – - – -+
| TCP | | Transport |
+- – - – - -+ +- – - – - – -+
| IP | | Internet |
+- – - – - -+ +- – - – - – -+
| NAS | | Network |
+- – - – - -+ +- – - – - – -+
| AS | | Link |
+- – - – - -+ +- – - – - – -+
| Channels | | Physical |
+- – - – - -+ +- – - – - – -+
Functionality
The following functions exist in the non-access stratum:
Mobility management: maintaining connectivity and active sessions with user equipment as the user moves
Call c |
https://en.wikipedia.org/wiki/OSEK | OSEK (Offene Systeme und deren Schnittstellen für die Elektronik in Kraftfahrzeugen; English: "Open Systems and their Interfaces for the Electronics in Motor Vehicles") is a standards body that has produced specifications for an embedded operating system, a communications stack, and a network management protocol for automotive embedded systems. It has produced related specifications, namely AUTOSAR. OSEK was designed to provide a reliable standard software architecture for the various electronic control units (ECUs) throughout a car.
OSEK was founded in 1993 by a German automotive company consortium (BMW, Robert Bosch GmbH, DaimlerChrysler, Opel, Siemens, and Volkswagen Group) and the University of Karlsruhe. In 1994, the French cars manufacturers Renault and PSA Peugeot Citroën, which had a similar project called VDX (Vehicle Distributed eXecutive), joined the consortium. Therefore, the official name was OSEK/VDX and OSEK was registered trademark of Continental Automotive GmbH (until 2007: Siemens AG).
Standards
OSEK is an open standard, published by a consortium founded by the automobile industry. Some parts of OSEK are standardized in ISO 17356.
ISO 17356-1:2005 Road vehicles—Open interface for embedded automotive applications—Part 1: General structure and terms, definitions and abbreviated terms
ISO 17356-2:2005 Road vehicles—Open interface for embedded automotive applications—Part 2: OSEK/VDX specifications for binding OS, COM and NM
ISO 17356-3:2005 Road vehicles—Open interface for embedded automotive applications—Part 3: OSEK/VDX Operating System (OS)
ISO 17356-4:2005 Road vehicles—Open interface for embedded automotive applications—Part 4: OSEK/VDX Communication (COM)
ISO 17356-5:2006 Road vehicles—Open interface for embedded automotive applications—Part 5: OSEK/VDX Network Management (NM)
ISO 17356-6:2006 Road vehicles—Open interface for embedded automotive applications—Part 6: OSEK/VDX Implementation Language (OIL)
before ISO
OSEK VDX Portal
|
https://en.wikipedia.org/wiki/Action%20semantics | Action semantics is a framework for the formal specification of semantics of programming languages invented by David Watt and Peter D. Mosses in the 1990s. It is a mixture of denotational, operational and algebraic semantics.
Action Semantics aims to be pragmatic. Action-Semantic Descriptions (ASDs) are designed to scale up to handle realistic programming languages. This is aided by the extensibility and modifiability of ASDs. This helps to ensure that extensions and changes do not require too many changes in the description. This is in contrast to the typical case when extending denotational or operational semantics, which may require reformulation of the entire description.
The Action Semantics framework was originally developed at the University of Aarhus and the University of Glasgow. Groups and individuals around the world have since contributed further to the approach.
Semantic entities
An important part of action semantics that gives it a modularity not seen in previous programming language semantics is the use of first-order semantic entities. First-order refers to how, unlike in denotational semantics, where a semantic function can be applied to another semantic function, in action semantics, a semantic entity cannot be applied to another semantic entity of its kind. Furthermore, the semantic entities utilized by action semantics broaden the framework’s ability to describe a programming language’s constructs by serving to denote both program behavior that is independent of any particular implementation and the way in which parts of a program influence the overall performance of the whole. The appropriately named action notation is employed to express the three types of semantic entities found in action semantics: actions, data, and yielders. The central semantic entity in this framework is actions, with data and yielders occupying supplementary roles. More specifically, actions are the mechanisms through which yielders and data are processed. An action, |
https://en.wikipedia.org/wiki/Surface%20modification | Surface modification is the act of modifying the surface of a material by bringing physical, chemical or biological characteristics different from the ones originally found on the surface of a material.
This modification is usually made to solid materials, but it is possible to find examples of the modification to the surface of specific liquids.
The modification can be done by different methods with a view to altering a wide range of characteristics of the surface, such as: roughness, hydrophilicity, surface charge, surface energy, biocompatibility and reactivity.
Surface engineering
Surface engineering is the sub-discipline of materials science which deals with the surface of solid matter. It has applications to chemistry, mechanical engineering, and electrical engineering (particularly in relation to semiconductor manufacturing).
Solids are composed of a bulk material covered by a surface. The surface which bounds the bulk material is called the Surface phase. It acts as an interface to the surrounding environment. The bulk material in a solid is called the Bulk phase.
The surface phase of a solid interacts with the surrounding environment. This interaction can degrade the surface phase over time. Environmental degradation of the surface phase over time can be caused by wear, corrosion, fatigue and creep.
Surface engineering involves altering the properties of the Surface Phase in order to reduce the degradation over time. This is accomplished by making the surface robust to the environment in which it will be used.
Applications and Future of Surface Engineering
Surface engineering techniques are being used in the automotive, aerospace, missile, power, electronic, biomedical, textile, petroleum, petrochemical, chemical, steel, power, cement, machine tools, construction industries. Surface engineering techniques can be used to develop a wide range of functional properties, including physical, chemical, electrical, electronic, magnetic, mechanical, wear-r |
https://en.wikipedia.org/wiki/POSTNET | POSTNET (Postal Numeric Encoding Technique) is a barcode symbology used by the United States Postal Service to assist in directing mail. The ZIP Code or ZIP+4 code is encoded in half- and full-height bars. Most often, the delivery point is added, usually being the last two digits of the address or PO box number.
The barcode starts and ends with a full bar (often called a guard rail or frame bar and represented as the letter "S" in one version of the USPS TrueType Font) and has a check digit after the ZIP, ZIP+4, or delivery point. The encoding table is shown on the right.
Each individual digit is represented by a set of five bars, two of which are full bars (i.e. two-out-of-five code). The full bars represent "on" bits in a pseudo-binary code in which the places represent, from left to right: 7, 4, 2, 1, and 0. (Though in this scheme, zero is encoded as 11 in decimal, or in POSTNET "binary" as 11000.)
Encoding
The following table shows the encoding for decimal digits:
Example
The ZIP+4 of 55555-1237 yields a check digit of 2 for encoded data of 5555512372
Together with the initials and terminal frame bars, this would be represented as:
Image:POSTNET 5.svgImage:POSTNET 5.svgImage:POSTNET 5.svgImage:POSTNET 2.svgImage:POSTNET 7.svgImage:POSTNET BAR.png
Barcode formats
There have been four formats of Postnet barcodes used by the Postal Service:
A 5 digit (plus check digit) barcode, containing the basic ZIP Code only, referred to as the "A" code. 32 bars total.
A 6 digit (plus check digit) barcode, containing the last 2 digits of the ZIP Code and the 4 digits of the ZIP+4 Code, referred to as a "B" code. 37 bars total. In the early stages of Postal automated mail processing the B code was used to "upgrade" mail that had been coded only with a 5-digit "A" code. This barcode was only found on mail that received a 5-digit barcode on the initial coding by an OCR. Now obsolete.
A 9 digit (plus check digit) barcode, containing the ZIP Code and ZIP+4 Code, refe |
https://en.wikipedia.org/wiki/User-Agent%20header | In computing, the User-Agent header is an HTTP header intended to identify the user agent responsible for making a given HTTP request. Whereas the character sequence User-Agent comprises the name of the header itself, the header value that a given user agent uses to identify itself is colloquially known as its user agent string. The user agent for the operator of a computer used to access the Web has encoded within the rules that govern its behavior the knowledge of how to negotiate its half of a request-response transaction; the user agent thus plays the role of the client in a client–server system. Often considered useful in networks is the ability to identify and distinguish the software facilitating a network session. For this reason, the User-Agent HTTP header exists to identify the client software to the responding server.
Use in client requests
When a software agent operates in a network protocol, it often identifies itself, its application type, operating system, device model, software vendor, or software revision, by submitting a characteristic identification string to its operating peer. In HTTP, SIP, and NNTP protocols, this identification is transmitted in a header field User-Agent. Bots, such as Web crawlers, often also include a URL and/or e-mail address so that the Webmaster can contact the operator of the bot.
In HTTP, the "user agent string" is often used for content negotiation, where the origin server selects suitable content or operating parameters for the response. For example, the user agent string might be used by a web server to choose variants based on the known capabilities of a particular version of client software. The concept of content tailoring is built into the HTTP standard in RFC 1945 "for the sake of tailoring responses to avoid particular user agent limitations".
The user agent string is one of the criteria by which Web crawlers may be excluded from accessing certain parts of a website using the Robots Exclusion Standard ( |
https://en.wikipedia.org/wiki/IBM%207950%20Harvest | The IBM 7950, also known as Harvest, was a one-of-a-kind adjunct to the Stretch computer which was installed at the United States National Security Agency (NSA). Built by IBM, it was delivered in 1962 and operated until 1976, when it was decommissioned. Harvest was designed to be used for cryptanalysis.
Development
In April 1958, the final design for the NSA-customized version of IBM's Stretch computer had been approved, and the machine was installed in February 1962. The design engineer was James H. Pomerene, and it was built by IBM in Poughkeepsie, New York. Its electronics (fabricated of the same kind of discrete transistors used for Stretch) were physically about twice as big as the Stretch to which it was attached. Harvest added a small number of instructions to Stretch, and could not operate independently.
An NSA-conducted evaluation found that Harvest was more powerful than the best commercially available machine by a factor of 50 to 200, depending on the task.
Architecture
The equipment added to the Stretch computer consisted of the following special peripherals:
IBM 7951 — Stream coprocessor
IBM 7952 — High performance core storage
IBM 7955 — Magnetic tape system, also known as TRACTOR
IBM 7959 — High speed I/O exchange
With the stream processing unit, Harvest was able to process 3 million characters a second.
The TRACTOR tape system, part of the HARVEST system, was unique for its time. It included six tape drives, which handled tape in cartridges, along with a library mechanism that could fetch a cartridge from a library, mount it on a drive, and return it to the library. The transfer rates and library mechanism were balanced in performance such that the system could read two streams of data from tape, and write a third, for the entire capacity of the library, without any time wasted for tape handling.
Programming
Harvest's most important mode of operation was called "setup" mode, in which the processor was configured with several hundred bit |
https://en.wikipedia.org/wiki/Cover%20%28telecommunications%29 | In telecommunications and tradecraft, cover is the technique of concealing or altering the characteristics of communications patterns for the purpose of denying an unauthorized receiver information that would be of value.
The purpose of cover is not to make the communication secure, but to make it look like noise, rendering it uninteresting and not worth analysis. Even if an attacker recognizes the communication as interesting, cover makes traffic analysis more difficult since he must crack the cover before he can find out to whom it is addressed.
Usually, the covered communication is also encrypted. In this way, enemies have no idea you sent a message; friends know you sent a message, but don't know what you said; the intended recipient knows what you said.
Technically, cover sometimes refers to the specific process of modulo two addition of a pseudorandom bit stream generated by a cryptographic device with bits from the control message.
Source: from Federal Standard 1037C and from MIL-STD-188
Cryptography
es:cobertura |
https://en.wikipedia.org/wiki/40-bit%20encryption | 40-bit encryption refers to a (now broken) key size of forty bits, or five bytes, for symmetric encryption; this represents a relatively low level of security. A forty bit length corresponds to a total of 240 possible keys. Although this is a large number in human terms (about a trillion), it is possible to break this degree of encryption using a moderate amount of computing power in a brute-force attack, i.e., trying out each possible key in turn.
Description
A typical home computer in 2004 could brute-force a 40-bit key in a little under two weeks, testing a million keys per second; modern computers are able to achieve this much faster. Using free time on a large corporate network or a botnet would reduce the time in proportion to the number of computers available. With dedicated hardware, a 40-bit key can be broken in seconds. The Electronic Frontier Foundation's Deep Crack, built by a group of enthusiasts for US$250,000 in 1998, could break a 56-bit Data Encryption Standard (DES) key in days, and would be able to break 40-bit DES encryption in about two seconds.
40-bit encryption was common in software released before 1999, especially those based on the RC2 and RC4 algorithms which had special "7-day" export review policies, when algorithms with larger key lengths could not legally be exported from the United States without a case-by-case license. "In the early 1990s ... As a general policy, the State Department allowed exports of commercial encryption with 40-bit keys, although some software with DES could be exported to U.S.-controlled subsidiaries and financial institutions." As a result, the "international" versions of web browsers were designed to have an effective key size of 40 bits when using Secure Sockets Layer to protect e-commerce. Similar limitations were imposed on other software packages, including early versions of Wired Equivalent Privacy. In 1992, IBM designed the CDMF algorithm to reduce the strength of 56-bit DES against brute force attac |
https://en.wikipedia.org/wiki/Micron%20Technology | Micron Technology, Inc. is an American producer of computer memory and computer data storage including dynamic random-access memory, flash memory, and USB flash drives. It is headquartered in Boise, Idaho. Its consumer products, including the Ballistix line of memory modules, are marketed under the Crucial brand. Micron and Intel together created IM Flash Technologies, which produced NAND flash memory. It owned Lexar between 2006 and 2017.
History
1978–1999
Micron was founded in Boise, Idaho, in 1978 by Ward Parkinson, Joe Parkinson, Dennis Wilson, and Doug Pitman as a semiconductor design consulting company. Startup funding was provided by local Idaho businessmen Tom Nicholson, Allen Noble, Rudolph Nelson, and Ron Yanke. Later it received funding from Idaho billionaire J. R. Simplot, whose fortune was made in the potato business. In 1981, the company moved from consulting to manufacturing with the completion of its first wafer fabrication unit ("Fab 1"), producing 64K DRAM chips.
In 1984, the company went public.
In 1994, founder Joe Parkinson retired as CEO and Steve Appleton took over as Chairman, President, and CEO.
A 1996 3-way merger among ZEOS International, Micron Computer, and Micron Custom Manufacturing Services (MCMS) increased the size and scope of the company; this was followed rapidly with the 1997 acquisition of NetFrame Systems, in a bid to enter the mid-range server industry.
2000–present
In 2000, Gurtej Singh Sandhu and Trung T. Doan at Micron initiated the development of atomic layer deposition high-k films for DRAM memory devices. This helped drive cost-effective implementation of semiconductor memory, starting with 90 nm node DRAM. Pitch double-patterning was also pioneered by Gurtej Singh Sandhu at Micron during the 2000s, leading to the development of 30-nm class NAND flash memory, and it has since been widely adopted by NAND flash and RAM manufacturers worldwide.
Micron and Intel created a joint venture in 2005, based in IM Flash Techn |
https://en.wikipedia.org/wiki/Search/Retrieve%20Web%20Service | Search/Retrieve Web service (SRW) is a web service for search and retrieval. SRW provides a SOAP interface to queries, to augment the URL interface provided by its companion protocol Search/Retrieve via URL (SRU). Queries in SRU and SRW are expressed using the Contextual Query Language (CQL).
Standards for SRW, SRU, and CQL are promulgated by the United States Library of Congress.
The SRW service and SRU protocol were both created by as part of the ZING (Z39.50 International: Next Generation) initiative as successors to the Z39.50 protocol.
Example usage
See also
Z39.50
Implementations
refbase
RefDB
Te Ara: The Encyclopedia of New Zealand
External links
SRU: Search/Retrieve via URL
SRW: Search/Retrieve Web Service
CQL: Contextual Query Language
Web services
Library science terminology |
https://en.wikipedia.org/wiki/Prime%20ring | In abstract algebra, a nonzero ring R is a prime ring if for any two elements a and b of R, arb = 0 for all r in R implies that either a = 0 or b = 0. This definition can be regarded as a simultaneous generalization of both integral domains and simple rings.
Although this article discusses the above definition, prime ring may also refer to the minimal non-zero subring of a field, which is generated by its identity element 1, and determined by its characteristic. For a characteristic 0 field, the prime ring is the integers, and for a characteristic p field (with p a prime number) the prime ring is the finite field of order p (cf. Prime field).
Equivalent definitions
A ring R is prime if and only if the zero ideal {0} is a prime ideal in the noncommutative sense.
This being the case, the equivalent conditions for prime ideals yield the following equivalent conditions for R to be a prime ring:
For any two ideals A and B of R, AB = {0} implies A = {0} or B = {0}.
For any two right ideals A and B of R, AB = {0} implies A = {0} or B = {0}.
For any two left ideals A and B of R, AB = {0} implies A = {0} or B = {0}.
Using these conditions it can be checked that the following are equivalent to R being a prime ring:
All nonzero right ideals are faithful as right R-modules.
All nonzero left ideals are faithful as left R-modules.
Examples
Any domain is a prime ring.
Any simple ring is a prime ring, and more generally: every left or right primitive ring is a prime ring.
Any matrix ring over an integral domain is a prime ring. In particular, the ring of 2 × 2 integer matrices is a prime ring.
Properties
A commutative ring is a prime ring if and only if it is an integral domain.
A ring is prime if and only if its zero ideal is a prime ideal.
A nonzero ring is prime if and only if the monoid of its ideals lacks zero divisors.
The ring of matrices over a prime ring is again a prime ring.
Notes
References
Ring theory |
https://en.wikipedia.org/wiki/Matrix%20ring | In abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication . The set of all matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: Matn(R) and ). Some sets of infinite matrices form infinite matrix rings. Any subring of a matrix ring is a matrix ring. Over a rng, one can form matrix rngs.
When R is a commutative ring, the matrix ring Mn(R) is an associative algebra over R, and may be called a matrix algebra. In this setting, if M is a matrix and r is in R, then the matrix rM is the matrix M with each of its entries multiplied by r.
Examples
The set of all square matrices over R, denoted Mn(R). This is sometimes called the "full ring of n-by-n matrices".
The set of all upper triangular matrices over R.
The set of all lower triangular matrices over R.
The set of all diagonal matrices over R. This subalgebra of Mn(R) is isomorphic to the direct product of n copies of R.
For any index set I, the ring of endomorphisms of the right R-module is isomorphic to the ring of column finite matrices whose entries are indexed by and whose columns each contain only finitely many nonzero entries. The ring of endomorphisms of M considered as a left R-module is isomorphic to the ring of row finite matrices.
If R is a Banach algebra, then the condition of row or column finiteness in the previous point can be relaxed. With the norm in place, absolutely convergent series can be used instead of finite sums. For example, the matrices whose column sums are absolutely convergent sequences form a ring. Analogously of course, the matrices whose row sums are absolutely convergent series also form a ring. This idea can be used to represent operators on Hilbert spaces, for example.
The intersection of the row-finite and column-finite matrix rings forms a ring .
If R is commutative, then Mn(R) has a structure of a *-algebra over R, where the involution * on M |
https://en.wikipedia.org/wiki/Domain%20%28ring%20theory%29 | In algebra, a domain is a nonzero ring in which implies or . (Sometimes such a ring is said to "have the zero-product property".) Equivalently, a domain is a ring in which 0 is the only left zero divisor (or equivalently, the only right zero divisor). A commutative domain is called an integral domain. Mathematical literature contains multiple variants of the definition of "domain".
Examples and non-examples
The ring is not a domain, because the images of 2 and 3 in this ring are nonzero elements with product 0. More generally, for a positive integer , the ring is a domain if and only if is prime.
A finite domain is automatically a finite field, by Wedderburn's little theorem.
The quaternions form a noncommutative domain. More generally, any division algebra is a domain, since all its nonzero elements are invertible.
The set of all integral quaternions is a noncommutative ring which is a subring of quaternions, hence a noncommutative domain.
A matrix ring Mn(R) for n ≥ 2 is never a domain: if R is nonzero, such a matrix ring has nonzero zero divisors and even nilpotent elements other than 0. For example, the square of the matrix unit E12 is 0.
The tensor algebra of a vector space, or equivalently, the algebra of polynomials in noncommuting variables over a field, is a domain. This may be proved using an ordering on the noncommutative monomials.
If R is a domain and S is an Ore extension of R then S is a domain.
The Weyl algebra is a noncommutative domain.
The universal enveloping algebra of any Lie algebra over a field is a domain. The proof uses the standard filtration on the universal enveloping algebra and the Poincaré–Birkhoff–Witt theorem.
Group rings and the zero divisor problem
Suppose that G is a group and K is a field. Is the group ring a domain? The identity
shows that an element g of finite order induces a zero divisor in R. The zero divisor problem asks whether this is the only obstruction; in other words,
Given a field |
https://en.wikipedia.org/wiki/Sympatric%20speciation | Sympatric speciation is the evolution of a new species from a surviving ancestral species while both continue to inhabit the same geographic region. In evolutionary biology and biogeography, sympatric and sympatry are terms referring to organisms whose ranges overlap so that they occur together at least in some places. If these organisms are closely related (e.g. sister species), such a distribution may be the result of sympatric speciation. Etymologically, sympatry is derived from the Greek roots ("together") and ("homeland"). The term was coined by Edward Bagnall Poulton in 1904, who explains the derivation.
Sympatric speciation is one of three traditional geographic modes of speciation. Allopatric speciation is the evolution of species caused by the geographic isolation of two or more populations of a species. In this case, divergence is facilitated by the absence of gene flow. Parapatric speciation is the evolution of geographically adjacent populations into distinct species. In this case, divergence occurs despite limited interbreeding where the two diverging groups come into contact. In sympatric speciation, there is no geographic constraint to interbreeding. These categories are special cases of a continuum from zero (sympatric) to complete (allopatric) spatial segregation of diverging groups.
In multicellular eukaryotic organisms, sympatric speciation is a plausible process that is known to occur, but the frequency with which it occurs is not known.
In bacteria, however, the analogous process (defined as "the origin of new bacterial species that occupy definable ecological niches") might be more common because bacteria are less constrained by the homogenizing effects of sexual reproduction and are prone to comparatively dramatic and rapid genetic change through horizontal gene transfer.
Evidence
Sympatric speciation events are quite common in plants, which are prone to acquiring multiple homologous sets of chromosomes, resulting in polyploidy. The polyp |
https://en.wikipedia.org/wiki/Communication%20source | A source or sender is one of the basic concepts of communication and information processing. Sources are objects which encode message data and transmit the information, via a channel, to one or more observers (or receivers).
In the strictest sense of the word, particularly in information theory, a source is a process that generates message data that one would like to communicate, or reproduce as exactly as possible elsewhere in space or time. A source may be modelled as memoryless, ergodic, stationary, or stochastic, in order of increasing generality.
Communication Source combines Communication and Mass Media Complete and Communication Abstracts to provide full-text access to more than 700 journals, and indexing and abstracting for more than 1,000 core journals. Coverage dating goes back to 1900.
Content is derived from academic journals, conference papers, conference proceedings, trade publications, magazines and periodicals.
A transmitter can be either a device, for example, an antenna, or a human transmitter, for example, a speaker. The word "transmitter" derives from an emitter, that is to say, that emits using the Hertzian waves.
In sending mail it also refers to the person or organization that sends a letter and whose address is written on the envelope of the letter.
In finance, an issuer can be, for example, the bank system of elements.
In education, an issuer is any person or thing that gives knowledge to the student, for example, the professor.
For communication to be effective, the sender and receiver must share the same code. In ordinary communication, the sender and receiver roles are usually interchangeable.
Depending on the language's functions, the issuer fulfills the expressive or emotional function, in which feelings, emotions, and opinions are manifested, such as The way is dangerous.
In economy
In the economy, the issuer is a legal entity, foundation, company, individual firm, national or foreign governments, investment companies o |
https://en.wikipedia.org/wiki/Directional%20derivative | A directional derivative is a concept in multivariable calculus that measures the rate at which a function changes in a particular direction at a given point.
The directional derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v.
The directional derivative of a scalar function f with respect to a vector v at a point (e.g., position) x may be denoted by any of the following:
It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the curvilinear coordinate curves, all other coordinates being constant.
The directional derivative is a special case of the Gateaux derivative.
Definition
The directional derivative of a scalar function
along a vector
is the function defined by the limit
This definition is valid in a broad range of contexts, for example where the norm of a vector (and hence a unit vector) is undefined.
For differentiable functions
If the function f is differentiable at x, then the directional derivative exists along any unit vector v at x, and one has
where the on the right denotes the gradient, is the dot product and v is a unit vector. This follows from defining a path and using the definition of the derivative as a limit which can be calculated along this path to get:
Intuitively, the directional derivative of f at a point x represents the rate of change of f, in the direction of v with respect to time, when moving past x.
Using only direction of vector
In a Euclidean space, some authors define the directional derivative to be with respect to an arbitrary nonzero vector v after normalization, thus being independent of its magnitude and depending only on its direction.
This definition gives the rate of increase of per unit of distance moved in the direction given by . In this case, one has
or in case f is |
https://en.wikipedia.org/wiki/List%20of%20wiki%20software |
Standard wiki programs, by programming language
JavaScript-based
TiddlyWiki is a HTML-JavaScript-based server-less wiki in which the entire site/wiki is contained in a single file, or as a Node.js-based wiki application. It is designed for maximum customization possibilities.
Wiki.js is an open-source, Node.js-based wiki application using git as the back end storage mechanism and automatically syncs with any git repository. It provides a visual Markdown editor with assets management, authentication system and a built-in search engine.
Java-based
XWiki is a free wiki software platform written in Java with a design emphasis on extensibility. XWiki is an enterprise wiki engine with a complete wiki feature set (version control, attachments, etc.) and a database engine and programming language which allows database driven applications to be created using the wiki interface.
Perl-based
Foswiki is a structured wiki, typically used to run a collaboration platform, knowledge or document management system a knowledge based, or team portal. is a structured wiki, which enables users to create "wiki applications".
ikiwiki, a "wiki compiler" - can use Subversion or git as the back end storage mechanism. ikiwiki converts wiki pages into HTML pages suitable for publishing on a website.
TWiki is a flexible, powerful, secure, simple Enterprise wiki and application platform. is a structured wiki, typically used to run a project development space, a document management system, a knowledge base, or any other groupware tool. Also available as a VMware appliance.
UseModWiki is a wiki software written in Perl and licensed under General Public License. Created by Clifford Adams in 2000, it is a clone of AtisWiki.
WikiWikiWeb, the first wiki and its associated software.
PHP-based
BookStack is released under the MIT License. It uses the ideas of books to organize pages and store information.
DokuWiki is a wiki application licensed under GPLv2 and written in PHP. It is aime |
https://en.wikipedia.org/wiki/Inverted%20sugar%20syrup | Inverted sugar syrup, also called invert syrup, invert sugar, simple syrup, sugar syrup, sugar water, bar syrup, syrup USP, or sucrose inversion, is a syrup mixture of the monosaccharides glucose and fructose, that is made by hydrolytic saccharification of the disaccharide sucrose. This mixture's optical rotation is opposite to that of the original sugar, which is why it is called an invert sugar.
It is 1.3x sweeter than table sugar, and foods that contain invert sugar retain moisture better and crystallize less easily than do those that use table sugar instead. Bakers, who call it invert syrup, may use it more than other sweeteners.
Production
Plain water
Inverted sugar syrup can be made without acids or enzymes by heating it up alone: two parts granulated sugar and one part water, simmered for five to seven minutes, will be partly inverted.
The amount of water can be increased to increase the time it takes to reach the desired final temperature, and increasing the time increases the amount of inversion that occurs. In general, higher final temperatures result in thicker syrups, and lower final temperatures, in thinner ones.
Additives
Commercially prepared enzyme-catalyzed solutions are inverted at . The optimum pH for inversion is 5.0. Invertase is added at a rate of about 0.15% of the syrup's weight, and inversion time will be about 8 hours. When completed the syrup temperature is raised to inactivate the invertase, but the syrup is concentrated in a vacuum evaporator to preserve color.
Though inverted sugar syrup can be made by heating table sugar in water alone, the reaction can be sped up by adding lemon juice, cream of tartar, or other catalysts, often without changing the flavor noticeably. Common sugar can be inverted quickly by mixing sugar and citric acid or cream of tartar at a ratio of about 1000:1 by weight and adding water. If lemon juice which is about five percent citric acid by weight is used instead then the ratio becomes 50:1. Such a mixtu |
https://en.wikipedia.org/wiki/Magnetic%20cartridge | A magnetic cartridge, more commonly called a phonograph cartridge or phono cartridge or (colloquially) a pickup, is an electromechanical transducer that is used to play records on a turntable.
The cartridge contains a removable or permanently mounted stylus, the tip - usually a gemstone, such as diamond or sapphire - of which makes physical contact with the record's groove. In popular usage and in disc jockey jargon, the stylus, and sometimes the entire cartridge, is often called the needle. As the stylus tracks the serrated groove, it vibrates a cantilever on which is mounted a permanent magnet which moves between the magnetic fields of sets of electromagnetic coils in the cartridge (or vice versa: the coils are mounted on the cantilever, and the magnets are in the cartridge). The shifting magnetic fields generate an electrical current in the coils. The electrical signal generated by the cartridge can be amplified and then converted into sound by a loudspeaker.
History
The first commercially successful type of electrical phonograph pickup was introduced in 1925. Although electromagnetic, its resemblance to later magnetic cartridges is remote: it contained a bulky horseshoe magnet and employed the same imprecisely mass-produced single-use steel needles which had been standard since the first crude disc record players appeared in the 1890s. Its tracking weight was specified in ounces, not grams. This early type of magnetic pickup completely dominated the market well into the 1930s, but by the end of that decade it had been superseded by a comparatively lightweight piezoelectric crystal pickup type. The use of short-lived disposable metal needles remained standard. During the years of affluence and long-deferred consumer demand immediately following World War II, as old record players with very heavy pickups were replaced, precision-ground and conveniently long-lasting stylus tips made of sapphire or the exotic hard metal osmium were increasingly popular. However, |
https://en.wikipedia.org/wiki/Dynode | A dynode is an electrode in a vacuum tube that serves as an electron multiplier through secondary emission. The first tube to incorporate a dynode was the dynatron, an ancestor of the magnetron, which used a single dynode. Photomultiplier and video camera tubes generally include a series of dynodes, each at a more positive electrical potential than its predecessor. Secondary emission occurs at the surface of each dynode. Such an arrangement is able to amplify the tiny current emitted by the photocathode, typically by a factor of one million.
Operation
The electrons emitted from the cathode are accelerated toward the first dynode, which is maintained 90 to 100 V positive concerning the cathode. Each accelerated photoelectron that strikes the dynode surface produces several electrons. These electrons are then accelerated toward the second dynode, held 90 to 100 V more positive than the first dynode. Each electron that strikes the surface of the second dynode produces several more electrons, which are then accelerated toward the third dynode, and so on. By the time this process has been repeated at each of the dynodes, 105 to 107 electrons have been produced for each incident photon, dependent on the number of dynodes. For conventional dynode materials, such as BeO and MgO, a multiplication factor of 10 can normally be achieved by each dynode stage.
Naming
The dynode takes its name from the dynatron. Albert Hull did not use the term dynode in his 1918 paper on the dynatron, but used the term extensively in his 1922 paper. In the latter paper, he defined a dynode as a "plate that emits impact electrons ... when it is part of a dynatron."
See also
Microchannel plate detector
Photoelectric effect
Particle detector
Photodetector
References
Electronic amplifiers
Particle detectors |
https://en.wikipedia.org/wiki/Codd%27s%2012%20rules | Codd's twelve rules are a set of thirteen rules (numbered zero to twelve) proposed by Edgar F. Codd, a pioneer of the relational model for databases, designed to define what is required from a database management system in order for it to be considered relational, i.e., a relational database management system (RDBMS). They are sometimes referred to as "Codd's Twelve Commandments".
History
Codd originally set out the rules in 1970, and developed them further in a 1974 conference paper. His aim was to prevent the vision of the original relational database from being diluted, as database vendors scrambled in the early 1980s to repackage existing products with a relational veneer. Rule 12 was particularly designed to counter such a positioning.
While in 1999, a textbook stated "Nowadays, most RDBMSs ... pass the test". another in 2007 suggested "no database system complies with all twelve rules." Codd himself, in his book "The Relational Model for Database Management: Version 2", acknowledged that while his original set of 12 rules can be used for coarse distinctions, the 333 features of his Relational Model Version 2 (RM/V2) are needed for distinctions of a finer grain.
Rules
Rule 0: The foundation rule:
For any system that is advertised as, or claimed to be, a relational data base management system, that system must be able to manage data bases entirely through its relational capabilities.
Rule 1: The information rule:
All information in a relational data base is represented explicitly at the logical level and in exactly one way by values in tables.
Rule 2: The guaranteed access rule:
Each and every datum (atomic value) in a relational data base is guaranteed to be logically accessible by resorting to a combination of table name, primary key value and column name.
Rule 3: Systematic treatment of null values:
Null values (distinct from the empty character string or a string of blank characters and distinct from zero or any other number) are supported in fully |
https://en.wikipedia.org/wiki/Open-source%20journalism | Open-source journalism, a close cousin to citizen journalism or participatory journalism, is a term coined in the title of a 1999 article by Andrew Leonard of Salon.com. Although the term was not actually used in the body text of Leonard's article, the headline encapsulated a collaboration between users of the internet technology blog Slashdot and a writer for Jane's Intelligence Review. The writer, Johan J. Ingles-le Nobel, had solicited feedback on a story about cyberterrorism from Slashdot readers, and then re-wrote his story based on that feedback and compensated the Slashdot writers whose information and words he used.
This early usage of the phrase clearly implied the paid use, by a mainstream journalist, of copyright-protected posts made in a public online forum. It thus referred to the standard journalistic techniques of news gathering and fact checking, and reflected a similar term—open-source intelligence—that was in use from 1992 in military intelligence circles.
The meaning of the term has since changed and broadened, and it is now commonly used to describe forms of innovative publishing of online journalism, rather than the sourcing of news stories by a professional journalist.
The term open-source journalism is often used to describe a spectrum on online publications: from various forms of semi-participatory online community journalism (as exemplified by projects such as the copyright newspaper NorthWest Voice), through to genuine open-source news publications (such as the Spanish 20 minutos, and Wikinews).
A relatively new development is the use of convergent polls, allowing editorials and opinions to be submitted and voted on. Over time, the poll converges on the most broadly accepted editorials and opinions. Examples of this are Opinionrepublic.com and Digg. Scholars are also experimenting with the process of journalism itself, such as open-sourcing the story skeletons that journalists build.
Usage
At first sight, it would appear to many that |
https://en.wikipedia.org/wiki/Mining%20engineering | Mining in the engineering discipline is the extraction of minerals from underneath, open pit, above, or on the ground. Mining engineering is associated with many other disciplines, such as mineral processing, exploration, excavation, geology, and metallurgy, geotechnical engineering and surveying. A mining engineer may manage any phase of mining operations, from exploration and discovery of the mineral resources, through feasibility study, mine design, development of plans, production and operations to mine closure.
With the process of mineral extraction, some amount of waste and uneconomic material are generated, which are the primary source of pollution in the vicinity of mines. Mining activities, by their nature, cause a disturbance of the natural environment in and around which the minerals are located. Mining engineers must therefore be concerned not only with the production and processing of mineral commodities but also with the mitigation of damage to the environment both during and after mining as a result of the change in the mining area. Such industries go through stringent laws to control the pollution and damage caused to the environment and are periodically governed by the concerned departments.
History of mining engineering
From prehistoric times to the present, mining has played a significant role in the existence of the human race. Since the beginning of civilization, people have used stone and ceramics and, later, metals found on or close to the Earth's surface. These were used to manufacture early tools and weapons. For example, high-quality flint found in northern France and southern England were used to set fire and break rock. Flint mines have been found in chalk areas where seams of the stone were followed underground by shafts and galleries. The oldest known mine on archaeological record is the "Lion Cave" in Eswatini. At this site, which radiocarbon dating indicates to be about 43,000 years old, paleolithic humans mined mineral hematite, wh |
https://en.wikipedia.org/wiki/Jacobson%20density%20theorem | In mathematics, more specifically non-commutative ring theory, modern algebra, and module theory, the Jacobson density theorem is a theorem concerning simple modules over a ring .
The theorem can be applied to show that any primitive ring can be viewed as a "dense" subring of the ring of linear transformations of a vector space. This theorem first appeared in the literature in 1945, in the famous paper "Structure Theory of Simple Rings Without Finiteness Assumptions" by Nathan Jacobson. This can be viewed as a kind of generalization of the Artin-Wedderburn theorem's conclusion about the structure of simple Artinian rings.
Motivation and formal statement
Let be a ring and let be a simple right -module. If is a non-zero element of , (where is the cyclic submodule of generated by ). Therefore, if are non-zero elements of , there is an element of that induces an endomorphism of transforming to . The natural question now is whether this can be generalized to arbitrary (finite) tuples of elements. More precisely, find necessary and sufficient conditions on the tuple and separately, so that there is an element of with the property that for all . If is the set of all -module endomorphisms of , then Schur's lemma asserts that is a division ring, and the Jacobson density theorem answers the question on tuples in the affirmative, provided that the are linearly independent over .
With the above in mind, the theorem may be stated this way:
The Jacobson density theorem. Let be a simple right -module, , and a finite and -linearly independent set. If is a -linear transformation on then there exists such that for all in .
Proof
In the Jacobson density theorem, the right -module is simultaneously viewed as a left -module where , in the natural way: . It can be verified that this is indeed a left module structure on . As noted before, Schur's lemma proves is a division ring if is simple, and so is a vector space over .
The proof also relies on the fol |
https://en.wikipedia.org/wiki/Newtonian%20limit | In physics, the Newtonian limit is a mathematical approximation applicable to physical systems exhibiting (1) weak gravitation, (2) objects moving slowly compared to the speed of light, and (3) slowly changing (or completely static) gravitational fields. Under these conditions, Newton's law of universal gravitation may be used to obtain values that are accurate. In general, and in the presence of significant gravitation, the general theory of relativity must be used.
In the Newtonian limit, spacetime is approximately flat and the Minkowski metric may be used over finite distances. In this case 'approximately flat' is defined as space in which gravitational effect approaches 0, mathematically actual spacetime and Minkowski space are not identical, Minkowski space is an idealized model.
Special relativity
In special relativity, Newtonian behaviour can in most cases be obtained by performing the limit . In this limit, the often appearing gamma factor becomes 1
and the Lorentz transformations between reference frames turn into Galileo transformations
General relativity
The geodesic equation for a free particle on curved spacetime with metric can be derived from the action
If the spacetime-metric is
then, ignoring all contributions of order the action becomes
which is the action that reproduces the Newtonian equations of motion of a particle in a gravitational potential
See also
Classical limit
References
Special relativity
Dynamical systems |
https://en.wikipedia.org/wiki/Eugene%20Koonin | Eugene Viktorovich Koonin (Russian: Евге́ний Ви́кторович Ку́нин; born October 26, 1956) is a Russian-American biologist and Senior Investigator at the National Center for Biotechnology Information (NCBI). He is a recognised expert in the field of evolutionary and computational biology.
Education
Koonin gained a Master of Science in 1978 and a PhD in 1983 in molecular biology, both from the Department of Biology at Moscow State University. His PhD thesis, titled "Multienzyme organization of encephalomyocarditis virus replication complexes", was supervised by Vadim I. Agol.
Research
From 1985 until 1991, Koonin worked as a research scientist in computational biology in the Institutes of Poliomyelitis and Microbiology at the USSR Academy of Medical Sciences, studying virus biochemistry and bacterial genetics. In 1991, Koonin moved to the NCBI, where he has held a Senior Investigator position since 1996.
Koonin's principal research goals include the comparative analysis of sequenced genomes and automatic methods for genome-scale annotation of gene functions. He also researches in the application of comparative genomics for phylogenetic analysis, reconstruction of ancestral life forms and building large-scale evolutionary scenarios, as well as mathematical modeling of genome evolution. Koonin's research also investigates computational study of the major transitions in the evolution of life (such as the origin of eukaryotes), the evolution of eukaryotic signaling and developmental pathways from the comparative-genomic perspective.
Career
Koonin has worked as Adjunct Professor at the Georgia Institute of Technology, Boston University and the University of Haifa.
As of 2014, Koonin serves on the advisory editorial board of Trends in Genetics, and is co-Editor-in-Chief of the open access journal Biology Direct. He served on the editorial board of Bioinformatics from 1999 until 2001. Koonin is also an advisory board member in bioinformatics at Faculty of 1000.
In 2016 h |
https://en.wikipedia.org/wiki/Simics | Simics is a full-system simulator or virtual platform used to run unchanged production binaries of the target hardware. Simics was originally developed by the Swedish Institute of Computer Science (SICS), and then spun off to Virtutech for commercial development in 1998. Virtutech was acquired by Intel in 2010. Currently, Simics is provided by Intel in a public release and sold commercially by Wind River Systems, which was in the past a subsidiary of Intel.
Simics contains both instruction set simulators and hardware models, and is or has been used to simulate systems such as Alpha, ARM (32- and 64-bit), IA-64, MIPS (32- and 64-bit), MSP430, PowerPC (32- and 64-bit), RISC-V (32- and 64-bit), SPARC-V8 and V9, and x86 and x86-64 CPUs.
Many different operating systems have been run on various simulated virtual platforms, including Linux, MS-DOS, Windows, VxWorks, OSE, Solaris, FreeBSD, QNX, RTEMS, UEFI, and Zephyr.
The NetBSD AMD64 port was initially developed using Simics before the public release of the chip. The purpose of simulation in Simics is often to develop software for a particular type of hardware without requiring access to that precise hardware, using Simics as a virtual platform. This can applied both to pre-release and pre-silicon software development for future hardware, as well as for existing hardware. Intel uses Simics to provide its ecosystem with access to future platform months or years ahead of the hardware launch.
The current version of Simics is 6 which was released publicly in 2019. Simics runs on 64-bit x86-64 machines running Microsoft Windows and Linux (32-bit support was dropped with the release of Simics 5, since 64-bit provides significant performance advantages and is universally available on current hardware). The previous version, Simics 5, was released in 2015.
Simics has the ability to execute a system in forward and reverse direction. Reverse debugging can illuminate how an exceptional condition or bug occurred. When execu |
https://en.wikipedia.org/wiki/List%20of%20engineering%20societies | An engineering society is a professional organization for engineers of various disciplines. Some are umbrella type organizations which accept many different disciplines, while others are discipline-specific. Many award professional designations, such as European Engineer, professional engineer, chartered engineer, incorporated engineer or similar. There are also many student-run engineering societies, commonly at universities or technical colleges.
Africa
Ghana
Ghana Institution of Engineers
South Africa
South African Institute of Electrical Engineers
Engineering Council of South Africa
Zimbabwe
Zimbabwe Institution of Engineers
Americas
Canada
In Canada, the term "engineering society" sometimes refers to organizations of engineering students as opposed to professional societies of engineers. The Canadian Federation of Engineering Students, whose membership consists of most of the engineering student societies from across Canada (see below), is the national association of undergraduate engineering student societies in Canada.
Canada also has many traditions related to the calling of an engineer.
The Engineering Institute of Canada (French: l'Institut Canadien des ingénieurs) has the following member societies:
Institution of Mechanical Engineers (Canadian Branch of the IMechE)
Canadian Maritime Section of the Marine Technology Society
Canadian Nuclear Society
Canadian Society for Chemical Engineering
Canadian Society for Civil Engineering
Ontario
Professional Engineers Ontario
Engineering Society of Queen's University
Lassonde Engineering Society
United States
Alpha Omega Epsilon
Alpha Pi Mu
American Academy of Environmental Engineers
American Association of Engineering Societies
American Indian Council of Architects and Engineers
American Indian Science and Engineering Society
American Institute of Aeronautics and Astronautics
American Institute of Chemical Engineers
American Nuclear Society
American Railway Engineering Association
American Society for |
https://en.wikipedia.org/wiki/Eckmann%E2%80%93Hilton%20argument | In mathematics, the Eckmann–Hilton argument (or Eckmann–Hilton principle or Eckmann–Hilton theorem) is an argument about two unital magma structures on a set where one is a homomorphism for the other. Given this, the structures are the same, and the resulting magma is a commutative monoid. This can then be used to prove the commutativity of the higher homotopy groups. The principle is named after Beno Eckmann and Peter Hilton, who used it in a 1962 paper.
The Eckmann–Hilton result
Let be a set equipped with two binary operations, which we will write and , and suppose:
and are both unital, meaning that there are identity elements and of such that and , for all .
for all .
Then and are the same and in fact commutative and associative.
Remarks
The operations and are often referred to as monoid structures or multiplications, but this suggests they are assumed to be associative, a property that is not required for the proof. In fact, associativity follows. Likewise, we do not have to require that the two operations have the same neutral element; this is a consequence.
Proof
First, observe that the units of the two operations coincide:
.
Now, let .
Then . This establishes that the two operations coincide and are commutative.
For associativity, .
Two-dimensional proof
The above proof also has a "two-dimensional" presentation that better illustrates the application to higher homotopy groups.
For this version of the proof, we write the two operations as vertical and horizontal juxtaposition, i.e., and . The interchange property can then be expressed as follows:
For all , , so we can write
without ambiguity.
Let and be the units for vertical and horizontal composition respectively. Then , so both units are equal.
Now, for all , , so horizontal composition is the same as vertical composition and both operations are commutative.
Finally, for all ,
, so composition is associative.
Remarks
If the operations are associative, each one defines the |
https://en.wikipedia.org/wiki/Silver%20sulfide | Silver sulfide is an inorganic compound with the formula . A dense black solid, it is the only sulfide of silver. It is useful as a photosensitizer in photography. It constitutes the tarnish that forms over time on silverware and other silver objects. Silver sulfide is insoluble in most solvents, but is degraded by strong acids. Silver sulfide is a network solid made up of silver (electronegativity of 1.98) and sulfur (electronegativity of 2.58) where the bonds have low ionic character (approximately 10%).
Formation
Silver sulfide naturally occurs as the tarnish on silverware. When combined with silver, hydrogen sulfide gas creates a layer of black silver sulfide patina on the silver, protecting the inner silver from further conversion to silver sulfide. Silver whiskers can form when silver sulfide forms on the surface of silver electrical contacts operating in an atmosphere rich in hydrogen sulfide and high humidity. Such atmospheres can exist in sewage treatment and paper mills.
Structure and properties
Three forms are known: monoclinic acanthite (β-form), stable below 179 °C, body centered cubic so-called argentite (α-form), stable above 180 °C, and a high temperature face-centred cubic (γ-form) stable above 586 °C. The higher temperature forms are electrical conductors. It is found in nature as relatively low temperature mineral acanthite. Acanthite is an important ore of silver. The acanthite, monoclinic, form features two kinds of silver centers, one with two and the other with three near neighbour sulfur atoms. Argentite refers to a cubic form, which, due to instability in "normal" temperatures, is found in form of the pseudomorphosis of acanthite after argentite.
History
In 1833 Michael Faraday noticed that the resistance of silver sulfide decreased dramatically as temperature increased. This constituted the first report of a semiconducting material.
Silver sulfide is a component of classical qualitative inorganic analysis.
References
External link |
https://en.wikipedia.org/wiki/Tribology | Tribology is the science and engineering of understanding friction, lubrication and wear phenomena for interacting surfaces in relative motion. It is highly interdisciplinary, drawing on many academic fields, including physics, chemistry, materials science, mathematics, biology and engineering. The fundamental objects of study in tribology are tribosystems, which are physical systems of contacting surfaces. Subfields of tribology include biotribology, nanotribology and space tribology. It is also related to other areas such as the coupling of corrosion and tribology in tribocorrosion and the contact mechanics of how surfaces in contact deform.
Approximately 20% of the total energy expenditure of the world is due to the impact of friction and wear in the transportation, manufacturing, power generation, and residential sectors.
This section will provide an overview of tribology, with links to many of the more specialized areas.
Etymology
The word tribology derives from the Greek root τριβ- of the verb , tribo, "I rub" in classic Greek, and the suffix -logy from , -logia "study of", "knowledge of". Peter Jost coined the word in 1966, in the eponymous report which highlighted the cost of friction, wear and corrosion to the UK economy.
History
Early history
Despite the relatively recent naming of the field of tribology, quantitative studies of friction can be traced as far back as 1493, when Leonardo da Vinci first noted the two fundamental 'laws' of friction. According to Leonardo, frictional resistance was the same for two different objects of the same weight but making contact over different widths and lengths. He also observed that the force needed to overcome friction doubles as weight doubles. However, Leonardo's findings remained unpublished in his notebooks.
The two fundamental 'laws' of friction were first published (in 1699) by Guillaume Amontons, with whose name they are now usually associated. They state that:
the force of friction acting between two s |
https://en.wikipedia.org/wiki/Artinian%20ring | In mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on (one-sided) ideals; that is, there is no infinite descending sequence of ideals. Artinian rings are named after Emil Artin, who first discovered that the descending chain condition for ideals simultaneously generalizes finite rings and rings that are finite-dimensional vector spaces over fields. The definition of Artinian rings may be restated by interchanging the descending chain condition with an equivalent notion: the minimum condition.
Precisely, a ring is left Artinian if it satisfies the descending chain condition on left ideals, right Artinian if it satisfies the descending chain condition on right ideals, and Artinian or two-sided Artinian if it is both left and right Artinian. For commutative rings the left and right definitions coincide, but in general they are distinct from each other.
The Wedderburn–Artin theorem characterizes every simple Artinian ring as a ring of matrices over a division ring. This implies that a simple ring is left Artinian if and only if it is right Artinian.
The same definition and terminology can be applied to modules, with ideals replaced by submodules.
Although the descending chain condition appears dual to the ascending chain condition, in rings it is in fact the stronger condition. Specifically, a consequence of the Akizuki–Hopkins–Levitzki theorem is that a left (resp. right) Artinian ring is automatically a left (resp. right) Noetherian ring. This is not true for general modules; that is, an Artinian module need not be a Noetherian module.
Examples and counterexamples
An integral domain is Artinian if and only if it is a field.
A ring with finitely many, say left, ideals is left Artinian. In particular, a finite ring (e.g., ) is left and right Artinian.
Let k be a field. Then is Artinian for every positive integer n.
Similarly, is an Artinian ring with maximal ideal |
https://en.wikipedia.org/wiki/JIS%20encoding | In computing, JIS encoding refers to several Japanese Industrial Standards for encoding the Japanese language. Strictly speaking, the term means either:
A set of standard coded character sets for Japanese, notably:
JIS X 0201, the Japanese version of ISO 646 (ASCII) containing the base 7-bit ASCII characters (with some modifications) and 64 half-width katakana characters.
JIS X 0208, the most common kanji character set containing 6,879 characters, including 6,355 kanji and 524 other characters (one 94 by 94 plane)
JIS X 0212, a supplement for JIS X 0208 which adds 5,801 kanji, totaling 12,156 kanji (a second 94 by 94 plane)
JIS X 0213, which extends JIS X 0208 (two planes)
JIS X 0202 (also known as ISO-2022-JP), a set of encoding mechanisms for sending JIS character data over transmission mediums that only support 7-bit data.
In practice, "JIS encoding" usually refers to JIS X 0208 character data encoded with JIS X 0202. For instance, the IANA uses the JIS_Encoding label to refer to JIS X 0202, and the ISO-2022-JP label to refer to the profile thereof defined by .
Other encoding mechanisms for JIS characters include the Shift JIS encoding and EUC-JP. Shift JIS adds the kanji, full-width hiragana and full-width katakana from JIS X 0208 to JIS X 0201 in a backward compatible way. Shift JIS is perhaps the most widely used encoding in Japan, as the compatibility with the single-byte JIS X 0201 character set made it possible for electronic equipment manufacturers (such as cash register manufacturers) to offer an upgrade from older cheaper equipment that was not capable of displaying kanji to newer equipment while retaining character-set compatibility.
EUC-JP is used on UNIX systems, where the JIS encodings are incompatible with POSIX standards.
A more recent alternative to JIS coded characters is Unicode (UCS coded characters), particularly in the UTF-8 encoding mechanism.
Encoding comparison
The following table compares the features of the three main encodin |
https://en.wikipedia.org/wiki/Bran | Bran, also known as miller's bran, is the hard layers of cereal grain surrounding the endosperm. It consists of the combined aleurone and pericarp. Corn (maize) bran also includes the pedicel (tip cap). Along with the germ, it is an integral part of whole grains, and is often produced as a byproduct of milling in the production of refined grains.
Bran is present in cereal grain, including rice, corn (maize), wheat, oats, barley, rye, and millet. Bran is not the same as chaff, which is a coarser, scaly material surrounding the grain, but does not form part of the grain itself, and which is indigestible by humans.
Composition
Bran is particularly rich in dietary fiber and essential fatty acids, and contains significant quantities of starch, protein, vitamins, and dietary minerals. It is also a source of phytic acid, an antinutrient that prevents nutrient absorption.
The high oil content of bran makes it subject to rancidification, one of the reasons that it is often separated from the grain before storage or further processing. Bran is often heat-treated to increase its shelf life.
Rice bran
Rice bran is a byproduct of the rice-milling process (the conversion of brown rice to white rice), and it contains various antioxidants. A major rice bran fraction contains 12%–13% oil and highly unsaponifiable components (4.3%). This fraction contains tocotrienols (a form of vitamin E), gamma-oryzanol, and beta-sitosterol; all these constituents may contribute to the lowering of the plasma levels of the various parameters of the lipid profile. Rice bran also contains a high level of dietary fiber (beta-glucan, pectin, and gum). It also contains ferulic acid, which is also a component of the structure of nonlignified cell walls. Some research suggests, though, inorganic arsenic is present at some level in rice bran. One study found the levels to be 20% higher than in contaminated drinking water.
Uses
Bran is often used to enrich breads (notably muffins) and breakfast cerea |
https://en.wikipedia.org/wiki/Schl%C3%A4fli%20symbol | In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, who generalized Euclidean geometry to more than three dimensions and discovered all their convex regular polytopes, including the six that occur in four dimensions.
Definition
The Schläfli symbol is a recursive description, starting with {p} for a p-sided regular polygon that is convex. For example, {3} is an equilateral triangle, {4} is a square, {5} a convex regular pentagon, etc.
Regular star polygons are not convex, and their Schläfli symbols {p/q} contain irreducible fractions p/q, where p is the number of vertices, and q is their turning number. Equivalently, {p/q} is created from the vertices of {p}, connected every q. For example, is a pentagram; is a pentagon.
A regular polyhedron that has q regular p-sided polygon faces around each vertex is represented by {p,q}. For example, the cube has 3 squares around each vertex and is represented by {4,3}.
A regular 4-dimensional polytope, with r {p,q} regular polyhedral cells around each edge is represented by {p,q,r}. For example, a tesseract, {4,3,3}, has 3 cubes, {4,3}, around an edge.
In general, a regular polytope {p,q,r,...,y,z} has z {p,q,r,...,y} facets around every peak, where a peak is a vertex in a polyhedron, an edge in a 4-polytope, a face in a 5-polytope, and an (n-3)-face in an n-polytope.
Properties
A regular polytope has a regular vertex figure. The vertex figure of a regular polytope {p,q,r,...,y,z} is {q,r,...,y,z}.
Regular polytopes can have star polygon elements, like the pentagram, with symbol , represented by the vertices of a pentagon but connected alternately.
The Schläfli symbol can represent a finite convex polyhedron, an infinite tessellation of Euclidean space, or an infinite tessellation of hyperbolic space, depending on the angle defect of the construction. A positive angle defe |
https://en.wikipedia.org/wiki/Automatic%20Packet%20Reporting%20System | Automatic Packet Reporting System (APRS) is an amateur radio-based system for real time digital communications of information of immediate value in the local area. Data can include object Global Positioning System (GPS) coordinates, weather station telemetry, text messages, announcements, queries, and other telemetry. APRS data can be displayed on a map, which can show stations, objects, tracks of moving objects, weather stations, search and rescue data, and direction finding data.
APRS data is typically transmitted on a single shared frequency (depending on country) to be repeated locally by area relay stations (digipeaters) for widespread local consumption. In addition, all such data are typically ingested into the APRS Internet System (APRS-IS) via an Internet-connected receiver (IGate) and distributed globally for ubiquitous and immediate access. Data shared via radio or Internet are collected by all users and can be combined with external map data to build a shared live view.
APRS was developed from the late 1980s forward by Bob Bruninga, call sign WB4APR, a senior research engineer at the United States Naval Academy. He maintained the main APRS Web site until his death in 2022. The initialism "APRS" was derived from his call sign.
History
Bob Bruninga, a senior research engineer at the United States Naval Academy, implemented the earliest ancestor of APRS on an Apple II computer in 1982. This early version was used to map high frequency Navy position reports. The first use of APRS was in 1984, when Bruninga developed a more advanced version on a VIC-20 for reporting the position and status of horses in a endurance run.
During the next two years, Bruninga continued to develop the system, which he then called the Connectionless Emergency Traffic System (CETS). Following a series of Federal Emergency Management Agency (FEMA) exercises using CETS, the system was ported to the IBM Personal Computer. During the early 1990s, CETS (then known as the Automatic |
https://en.wikipedia.org/wiki/General%20Mobile%20Radio%20Service | The General Mobile Radio Service (GMRS) is a land-mobile FM UHF radio service designed for short-range two-way voice communication and authorized under part 95 of the US FCC code. It requires a license in the United States, but some GMRS compatible equipment can be used license-free in Canada. The US GMRS license is issued for a period of 10 years by the FCC. The United States permits use by adult individuals who possess a valid GMRS license, as well as their immediate family members. Immediate relatives of the GMRS system licensee are entitled to communicate among themselves for personal or business purposes, but employees of the licensee who are not family members are not covered by the license. Non-family members must be licensed separately.
GMRS radios are typically handheld portable (walkie-talkies) much like Family Radio Service (FRS) radios, and they share a frequency band with FRS near 462 and 467 MHz. Mobile and base station-style radios are available as well, but these are normally commercial UHF radios as often used in the public service and commercial land mobile bands. These are legal for use in this service as long as they are certified for GMRS under USC 47 Part 95.
GMRS licensees are allowed to establish repeaters to extend their communications range. GMRS repeaters are permitted to be linked with other GMRS repeaters but are not authorized to connect to the public switched telephone network.
Licensing
Any individual in the United States who is at least 18 years of age and not a representative of a foreign government may apply for a GMRS license by completing the application form, online through the FCC's Universal Licensing System. No exam is required. A GMRS license is issued for a 10–year term.
The current fee was reduced to $35 for all applicants on April 19, 2022.
A GMRS individual license extends to immediate family members and authorizes them to use the licensed system. GMRS license holders are allowed to communicate with FRS users on |
https://en.wikipedia.org/wiki/Backhoe | A backhoe—also called rear actor or back actor—is a type of excavating equipment, or digger, consisting of a digging bucket on the end of a two-part articulated arm. It is typically mounted on the back of a tractor or front loader, the latter forming a "backhoe loader" (a US term, but known as a "JCB" in Ireland and the UK). The section of the arm closest to the vehicle is known as the boom, while the section that carries the bucket is known as the dipper (or dipper-stick), both terms derived from steam shovels. The boom, which is the long piece of the backhoe arm attached to the tractor through a pivot called the king-post, is located closest to the cab. It allows the arm to pivot left and right, typically through a range of 180 to 200 degrees, and also enables lifting and lowering movements.
Description
The term "backhoe" refers to the action of the bucket, not its location on the vehicle. That is, a backhoe digs by drawing earth backwards, rather than lifting it with a forward motion like a person shovelling, a steam shovel, or a bulldozer. The buckets on some backhoes may be reconfigured facing forward, making them "hoes".
A tractor-loader backhoe (TLB) is a tractor-like vehicle with a backhoe at the rear, a front loader on the other and a swivelling seat to position the operator facing whichever direction is needed at the time. In North America, this arrangement is often referred to as simply a backhoe, or when on a chassis originally derived from farm tractors, a tractor-loader backhoe. To differentiate, a backhoe on its own dedicated chassis may then be referred to as an excavator.
Backhoe loaders can be designed and manufactured from the start as such, or can be the result of a farm tractor equipped with a front end loader (FEL) and rear backhoe. Though similar looking, the purpose-designed backhoe loaders are much stronger, with the farm variation unsuitable for heavy work.
With the advent of hydraulic powered attachments such as a tiltrotator, b |
https://en.wikipedia.org/wiki/Nd%3AYAG%20laser | Nd:YAG (neodymium-doped yttrium aluminum garnet; Nd:Y3Al5O12) is a crystal that is used as a lasing medium for solid-state lasers. The dopant, triply ionized neodymium, Nd(III), typically replaces a small fraction (1%) of the yttrium ions in the host crystal structure of the yttrium aluminum garnet (YAG), since the two ions are of similar size. It is the neodymium ion which provides the lasing activity in the crystal, in the same fashion as red chromium ion in ruby lasers.
Laser operation of Nd:YAG was first demonstrated by J.E. Geusic et al. at Bell Laboratories in 1964.
Technology
Nd:YAG lasers are optically pumped using a flashtube or laser diodes. These are one of the most common types of laser, and are used for many different applications.
Nd:YAG lasers typically emit light with a wavelength of 1064 nm, in the infrared. However, there are also transitions near 946, 1120, 1320, and 1440 nm. Nd:YAG lasers operate in both pulsed and continuous mode. Pulsed Nd:YAG lasers are typically operated in the so-called Q-switching mode: An optical switch is inserted in the laser cavity waiting for a maximum population inversion in the neodymium ions before it opens. Then the light wave can run through the cavity, depopulating the excited laser medium at maximum population inversion. In this Q-switched mode, output powers of 250 megawatts and pulse durations of 10 to 25 nanoseconds have been achieved. The high-intensity pulses may be efficiently frequency doubled to generate laser light at 532 nm, or higher harmonics at 355, 266 and 213 nm.
Nd:YAG absorbs mostly in the bands between 730–760 nm and 790–820 nm. At low current densities krypton flashlamps have higher output in those bands than do the more common xenon lamps, which produce more light at around 900 nm. The former are therefore more efficient for pumping Nd:YAG lasers.
The amount of the neodymium dopant in the material varies according to its use. For continuous wave output, the doping is significantly lowe |
https://en.wikipedia.org/wiki/Hasse%20principle | In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the p-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in the real numbers and in the p-adic numbers for each prime p.
Intuition
Given a polynomial equation with rational coefficients, if it has a rational solution, then this also yields a real solution and a p-adic solution, as the rationals embed in the reals and p-adics: a global solution yields local solutions at each prime. The Hasse principle asks when the reverse can be done, or rather, asks what the obstruction is: when can you patch together solutions over the reals and p-adics to yield a solution over the rationals: when can local solutions be joined to form a global solution?
One can ask this for other rings or fields: integers, for instance, or number fields. For number fields, rather than reals and p-adics, one uses complex embeddings and -adics, for prime ideals .
Forms representing 0
Quadratic forms
The Hasse–Minkowski theorem states that the local–global principle holds for the problem of representing 0 by quadratic forms over the rational numbers (which is Minkowski's result); and more generally over any number field (as proved by Hasse), when one uses all the appropriate local field necessary conditions. Hasse's theorem on cyclic extensions states that the local–global principle applies to the condition of being a relative norm for a cyclic extension of number fields.
Cubic forms
A counterexample by Ernst S. Selmer shows that the Hasse–Minkowski theorem cannot be extended to forms of degree 3: The cubic equation 3x3 + |
https://en.wikipedia.org/wiki/Viktor%20Schauberger | Viktor Schauberger (30 June 1885 – 25 September 1958) was an Austrian forest caretaker, naturalist, philosopher, inventor and pseudoscientist.
Early life
Schauberger was born in Holzschlag, Upper Austria on 30 June 1885. His parents were Leopold Schauberger and Josefa, née Klimitsch. From 1891 to 1897 he attended the elementary school in Aigen, then until 1900 the state grammar school in Linz. Until 1904 he went to the forestry school in Aggsbach in the Kartause Aggsbach, where he passed the exam as a forester. From 1904 to 1906 he was forest clerk in Groß-Schweinbarth in Lower Austria.
Films
In 1930, "Tragendes Wasser" was filmed, showing the functioning of the log flumes.
Nature Was My Teacher, narrated by Tom Brown (1993, Borderland Science Research Foundation)
Sacred Living Geometry: The Enlightened Environmental Theories of Viktor Schauberger, narrated by Callum Coats (1995, Talkstudio)
Extraordinary Nature of Water, narrated by Callum Coats (2000, Filmstream)
Viktor Schauberger: Comprehend and Copy Nature, directed by Franz Fitzke (2007, Schauberger Verlag)
Books
Schauberger, Viktor: Unsere sinnlose Arbeit – Die Quelle der Weltkrise, Der Aufbau durch Atomverwandlung, nicht Atomzertrümmerung (1933, Krystall-Verlag GmbH, 2001, Jörg Schauberger, ) (Released in English as "Our Senseless Toil – The Cause of the World Crisis – Progress Through Transformation of the Atom – Not its destruction!")
Schauberger, Viktor & Coats, Callum: Eco-Technology 1: The Water Wizard – The Extraordinary Properties of Natural Water (1998, Gateway Books, )
Schauberger, Viktor & Coats, Callum: Eco-Technology 2: Nature as Teacher – New Principles in the Working of Nature (1999, Gateway Books, )
Schauberger, Viktor & Coats, Callum: Eco-Technology 3: The Fertile Earth – Nature's Energies in Agriculture, Soil Fertilisation and Forestry (1999, Gateway Books, )
Schauberger, Viktor & Coats, Callum: Eco-Technology 4: Energy Evolution – Harnessing Free Energy from Nature (2000 |
https://en.wikipedia.org/wiki/Furfural | Furfural is an organic compound with the formula C4H3OCHO. It is a colorless liquid, although commercial samples are often brown. It has an aldehyde group attached to the 2-position of furan. It is a product of the dehydration of sugars, as occurs in a variety of agricultural byproducts, including corncobs, oat, wheat bran, and sawdust. The name furfural comes from the Latin word , meaning bran, referring to its usual source. Furfural is only derived from lignocellulosic biomass, i.e., its origin is non-food or non-coal/oil based. In addition to ethanol, acetic acid, and sugar, furfural is one of the oldest organic chemicals available readily purified from natural precursors.
History
Furfural was first isolated in 1821 (published in 1832) by the German chemist Johann Wolfgang Döbereiner, who produced a small sample as a byproduct of formic acid synthesis. In 1840, the Scottish chemist John Stenhouse found that the same chemical could be produced by distilling a wide variety of crop materials, including corn, oats, bran, and sawdust, with aqueous sulfuric acid; he also determined furfural's empirical formula (C5H4O2). George Fownes named this oil "furfurol" in 1845 (from furfur (bran), and oleum (oil)). In 1848, the French chemist Auguste Cahours determined that furfural was an aldehyde. Determining the structure of furfural required some time: the furfural molecule contains a cyclic ether (furan), which tends to break open when it's treated with harsh reagents. In 1870, German chemist Adolf von Baeyer speculated about the structure of the chemically similar compounds furan and 2-furoic acid. Additional research by German chemist Heinrich Limpricht supported this idea. From work published in 1877, Baeyer had confirmed his previous belief on the structure of furfural. By 1886, furfurol was being called "furfural" (short for "furfuraldehyde") and the correct chemical structure for furfural was being proposed. By 1887, the German chemist Willy Marckwald had inferred t |
https://en.wikipedia.org/wiki/List%20of%20exponential%20topics | This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics.
Accelerating change
Approximating natural exponents (log base e)
Artin–Hasse exponential
Bacterial growth
Baker–Campbell–Hausdorff formula
Cell growth
Barometric formula
Beer–Lambert law
Characterizations of the exponential function
Catenary
Compound interest
De Moivre's formula
Derivative of the exponential map
Doléans-Dade exponential
Doubling time
e-folding
Elimination half-life
Error exponent
Euler's formula
Euler's identity
e (mathematical constant)
Exponent
Exponent bias
Exponential (disambiguation)
Exponential backoff
Exponential decay
Exponential dichotomy
Exponential discounting
Exponential diophantine equation
Exponential dispersion model
Exponential distribution
Exponential error
Exponential factorial
Exponential family
Exponential field
Exponential formula
Exponential function
Exponential generating function
Exponential-Golomb coding
Exponential growth
Exponential hierarchy
Exponential integral
Exponential integrator
Exponential map (Lie theory)
Exponential map (Riemannian geometry)
Exponential map (discrete dynamical systems)
Exponential notation
Exponential object (category theory)
Exponential polynomials—see also Touchard polynomials (combinatorics)
Exponential response formula
Exponential sheaf sequence
Exponential smoothing
Exponential stability
Exponential sum
Exponential time
Sub-exponential time
Exponential tree
Exponential type
Exponentially equivalent measures
Exponentiating by squaring
Exponentiation
Fermat's Last Theorem
Forgetting curve
Gaussian function
Gudermannian function
Half-exponential function
Half-life
Hyperbolic function
Inflation, inflation rate
Interest
Lambert W function
Lifetime (physics)
Limiting factor
Lindemann–Weierstrass theorem |
https://en.wikipedia.org/wiki/Blinding%20%28cryptography%29 | In cryptography, blinding is a technique by which an agent can provide a service to (i.e., compute a function for) a client in an encoded form without knowing either the real input or the real output. Blinding techniques also have applications to preventing side-channel attacks on encryption devices.
More precisely, Alice has an input x and Oscar has a function f. Alice would like Oscar to compute for her without revealing either x or y to him. The reason for her wanting this might be that she doesn't know the function f or that she does not have the resources to compute it.
Alice "blinds" the message by encoding it into some other input E(x); the encoding E must be a bijection on the input space of f, ideally a random permutation. Oscar gives her f(E(x)), to which she applies a decoding D to obtain .
Not all functions allow for blind computation. At other times, blinding must be applied with care. An example of the latter is Rabin–Williams signatures. If blinding is applied to the formatted message but the random value does not honor Jacobi requirements on p and q, then it could lead to private key recovery. A demonstration of the recovery can be seen in discovered by Evgeny Sidorov.
The most common application of blinding is the blind signature. In a blind signature protocol, the signer digitally signs a message without being able to learn its content.
The one-time pad (OTP) is an application of blinding to the secure communication problem, by its very nature. Alice would like to send a message to Bob secretly, however all of their communication can be read by Oscar. Therefore, Alice sends the message after blinding it with a secret key or OTP that she shares with Bob. Bob reverses the blinding after receiving the message. In this example, the function
f is the identity and E and D are both typically the XOR operation.
Blinding can also be used to prevent certain side-channel attacks on asymmetric encryption schemes. Side-channel attacks allow an advers |
https://en.wikipedia.org/wiki/Backhoe%20loader | A backhoe loader, also called a loader backhoe, loader excavator, tractor excavator, digger or colloquially shortened to backhoe within the industry, is a heavy equipment vehicle that consists of a tractor-like unit fitted with a loader-style shovel/bucket on the front and a backhoe on the back. Due to its (relatively) small size and versatility, backhoe loaders are very common in urban engineering and small construction projects (such as building a small house, fixing urban roads, etc.) as well as developing countries. This type of machine is similar to and derived from what is now known as a TLB (Tractor-Loader-Backhoe), which is to say, an agricultural tractor fitted with a front loader and rear backhoe attachment.
The true development of the backhoe actually began in 1947 by the inventors that started the Wain-Roy Corporation of Hubbardston, Massachusetts. In 1947 Wain-Roy Corporation developed and tested the first actual backhoes. In April 1948 Wain-Roy Corporation sold the first all-hydraulic backhoes, mounted to a Ford Model 8N tractor, to the Connecticut Light and Power Company for $705.
History
Evolving in parallel to development in the U.S., backhoes were first produced in the UK in 1953 by JCB, but it was just a prototype. The world's first backhoe loader with factory warranty was introduced in the U.S. by J.I. Case in 1957. Their Model 320 was the world's first serial backhoe loader. Although based on a tractor, a backhoe loader was and is almost never called a tractor when both the loader and the backhoe are permanently attached. Backhoe loaders are also not generally used for towing and usually do not have a power take-off (PTO) as often this is used to drive the hydraulic pump operating the attachments. When the backhoe is permanently attached, the machine usually has a seat that can swivel to the rear to face the hoe controls. Removable backhoe attachments almost always have a separate seat on the attachment itself.
In Britain and Ireland they ar |
https://en.wikipedia.org/wiki/Homological%20conjectures%20in%20commutative%20algebra | In mathematics, homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of interrelated (sometimes surprisingly so) conjectures relating various homological properties of a commutative ring to its internal ring structure, particularly its Krull dimension and depth.
The following list given by Melvin Hochster is considered definitive for this area. In the sequel, , and refer to Noetherian commutative rings; will be a local ring with maximal ideal , and and are finitely generated -modules.
The Zero Divisor Theorem. If has finite projective dimension and is not a zero divisor on , then is not a zero divisor on .
Bass's Question. If has a finite injective resolution then is a Cohen–Macaulay ring.
The Intersection Theorem. If has finite length, then the Krull dimension of N (i.e., the dimension of R modulo the annihilator of N) is at most the projective dimension of M.
The New Intersection Theorem. Let denote a finite complex of free R-modules such that has finite length but is not 0. Then the (Krull dimension) .
The Improved New Intersection Conjecture. Let denote a finite complex of free R-modules such that has finite length for and has a minimal generator that is killed by a power of the maximal ideal of R. Then .
The Direct Summand Conjecture. If is a module-finite ring extension with R regular (here, R need not be local but the problem reduces at once to the local case), then R is a direct summand of S as an R-module. The conjecture was proven by Yves André using a theory of perfectoid spaces.
The Canonical Element Conjecture. Let be a system of parameters for R, let be a free R-resolution of the residue field of R with , and let denote the Koszul complex of R with respect to . Lift the identity map to a map of complexes. Then no matter what the choice of system of parameters or lifting, the last map from is not 0.
Existence of Balanced Big Cohen–Macaulay Modul |
https://en.wikipedia.org/wiki/Basel%20problem | The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty-eight. Euler generalised the problem considerably, and his ideas were taken up more than a century later by Bernhard Riemann in his seminal 1859 paper "On the Number of Primes Less Than a Given Magnitude", in which he defined his zeta function and proved its basic properties. The problem is named after Basel, hometown of Euler as well as of the Bernoulli family who unsuccessfully attacked the problem.
The Basel problem asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite series:
The sum of the series is approximately equal to 1.644934. The Basel problem asks for the exact sum of this series (in closed form), as well as a proof that this sum is correct. Euler found the exact sum to be and announced this discovery in 1735. His arguments were based on manipulations that were not justified at the time, although he was later proven correct. He produced an accepted proof in 1741.
The solution to this problem can be used to estimate the probability that two large random numbers are coprime. Two random integers in the range from 1 to , in the limit as goes to infinity, are relatively prime with a probability that approaches , the reciprocal of the solution to the Basel problem.
Euler's approach
Euler's original derivation of the value essentially extended observations about finite polynomials and assumed that these same properties hold true for infinite series.
Of course, Euler's original reasoning requires justification (100 years later, Karl Weierstrass proved |
https://en.wikipedia.org/wiki/121%20%28number%29 | 121 (one hundred [and] twenty-one) is the natural number following 120 and preceding 122.
In mathematics
One hundred [and] twenty-one is
a square (11 times 11)
the sum of the powers of 3 from 0 to 4, so a repunit in ternary. Furthermore, 121 is the only square of the form , where p is prime (3, in this case).
the sum of three consecutive prime numbers (37 + 41 + 43).
As , it provides a solution to Brocard's problem. There are only two other squares known to be of the form . Another example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form (with being 2 and 5, respectively).
It is also a star number, a centered tetrahedral number, and a centered octagonal number.
In decimal, it is a Smith number since its digits add up to the same value as its factorization (which uses the same digits) and as a consequence of that it is a Friedman number (). But it cannot be expressed as the sum of any other number plus that number's digits, making 121 a self number.
In other fields
121 is also:
The electricity emergency telephone number in Egypt
The number for voicemail for mobile phones on the Vodafone network
The undiscovered chemical element unbiunium has the atomic number 121
The official end score for cribbage
The pennant number of RTS Moskva, the Russian Navy’s Black Sea flagship, which was damaged beyond repair on April 13, 2022.
See also
List of highways numbered 121
United States House of Representatives House Resolution 121
United Nations Security Council Resolution 121
References
Integers |
https://en.wikipedia.org/wiki/2000%20%28number%29 | 2000 (two thousand) is a natural number following 1999 and preceding 2001.
It is:
the highest number expressible using only two unmodified characters in Roman numerals (MM)
an Achilles number
smallest four digit eban number
Selected numbers in the range 2001–2999
2001 to 2099
2001 – sphenic number
2002 – palindromic number
2003 – Sophie Germain prime and the smallest prime number in the 2000s
2004 – Area of the 24th crystagon
2005 – A vertically symmetric number
2006 – number of subsets of {1,2,3,4,5,6,7,8,9,10,11} with relatively prime elements
2007 – 22007 + 20072 is prime
2008 – number of 4 X 4 matrices with nonnegative integer entries and row and column sums equal to 3
2009 = 74 − 73 − 72
2010 – number of compositions of 12 into relatively prime parts
2011 – sexy prime with 2017, sum of eleven consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211
2012 – The number 8 × 102012 − 1 is a prime number
2013 – number of widely totally strongly normal compositions of 17
2014 – 5 × 22014 - 1 is prime
2015 – Lucas–Carmichael number
2016 – triangular number, number of 5-cubes in a 9-cube, Erdős–Nicolas number, 211-25.
2017 – Mertens function zero, sexy prime with 2011
2018 – Number of partitions of 60 into prime parts
2019 – smallest number that can be represented as the sum of 3 prime squares 6 different ways: 2019 = 72 + 112 + 432 = 72 + 172 + 412 = 132 + 132 + 412 = 112 + 232 + 372 = 172 + 192 + 372 = 232 + 232 + 312.
2020 – sum of the totient function for the first 81 integers
2021 = 43 * 47, consecutive prime numbers, next is 2491
2022 – non-isomorphic colorings of a toroidal 3 × 3 grid using exactly three colors under translational symmetry, beginning of a run of 4 consecutive Niven numbers
2023 = 7 * 17 * 17 – multiple of 7 with digit sum equal to 7, sum of squares of digits equals 17
2024 – tetrahedral number
2025 = 452, sum of the cubes of the first nine integers, centered octagonal number
2027 – s |
https://en.wikipedia.org/wiki/VLC%20media%20player | VLC media player (previously the VideoLAN Client and commonly known as simply VLC) is a free and open-source, portable, cross-platform media player software and streaming media server developed by the VideoLAN project. VLC is available for desktop operating systems and mobile platforms, such as Android, iOS and iPadOS. VLC is also available on digital distribution platforms such as Apple's App Store, Google Play, and Microsoft Store.
VLC supports many audio- and video-compression-methods and file-formats, including DVD-Video, Video CD, and streaming-protocols. It is able to stream media over computer networks and can transcode multimedia files.
The default distribution of VLC includes many free decoding and encoding libraries, avoiding the need for finding/calibrating proprietary plugins. The libavcodec library from the FFmpeg project provides many of VLC's codecs, but the player mainly uses its own muxers and demuxers. It also has its own protocol implementations. It also gained distinction as the first player to support playback of encrypted DVDs on Linux and macOS by using the libdvdcss DVD decryption library; however, this library is legally controversial and is not included in many software repositories of Linux distributions as a result. It is available on iOS under the MPLv2.
History
The VideoLAN software originated as a French academic project in 1996. VLC used to stand for "VideoLAN Client" when VLC was a client of the VideoLAN project. Since VLC is no longer merely a client, that initialism no longer applies. It was intended to consist of a client and server to stream videos from satellite dishes across a campus network. Originally developed by students at the École Centrale Paris, it is now developed by contributors worldwide and is coordinated by VideoLAN, a non-profit organization. Rewritten from scratch in 1998, it was released under GNU General Public License on February 1, 2001, with authorization from the headmaster of the École Centrale Paris. T |
https://en.wikipedia.org/wiki/Contra%20%28video%20game%29 | is a run and gun video game developed and published by Konami, originally developed as a coin-operated arcade video game in 1986 and released on February 20, 1987. A home version was released for the Nintendo Entertainment System in 1988, along with ports for various home computer formats, including the MSX2. The arcade and computer versions were localized as Gryzor in Europe, and the NES version as Probotector in PAL regions.
The arcade game was a commercial success worldwide, becoming one of the top four highest-grossing dedicated arcade games of 1987 in the United States. The NES version was also a critical and commercial success, with Electronic Gaming Monthly awarding it for being the Best Action Game of 1988. Several Contra sequels were produced following the original game.
Gameplay
Contra employs a variety of playing perspectives, which include a standard side view, a pseudo-3D view (in which the player proceeds by shooting and moving towards the background, in addition to left or right) and a fixed screen format (in which the player has their gun aimed upwards by default). Up to two people can play simultaneously, with one player as Bill (the blond-haired commando wearing a white tank top and blue bandana), and the other player as Lance (the shirtless dark-haired commando with a red bandana). The controls consists of an eight-way joystick and two action buttons for shooting (left) and jumping (right). When one of the protagonists jumps, he curls into a somersault instead of doing a conventional jump like in other games. The joystick controls not only the player's movement while running and jumping, but also his aiming. During side view stages, the player can shoot leftward, rightward or upward while standing, as well as horizontally and diagonally while running. The player can also shoot in any of eight directions, including downwards, while jumping. Pressing the joystick downwards while standing will cause the character to lie down on his stomach, allowi |
https://en.wikipedia.org/wiki/Glossary%20of%20Riemannian%20and%20metric%20geometry | This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology.
The following articles may also be useful; they either contain specialised vocabulary or provide more detailed expositions of the definitions given below.
Connection
Curvature
Metric space
Riemannian manifold
See also:
Glossary of general topology
Glossary of differential geometry and topology
List of differential geometry topics
Unless stated otherwise, letters X, Y, Z below denote metric spaces, M, N denote Riemannian manifolds, |xy| or denotes the distance between points x and y in X. Italic word denotes a self-reference to this glossary.
A caveat: many terms in Riemannian and metric geometry, such as convex function, convex set and others, do not have exactly the same meaning as in general mathematical usage.
A
Alexandrov space a generalization of Riemannian manifolds with upper, lower or integral curvature bounds (the last one works only in dimension 2)
Almost flat manifold
Arc-wise isometry the same as path isometry.
Autoparallel the same as totally geodesic
B
Barycenter, see center of mass.
bi-Lipschitz map. A map is called bi-Lipschitz if there are positive constants c and C such that for any x and y in X
Busemann function given a ray, γ : [0, ∞)→X, the Busemann function is defined by
C
Cartan–Hadamard theorem is the statement that a connected, simply connected complete Riemannian manifold with non-positive sectional curvature is diffeomorphic to Rn via the exponential map; for metric spaces, the statement that a connected, simply connected complete geodesic metric space with non-positive curvature in the sense of Alexandrov is a (globally) CAT(0) space.
Cartan extended Einstein's General relativity to Einstein–Cartan theory, using Riemannian-Cartan geometry instead of Riemannian geometry. This extension provides affine torsion, which allows for non-symmetric curvature tensors and the inco |
https://en.wikipedia.org/wiki/Field%20%28computer%20science%29 | In computer science, data that has several parts, known as a record, can be divided into fields (data fields). Relational databases arrange data as sets of database records, so called rows. Each record consists of several fields; the fields of all records form the columns.
Examples of fields: name, gender, hair colour.
In object-oriented programming, a field (also called data member or member variable) is a particular piece of data encapsulated within a class or object. In the case of a regular field (also called instance variable), for each instance of the object there is an instance variable: for example, an Employee class has a Name field and there is one distinct name per employee. A static field (also called class variable) is one variable, which is shared by all instances. Fields are abstracted by properties, which allow them to be read and written as if they were fields, but these can be translated to getter and setter method calls.
Fixed length
Fields that contain a fixed number of bits are known as fixed length fields. A four byte field for example may contain a 31 bit binary integer plus a sign bit (32 bits in all). A 30 byte name field may contain a person's name typically padded with blanks at the end.
The disadvantage of using fixed length fields is that some part of the field may be wasted but space is still required for the maximum length case. Also, where fields are omitted, padding for the missing fields is still required to maintain fixed start positions within a record for instance.
Variable length
A variable length field is not always the same physical size.
Such fields are nearly always used for text fields that can be large, or fields that vary greatly
in length. For example, a bibliographical database like PubMed has many small fields such
as publication date and author name, but also has abstracts, which vary greatly in length.
Reserving a fixed-length field of some length would be inefficient because it would enforce a
maximum length o |
https://en.wikipedia.org/wiki/Weyl%20algebra | In abstract algebra, the Weyl algebra is the ring of differential operators with polynomial coefficients (in one variable), namely expressions of the form
More precisely, let F be the underlying field, and let F[X] be the ring of polynomials in one variable, X, with coefficients in F. Then each fi lies in F[X].
∂X is the derivative with respect to X. The algebra is generated by X and ∂X.
The Weyl algebra is an example of a simple ring that is not a matrix ring over a division ring. It is also a noncommutative example of a domain, and an example of an Ore extension.
The Weyl algebra is isomorphic to the quotient of the free algebra on two generators, X and Y, by the ideal generated by the element
The Weyl algebra is the first in an infinite family of algebras, also known as Weyl algebras. The n-th Weyl algebra, An, is the ring of differential operators with polynomial coefficients in n variables. It is generated by Xi and ∂Xi, .
Weyl algebras are named after Hermann Weyl, who introduced them to study the Heisenberg uncertainty principle in quantum mechanics. It is a quotient of the universal enveloping algebra of the Heisenberg algebra, the Lie algebra of the Heisenberg group, by setting the central element of the Heisenberg algebra (namely [X,Y]) equal to the unit of the universal enveloping algebra (called 1 above).
The Weyl algebra is also referred to as the symplectic Clifford algebra. Weyl algebras represent the same structure for symplectic bilinear forms that Clifford algebras represent for non-degenerate symmetric bilinear forms.
Generators and relations
One may give an abstract construction of the algebras An in terms of generators and relations. Start with an abstract vector space V (of dimension 2n) equipped with a symplectic form ω. Define the Weyl algebra W(V) to be
where T(V) is the tensor algebra on V, and the notation means "the ideal generated by".
In other words, W(V) is the algebra generated by V subject only to the relation . Th |
https://en.wikipedia.org/wiki/Variational%20principle | In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those functions. For example, the problem of determining the shape of a hanging chain suspended at both ends—a catenary—can be solved using variational calculus, and in this case, the variational principle is the following: The solution is a function that minimizes the gravitational potential energy of the chain.
Overview
Any physical law which can be expressed as a variational principle describes a self-adjoint operator. These expressions are also called Hermitian. Such an expression describes an invariant under a Hermitian transformation.
History
Felix Klein's Erlangen program attempted to identify such invariants under a group of transformations. In what is referred to in physics as Noether's theorem, the Poincaré group of transformations (what is now called a gauge group) for general relativity defines symmetries under a group of transformations which depend on a variational principle, or action principle.
Examples
In mathematics
The Rayleigh–Ritz method for solving boundary-value problems approximately
Ekeland's variational principle in mathematical optimization
The finite element method
The variation principle relating topological entropy and Kolmogorov-Sinai entropy.
In physics
Fermat's principle in geometrical optics
Maupertuis' principle in classical mechanics
The principle of least action in mechanics, electromagnetic theory, and quantum mechanics
The variational method in quantum mechanics
Gauss's principle of least constraint and Hertz's principle of least curvature
Hilbert's action principle in general relativity, leading to the Einstein field equations.
Palatini variation
Gibbons–Hawking–York boundary term
References
External links
The Feynman Lectures on Physics Vol. II Ch. 19: The Principle of Least |
https://en.wikipedia.org/wiki/Electrowetting | Electrowetting is the modification of the wetting properties of a surface (which is typically hydrophobic) with an applied electric field.
History
The electrowetting of mercury and other liquids on variably charged surfaces was probably first explained by Gabriel Lippmann in 1875 and was certainly observed much earlier. A. N. Frumkin used surface charge to change the shape of water drops in 1936. The term electrowetting was first introduced in 1981 by G. Beni and S. Hackwood to describe an effect proposed for designing a new type of display device for which they received a patent. The use of a "fluid transistor" in microfluidic circuits for manipulating chemical and biological fluids was first investigated by J. Brown in 1980 and later funded in 1984–1988 under NSF Grants 8760730 & 8822197, employing insulating dielectric and hydrophobic layer(s) (EWOD), immiscible fluids, DC or RF power; and mass arrays of miniature interleaved (saw tooth) electrodes with large or matching indium tin oxide (ITO) electrodes to digitally relocate nano droplets in linear, circular, and directed paths, pump or mix fluids, fill reservoirs, and control fluid flow electronically or optically. Later, in collaboration with J. Silver at the NIH, EWOD-based electrowetting was disclosed for single and immiscible fluids to move, separate, hold, and seal arrays of digital PCR sub-samples.
Electrowetting using an insulating layer on top of a bare electrode was later studied by Bruno Berge in 1993. Electrowetting on this dielectric-coated surface is called electrowetting-on-dielectric (EWOD) to distinguish it from the conventional electrowetting on the bare electrode. Electrowetting can be demonstrated by replacing the metal electrode in the EWOD system by a semiconductor. Electrowetting is also observed when a reverse bias is applied to a conducting droplet (e.g. mercury) which has been placed directly onto a semiconductor surface (e.g. silicon) to form a Schottky contact in a Schottky diode el |
https://en.wikipedia.org/wiki/Unit%20fraction | A unit fraction is a positive fraction with one as its numerator, 1/. 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. When an object is divided into equal parts, each part is a unit fraction of the whole.
Multiplying two unit fractions produces another unit fraction, but other arithmetic operations do not preserve unit fractions. In modular arithmetic, unit fractions can be converted into equivalent whole numbers, allowing modular division to be transformed into multiplication. Every rational number can be represented as a sum of distinct unit fractions; these representations are called Egyptian fractions based on their use in ancient Egyptian mathematics. Many infinite sums of unit fractions are meaningful mathematically.
In geometry, unit fractions can be used to characterize the curvature of triangle groups and the tangencies of Ford circles. Unit fractions are commonly used in fair division, and this familiar application is used in mathematics education as an early step toward the understanding of other fractions. Unit fractions are common in probability theory due to the principle of indifference. They also have applications in combinatorial optimization and in analyzing the pattern of frequencies in the hydrogen spectral series.
Arithmetic
The unit fractions are the rational numbers that can be written in the form where can be any positive natural number. They are thus the multiplicative inverses of the positive integers. When something is divided into equal parts, each part is a fraction of the whole.
Elementary arithmetic
Multiplying any two unit fractions results in a product that is another unit fraction:
However, adding, subtracting, or dividing two unit fractions produces a result that is generally not a unit fraction:
As the last of these formulas shows, every fraction can be expressed as a quotient of two unit fractions.
Modu |
https://en.wikipedia.org/wiki/UltraSPARC | The UltraSPARC is a microprocessor developed by Sun Microsystems and fabricated by Texas Instruments, introduced in mid-1995. It is the first microprocessor from Sun to implement the 64-bit SPARC V9 instruction set architecture (ISA). Marc Tremblay was a co-microarchitect.
Microarchitecture
The UltraSPARC is a four-issue superscalar microprocessor that executes instructions in in-order. It includes a nine-stage integer pipeline.
Functional units
The execution units were simplified relative to the SuperSPARC to achieve higher clock frequencies - an example of a simplification is that the ALUs were not cascaded, unlike the SuperSPARC, to avoid restricting clock frequency.
The integer register file has 32 64-bit entries. As the SPARC ISA uses register windows, of which the UltraSPARC has eight, the actual number of registers is 144. The register file has seven read and three write ports. The integer register file provides registers to two arithmetic logic units and the load/store unit. The two ALUs can both execute arithmetic, logic and shift instructions but only one can execute multiply and divide instructions.
The floating-point unit consists of five functional units. One executes floating point adds and subtracts, one multiplies, one divides and square-roots. Two units are for executing SIMD instructions defined by the Visual Instruction Set (VIS). The floating-point register file contains thirty-two 64-bit registers. It has five read ports and three write ports.
Cache
The UltraSPARC has two levels of cache, primary and secondary. There are two primary caches, one for instructions and one for data. Both have a capacity of 16 KB.
The UltraSPARC required a mandatory external secondary cache. The cache is unified, has a capacity of 512 KB to 4 MB and is direct-mapped. It can return data in a single cycle. The external cache is implemented with synchronous SRAMs clocked at the same frequency as the microprocessor, as ratios were not supported. It is accesse |
https://en.wikipedia.org/wiki/Heavy%20equipment | Heavy equipment, heavy machinery, earthmovers, construction vehicles, or construction equipment, refers to heavy-duty vehicles specially designed to execute construction tasks, most frequently involving earthwork operations or other large construction tasks. Heavy equipment usually comprises five equipment systems: the implement, traction, structure, power train, and control/information.
Heavy equipment has been used since at least the 1st century BC when the ancient Roman engineer Vitruvius described a crane in De architectura when it was powered via human or animal labor.
Heavy equipment functions through the mechanical advantage of a simple machine, the ratio between input force applied and force exerted is multiplied, making tasks which could take hundreds of people and weeks of labor without heavy equipment far less intensive in nature. Some equipment uses hydraulic drives as a primary source of motion.
The word plant, in this context, has come to mean any type of industrial equipment, including mobile equipment (e.g. in the same sense as powerplant). However, plant originally meant "structure" or "establishment" – usually in the sense of factory or warehouse premises; as such, it was used in contradistinction to movable machinery, e.g. often in the phrase "plant and equipment".
History
The use of heavy equipment has a long history; the ancient Roman engineer Vitruvius (1st century BCE) gave descriptions of heavy equipment and cranes in ancient Rome in his treatise De architectura. The pile driver was invented around 1500. The first tunnelling shield was patented by Marc Isambard Brunel in 1818.
From horses, through steam and diesel, to electric and robotic
Until the 19th century and into the early 20th century heavy machines were drawn under human or animal power. With the advent of portable steam-powered engines the drawn machine precursors were reconfigured with the new engines, such as the combine harvester. The design of a core tractor evolved arou |
https://en.wikipedia.org/wiki/Awareness | In philosophy and psychology, awareness is a concept about knowing, perceiving and being cognizant of events. Another definition describes it as a state wherein a subject is aware of some information when that information is directly available to bring to bear in the direction of a wide range of behavioral actions. The concept is often synonymous to consciousness and is also understood as being consciousness itself.
The states of awareness are also associated with the states of experience so that the structure represented in awareness is mirrored in the structure of experience.
Concept
Awareness is a relative concept. It may be focused on an internal state, such as a visceral feeling, or on external events by way of sensory perception. It is analogous to sensing something, a process distinguished from observing and perceiving (which involves a basic process of acquainting with the items we perceive). Awareness or "to sense" can be described as something that occurs when the brain is activated in certain ways, such as when the color red is what is seen once the retina is stimulated by light waves. This conceptualization is posited amid the difficulty in developing an analytic definition of awareness or sensory awareness.
Awareness is also associated with consciousness in the sense that this concept denotes a fundamental experience such as a feeling or intuition that accompanies the experience of phenomena. Specifically, this is referred to as awareness of experience. As for consciousness, it has been postulated to undergo continuously changing levels.
Peripheral awareness
Peripheral awareness refers to the human ability to process information at the periphery of attention, such as acknowledging distant sounds of people outside while siting indoors and concentrating on a specific task such as reading. Peripheral vision is defined as the perception of visual stimuli at or near the edge of the field of vision and the capacity to perceive such stimuli. Peripheral aw |
https://en.wikipedia.org/wiki/Lewy%20body | Lewy bodies are the inclusion bodies – abnormal aggregations of protein – that develop inside nerve cells affected by Parkinson's disease (PD), the Lewy body dementias (Parkinson's disease dementia and dementia with Lewy bodies (DLB)), and some other disorders. They are also seen in cases of multiple system atrophy, particularly the parkinsonian variant (MSA-P).
Lewy bodies appear as spherical masses in the cytoplasm that displace other cell components. For instance, some Lewy bodies tend to displace the nucleus to one side of the cell. There are two main kinds of Lewy bodies: classical and cortical. Lewy bodies may be found in the midbrain (within the substantia nigra) or within the cortex. A classical Lewy body is an eosinophilic cytoplasmic inclusion consisting of a dense core surrounded by a halo of 10 nm wide radiating fibrils, the primary structural component of which is alpha-synuclein.
History
In 1910, Fritz Heinrich Lewy was studying in Berlin for his doctorate. He was the first doctor to notice some unusual proteins in the brain, comparing them to earlier findings by Gonzalo Rodríguez Lafora. In 1913, Lafora described another case, and acknowledged Lewy as the discoverer, naming them cuerpos intracelulares de Lewy (intracellular Lewy bodies). Konstantin Nikolaevich Trétiakoff found them in 1919 in the substantia nigra of PD brains, called them corps de Lewy and is credited with the eponym. In 1923, Lewy published his findings in a book, The Study on Muscle Tone and Movement. Including Systematic Investigations on the Clinic, Physiology, Pathology, and Pathogenesis of Paralysis agitans. Eliasz Engelhardt, who is in the neurology department at Federal University of Rio de Janeiro, argued in 2017 that Lafora should be credited with the eponym, because he named them six years before Trétiakoff. Nonetheless, Trétiakoff is still the primary figure acknowledged for coining the term, “Lewy bodies.”
According to the Journal of the History of the Neurosciences, |
https://en.wikipedia.org/wiki/Thue%E2%80%93Morse%20sequence | In mathematics, the Thue–Morse sequence or Prouhet–Thue–Morse sequence or parity sequence is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far. The first few steps of this procedure yield the strings 0 then 01, 0110, 01101001, 0110100110010110, and so on, which are prefixes of the Thue–Morse sequence. The full sequence begins:
01101001100101101001011001101001....
The sequence is named after Axel Thue and Marston Morse.
Definition
There are several equivalent ways of defining the Thue–Morse sequence.
Direct definition
To compute the nth element tn, write the number n in binary. If the number of ones in this binary expansion is odd then tn = 1, if even then tn = 0. That is, tn is the even parity bit for n. John H. Conway et al. called numbers n satisfying tn = 1 odious (for odd) numbers and numbers for which tn = 0 evil (for even) numbers. In other words, tn = 0 if n is an evil number and tn = 1 if n is an odious number.
Fast sequence generation
This method leads to a fast method for computing the Thue–Morse sequence: start with , and then, for each n, find the highest-order bit in the binary representation of n that is different from the same bit in the representation of . If this bit is at an even index, tn differs from , and otherwise it is the same as .
In pseudo-code form:
def generate_sequence(seq_length: int):
"""Thue–Morse sequence."""
value = 0
for n = 0 to seq_length-1 by 1:
# Note: assumes an even number of bits in the word size, and two's complement arithmetic so that when n == 0, x is odd (e.g. 31 or 63)
x = index_of_highest_one_bit(n ^ (n - 1))
if ((x & 1) == 0):
# bit index is even, so toggle value
value = 1 - value
yield value
The resulting algorithm takes constant time to generate each sequence element, using only a logarithmic nu |
https://en.wikipedia.org/wiki/Respiration%20%28physiology%29 | In physiology, respiration is the movement of oxygen from the outside environment to the cells within tissues, and the removal of carbon dioxide in the opposite direction that's to the environment.
The physiological definition of respiration differs from the biochemical definition, which refers to a metabolic process by which an organism obtains energy (in the form of ATP and NADPH) by oxidizing nutrients and releasing waste products. Although physiologic respiration is necessary to sustain cellular respiration and thus life in animals, the processes are distinct: cellular respiration takes place in individual cells of the organism, while physiologic respiration concerns the diffusion and transport of metabolites between the organism and the external environment.
Gas exchanges in the lung occurs by ventilation and perfusion. Ventilation refers to the in and out movement of air of the lungs and perfusion is the circulation of blood in the pulmonary capillaries. In mammals, physiological respiration involves respiratory cycles of inhaled and exhaled breaths. Inhalation (breathing in) is usually an active movement that brings air into the lungs where the process of gas exchange takes place between the air in the alveoli and the blood in the pulmonary capillaries. Contraction of the diaphragm muscle cause a pressure variation, which is equal to the pressures caused by elastic, resistive and inertial components of the respiratory system. In contrast, exhalation (breathing out) is usually a passive process, though there are many exceptions: when generating functional overpressure (speaking, singing, humming, laughing, blowing, snorting, sneezing, coughing, powerlifting); when exhaling underwater (swimming, diving); at high levels of physiological exertion (running, climbing, throwing) where more rapid gas exchange is necessitated; or in some forms of breath-controlled meditation. Speaking and singing in humans requires sustained breath control that many mammals are not |
https://en.wikipedia.org/wiki/Cat%27s%20cradle | Cat's cradle is a game involving the creation of various string figures between the fingers, either individually or by passing a loop of string back and forth between two or more players. The true origin of the name is debated, though the first known reference is in The light of nature pursued by Abraham Tucker in 1768. The type of string, the specific figures, their order, and the names of the figures vary. Independent versions of this game have been found in indigenous cultures throughout the world, including in Africa, Eastern Asia, the Pacific Islands, Australia, the Americas, and the Arctic.
Play
The simplest version of the game involves a player using a long string loop to make a complex figure using their fingers and hands.
Another version of the game consists of two or more players making a sequence of string figures, each altering the figure made by the previous player. The game begins with one player making the eponymous figure Cat's Cradle (above). After each figure, the next player manipulates that figure and removes the string figure from the hands of the previous player with one of a few simple motions and tightens the loop to create another figure, for example, Diamonds. Diamonds might then lead to Candles (which is also known as Pinkies), for example, and then Manger—an inverted Cat's Cradle—and so on. Most of the core figures allow a choice between two or more subsequent figures: for example, Fish in a Dish can become Cat's Eye or Manger. The game ends when a player makes a mistake or creates a dead-end figure, which cannot be turned into anything else. Many players believe that Two Crowns or King's Crown is one such dead-end figure, although more experienced players recognize that it can be creatively maneuvered into Candles or Pinkies, which allows the game to continue.
History
The origin of the name "cat's cradle" is debated but the first known reference is in The light of nature pursued by Abraham Tucker in 1768. "An ingenious play they cal |
https://en.wikipedia.org/wiki/Video4Linux | Video4Linux (V4L for short) is a collection of device drivers and an API for supporting realtime video capture on Linux systems. It supports many USB webcams, TV tuners, and related devices, standardizing their output, so programmers can easily add video support to their applications.
Video4Linux is responsible for creating V4L2 device nodes aka a device file (/dev/videoX, /dev/vbiX and /dev/radioX) and tracking data from these nodes. The device node creation is handled by V4L device drivers using the video_device struct (v4l2-dev.h) and it can either be allocated dynamically or embedded in another larger struct.
Video4Linux was named after Video for Windows (which is sometimes abbreviated "V4W"), but is not technically related to it.
While Video4Linux is only available on Linux, there is a compatibility layer available for FreeBSD called Video4BSD. This provides a way for many programs that depend on V4L to also compile and run on the FreeBSD operating system.
History
V4L had been introduced late into the 2.1.X development cycle of the Linux kernel. V4L1 support was dropped in kernel 2.6.38.
V4L2 is the second version of V4L. Video4Linux2 fixed some design bugs and started appearing in the 2.5.x kernels. Video4Linux2 drivers include a compatibility mode for Video4Linux1 applications, though the support can be incomplete and it is recommended to use Video4Linux1 devices in V4L2 mode. The project DVB-Wiki is now hosted on LinuxTV web site.
Some programs support V4L2 through the media resource locator v4l2://.
Software support
aMSN
Cheese (software)
Cinelerra
CloudApp
Ekiga
FFmpeg
FreeJ
GStreamer
Guvcview
kdetv
Kopete
Libav
Linphone
LiVES
MPlayer
mpv
MythTV
Open Broadcaster Software
OpenCV
Peek
PyGame
Skype
Tvheadend
VLC media player
xawtv
Xine
ZoneMinder
Criticism
Video4Linux has a complex negotiation process, which caused not all applications having support for all cameras.
See also
Direct Rendering Manager – defines a kerne |
https://en.wikipedia.org/wiki/Monochord | A monochord, also known as sonometer (see below), is an ancient musical and scientific laboratory instrument, involving one (mono-) string (chord). The term monochord is sometimes used as the class-name for any musical stringed instrument having only one string and a stick shaped body, also known as musical bows. According to the Hornbostel–Sachs system, string bows are bar zithers (311.1) while monochords are traditionally board zithers (314). The "harmonical canon", or monochord is, at its least, "merely a string having a board under it of exactly the same length, upon which may be delineated the points at which the string must be stopped to give certain notes," allowing comparison.
A string is fixed at both ends and stretched over a sound box. One or more movable bridges are then manipulated to demonstrate mathematical relationships among the frequencies produced. "With its single string, movable bridge and graduated rule, the monochord (kanōn [Greek: law]) straddled the gap between notes and numbers, intervals and ratios, sense-perception and mathematical reason." However, "music, mathematics, and astronomy were [also] inexorably linked in the monochord." As a pedagogical tool for demonstrating mathematical relationships between intervals, the monochord remained in use throughout the Middle Ages.
Experimental use
The monochord can be used to illustrate the mathematical properties of musical pitch and to illustrate Mersenne's laws regarding string length and tension: "essentially a tool for measuring musical intervals". For example, when a monochord's string is open it vibrates at a particular frequency and produces a pitch. When the length of the string is halved, and plucked, it produces a pitch an octave higher and the string vibrates at twice the frequency of the original (2:1) . Half of this length will produce a pitch two octaves higher than the original—four times the initial frequency (4:1)—and so on. Standard diatonic Pythagorean tuning (Ptolemy's Di |
https://en.wikipedia.org/wiki/Smith%20chart | The Smith chart (sometimes also called Smith diagram, Mizuhashi chart (), Mizuhashi–Smith chart (), Volpert–Smith chart () or Mizuhashi–Volpert–Smith chart), is a graphical calculator or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits.
It was independently proposed by Tōsaku Mizuhashi () in 1937, and by () and Phillip H. Smith in 1939.
Starting with a rectangular diagram, Smith had developed a special polar coordinate chart by 1936, which, with the input of his colleagues Enoch B. Ferrell and James W. McRae, who were familiar with conformal mappings, was reworked into the final form in early 1937, which was eventually published in January 1939.
While Smith had originally called it a "transmission line chart" and other authors first used names like "reflection chart", "circle diagram of impedance", "immittance chart" or "Z-plane chart", early adopters at MIT's Radiation Laboratory started to refer to it simply as "Smith chart" in the 1940s, a name generally accepted in the Western world by 1950.
The Smith chart can be used to simultaneously display multiple parameters including impedances, admittances, reflection coefficients, scattering parameters, noise figure circles, constant gain contours and regions for unconditional stability, including mechanical vibrations analysis. The Smith chart is most frequently used at or within the unity radius region. However, the remainder is still mathematically relevant, being used, for example, in oscillator design and stability analysis.
While the use of paper Smith charts for solving the complex mathematics involved in matching problems has been largely replaced by software based methods, the Smith chart is still a very useful method of showing how RF parameters behave at one or more frequencies, an alternative to using tabular information.
Thus most RF circuit analysis software includes a |
https://en.wikipedia.org/wiki/Compass%20%28drawing%20tool%29 | A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses can be used for mathematics, drafting, navigation and other purposes.
Prior to computerization, compasses and other tools for manual drafting were often packaged as a set with interchangeable parts. By the mid-twentieth century, circle templates supplemented the use of compasses. Today those facilities are more often provided by computer-aided design programs, so the physical tools serve mainly a didactic purpose in teaching geometry, technical drawing, etc.
Construction and parts
Compasses are usually made of metal or plastic, and consist of two "legs" connected by a hinge which can be adjusted to allow changing of the radius of the circle drawn. Typically one leg has a spike at its end for anchoring, and the other leg holds a drawing tool, such as a pencil, a short length of just pencil lead or sometimes a pen.
Handle
The handle, a small knurled rod above the hinge, is usually about half an inch long. Users can grip it between their pointer finger and thumb.
Legs
There are two types of leg in a pair of compasses: the straight or the steady leg and the adjustable one. Each has a separate purpose; the steady leg serves as the basis or support for the needle point, while the adjustable leg can be altered in order to draw different sizes of circles.
Hinge
The screw through the hinge holds the two legs in position. The hinge can be adjusted, depending on desired stiffness; the tighter the hinge-screw, the more accurate the compass's performance. The better quality compass, made of plated metal, is able to be finely adjusted via a small, serrated wheel usually set between the legs (see the "using a compass" animation shown above) and it has a (dangerously powerful) spring encompassing the hinge. This sort of compass is often kno |
https://en.wikipedia.org/wiki/Passive%20matrix%20addressing | Passive matrix addressing is an addressing scheme used in early LCDs. This is a matrix addressing scheme meaning that only m + n control signals are required to address an m × n display. A pixel in a passive matrix must maintain its state without active driving circuitry until it can be refreshed again.
The signal is divided into a row or select signal and a column or video signal. The select voltage determines the row that is being addressed and all n pixels on a row are addressed simultaneously. When pixels on a row are being addressed, a Vsel potential is applied, and all other rows are unselected with a Vunsel potential. The video signal or column potential is then applied with a potential for each m columns individually. An on-switched (lit) pixel corresponds to a Von, an off-switched (unlit) corresponds to a Voff potential.
The potential across pixel at selected row i and column j is
and
for the unselected rows.
This scheme has been expanded to define the limits of this type of addressing typical LCDs.
Passive matrix addressed displays, such as Ferro Liquid Display, do not need the switch component of an active matrix display, because they have built-in bistability. Technology for electronic paper also has a form of bistability. Displays with bistable pixel elements are addressed with a passive matrix addressing scheme, whereas TFT LCD displays are addressed using active addressing.
See also
Active matrix addressing
Pixel geometry
Liquid crystal display
References
Digital imaging
Liquid crystal displays |
https://en.wikipedia.org/wiki/Inclusion%20map | In mathematics, if is a subset of then the inclusion map (also inclusion function, insertion, or canonical injection) is the function that sends each element of to treated as an element of
A "hooked arrow" () is sometimes used in place of the function arrow above to denote an inclusion map; thus:
(However, some authors use this hooked arrow for any embedding.)
This and other analogous injective functions from substructures are sometimes called natural injections.
Given any morphism between objects and , if there is an inclusion map into the domain , then one can form the restriction of In many instances, one can also construct a canonical inclusion into the codomain known as the range of
Applications of inclusion maps
Inclusion maps tend to be homomorphisms of algebraic structures; thus, such inclusion maps are embeddings. More precisely, given a substructure closed under some operations, the inclusion map will be an embedding for tautological reasons. For example, for some binary operation to require that
is simply to say that is consistently computed in the sub-structure and the large structure. The case of a unary operation is similar; but one should also look at nullary operations, which pick out a constant element. Here the point is that closure means such constants must already be given in the substructure.
Inclusion maps are seen in algebraic topology where if is a strong deformation retract of the inclusion map yields an isomorphism between all homotopy groups (that is, it is a homotopy equivalence).
Inclusion maps in geometry come in different kinds: for example embeddings of submanifolds. Contravariant objects (which is to say, objects that have pullbacks; these are called covariant in an older and unrelated terminology) such as differential forms restrict to submanifolds, giving a mapping in the other direction. Another example, more sophisticated, is that of affine schemes, for which the inclusions
and
may be different morphi |
https://en.wikipedia.org/wiki/Bimodule | In abstract algebra, a bimodule is an abelian group that is both a left and a right module, such that the left and right multiplications are compatible. Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in the sense that many of the relationships between left and right modules become simpler when they are expressed in terms of bimodules.
Definition
If R and S are two rings, then an R-S-bimodule is an abelian group such that:
M is a left R-module and a right S-module.
For all r in R, s in S and m in M:
An R-R-bimodule is also known as an R-bimodule.
Examples
For positive integers n and m, the set Mn,m(R) of matrices of real numbers is an R-S-bimodule, where R is the ring Mn(R) of matrices, and S is the ring Mm(R) of matrices. Addition and multiplication are carried out using the usual rules of matrix addition and matrix multiplication; the heights and widths of the matrices have been chosen so that multiplication is defined. Note that Mn,m(R) itself is not a ring (unless ), because multiplying an matrix by another matrix is not defined. The crucial bimodule property, that , is the statement that multiplication of matrices is associative (which, in the case of a matrix ring, corresponds to associativity).
Any algebra A over a ring R has the natural structure of an R-bimodule, with left and right multiplication defined by and respectively, where is the canonical embedding of R into A.
If R is a ring, then R itself can be considered to be an R-R-bimodule by taking the left and right actions to be multiplication—the actions commute by associativity. This can be extended to Rn (the n-fold direct product of R).
Any two-sided ideal of a ring R is an R-R-bimodule, with the ring multiplication both as the left and as the right multiplication.
Any module over a commutative ring R has the natural structure of a bimodule. For example, if M is a left module, we can define multiplication on the right to be the same |
https://en.wikipedia.org/wiki/Flat%20module | In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion free modules. Formally, a module M over a ring R is flat if taking the tensor product over R with M preserves exact sequences. A module is faithfully flat if taking the tensor product with a sequence produces an exact sequence if and only if the original sequence is exact.
Flatness was introduced by in his paper Géometrie Algébrique et Géométrie Analytique.
Definition
A left module over a ring is flat if the following condition is satisfied: for every injective linear map of right -modules, the map
is also injective, where is the map
induced by
For this definition, it is enough to restrict the injections to the inclusions of finitely generated ideals into .
Equivalently, an -module is flat if the tensor product with is an exact functor; that is if, for every short exact sequence of -modules the sequence is also exact. (This is an equivalent definition since the tensor product is a right exact functor.)
These definitions apply also if is a non-commutative ring, and is a left -module; in this case, , and must be right -modules, and the tensor products are not -modules in general, but only abelian groups.
Characterizations
Flatness can also be characterized by the following equational condition, which means that -linear relations in stem from linear relations in .
A left -module is flat if and only if, for every linear relation
with and , there exist elements and such that
for
and
for
It is equivalent to define elements of a module, and a linear map from to this module, which maps the standard basis of to the elements. This allows rewriting the previous characterization in terms of homomorphisms, as follows.
An -module is flat if and only if the following condition holds: for every map where is a finitely generated free -module, and for every finitely generated -submodule of the map factors through a m |
https://en.wikipedia.org/wiki/Index%20of%20logarithm%20articles | This is a list of logarithm topics, by Wikipedia page. See also the list of exponential topics.
Acoustic power
Antilogarithm
Apparent magnitude
Baker's theorem
Bel
Benford's law
Binary logarithm
Bode plot
Henry Briggs
Bygrave slide rule
Cologarithm
Common logarithm
Complex logarithm
Discrete logarithm
Discrete logarithm records
e
Representations of e
El Gamal discrete log cryptosystem
Harmonic series
History of logarithms
Hyperbolic sector
Iterated logarithm
Otis King
Law of the iterated logarithm
Linear form in logarithms
Linearithmic
List of integrals of logarithmic functions
Logarithmic growth
Logarithmic timeline
Log-likelihood ratio
Log-log graph
Log-normal distribution
Log-periodic antenna
Log-Weibull distribution
Logarithmic algorithm
Logarithmic convolution
Logarithmic decrement
Logarithmic derivative
Logarithmic differential
Logarithmic differentiation
Logarithmic distribution
Logarithmic form
Logarithmic graph paper
Logarithmic growth
Logarithmic identities
Logarithmic number system
Logarithmic scale
Logarithmic spiral
Logarithmic timeline
Logit
LogSumExp
Mantissa is a disambiguation page; see common logarithm for the traditional concept of mantissa; see significand for the modern concept used in computing.
Matrix logarithm
Mel scale
Mercator projection
Mercator series
Moment magnitude scale
John Napier
Napierian logarithm
Natural logarithm
Natural logarithm of 2
Neper
Offset logarithmic integral
pH
Pollard's kangaroo algorithm
Pollard's rho algorithm for logarithms
Polylogarithm
Polylogarithmic function
Prime number theorem
Richter magnitude scale
Grégoire de Saint-Vincent
Alphonse Antonio de Sarasa
Schnorr signature
Semi-log graph
Significand
Slide rule
Smearing retransformation
Sound intensity level
Super-logarithm
Table of logarithms
Weber-Fechner law
Exponentials
Logarithm topics |
https://en.wikipedia.org/wiki/10%2C000 | 10,000 (ten thousand) is the natural number following 9,999 and preceding 10,001.
Name
Many languages have a specific word for this number: in Ancient Greek it is (the etymological root of the word myriad in English), in Aramaic , in Hebrew [], in Chinese (Mandarin , Cantonese , Hokkien bān), in Japanese [], in Khmer [], in Korean [], in Russian [], in Vietnamese , in Sanskrit अयुत [ayuta], in Thai [], in Malayalam [], and in Malagasy alina. In many of these languages, it often denotes a very large but indefinite number.
The classical Greeks used letters of the Greek alphabet to represent Greek numerals: they used a capital letter mu (Μ) to represent ten thousand. This Greek root was used in early versions of the metric system in the form of the decimal prefix myria-.
The Number ten thousand can also be written as 10,000 (U.K. and U.S.), 10,000 (Central America and South America, as well as mainland Europe), 10,000 (transition metric), or 10,000 (with the dot raised to the middle of the zeroes; metric).
In mathematics
In scientific notation it is written as 104 or 1 E+4 (equivalently 1 E4) in E notation.
It is the square of 100 and the square root of 100,000,000.
The value of a myriad to the power of itself, 1000010000 = 1040000.
It has a total of 25 divisors, whose geometric mean averages a whole number, 100.
It has a reduced totient of 500, and a totient of 4,000, with a total of 16 integers having a totient value of 10,000.
There are a total of 1,229 prime numbers less than ten thousand, a count that is itself prime.
A myriagon is a polygon with ten thousand edges and a total of 25 dihedral symmetry groups when including the myriagon itself, alongside 25 cyclic groups as subgroups.
In science
In astronomy,
asteroid Number: 10000 Myriostos, Provisional Designation: , Discovery Date: September 30, 1951, by A. G. Wilson:List of asteroids (9001-10000).
In climate, Summary of 10000 Years is one of several pages of the Climate Timeline Tool |
https://en.wikipedia.org/wiki/Order%20%28group%20theory%29 | In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element of a group, is thus the smallest positive integer such that , where denotes the identity element of the group, and denotes the product of copies of . If no such exists, the order of is infinite.
The order of a group is denoted by or , and the order of an element is denoted by or , instead of where the brackets denote the generated group.
Lagrange's theorem states that for any subgroup of a finite group , the order of the subgroup divides the order of the group; that is, is a divisor of . In particular, the order of any element is a divisor of .
Example
The symmetric group S3 has the following multiplication table.
{| class="wikitable"
|-
! •
! e || s || t || u || v || w
|-
! e
| e || s || t || u || v || w
|-
! s
| s || e || v || w || t || u
|-
! t
| t || u || e || s || w || v
|-
! u
| u || t || w || v || e || s
|-
! v
| v || w || s || e || u || t
|-
! w
| w || v || u || t || s || e
|}
This group has six elements, so . By definition, the order of the identity, , is one, since . Each of , , and squares to , so these group elements have order two: . Finally, and have order 3, since , and .
Order and structure
The order of a group G and the orders of its elements give much information about the structure of the group. Roughly speaking, the more complicated the factorization of |G|, the more complicated the structure of G.
For |G| = 1, the group is trivial. In any group, only the identity element a = e has ord(a) = 1. If every non-identity element in G is equal to its inverse (so that a2 = e), then ord(a) = 2; this implies G is abelian since . The converse is not true; for example, the (additive) cyclic g |
https://en.wikipedia.org/wiki/ISO/IEC%202022 | ISO/IEC 2022 Information technology—Character code structure and extension techniques, is an ISO/IEC standard in the field of character encoding. It is equivalent to the ECMA standard ECMA-35, the ANSI standard ANSI X3.41 and the Japanese Industrial Standard JIS X 0202. Originating in 1971, it was most recently revised in 1994.
ISO 2022 specifies a general structure which character encodings can conform to, dedicating particular ranges of bytes (0x00–1F and 0x7F–9F) to be used for non-printing control codes for formatting and in-band instructions (such as line breaks or formatting instructions for text terminals), rather than graphical characters. It also specifies a syntax for escape sequences, multiple-byte sequences beginning with the control code, which can likewise be used for in-band instructions. Specific sets of control codes and escape sequences designed to be used with ISO 2022 include ISO/IEC 6429, portions of which are implemented by ANSI.SYS and terminal emulators.
ISO 2022 itself also defines particular control codes and escape sequences which can be used for switching between different coded character sets (for example, between ASCII and the Japanese JIS X 0208) so as to use multiple in a single document, effectively combining them into a single stateful encoding (a feature less important since the advent of Unicode). It is designed to be usable in both 8-bit environments and 7-bit environments (those where only seven bits are usable in a byte, such as e-mail without 8BITMIME).
Encodings and conformance
Writing systems with relatively few characters, such as Greek, Cyrillic, Arabic, or Hebrew, as well as forms of the Latin alphabet using diacritics or letters absent in the ISO Basic Latin alphabet, have historically been represented on computers with different 8-bit, single byte, extended ASCII encodings. Some of these, such as the ISO 8859 series, conform to ISO 2022, while others such as DOS code page 437 do not, usually due to not reserving the |
https://en.wikipedia.org/wiki/Cranial%20electrotherapy%20stimulation | Cranial electrotherapy stimulation (CES) is a form of neurostimulation that delivers a small, pulsed, alternating current via electrodes on the head. CES is used with the intention of treating a variety of conditions such as anxiety, depression and insomnia. CES has been suggested as a possible treatment for headaches, fibromyalgia, smoking cessation, and opiate withdrawal, but there is little evidence of effectiveness for many of these conditions and the evidence for use in acute depression is not sufficient to justify it.
Medical uses
A 2014 Cochrane review found insufficient evidence to determine whether or not CES with alternating current is safe and effective for treating depression. The FDA came to the same conclusion in December 2019.
A 2018 systematic review found that evidence is insufficient that CES has clinically important effects on fibromyalgia, headache, neuromusculoskeletal pain, degenerative joint pain, depression, or insomnia; low-strength evidence suggests modest benefit in patients with anxiety and depression.
Description
Electrodes are placed on the earlobes, maxilla-occipital junction, mastoid processes or temples.
Despite the long history of CES, its underlying principles and mechanisms are still not clear.
CES stimulation of 1 mA (milliampere) has shown to reach the thalamic area at a radius of 13.30 mm. CES has shown to induce changes in the electroencephalogram, increasing alpha relative power and decreasing relative power in delta and beta frequencies.
CES has also shown to reach cortical and subcortical areas of the brain, in electromagnetic tomography and functional MRI studies. CES treatments have been found to induce changes in neurohormones and neurotransmitters that have been implicated in psychiatric disorders: substantial increases in beta endorphins, adrenocorticotrophic hormone, and serotonin; moderate increases in melatonin and norepinephrine, modest or unquantified increases in cholinesterase, gamma-aminobutyric acid, and |
https://en.wikipedia.org/wiki/DEC%20PRISM | PRISM (Parallel Reduced Instruction Set Machine) was a 32-bit RISC instruction set architecture (ISA) developed by Digital Equipment Corporation (DEC). It was the outcome of a number of DEC research projects from the 1982–1985 time-frame, and the project was subject to continually changing requirements and planned uses that delayed its introduction. This process eventually decided to use the design for a new line of Unix workstations. The arithmetic logic unit (ALU) of the microPrism version had completed design in April 1988 and samples were fabricated, but the design of other components like the floating point unit (FPU) and memory management unit (MMU) were still not complete in the summer when DEC management decided to cancel the project in favor of MIPS-based systems. An operating system codenamed MICA was developed for the PRISM architecture, which would have served as a replacement for both VAX/VMS and ULTRIX on PRISM.
PRISM's cancellation had significant effects within DEC. Many of the team members left the company over the next year, notably Dave Cutler who moved to Microsoft and led the development of Windows NT. The MIPS-based workstations were moderately successful among DEC's existing Ultrix users but had little success competing against companies like Sun Microsystems. Meanwhile, DEC's cash-cow VAX line grew increasingly less performant as new RISC designs outperformed even the top-of-the-line VAX 9000. As the company explored the future of the VAX they concluded that a PRISM-like processor with a few additional changes could address all of these markets. Starting where PRISM left off, the DEC Alpha program started in 1989.
History
Background
Introduced in 1977, the VAX was a runaway success for DEC, cementing its place as the world's #2 computer vendor behind IBM. The VAX was noted for its rich instruction set architecture (ISA), which was implemented in complex microcode. The VMS operating system was layered on top of this ISA, which drove it to h |
https://en.wikipedia.org/wiki/Alternating%20series | In mathematics, an alternating series is an infinite series of the form
or
with for all . The signs of the general terms alternate between positive and negative. Like any series, an alternating series converges if and only if the associated sequence of partial sums converges.
Examples
The geometric series 1/2 − 1/4 + 1/8 − 1/16 + ⋯ sums to 1/3.
The alternating harmonic series has a finite sum but the harmonic series does not.
The Mercator series provides an analytic expression of the natural logarithm:
The functions sine and cosine used in trigonometry can be defined as alternating series in calculus even though they are introduced in elementary algebra as the ratio of sides of a right triangle. In fact,
and
When the alternating factor is removed from these series one obtains the hyperbolic functions sinh and cosh used in calculus.
For integer or positive index α the Bessel function of the first kind may be defined with the alternating series
where is the gamma function.
If is a complex number, the Dirichlet eta function is formed as an alternating series
that is used in analytic number theory.
Alternating series test
The theorem known as "Leibniz Test" or the alternating series test tells us that an alternating series will converge if the terms converge to 0 monotonically.
Proof: Suppose the sequence converges to zero and is monotone decreasing. If is odd and , we obtain the estimate via the following calculation:
Since is monotonically decreasing, the terms are negative. Thus, we have the final inequality: . Similarly, it can be shown that . Since converges to , our partial sums form a Cauchy sequence (i.e., the series satisfies the Cauchy criterion) and therefore converge. The argument for even is similar.
Approximating sums
The estimate above does not depend on . So, if is approaching 0 monotonically, the estimate provides an error bound for approximating infinite sums by partial sums:
That does not mean that this estimate always |
https://en.wikipedia.org/wiki/SSE3 | SSE3, Streaming SIMD Extensions 3, also known by its Intel code name Prescott New Instructions (PNI), is the third iteration of the SSE instruction set for the IA-32 (x86) architecture. Intel introduced SSE3 in early 2004 with the Prescott revision of their Pentium 4 CPU. In April 2005, AMD introduced a subset of SSE3 in revision E (Venice and San Diego) of their Athlon 64 CPUs. The earlier SIMD instruction sets on the x86 platform, from oldest to newest, are MMX, 3DNow! (developed by AMD, no longer supported on newer CPUs), SSE, and SSE2.
SSE3 contains 13 new instructions over SSE2.
Changes
The most notable change is the capability to work horizontally in a register, as opposed to the more or less strictly vertical operation of all previous SSE instructions. More specifically, instructions to add and subtract the multiple values stored within a single register have been added. These instructions can be used to speed up the implementation of a number of DSP and 3D operations. There is also a new instruction to convert floating point values to integers without having to change the global rounding mode, thus avoiding costly pipeline stalls. Finally, the extension adds LDDQU, an alternative misaligned integer vector load that has better performance on NetBurst based platforms for loads that cross cacheline boundaries.
CPUs with SSE3
AMD:
Opteron (since Stepping E4)
Sempron (since Palermo. Stepping E3)
Athlon 64 (since Venice Stepping E3 and San Diego Stepping E4)
Athlon 64 FX (since San Diego Stepping E4)
Athlon 64 X2
Phenom 64 X2
Turion family
K10 family
APU family (including without GPU)
FX Series
Zen family
Intel:
Celeron D
Celeron (starting with Core microarchitecture)
Pentium 4 (since Prescott)
Pentium D
Pentium Extreme Edition (but NOT Pentium 4 Extreme Edition)
Pentium Dual-Core
Pentium (starting with Core microarchitecture)
Core
Xeon (since Nocona)
Atom
VIA/Centaur:
C7
Nano
Transmeta Efficeon TM88xx (NOT Model Numbers TM86xx)
New instructions
Common instr |
https://en.wikipedia.org/wiki/Free%20algebra | In mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since its elements may be described as "polynomials" with non-commuting variables. Likewise, the polynomial ring may be regarded as a free commutative algebra.
Definition
For R a commutative ring, the free (associative, unital) algebra on n indeterminates {X1,...,Xn} is the free R-module with a basis consisting of all words over the alphabet {X1,...,Xn} (including the empty word, which is the unit of the free algebra). This R-module becomes an R-algebra by defining a multiplication as follows: the product of two basis elements is the concatenation of the corresponding words:
and the product of two arbitrary R-module elements is thus uniquely determined (because the multiplication in an R-algebra must be R-bilinear). This R-algebra is denoted R⟨X1,...,Xn⟩. This construction can easily be generalized to an arbitrary set X of indeterminates.
In short, for an arbitrary set , the free (associative, unital) R-algebra on X is
with the R-bilinear multiplication that is concatenation on words, where X* denotes the free monoid on X (i.e. words on the letters Xi), denotes the external direct sum, and Rw denotes the free R-module on 1 element, the word w.
For example, in R⟨X1,X2,X3,X4⟩, for scalars α, β, γ, δ ∈ R, a concrete example of a product of two elements is
.
The non-commutative polynomial ring may be identified with the monoid ring over R of the free monoid of all finite words in the Xi.
Contrast with polynomials
Since the words over the alphabet {X1, ...,Xn} form a basis of R⟨X1,...,Xn⟩, it is clear that any element of R⟨X1, ...,Xn⟩ can be written uniquely in the form:
where are elements of R and all but finitely many of these elements are zero. This explains why the elements of R⟨X1,...,Xn⟩ are often denoted as "non-commutative polynomials" in the "variables" (or "indeterminates") X1,...,Xn; the elements are |
https://en.wikipedia.org/wiki/Pullback%20%28differential%20geometry%29 | Let be a smooth map between smooth manifolds and . Then there is an associated linear map from the space of 1-forms on (the linear space of sections of the cotangent bundle) to the space of 1-forms on . This linear map is known as the pullback (by ), and is frequently denoted by . More generally, any covariant tensor field – in particular any differential form – on may be pulled back to using .
When the map is a diffeomorphism, then the pullback, together with the pushforward, can be used to transform any tensor field from to or vice versa. In particular, if is a diffeomorphism between open subsets of and , viewed as a change of coordinates (perhaps between different charts on a manifold ), then the pullback and pushforward describe the transformation properties of covariant and contravariant tensors used in more traditional (coordinate dependent) approaches to the subject.
The idea behind the pullback is essentially the notion of precomposition of one function with another. However, by combining this idea in several different contexts, quite elaborate pullback operations can be constructed. This article begins with the simplest operations, then uses them to construct more sophisticated ones. Roughly speaking, the pullback mechanism (using precomposition) turns several constructions in differential geometry into contravariant functors.
Pullback of smooth functions and smooth maps
Let be a smooth map between (smooth) manifolds and , and suppose is a smooth function on . Then the pullback of by is the smooth function on defined by . Similarly, if is a smooth function on an open set in , then the same formula defines a smooth function on the open set in . (In the language of sheaves, pullback defines a morphism from the sheaf of smooth functions on to the direct image by of the sheaf of smooth functions on .)
More generally, if is a smooth map from to any other manifold , then is a smooth map from to .
Pullback of bundles and sections
I |
https://en.wikipedia.org/wiki/Electrodynamic%20suspension | Electrodynamic suspension (EDS) is a form of magnetic levitation in which there are conductors which are exposed to time-varying magnetic fields. This induces eddy currents in the conductors that creates a repulsive magnetic field which holds the two objects apart.
These time varying magnetic fields can be caused by relative motion between two objects. In many cases, one magnetic field is a permanent field, such as a permanent magnet or a superconducting magnet, and the other magnetic field is induced from the changes of the field that occur as the magnet moves relative to a conductor in the other object.
Electrodynamic suspension can also occur when an electromagnet driven by an AC electrical source produces the changing magnetic field, in some cases, a linear induction motor generates the field.
EDS is used for maglev trains, such as the Japanese SCMaglev. It is also used for some classes of magnetically levitated bearings.
Types
Many examples of this have been used over the years.
Bedford levitator
In this early configuration by Bedford, Peer, and Tonks from 1939, an aluminum plate is placed on two concentric cylindrical coils, and driven with an AC current. When the parameters are correct, the plate exhibits 6-axis stable levitation.
Levitation melting
In the 1950s, a technique was developed where small quantities of metal were levitated and melted by a magnetic field of a few tens of kHz. The coil was a metal pipe, allowing coolant to be circulated through it. The overall form was generally conical, with a flat top. This permitted an inert atmosphere to be employed, and was commercially successful.
Linear induction motor
Eric Laithwaite and colleagues took the Bedford levitator, and by stages developed and improved it.
First they made the levitator longer along one axis, and were able to make a levitator that was neutrally stable along one axis, and stable along all other axes.
Further development included replacing the single phase energising curre |
https://en.wikipedia.org/wiki/Limiter | In electronics, a limiter is a circuit that allows signals below a specified input power or level to pass unaffected while attenuating (lowering) the peaks of stronger signals that exceed this threshold. Limiting is a type of dynamic range compression. Clipping is an extreme version of limiting.
Limiting is any process by which the amplitude of a signal is prevented from exceeding a predetermined value.
Limiters are common as a safety device in live sound and broadcast applications to prevent sudden volume peaks from occurring. Limiters are also used as protective features in some components of sound reinforcement systems (e.g., powered mixing boards and power amplifiers) and in some bass amplifiers, to prevent unwanted distortion or loudspeaker damage.
Types
Limiting can refer to a range of treatments designed to limit the maximum level of a signal. Treatments in order of decreasing severity range from clipping, in which a signal is passed through normally but sheared off when it would normally exceed a certain threshold; soft clipping which squashes peaks instead of shearing them; a hard limiter, a type of variable-gain audio level compression, in which the gain of an amplifier is changed very quickly to prevent the signal from going over a certain amplitude or a soft limiter which reduces maximum output through gain compression.
In amplifiers
Bass instrument amplifiers and power amplifiers are more commonly equipped with limiter circuitry to prevent overloading the power amplifier and to protect speakers. Electric guitar amps do not usually have limiters.
PIN diodes can be used in limiter circuits to reflect the energy back to the source or clip the signal.
In FM radio
An FM radio receiver usually has at least one stage of amplification that performs a limiting function. This stage provides a constant level of signal to the FM demodulator stage, reducing the effect of input signal level changes to the output. If two or more signals are received at the same |
https://en.wikipedia.org/wiki/Powder%20metallurgy | Powder metallurgy (PM) is a term covering a wide range of ways in which materials or components are made from metal powders. PM processes can reduce or eliminate the need for subtractive processes in manufacturing, lowering material losses and reducing the cost of the final product.
Powder metallurgy is also used to make unique materials impossible to get from melting or forming in other ways. A very important product of this type is tungsten carbide. Tungsten carbide is used to cut and form other metals and is made from tungsten carbide particles bonded with cobalt. It is very widely used in industry for tools of many types and globally ~50,000 tonnes per year is made with powder metallurgy. Other products include sintered filters, porous oil-impregnated bearings, electrical contacts and diamond tools.
Since the advent of industrial production-scale metal powder-based additive manufacturing in the 2010s, selective laser sintering and other metal additive manufacturing processes are a new category of commercially important powder metallurgy applications.
Overview
The powder metallurgy "press and sinter" process generally consists of three basic steps: powder blending (or pulverisation), die compaction, and sintering. Compaction of the powder in the die is generally performed at room temperature. Sintering is the process of binding a material together with heat without liquefying it. It is usually conducted at atmospheric pressure, and under carefully controlled atmosphere composition. To obtain special properties or enhanced precision, secondary processing like coining or heat treatment often follows.
One of the older such methods is the process of blending fine (<180 microns) metal powders with additives, pressing them into a die of the desired shape, and then sintering the compressed material together, under a controlled atmosphere. The metal powder is usually iron, and additives include a lubricant wax, carbon, copper, and/or nickel. This produces precise par |
https://en.wikipedia.org/wiki/Sound%20pressure | Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a sound wave. In air, sound pressure can be measured using a microphone, and in water with a hydrophone. The SI unit of sound pressure is the pascal (Pa).
Mathematical definition
A sound wave in a transmission medium causes a deviation (sound pressure, a dynamic pressure) in the local ambient pressure, a static pressure.
Sound pressure, denoted p, is defined by
where
ptotal is the total pressure,
pstat is the static pressure.
Sound measurements
Sound intensity
In a sound wave, the complementary variable to sound pressure is the particle velocity. Together, they determine the sound intensity of the wave.
Sound intensity, denoted I and measured in W·m−2 in SI units, is defined by
where
p is the sound pressure,
v is the particle velocity.
Acoustic impedance
Acoustic impedance, denoted Z and measured in Pa·m−3·s in SI units, is defined by
where
is the Laplace transform of sound pressure,
is the Laplace transform of sound volume flow rate.
Specific acoustic impedance, denoted z and measured in Pa·m−1·s in SI units, is defined by
where
is the Laplace transform of sound pressure,
is the Laplace transform of particle velocity.
Particle displacement
The particle displacement of a progressive sine wave is given by
where
is the amplitude of the particle displacement,
is the phase shift of the particle displacement,
k is the angular wavevector,
ω is the angular frequency.
It follows that the particle velocity and the sound pressure along the direction of propagation of the sound wave x are given by
where
vm is the amplitude of the particle velocity,
is the phase shift of the particle velocity,
pm is the amplitude of the acoustic pressure,
is the phase shift of the acoustic pressure.
Taking the Laplace transforms of v and p with respect to time yields
Since , the amplitude of the specific acoust |
https://en.wikipedia.org/wiki/Dialysis%20%28chemistry%29 | In chemistry, dialysis is the process of separating molecules in solution by the difference in their rates of diffusion through a semipermeable membrane, such as dialysis tubing.
Dialysis is a common laboratory technique that operates on the same principle as medical dialysis. In the context of life science research, the most common application of dialysis is for the removal of unwanted small molecules such as salts, reducing agents, or dyes from larger macromolecules such as proteins, DNA, or polysaccharides. Dialysis is also commonly used for buffer exchange and drug binding studies.
The concept of dialysis was introduced in 1861 by the Scottish chemist Thomas Graham. He used this technique to separate sucrose (small molecule) and gum Arabic solutes (large molecule) in aqueous solution. He called the diffusible solutes crystalloids and those that would not pass the membrane colloids.
From this concept dialysis can be defined as a spontaneous separation process of suspended colloidal particles from dissolved ions or molecules of small dimensions through a semi permeable membrane. Most common dialysis membrane are made of cellulose, modified cellulose or synthetic polymer (cellulose acetate or nitrocellulose).
Etymology
Dialysis derives from the Greek , 'through', and , 'to loosen'.
Principles
Dialysis is the process used to change the matrix of molecules in a sample by differentiating molecules by the classification of size. It relies on diffusion, which is the random, thermal movement of molecules in solution (Brownian motion) that leads to the net movement of molecules from an area of higher concentration to a lower concentration until equilibrium is reached. Due to the pore size of the membrane, large molecules in the sample cannot pass through the membrane, thereby restricting their diffusion from the sample chamber. By contrast, small molecules will freely diffuse across the membrane and obtain equilibrium across the entire solution volume, thereby changi |
https://en.wikipedia.org/wiki/Spheroplast | A spheroplast (or sphaeroplast in British usage) is a microbial cell from which the cell wall has been almost completely removed, as by the action of penicillin or lysozyme. According to some definitions, the term is used to describe Gram-negative bacteria. According to other definitions, the term also encompasses yeasts. The name spheroplast stems from the fact that after the microbe's cell wall is digested, membrane tension causes the cell to acquire a characteristic spherical shape. Spheroplasts are osmotically fragile, and will lyse if transferred to a hypotonic solution.
When used to describe Gram-negative bacteria, the term spheroplast refers to cells from which the peptidoglycan component but not the outer membrane component of the cell wall has been removed.
Spheroplast formation
Antibiotic-induced spheroplasts
Various antibiotics convert Gram-negative bacteria into spheroplasts. These include peptidoglycan synthesis inhibitors such as fosfomycin, vancomycin, moenomycin, lactivicin and the β-lactam antibiotics. Antibiotics that inhibit biochemical pathways directly upstream of peptidoglycan synthesis induce spheroplasts too (e.g. fosmidomycin, phosphoenolpyruvate).
In addition to the above antibiotics, inhibitors of protein synthesis (e.g. chloramphenicol, oxytetracycline, several aminoglycosides) and inhibitors of folic acid synthesis (e.g. trimethoprim, sulfamethoxazole) also cause Gram-negative bacteria to form spheroplasts.
Enzyme-induced spheroplasts
The enzyme lysozyme causes Gram-negative bacteria to form spheroplasts, but only if a membrane permeabilizer such as lactoferrin or ethylenediaminetetraacetate (EDTA) is used to ease the enzyme's passage through the outer membrane. EDTA acts as a permeabilizer by binding to divalent ions such as Ca2+ and removing them from the outer membrane.
The yeast Candida albicans can be converted to spheroplasts using the enzymes lyticase, chitinase and β-glucuronidase.
Uses and applications
Antibiotic discov |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.